axial flux permanent magnet brushless machines

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Axial Flux Permanent MagnetBrushless Machines

by

JACEK F. GIERASUnited Te chnolo gie s Re s e arch C ente 4East Harford, Connecticut, U.S.A.

RONG-JIE WANGUniv ersity of Stellenbosch,Stellenbosch, Western Cape, South Africa

and

MAARTEN J. KAMPERUniv e rsity of Ste llenbo s ch,Stellenbosch, Westem Cape, South Africa

W&wwKLUWER ACADEMIC PUBLISHERSDORDRECHT / BOSTON / LONDON

1 .

Contents

Preface

INTRODUCTION

1.1 Scope

I.2 Features

I.3 Development of AFPM machines

I.4 Types of axial flux PM machines

1.5 Topologies and geometries

1.6 Axial magnetic field excited by PMs

I.1 PM eddy-current brake as the simplest AFPMbrushless machine

1.8 AFPM machines versus RFPM machines

I.9 Power limitation of AFPM machines

Numerical examples

PRINCIPLES OF AFPM MACHINES

2.I Magnetic circuits2.I.1 Single-sidedmachines

2.I.2 Double-sided machines with internal PM disc rotor2.1.3 Double-sided machines with internal ring-shaped

core stator2.I.4 Double-sided machines with internal slotted stator2.1.5 Double-sided machines with internal coreless stator2.I.6 Multidiscmachines

2.2 Windings2.2.1 Three-phase windings distributed in slots2.2.2 Drum-type winding

xi

I

1

IaJ

2.

4

6

10

t3

I6

t9

I9

27

272727

293 l) L

3 Z

a aJ J

a aJ J

35

Vi AXIAL FLUX PERMANENT MAGNET BRUSHLESS MACHINES

2.2.3 Coreless stator winding2.2.4 Salient pole windings

2.3 Torque production

2.4 Magnetic flux

2.5 Electromagnetic torque and EMF

2.6 Losses and efficiency2.6.1 Stator winding losses2.6.2 Stator core losses2.6.3 Core loss finite element model2.6.4 Losses in permanent magnets

2.6.5 Rotor core losses

2.6.6 Eddy current losses in stator conductors

2.6.7 Rotationallosses2.6.8 Losses for nonsinusoidal current2.6.9 Efficiency

Phasor diagrams

Sizing equations

Armature reaction

AFPM motor2.10.1 Sine-wave motor2.10.2 Square-wave motor

AFPM synchronous generator

2.IIl Performance characteristics of a stand alonegenerator

2.II.2 Synchronization with utility grid

2.1

2.8

2.9

2.r0

3537

3739

40

42424445454l48495050

51

54

57

616 l62

65

6566

68

79

7979838487

90909599

103

2 . l l

Numerical examples

3. MATERIALS AND FABRICATION

3.1 Stator cores

3.1.1 Nonoriented electrical steels

3.1.2 Amorphous ferromagnetic alloys

3.1.3 Soft magnetic powder composites3.L4 Fabrication of stator cores

3.2 Rotor magnetic circuits

3.2.1 PM materials

3.2.2 Characteristics of PM materials

3.2.3 Operating diagram3.2.4 Permeances for main and leakage fluxes

Contents

3.2.5 Calculation of magnetic circuits with PMs3.2.6 Fabrication of rotor masnetic circuits

3.3 Windings3.3.I Conductors3.3.2 Fabrication of slotted windings3.3.3 Fabrication of coreless windines

Numerical examples

4. AFPM MACHINES WITH IRON CORES 125

4.I Geometries I25

4.2 Commercial AFPM machines with stator ferromagnetic cores 126

4.3 Some features of iron-cored AFPM machines 127

4.4 Magnetic flux density distribution in the air gap I28

4.5 Calculation of reactances 1304.5.I Synchronous and armature reaction reactances 1304.5.2 Stator leakage reactance I3I

4.6 Performance characteristics I34

4.7 Performance calculation 1364.7.I Sine-wave AFPM machine 1364.7.2 Synchronous generator 1384.7.3 Square-wave AFPM machine l4I

4.8 Finite element calculations I4l

Numerical examples 144

5. AFPM MACHINES WITHOUT STATOR CORES

5.1 Advantages and disadvantages

5.2 Commercial coreless stator AFPM machines

5.3 Performance calculation5.3.1 Steady-state performance

5.3.2 Dynamicperformance

5.4 Calculation of coreless winding inductances5.4.1 Classical approach5.4.2 FEM approach

5.5 Performance characteristics

5.6 Eddy current losses in the stator windings5.6.1 Eddy current loss resistance5-6.2 Reduction of eddy current losses5.6.3 Reduction of circulatins current losses

vll

107109It2l 12I12tt4

116

153r53r53155155r57r59159160162

r63r63r67168

vllt AXIAL FLUX PERMANENT MAGNET BRUSHLESS MACHINES

5.6.4 Measurement of eddy current losses

5.7 Armature Reaction

5.8 Mechanical design features5.8.1 Mechanical strength analysis5.8.2 Imbalanced axial force on the stator

5.9 Thermal problems

Numerical examples

6. AFPM MACHINES WITHOUT STA|OR AND ROTOR CORES 189

6.I Advantages and disadvantages 189

6.2 Topology and construction 189

6.3 Air gap magnetic flux density I92

6.4 Electromagnetic torque and EMF I93

6.5 Commercial coreless AFPM motors I94

6.6 Case study: low-speed AFPM coreless brushless motor 1976.6.1 Performance characteristics 197

6.6.2 Cost analysis 198

6.6.3 Comparison with cylindrical motor with laminatedstator and rotor cores 199

6.7 Case study: low-speed coreless AFPM brushless generator 200

6.8 Characteristics of coreless AFPM machines 20I

Numerical examples 204

170

n0173174t77

179

n9

7. CONTROL

7 .I Control of trapezoidal AFPM machine7.1.I Voltageequations7.1.2 Solid-stateconverter7.I.3 Current control7.1.4 Speed control

7.1.5 High speed operation

7.2 Control of sinusoidal AFPM machine7.2.I Mathematical model and dq equivalent circuits7.2.2 Current control1.2.3 Speed control7.2.4 Hardware of sinusoidal AFPM machine drive

7.3 Sensorless position control

Numerical examples

2t32t3214216219222222223224229230234^ a aL J I

239

8 .

Contents

COOLING AND HEAT TRANSFER

8.1 Importance of thermal analysis

8.2 Heat transfer modes8.2.1 Conduct ion8.2.2 Radiation

8.2.3 Convect ion

8.3 Cooling of AFPM machines8.3.1 AFPM machines with self-ventilation8.3.2 AFPM machines with external ventilation

8.4 Lumped parameter thermal model

8.4.1 Thermal equivalent circuit

8.4.2 Conservation of energy

8.5 Machine duties8.5.1 Continuous duty8.5.2 Short-time duty8.5.3 Intermittentdutv

Numerical examples

APPLICATIONS

9.1 Power generation

9.I.1 High speed generators

9.I.2 Low speed generators

9.2 Electric vehicles

9.2.1 Hybrid electric vehicles

9.2.2 Battery electric vehicles

9.3 Ship propulsion9.3.1 Large AFPM motors9.3.2 Propulsion of unmanned submarines

9.3.3 Counterrotating rotor marine propulsion system

9.4 Elecffomagnetic aircraft launch system

9.5 Mobile drill rigs

9.6 Elevators

9.7 Miniature AFPM brushless motors

9.8 Vibration motors

9.9 Computer hard disc drives

Numerical examples

IX

249

24924925025025r255255264267268269

27027027r272

272

281

28128r282

285287289

291291292292

295

297299302304

306

307

9.

AXIAL FLUX PERMANENT MAGNET BRUSHLESS MACHINES

Symbols and Abbreviations

References

Index

3II

32r

J J I

Preface

The drop in prices of rare-earth permanent magnet (PM) materials and pro-

gress in power electronics have played an important role in the development of

PM brushless machines in the last three decades. These machines have recently

become mature and their high efficiency, power density and reliability has led

to PM brushless machines successfully replacing d.c. commutator machines

and cage induction machines in many areas.The axial flux PM (AFPM) brushless machine, also called the disc-type ma-

chine, is an attractive alternative to its cylindrical radial flux counterpart due to

the pancake shape, compact construction and high torque density. AFPM mo-

tors are particulady suitable for electrical vehicles, pumps, valve control, cen-

trifuges, fans, machine tools, hoists, robots and manufacturing. They have be-

come widely used for low-torque servo and speed control systems. The appli-

cation of AFPM machines as generators is justified in wind turbines, portable

generator sets and road vehicles. The power range of AFPM brushless ma-

chines is now from a fraction of a watt to sub-MW.Disc-type rotors can be embedded in power-transmission components or

flywheels to optimize the volume, mass, number of parts, power transfer and

assembly time. For electric vehicles with builfin wheel motors the payoff is

a simpler power train, higher effrciency and lower cost. Dual-function rotors

may also appear in pumps, elevators, energy storages and other machinery,

bringing added values and new levels ofperfonnance to these products.

The authors believe that this first book in English devoted entirely to AFPM

brushless machines will serve as a textbook, useful reference and design hand-

book of AFPM machines and will stimulate innovations in this field.

J.F. Grpnas, R. WRIrtc AND M.J. Kavppn

Chapter 1

INTRODUCTION

1.1 Scope

The term axialfl.ux permanent magnel (AFPM) machine in this book relates

only to permanent magnet (PM) machines with disc type rotors. Other AFPM

machine topologies, e.g. transverse flux machines, have not been considered.

In principle, the electromagnetic design of AFPM machines is similar to its

radial flux PM (RFPM) counterparts with cylindrical rotors. However, the me-

chanical design, thermal analysis and assembly process are more complex.

1,2 Features

The AFPM machine, also called the disc-type machine, is an attractive a1-

ternative to the cylindrical RFPM machine due to its pancake shape, compact

construction and high power density. AFPM motors are particularly suitablefor electrical vehicles, pumps, fans, valve control, centrifuges, machine tools,

robots and industrial equipment. The large diameter rotor with its high mo-

ment of inertia can be utilised as a flywheel. AFPM machines can also operate

as small to medium power generators. Since a large number of poles can be

accommodated, these machines are ideal for low speed applications, as for

example, electromechanical traction drives, hoists or wind generators.

The unique disc-type profile of the rotor and stator of AFPM machines

makes it possible to generate diverse and interchangeable designs. AFPM ma-

chines can be designed as single air gap or multiple air gaps machines, with

slotted, slotless or even totally ironless armature. Low power AFPM machines

are frequently designed as machines with slotless windings and surface PMs.

As the output power of the AFPM machines increases, the contact surface

between the rotor and the shaft in proportion to the power becomes smaller.


Table 1.1. Specifications of double-sided disc type AFPM brushless servo motors manufac-tured by E Bautz GmbH, Weiterstadt, Germany

Quantity S632D S634D S712F 5714F S8O2F S8O4F

Rated power, WRated torque, NmMaximumtorque, NmStandstilltorque, NmRated current, AMaximum current, AStandstill current. ARated speed, rpmMaximumspeed, rpmArmature constant,V/l000 rpmTorque constant,Nm/AResistance, QInductance, mHMoment of inertia,kgm2 x 10-3Mass, kgDiameterof frame, mmLengthof frame, mmPowerdensity, WkgTorquedensity, Nmlkg

6801 . 3

7

t . 74.02 l5 .3

5000

6000

23

0.352.5- ) -L

0.084.5

150

82

1 5 1 . 1

0.289

940t . 8

o

2.34.9256.3

5000

6000

25

0.39t . 82.8

0 . 1 25 .0

150

82

188 .0

0.16

9 1 02.9

I4

3 .54.9245 .9

3000

6000

^ a

0.642.45.4

0 .216.2

174

89

146.8

0.468

r2604 .0

t 8

4.76.6307.8

3000

6000

42

0.641 . 54.2

0.3o . o

t74

89

190 .9

0.606

1 8s05 .9

28

7.09.9471t.73000

6000

42

0.640.763 .0

0.69.7

210

103

t90.7

0.608

26708.5

40

10 .0I 1 .956

14.03000

6000

50

0.770.623 .0

1 . 010 .5

210

103

254.3

0.809

Careful attention must be given to the design of the rotor-shaft mechanicaljoint as this is usually the cause of failures of disc type machines.

In some cases, rotors are embedded in power-transmission components tooptimise the number of parts, volume, mass, power transfer and assembly time.For electric vehicles (EVs) with built-in wheel motors the payoff is a sim-pler electromechanical drive system, higher efficiency and lower cost. Dual-function rotors may also appear in pumps, elevators, fans and other types ofmachinery bringing new levels of performance to these products.

Introduction 3

Most applications use the AFPM machine as a d.c. brushless motor' En-

coders, resolvers or other rotor position sensofs are thus a vital part of brushless

disc motors.Table 1 .1 shows specifications of AFPM brushless servo motors rated up to

2.7 kW, manufacturedby E. Bautz GmbH, Weiterstadt, Germany.

1.3 Development of AFPM machinesThe history of electrical machines reveals that the earliest machines were

axial flux machines (M. Faraday, 1831, anonymous inventor with initials P.M.,

1832. W. Ritchie, 1833, B. Jacobi, 1834). However, shortly after T. Davenport(1837) claimed the first patent [66] for a radial flux machine, conventional ta-

dial flux machines have been widely accepted as the mainstream configuration

for electrical machines [30, 49].The first primitive working prototype of an axial flux machine ever recorded

was M. Faraday's disc (1831) - see Numerical Example l.l. The disc type

construction of electrical machines also appears in N. Tesla's patents, e.g. U.S.patent No. 405 858 12251entitled Electro-Magnetic Motor and published in

1889 (Fig. l.l). The reasons for shelving the axial flux machine were multi-

fold and mav be summarised as follows:

strong axial (normal) magnetic attraction force between the stator and rotor;

fabrication difficulties, such as cutting slots in laminated cores and other

methods of making slotted stator cores;

high costs involved in manufacturing the laminated stator cores;

difficulties in assembling the machine and keeping the uniform aft gap-

Although, the first PM excitation system was applied to electrical machines as

early as the 1830s, the poor quality of hard magnetic materials soon discour-

aged their use. The invention of Alnico in I 93 1, barium ferrite in the 1 950s and

especially the rare-earth neodymium-iron-boron (NdFeB) material (announced

in 1983) have made a comeback of the PM excitation system possible.

It is generally believed that the availability of high energy PM materials

(especially rare earth PMs) is the main driving force for exploitation of novel

PM machine topologies and has thus revived AFPM machines. Prices of rare-

earth PMs have been following a descending curve in the last decade of the

20th century with a sharp decline in the last three years. A recent market

survey shows that the NdFeB PMs can now be purchased in the Far East for

less than U.S.$ 20 per kilogram. With the availability of more affordable PM

materials, AFPM machines may play a more important role in the near future.

Figure l.l. Electro-magnetic858, 1889 [225] .

AXTAL FLUX PERMANENT MAGNET BRUSHLESS MACHINES

I n t v f : T n n

motor with disc rotor according to N. Tesla's patent No. 405

1.4 Types of axial flux PM machinesIn principle, each type of a radial flux machine should have its correspond-

ing axial flux (disc type) version. In practice, disc type machines are limited tothe following three types:

r PM d.c. commutator machines;

r PM brushless d.c. and synchronous machines;

r induction machines

Similar to its RFPM counterpart, the AFPM d.c. commutator machine usesPMs to replace the electromagnetic field excitation system. The rotor (arma-ture) can be designed as a wound rotor or printed winding rotor.

Introduction

Figure 1.2. AFMPM 8-pole d.c. commutator motor with printed rotor winding: (a) stator withPMs, (b) cross section, (c) rotor (armature) windings and brushes, (d) construction of 2p : gwinding with 145 bars. I - rotor with double-sided printed winding, 2 - pMs, 3 - brushes.

In the wound rotor, the almature winding is made of copper wires andmoulded with resin. The commutator is similar to that of the conventionaltype, i.e. it can be either a cylindrical or radial commutator.

The disc-fiipe printed armature winding motor is shown in Fig. 1.2. Therotor (armature) does not have a ferromagnetic core and its winding is similarto the wave winding of conventional d.c. commutator machines. The coilsare stamped from pieces of sheet copper and then welded, forming a wavewinding. When this motor was invented by J. Henry Baudot [16], the armaturewas made using a similar method to that by which printed circuit boards arefabricated. Hence, this is called the printed winding motor. The magneticflux of a d.c. printed winding commutator motor with a large air gap can beproduced using cost effective Alnico magnets with high remanence.

AFPM d.c. commutator motors are still a versatile and economical choicefor certain industrial, automotive and domestic applications such as fans, blow-ers, small EVs, power tools, appliances, etc.

Practically, d.c. brushless and a.c. synchronous machines have almost thesame structure, though their theory and operation principles are somewhat dif-ferent [96, 112, 172]. The main difference is in the shape of the operationcurrent waveform (Fig. 1.3), i.e.:

r the d.c. brushless machine generates a trapezoidal EMF waveform and isoperated with a rectangular line current waveform (also called a square-wqve mzchine):

ANAL FLUX PERMANENT MAGNET BRUSHLESS MACHTNES

?1

Phnse A

PlusE B

130 t80 240 300 16f{ B }

0 t20 240(b)

Figtre 1.3. Cunent waveforms for AFPM brushless machines: (a) square-wave machine, (b)

sinewave machine.

r the a.c. synchronous machine generates a sinusoidal EMF waveform and isoperated with sinewave currents (also called a sinewave machine).

It is difficult to manufacture a laminated rotor with cage winding for a disc-typeinduction machine 11481. If the cage winding is replaced with a non-magnetichigh conductivity (Cu or Al) homogenous disc or steel disc coated with copperlayer, the performance of the machine drastically deteriorates. Therefore, thereis little interest in disc type induction machines so far 1148, 238].

1.5 Topologies and geometriesFrom a consfiuction point of view, brushless AFPM machines can be de-

signed as single-sided or double-sided, with or without armature slots, withor without armature core, with intemal or external PM rotors, with surfacemounted or interior PMs and as single stage or multi-stage machines.

In the case of double-sided configurations, either the external stator or ex-ternal rotor affangement can be adopted. The first choice has the advantage ofusing fewer PMs at the expense of poor winding utilisation while the secondone is considered as a particularly advantageous machine topology [34]. Thediverse topologies of AFPM brushless machines may be classified as follows:

r single-sided AFPM machines

with slotted stator (Fig. 1.4a)

with slotless stator

with salient-pole stator

Introduction

double-sided AFPM machines

with internal stator (Fig. l.ab)

x with slotted statorx with slotless stator

. with iron core stator

. with coreless stator (Fig. l.4d)

. without both rotor and stator cores

Figure 1.4. Basic topologies of AFPM machines: (a) single-sided slotted machine, (b) double-

sided slotless machines with internal stator and twin PM rotor, (c) double sided machine with

slotted stator and internal PM rotor, (d) double-sided coreless motor with intemal stator. Istatorcore, 2 - statorwinding, 3 -rotor, 4-PM, 5 -frame, 6-bearing, 7 shaft.

AXIAL FLUX PERMANENT MAGNET BRUSHLESS MACHII,{ES

* with salient pole stator (Fig. 1.5)

with internal rotor (Fig. 1.ac)

x with slotted statorx with slotless stator

x with salient pole stator (Fig. L6)

multi-stage (multidisc) AFPM machines (Fig. 1.7)

Figure 1.5. Double-sided AFPM brushless machine with internal salient-pole stator and twinextemal rotor [170]: (a) construction; (b) stator; (c) rotor. 1 PM,2 rotor backing steeldisc, 3 - stator pole, 4 - stator coi1.

The air gap of the slotted armature AFPM machine is relatively small. Themean magnetic flux density in the air gap decreases under each slot openingdue to increase in the reluctance. The change in the mean magnetic flux densitycaused by slot openings corresponds to a fictitious increase in the air gap I I I 1 ].The relation between fictitious g' and physical air gap g is expressed with theaid of Carter coefficient kc ) I,i.e.

g' : gkc

, t 1

4 * 7 9

( 1 .1 )

( r .2)

+l*arc,an (*) (1 .3 )

Introduction

Figure 1.6. Double-sided AFPM brushless machine with three-phase, 9-coil extemal salient-pole stator and 8-pole intemal rotor. 1 - PM ,2 - stator backing ferromagnetic disc, 3 statorpole,4-statorcoi l .

where 11 is the average slot pitch and b1a is the width of slot opening.For AFPM machines with slotless windings the air gap is much larger and

equal to the mechanical clearance plus the thickness of all non-magnetic ma-terials (winding, insulation, potting, suppofting structure) that is passed bythe main magnetic flux. Since there are no slots, Carter coefficient kc : I.Compared to a conventional slotted winding, the slotless arrnature winding hasadvantages such as simple stator assembly, elimination of the cogging torqueand reduction of rotor surface losses, magnetic safuration and acoustic noise.The disadvantages include the use of more PM material, lower winding in-ductances sometimes causing problems for inverter-fed motors and significanteddy current losses in slotless conductors [45].

In the double-sided, salient-pole AFPM brushless machine shown in Fig.1.5, the stator coils with concentrated parameters are wound on axially lam-inated poles. To obtain a three-phase self-starting motor, the number of thestator poles should be different from the number of the rotor poles, e.g. 12stator poles and 8 rotor poles [60, 161, 170]. Fig. 1.6 shows a double-sidedAFPM machine with external salient pole stators and internal PM rotor. Thereare nine stator coils and eight rotor poles for a three-phase AFPM machine.

Depending on the application and operating environment, slotless statorsmay have ferromagnetic cores or be completely coreless. Coreless stator con-

l 0 AXIAL FLUX PERMANENT MAGNET BRUSHLESS MACHINES

figurations eliminate any fenomagnetic material from the stator (armature)system, thus making the associated eddy cuffent and hysteresis core lossesnonexisting. This type of configuration also eliminates axial magnetic attrac-tion forces between the stator and rotor at zero-current state. It is interestingthat slotless AFPM machines are often classified according to their windingalrangements and coil shapes, namely, toroidal, trapezoidal and rhomboidalforms [34, 45,79J.

Figure I .7. Coreless multidisc AFPM machine with three coreless stators and four PM rotoruaits: 1 statorwinding, 2 rotorunit, 4-PM, 3 -frame, 4 bearing, 5 shaft.

1.6 Axial magnetic field excited by PMsA double-sided AFPM machine with twin PM rotor in ryz rectangular co-

ordinate system is shown in Fig. l.B. Assuming that the radius of curvatureis higher than the pole pitch and the centre axes of the opposite rotor polesare shifted by a linear distance 16, the normal component of the magnetic fluxdensity on the surface ofthe rotor can be described in the stationary rAz coot-dinate system by the following equations:

. a t z :0 .Ysd

oo^ \ - -B - , t ( r . t ) - B o \ , b , c o s ( " ; " ! , d , r -

; )" ' 2u - l

t a t z : - 0 . 5 d

(1 .4)

Introduction

\ Pole Pitch

Figure 1.8. Twin-stator double-sided AFPM machine in Cartesian coordinate system.

l l

where .86 is the value of the nornal component in the center axis of the Northpole, and

(1 .6)

er: ]uu - BrrrDn ( r .7)

^ 1 7lJu - I/*

T

.:l#"*' (;)' h -#] *,n *"i, (,;) cos (p,b1)

oo

B,n,z(r,t) : Bo\U"cosl.,.,tT A,@ ,o) ; | (1.5)I l l- J

l*sinha - t (t)^ fr .o.r, ". t (*)' :o".,h *]

x sin@[) "rn(r&)

. 4A _u u - -

r

pole pitch

( 1 .8 )

12 AXTAL FLUX PERMANENT MAGNET BRUSHLESS MACHINES

(a) 0.9

B m z t ( x , r )

B mzz ( x. i )

0.9 09

0.3B mz1 (x,t)

: - 0B n r a r x ' t )

-0.1

0.3 l l i i I i i l l, I l l i i lr i l r:i \i\ / ,n \ \r/ i \ \ l','\'rl l i t . l lllitli:llililifrLli---.---.L r l--ll-i UJ-t lJI I I l l I r i l , l

i i i l

: l

(b)

0.1 0 . l5 0 .2 0 .25 0 .1

x z/r

0.05 0 .1 0 . r5 0 .2 0 .25 0 .3

x zpr

Q.o4 ;

on

rD) t t

ft* fft'l ifflr.Ylrl N,4ri iM,i M,1l l i l i r l r , l t l l l , r l l ,' ,j \ \ l l \ \i/i \ r lir \liliilillil.i trr{-u, rtj i[i]'i [il

'0 9 -0.90

0

Figure 1.9. Distribution of the normal components of the magnetic flux density according toeqns (1 .4 ) , (1 .5 ) and (1 .8 ) fo r r - 0 .04 ,m,b , :0 .03 m, Bo : 0 .6 T , t : 0 , ro : 0 .52 : (a )a : 0. (b) cv - 0.8.

In the above eqns (1.4), (1.5), (1.6), (1.7), and (1.8) u : ?rr is the linear speedof the rotor in the z-direction, n - n D lu is the rotational speed in rev/s and theparameter a depends on the shape of the distribution of the normal componentof the magnetic flux density (Fig. 1.9). Forthe flat-topped curve a : 0 andfor the concave curve (armature or eddy-current reaction) 0 < <-v < 1. Thecoefficient b, according to eqn (1.8) has been derived in [93].

The average diameter D of the PM excitation system and correspondingaverage pole pitch are:

, T * b ," 2

D : 0 . 5 ( D o u t * D i n ) ( l e)

Introduction

where Din is the inner diameter of PMs, Do6 is the outer diameter of PMs and2p is the number of poles.

The electromagnetic field analysis in AFPM brushless machines has beendiscussed in e.g. 190, 91, 250,251).

1.7 PM eddy-current brake as the simplest AFPMbrushless machine

A double-sided, PM excited eddy-current brake with high conductivity non-magnetic disc-type rotor is one of the simplest brushless AFPM machines (Fig.1.8). In an eddy-current brake the PM excitation system is stationary and theconductive rotor rotates at the speed n. Eqns (l.a) to (1.9) are valid sincethe stationary PM excitation system and rotating electric circuit (armature) areequivalent to the rotating PMs and the stationary electric circuit.

It is assumed that the eddy currents in the non-magnetic conductive discflow only in the radial direction, i.e., in the gr-direction (Fig. 1.8). Thus, themagnetic vector potential ,4 in the disc is described by the following scalarequation (2D analysis):

t3

o, A^0, * o, A^0, = ^- aF-

t ar,

: ()'AmY' ( 1 .10 )

where

a, - t/ ja,Fo4ro : (I + j)k" ( 1 .11 )

(1 .12 )

In eqns (1.11) and (1.12) the electric conductivity o depends on the disc tem-perature. The relative magnetic permeability of paramagnetic (A1) or diamag-netic (Cu) materials Fr x I. The angular frequency forhigher space harmonicsis according to eqn (1.7) or

u , :Z t r f , ; f " - - u f ; u : I , 3 , 5 , . . .

General solution to eqn ( I . l0) can be written, for example, as

(1 . l 3 )

A,na :i sio(ur,t * g,r - T)lOr,exp(-n,z) * A',exp(n,z)) (1.14)

l 4

where


az"+03 : (an , *ax , )k , ( l . l s )

u t l u - ( 1 . I 6 )

(1 .17 )

Since the curents in the disc flow only in the radial direction U, E*, : 0Ern" : 0 and Brno

_: 0 for *0.5d I z ( 0.5d. Using the magnetic vector

potential Y x A : E andthe second Maxwell's equation i "

E : *08 lAt,the remaining electric and magnetic components in the disc can be found as

E^y: - jarA*u

coti-

I j t "s in ( -u ,1 I 3 , ru:1

rc\,-2

u : l

[)lot" exp(- n,z) * Az, exp(n,z')l ( 1. 18)

12 flAmaurnr - -

0,

[ ) l^ r " exp(- n,z) - Az, exp(n,z)) (1.19)

Brn":9+*O T

: I p, rlos(a,t * p,r * I)(Or, exp(.* n,z) I Az, exp(n,z)) (1 .20)

u I

The integration constants 41, and 42, can be found on the basis of equalityof normal components of the magnetic flux density in the air and in the disc atz - A.Sd and z : -0.5d. i .e.

Introduction 15

r a t z : 0 . 5 d

p, cos(u,t * g,r - I)Vr, exp(-n,d,f 2) -t Az, exp(n,d,l2))z -

: Bobrcos(wrt * 0rr -

t a t z : - 0 . 5 d

p, coslw,t + g,@ - ro) - Xllqr" exp(-n,d,f 2) + 42, exp(n,cll2)l

: Bob, coslu,t + 0,(r - *ol - [l

There is only backward-rotating magnetic field in the air gap of an eddy-currentbrake, so that the terms p,r and 0"@ * 16) in eqns (1.4) and (1.5) are withthe * sign. Thus,

1 - , s i nh ( r c ,d "12 ) 11 - , 1Atu: 42,:

nBob"?ffi# :

z 6,nou,ffiG;I6sinh(rc"d)(r.21)

because sinh(2e) : 2 sinh r cosh r. Putting eqn (1.2 1) into (1. 1 8), (1. 1 9) and(1.20), the particular solution to eqn (1.10) for E*0, B*, and B^" compo-nents are

c c o ) b r l , ^ 7 7

Ems: -2t""TeCiqsin(u,t t g,r - 7)cosh(rc,2)

( t .22)

B'n':f-""T^#rtrsin(u't * 0'r - |)'i'n@'") (r'23)

Bn " :2uru"^"iOncos(a,t * F,r - [) cosh(n,z) (r.24)

f r \

t)

16 AXIAL FLUX PERMANENT MAGI,{ET BRUSHLESS MACHINES

The surface wave impedance for the uth space harmonic is calculated on thebasis of eqns (1.22') and (1.23)

zu - r u * j r , : - t r o t i r l * , ) z o i : r j : * : " n t t , { o , f ; )

: l(Bp,Ap, - Bx,Ax,) + j(Bx,Aa, - Po,Ar,) l? Q.25)

where

a - ,t L t T u -sinh(ap"k"d)

cosh(ct prk,d) - cos(ay,k,d)(r .26)

( t .27)

(r.28)

- sin(ay"k"r|)cosh(a p, k, d) - cos(a y

"k " d)

The impedance of the disc for the yth space harmonic

BR,:G#Te)

0.5(Do.t - Dn) ,- -;- Kzur / u

vL u - a u

(r .29)

where Do6 is the outer diameter of PMs, D;n is the inner diameter of pMs,z is the average pole pitch (1.9) and k"r rsthe impedance increase factor dueto circumferential cunents (in the r direction). The impedance increase factorfor the zth harmonic is [62]

k " , : 71 I(1 .30 )

u2 o.b(Dou, - Dm)

1.8 AFPM machines versus RFPM machinesIn pace with the application of new materials, innovation in manufacturing

technology and improvements in cooling techniques, further increase in thepower density (output power per mass or volume) of the electrical machine hasbeen made possible. There is an inherent limit to this increase for conventionalradial flux PM (RFPM) machines because of 127 , 49,96, 153, l77l:

a2, t 0.b1D.,, -

0 Ku r lu

Din ) . d .- Kru cotlr\ti,ur)

Introduction

r the bottle-neck feature for the flux path at the root of the rotor tooth in thecase of induction and d.c. commutator machines or brushless machineswith external rotors (Fig. 1.10);

r much of the rotor core around the shaft (rotor yoke) is hardly utilised as amagnetic circuit;

r heat from the stator winding is transferred to the stator core and then to theframe - there is poor heat removal through the stator air gap, rotor andshaft without forced cooling arrangements.

These limitations are inherently bound with radial flux structures and cannotbe removed easily unless a new topology is adopted. The AFPM machine,recognised as having a higher power density than the RI'PM machine, is morecompact than its radial flux counterpart L26,49,96, 153].

(a) 0)

Figure 1.10. Topologies of (a) RFPM machine (b) AFPM machine.

Moreover. since the inner diameter of the core of an AFPM machine is usu-ally much greater than the shaft diameter (see Fig. 1.4), better ventilation andcooling can be expected. In general, the special properties of AIPM machines,which are considered advantageous over RFPM machines in certain applica-tions, can be summarised as follows [48, 96]:

r AFPM machines have much larser diameter to lensth ratio than RFPMmachines;

r AFPM machines have a planar and somewhat adjustable ak gap;

L7

18 AXIAL FLUX PERMANENT MAG],{ET BRUSHLESS MACHINES

r capability of being designed to possess a higher power density with somesaving in core material;

r the topology of an AFPM machine is ideal to design a modular machinein which the number of the same modules is adjusted to power or torquerequirements;

r the larger the outer diameter of the core, the higher the number of poles thatcan be accommodated, making the AFPM machines a suitable choice forhigh frequency or 1ow speed operations.

Consequently, AFPM type machines are particularly suitable for servo, trac-tion, distributed generation and special-purpose applications where their prop-erties offer distinct advantases over their conventional RFPM countemarts.

600

? soo

:.i

.i :oo

L 2009i* roo

a

9m

80m

- 7000

I uooo

E 5oo()Ei cmo

$ rooo

&.*rm0

0

500

t 400

'6' 100

!: ?00

1S

0.25

o ,EEE 2001

1 l

Odpdpowr, kv

l l 5

Outd Fwr, kW

0.25

O IEEE 2OOI

0,25

cJ l rEE t00l0.25

o IEEE 2001

I ] J ] O

Or&u pow. kW Odpd powr, kW

Figure I . I I . Perfomance comparison of RFPM and AFPM machines [2 14].

The quantitative comparison between traditional RFPM machine and AFPMmachine is always difficult as it may raise the question of this comparison'sfairness. Some published work dealt with quantitative investigations of RFPMand AFPM machine configurations in terms of sizing and power density equa-tions [8, 49, 121, 2a71. Fig. 1 . 1 I gives the performance comparison betweena conventional RFPM machine and a number of AFPM machines of different

Introduction

configurations at five different power levels [214], which shows that the AFPMmachine has a smaller volume and less active material mass for a given powerrating than the RFPM machine.

1.9 Power limitation of AFPM machinesThe power range of AFPM disc-type brushless machines is now from a

fraction of a Watt to sub-MW. As the output power of the AFPM machineincreases, the contact surface between the rotor and shaft becomes smaller incomparison with the rated power. It is more difficult to design a high me-chanical integrity rotor-shaft mechanical joint in the higher range of the outputpower. A common solution to the improvement of the mechanical integrity ofthe rotor-shaft joint is to design a multidisc (multi-stage) machine (Fig. 1.7).

Since the scaling of the torque capability of the AFPM machine as the cubeof the diameter (see eqn (2.9\) while the torque of a RFPM machines scale asthe square of the diameter times the length, the benefits associated with axialflux geometries may be lost as the power level or the geometric ratio of thelength to diameter of the motor is increasedLlT4l. The transition occurs nearthe point where the radius equals twice the length of RFPM machine. Thismay be a limiting design consideration for the power rating of a single-stagedisc machine as the power level can always be increased by simply stacking ofdisc machines on the same shaft and in the same enclosure.

Numerical example 1.1A copper disc with its dimensions as shown in Fig. 1.12 rotates with the

speed of 12 000 rpm between U-shaped laminated pole shoes of a PM. A slid-ing contact consisting of two brushes is used to collect the electric current gen-erated by this primitive homopolar generator: one brush slides on the externaldiameter D,tut : 0.232 m and the second brush is located directly below oneof the poles at the distance of O.\Din : 0.03 m from the axis of the disc. Theremanent magnetic flux density of the NdFeB PM is B, : 7.25 T, coercivityis H. : 950 000 A/m and height 2hp1 :0.016 m. The thickness of the discis d : 0.005 m, one-sided a* gap is 9 : 0.0015 m and the width of the poleis bo : 20 mm. The relative magnetic permeability of the laminated core is

F, : 1000 and the conductivity of the disc is o : 57 x 106 S/m at 20"C. Thelength of the flux path in the laminated core is lp" - 0.328 m. Find:

(a) the magnetic flux density in the air gap;

(b) the EMF between brushes;

(c) the current, if the line resistance is El : 0.001 f, and load resistance isRr - 0.02 O.

t9

20 AXIAL FLUX PERMANENT MAGNET BRUSHLESS MACHINES

Figure 1,12. Faraday's disc: a nonmagnetic conductive disc rotating in a stationary magneticfield according to Numerical examole I .I .

The magnetic flux fringing effect in the air gap, the variation of magnetic per-meability with the magnetic field intensity in the laminated core and brushvoltage drop are neglected.

Solution

This is a homopolar type d.c. generator known as Faraday's disc and can beused as a cunent source, e.g. for electrolysis.

(a) Magnetic ffux density in the air gap

The relative recoil magnetic permeability

IAB \ 1 .25 -0t ' r t 'e( po LH

- 0.4r x lO-b 950000 0

r.047

The magnetic flux density in the air gap and saturation factor of the magneticcircuit can be found on the basis of Kirchhoff's magnetic voltage law, i.e.

u' 'ont :

Bn 2tttt +

Fjllrrec F}Frrec

where the saturation factor of the masnetic circuit

B" B" f?' ' 2 h n t - " e 2 h y + 1 ! 2 g + H r r l r "

l-LO Frrec llollrrec LtO

Ra2gk"otP0

L F".I .k s a t : 7 *

2p, (g + 0 .5d)- 1 |- T T

2 x 1000(0.001i * 0 .5 x 0.005):7 .042

Introduction

Thus, the air gap magnetic flux density is

2 l

8,,k

" I + (g + 0.5d)k"otH,," , fh.11

: t ' 25 , , :o .8o9T

1+(0 .0015*0 .5 x 0 .005)1 .042 x 1000/0 .008 " '

(b) EMF between brushes

Since Elt : ?- x En o, d,E : Bnudr where n : ,ur : Ztrrn is thelinear speed, r is the radius ofthe disc and n is the rotational speed in rev/s,dE : Bs(2nrn)dr. Thlus

p0.5Dea1 *- 12n : I Bnl2rrn)d7 -' l l ' ! '-e (n7"., - n?^\

J o . s D ; , , Y \ 4 \ - o u r

* ' ' )

: 4#ry (o.zsz, _ 0.006,) :6 83v(c) Current, if the line resistance is El : 0.001 Q and load resistance is /?1 :0.02 0.

Neglecting the current fringing effect in the disc, the resistance of the discfor induced current at 20oC is

n 0 .5 (Dod - D" ) 0 .5 (0 .232 - 0 .06)Hax- - -# :+ :0 .0000151 Q- odbo 57 x 106 x 0.005 x 0.02

The current is

I : - - : _ : - . . , , , , , , 6 ' 8 ,3 , , : 325 . \- Ra-r RL ]- Rt 0.0000151 + 0.001 + 0.02

- " '

The te rm ina l vo l t age i sV : I x Ry :325 x 0 .02 :6 .5Vand the l i nevoltage drop is LV : I x R1 :325 x 0.001 : 0.325 V.

Numerical example 1.2Find the impedance of the aluminum disc of a double-sided eddy cument

brake at ambient temperature 20"C. The inner diameter of the PMs is Drr, :0.14 m, the outer diameter of the PMs rs Do6 : 0.242, thickness of the discd : 3 mm, number of poles 2p : 16 and speed n : 3000 rpm. Assumethe conductivity of the aluminum o : 30 x 106 S/m at2}oC and its relativemagnetic permeability Fr = t.

22 AATAL FLUX PERMANENT MAGNET BRUSHLESS MACHINES

Solution

The average diameter of the disc

D : 0 .5 (Dm * Do, t ) : 0 .5 (0 .14 + 0 .232) : 0 .191 m

The average pole pitch

rD n'0.191t : 2 p :

t 6 - o ' 0 3 7 m

The frequency and angular frequency of the curent in the disc for fundamentalspace harmonic u :7

. ^3000f p , - 8

i r r : 400H2 "'; : 2r f : 21400: 2513.3 t/s

The attenuation factor for the fundamental space harmonic u : I of the elec-tromagnetic field in the disc according to eqn ( 1 .12) is

t." - : 277.66 1lm

The coefficients according to eqns (1.6), (1.16), (1.17), (1.26), (1.27) and( 1 .28) for u : 1, are respectively

' t : #u :84'865l1lYn

1.038

ux :

s inh( l .038 x217.66 x 0.003)coslr(1.038 x217.66 x 0.003) - cos(0.964 x277.66 x 0.003)1 .699

- sin(0.964 x 217.66 x 0.003)cosh(1.038 x 277.66 x 0.003) - cos(O.964 x 277.66 x 0.003)-1 .369

Ap

Aa

2513.3 x 0.4r10-6 x 1.0 x 30 x 106

Introduction

. 0.0022. lo- '

0.0015

n(v)

tr o'oo1

s . to a

0 0

L-)

1 v 4 l

Figure I . I 3 . Resistance and reactance of the copper disc for higher space harmonics z accord-ingto Numerical example 1.2.

0.964B R : - 0.961

0.5(1.0382 + 0.9642)

B 1.038

x : o'5(10g82 + or9o42) : 1'035

The surface wave impedance for u : I according to eqn (1.25)

r : [0.9G1 x 1.699 - 1.0s5 x (-1.869)] f f i

:2.2128 x 10-5 Q

r : [1.035 x 1.699 + 0.961 x (-r.369)] H,6:^ :3.2L6 x 10 6 f)"57 x 10o

z : 2.2123 x 10-5 + j3.216 x 10-6 Q

The impedance increase factor due to circumferential currents (in the r- direc-tion) according to eqn (1.30) is

k,, : r+ I = =,= 9 '937 = r , , : 1.23312 0.5(0.242 - 0 .14)

The disc impedance per pole for the fundamental space harmonic u : 1 ac-cording to eqn (1.29)

1 3 5 7 9 1113 t517 r92 r2325n2931333537394 r

1 AL+ AXIAL FLUX PERMANENT MAG],{ET BRUSHLESS MACHII,IES

z - (2.2123 x l0 5 * f i .216x l0 6 l93f f i t . tou

: 5 .231 x 10-5 + j7 .605 x 10-6 o

R : 5.231 x 10-5 f) X : 7.605 x 10-6 O

The disc resistance R, and reactance X, for higher space harmonics v ) 1 isplotted in Fig. 1.13.

Numerical example 1.3Estimate the cost of materials of a 3-phase, 250 kW 2300 rpm brushless

AFPM machine. The internal stator does not have any ferromagnetic core.The twin-type external rotor (Fig. L4d) consists of sintered NdFeB PMs (40poles) glued to two solid steel discs. The mass of the stator copper conductorsrs'm6u: 18.7 kg, mass of the stator winding insulation (including encapsu-lation) is mirr: 1.87 kg, mass of PMs is rnpy : 32.1kg, mass of the twinrotor core is mr": 50.8 kg (two discs) and mass of the shaft is m"h : 48.5kg. The cost of materials in U.S. dollars per kilogram is: copper conduc-tor cgu : 5.51, insulating materials c'irts : 7.00, sintered NdFeB magnetscpM :20.00 and carbon steel c"1""7 : 0.65. The cost of frame, end discs(bells) and bearings is C1 : $164.00. The cost of components that are in-dependent of the machine geometry (encoder, terminal leads, terminal board,nameplate) is Cs : $140.00.

Coefficients taking into account the manufacturing and utilisation of steelfor the shaft and rotor core (steel discs) are as follows:

r total volume of the steel bar to the volume of the shaft, ku"h: 1.94

r coefHcient taking into account the cost of machining of the shaft, k-"7, :

2 . 1 5

r total volume of the steel plate to the volume of the rotor discs, kr, : !.1

. coefficient taking into account the cost of machining of the rotor steel discs,k^, : \ .8

Solution

The cost of the copper winding

C- : nlgrcC,: 78.7 x 5.51 : $103.12

Introduction

The cost of the insulation and encapsulation

Cir" : Tr l insc' in": 1.87 x 7'00 : $13'10

The cost of PMs

Cpt',r : rnpMcpM :32.7 x 20.00 : $640.80

The cost of the rotor core (two steel discs)

Cr.: kurkrn mr.csteel:2.1 x 1.8 x 50.8 X 0.65 : $tZ4.B5

The cost ofthe shaft

C"h - kr"7rk*rnr1"csteel: L.94 x 2.I5 x 48.5 x 0.65 : $131.55

Total cost of materials

C : Cf t Co + C. + C,rnr l Cpm * Cr.l Crn

: 164.00* 140.00+ 103.12+ 13.10+640.80+ 724.85+ 131.55 : $ t3t7.a5

Chapter 2

PRINCIPLES OF AFPM MACHINES

In this chapter the basic principles of the AFPM machine are explained indetails. Considerable attention is given to the magnetic circuits, windings,torque production, losses, equivalent circuits, sizing procedure, armature reac-tion and performance characteristics of AFPM machines.

2.1 Magnetic circuits

2.1.1 Single-sided machinesThe single-sided construction of an axial flux machine is simpler than the

double-sided one, but the torque production capacity is lower. Fig.2.1 showstypical constructions of single-sided AFPM brushless machines with surfacePM rotors and laminated stators wound from electromechanical steel strips.The single-sided motor according to Fig. 2.lahas a standard frame and shaft.It can be used in industrial, traction and servo electromechanical drives. Themotor for hoist applications shown in Fig. 2.1b is integrated with a sheave(drum for ropes) and brake (not shown). It is used in gearless elevators [103].

2.1.2 Double-sided machines with internalPM disc rotor

Inthe double-sided machine with internal PM disc rotor, the armature wind-ing is located on two stator cores. The disc with PMs rotates between twostators. An eight-pole configuration is shown in Fig. 2.2. P}ds are embeddedor glued in a nonmagnetic rotor skeleton. The nonmagnetic air gap is large,i.e. the total air gap is equal to two mechanical clearances plus the thicknessof a PM with its relative magnetic permeability close to unity. A double-sidedmachine with parallel connected stators can operate even if one stator winding

28 AXIAL FLUX PERMANENT MAGNET BRUSHLESS MACH]NES

Figure 2.1. Single sided disc type machines: (a) for industrial and traction electromechanical

drives, (b) for hoist applications. I - laminated stator, 2 - PM, 3 - rotor, 4 - frame, 5 -

shaft,6 sheave.

ROTOE STATOR

Figure 2.2. Configuration of double-sided AFPM brushless machine with internal disc rotor

1 rotor, 2 - PM, 3 stator core, 4 - stator winding.

is broken. On the other hand, a series connection is preferred because it canprovide equal but opposing axial attractive forces.

A practical three-phase, 200 H2,3000 rpm, double-sided AFPM brushlessmotor with built-in brake is shown in Fig. 2.3 [145]. The three-phase winding

/.3

2

Principles of AFPM machines

Figure 2.3. Double-sided AFPM brushless servo motor with built-in brake and encoder: 1 -

statorwinding,2- statorcore,3 discrotorwithPMs,4-shaft,5 -left frame,6 rightframe, 7 - flange, 8 - brake shield, 9 - brake flange, 10 - elecfromagnetic brake, 1l -

encoder or resolver. Courtesy of SlovakUniversity of Technologt STU, Bratislava and ElectricalResearch and ksting Institute,Nov| Dubnica, Slovakia.

is Y-connected, while phase windings of the two stators are in series. This

motor is used as a flange-mounted servo motor. The ratio X"alX"q t 1.0

so the motor can be analysed as a cylindrical non-salient rotor synchronousmachine [118, 143, 145].

2.1.3 Double-sided machines with internal ring-shapedcore stator

A double-sided machine with internal ring-shaped stator core has a poly-phase slotless armature winding (drum type) wound on the surface of the statorferromagnetic core. 192, 160,218, 2451. In this machine the ring-shaped statorcore is formed either from a continuous steel tape or sintered powders. Thetotal air gap is equal to the thickness of the stator winding with insulation,mechanical clearance and the thickness of the PM in the axial direction. The

double-sided rotor simply called twin rotor with PMs is located at two sides

of the stator. The configurations with intemal and external rotors are shownin Fig. 2.4. The three phase winding arrangement, magnet polarities and fluxpaths in the magnetic circuit are shown in Fig. 2.5.

29

30 AXIAL FLUX PERMANEIVT MAGNET BRUSHLESS MACHINES

Figure 2.4. Double-sided machines with one slotless stator: (a) internal rotor, (b) externalrotor. I -statorcore, 2 statorwinding, 3 -steel rotor, 4 PMs, 5 resin, 6 frame,7 - shaft.

Figure 2.5. Three-phase winding, PM polarities and magnetic flux paths of a double-sided discmachine with one intemal slotiess stator. 1 winding, 2 PM, 3 - stator yoke, 4 rotoryoke.

The AFPM machines designed as shown in Fig. 2.4acanbe used as a propul-sion motor or combustion engine synchronous generator. The machine withexternal rotor, as shown in Fig. 2.4b,has been designed for hoist applications.A similar machine can be designed as an electric car wheel propulsion mo-tor. Additional magnets on cylindrical parts of the rotor are sometimes added

[ 160] or U-shaped magnets can be designed. Such magnets embrace the arma-

Principles of AFPM machines 3l

ture winding from three sides and only the internal portion of the winding does

not produce any electromagnetic torque.Owing to the large air gap the maximum flux density does not exceed 0.65

T. To produce this flux density a large volume of PMs is usually required.

As the perrneance component of the flux ripple associated with the slots is

eliminated, the cogging torque is practically absent. The magnetic circuit is

unsaturated (slotless stator core). On the other hand, the machine structure

lacks the necessary robustness [218]. Both buried magnet and surface magnet

rotors can be used.There are a number of applications for medium and large power axial flux

motors with external PM rotors, especially in electrical vehicles [92, 245].

Disc-type motors with extemal rotors have a particular advantage in low speed

high torque applications, such as buses and shuttles, due to their large radius for

torque production. For small electric cars the electric motor mounted directly

into the wheel is recommendedl92l.

2.I.4 Double-sided machines with internal slotted stator

The ring-type stator core can also be made with slots (Fig. 2.6). For this

type of motor, slots ale proglessively notched into the steel tape as it is passed

from one mandrel to another and the polyphase winding is inserted 12451. ln

the case of the slotted stator the air gap is small (g < 1 mm) and the air gap

magnetic flux density can increase to 0.85 T 1921. The magnet volume is less

than 50Yo that of the previous design, shown in Figs 2.4 and2.5.

Figure 2.6. Double-sided machine with one intemal slotted stator and buried PMs. I - stator

core with slots, 2 - PM, 3 - mild steel core (pole), 4 - nonmagnetic rotor disc.

) L AXIAL FLUX PERMANENT MAGNET BRL|SHLESS MACHINES

Figure 2.7. Double-stator, triple-rotor AFPM brushless motor with water cooling system [55]I -PM,2-statorcore, 3 statorwinding.

2.1.5 Double-sided machines with internal coreless statorAFPM machines with coreless stators have the stator winding wound on a

non-magnetic and non-conductive supporting structure or mould. The statorcore losses, i.e. hysteresis and eddy current losses do not exist. The losses inPMs and rotor solid steel disc are negligible. This type of design offers higherefficiency at zero cogging torque. In order to maintain a reasonable level offlux density in the air gap, a much larger volume of PMs in comparison withlaminated stator core AFPM machine is required. The stator winding is placedin the air gap magnetic field generated by the PMs mounted on two opposingrotor discs (Fig. l.ad). When operating at relatively high frequency, significanteddy current losses in the stator winding conductors may ocun 12341.

2.1,6 MultidiscmachinesThere is a limit on the increase of motor torque that can be achieved by

enlarging the motor diameter. Factors limiting the single disc design are:

(a) axial force taken by bearings;

(b) integrity of mechanical joint between the disc and shaft;

(c) disc stiffness.

A more reasonable solution for large torques are double or triple disc motors.There are several configurations of multidisc motors l5-7 , 55,73, 7 41. Large

multidisc motors rated at least 300-kW have a water cooling system (Fig.2.7)

Principles of AFPM machines 33

with radiators around the winding end connections [55]. To minimize the

winding losses due to skin effect, variable cross section conductors may be

used so that the cross section of conductors is bigger in the slot area than in the

end connection region. Using a variable cross section means a gain of 40o/o in

the rated power [55]. However, variable cross section of conductors means an

increased cost of manufacturing. Owing to high mechanical stresses a titanium

alloy is recommended for disc rotors.

2.2 Windings2.2.1 Three-phase windings distributed in slots

In a single-layer winding, only one coil side is located in a single slot. The

number of all coils is s1 f 2 and the number of coils per phase is n. : s 1 I (2m1)

where si is the number of stator slots and rn1 is the number of phases. In a

double-layer winding two sides of different coils are accommodated in each

slot. The number of all coils is s1 and the number of coils per phase is n. :

stlmt.The number of slots per pole is

(2.r )

where 2p is the number of poles. The number of slots per pole per phase is

o'- h

S lq r :

2 p * ,

The number of conductors per coil can be calculated as

r for a single-layer winding

(2.2)

(2.3)

(2.4)

A I -L r c -

r for a double-laver windine

A r -r r c -

_ aoa*Nt _ aoa-Nt

s1l (2m1) PQt

aoa-Nt _ ara*Nt

stlmt 2pqt

aoa-N1

T1'c

ara-Nr _TLc

where ,Ay'l is the number ofturns in series per phase, oo is the number of parallel

current paths and a- is the number of parallel conductors. The number of

conductors per slot is the same for both single-layer and double-layer windings,

i .e.

1 AJ + AXIAL FLUX PERMANENT MAGNET BRUSHLESS MACHINES

ALt : ctoa*Nt

PQt(2.s)

The full coil pitch measured in terms of the number of slots is y1 : Q1 where

Q1 is according to eqn (2.1). The shorl coil pitch can be expressed as

(2.6)

where tu"(r) is the coil pitch measured in units of length at a given radius rand r(r) is the pole pitch measured at the same radius. The coil pitch-to-polepitch ratio is independent on the radius, i.e.

at:YPetr \ r )

- u t " \ t ' )t ' - / \

T \7 ' )

kpr : sin (Utr)

The distribution factor of a polyphase winding for the fundamental space har-monic u : 1 is defined as the ratio of the phasor sum-to-arithmetic sum ofEMFs induced in each coil and expressed by the following equation:

1 . , , -t r o | -

sin(nl2m)(2.8)

qlsin}t l(2m1q1)l

The pitch factor for the fundamental space harmonic u : I is defined as theratio of the phasor sum to-arithmetic sum of the EMFs per coil side andexpressed as:

(.2.7)

(2.rt)

(2.e)

The winding factor for fundamental is the product of the distribution factor(eqn (2.8)) times pitch factor (eqn (2.9)), i.e.

kur : ka tk r t

The angle in electrical degrees between neighbouring slots is

(2.r0)

360"t - - P

S 1

Fig. 2.8 shows a single layer winding distributed in s1 : 36 slots of a three-

Phase, 2p:6 AFPM machine.


Figure 2.8. SingleJayer winding of an AIPM machine with rnr : 3' 2p : 6, sr : 36'

A t : Q t : 6 a n d Q t - 2 .

2.2.2 Drum-type windingDrum-type stator windings are used in twin-rotor double-sided AFPM ma-

chines (Fig. 2.q. The drum-type stator winding of a three-phase, six-pole

AFPM machine with twin external rotor is shown in Fig. 2.9. Each phase

of the winding has an equal number of coils connected in opposition so as to

cancel the possible flux circulation in the stator core. Those coils are evenly

distributed along the stator core diametrically opposing each other so the only

possible number of poles are 2,6,10, . . . etc. The advantages of the drum-type

stator winding (sometimes called toroidal stator winding 146,219]) are short

end connection, simple stator core and easy design of any number of phases'

2.2.3 Coreless stator windingCoreless stator windings are used in twin-rotor double-sided AFPM ma-

chines (Fig. l. d). For the ease of construction, the stator winding normally

consists of a number of single layer ttapezoidally shaped coils. The assembly

of the stator is made possible by bending the ends of the coils by a certain angle,

so that the active conductors lie evenly in the same plane and the end windings

nest closely together. The windings are held together in position by using a

composite material of epoxy resin and hardener. Fig. 2.10 shows the coreless

stator winding of a three-phase, eight-pole AFPM machine. obviously, the

relations used in the slotted stator windings can be directly used for coreless

35

36 AXIAL FL\]X PERMANE]VT MAGNET BRT]SHLESS MACHINES

Figure 2.9. Drum-type winding of a three-phase, six-pole, 18-coil AFpM machine with fwinextemal rotor.

Figure 2.10. Coreless winding of a three-phase, eight-pole AFPM machine with twin externalrotor.

trapezoidal stator winding with the exception that the term "slot" is replacedby the "coil side". Another coil profi1e that has been used in coreless statorAFPM machines is the rhomboidal co1l. It has shorler end connections than


Figure 2.11. Connection diagram ofa three-phase, nine-coil winding ofan AFPM brushlessmachine.

the trapezoidal coils. The inclined arrangement of the coil's active sides makesit possible to place water cooling ducts inside the stator. The main drawbackof rhomboidal coils is the reduction of the torque.

2.2.4 Salient pole windingsA salient pole AFPM motor can be of single-sided or double sided construc-

tion (Figs 1.5, 1.6, 2.12). The stator winding consists of a number of coils withconcentrated parameters and separate ferromagnetic cores for each of the coil.In general, the number of stator poles (coils) is different than the number ofrotor poles. Fig. 1.5b shows a three-phase, 12-coi1 stator winding of a double-sided AFPM machines with 2p : 8 rotor poles. Figures 1.6, 2.ll and 2.12show a three-phase, 9-coil stator winding. The difference in the number of thestator and rotor poles is necessary to provide the starting torque for motors andthe reduction of torque pulsations.

2.3 Torque productionSince the dimensions of AFPM machines are functions of the radius, the

electromagnetic torque is produced over a continuum of radii, not just at aconstant radius as in cylindrical machines.

The pole pitch r(r) and pole width br(r) of an axial flux machine are func-tions of the radius r, i.e.

3 /

38 AXIAL FLUX PERMANEI{T MAGNET BRUSHLESS MACHINES

Figure 2.12. Three-phase, nine-coil stator of a single-sided AFPM brushless machine with

salient poles stator. Photo-courtesy of Mii Technologies, West Lebanon, NH, U.S.A.

(2.r2)2trr m

2 p p

where a; is the ratio of the average Born to peak value B-,n of the magneticf fux density in the air gap. i .e.

7f f'o , , l r l : 0 ; T l r l : ( ) ;

P w P

Bo un b r ( ' )a i :

B * , o r a i :

r ( r )

^ , \ m t J | N r t o m r f i N t l or L m v J p'r \t ' ) 7T r

(2 . 1 3 )

(2.14)

Both the pole pitch r(r) and pole width br(r) are functions of the radius r, theparameter a; is notmally independent of the radius.

The line current densiQ is also a function of the radius r. Thus the peak

value of the line current density is

(2.rs)

The tangential force acting on the disc can be calculated on the basis of Am-pere's equation

dh, - Io(rir x En1 : A(r)(d-s, nn) (2.r6)


where lod,; : AQ)d,3, AQ) : A*(ilt/2 according to eqn (2.15), di is tne

radius element, d3 is the surface element and En is the vector of the normalcomponent (perpendicular to the disc surface) of the magnetic flux density inthe air gap. An AFPM disc-type machine provides Bn practically independentof the radius r.

Assuming the magnetic flux density in the air gap B,nn is independent ofthe radius r, dS : 2nrdr and Born : a,iBrns according to eqn (2.I4), theelectromagnetic torque on the basis of eqn (2.16) is

d,T6 : rd,F, : rlk6A(r)Bousd,Sl : 2ratk-rA(r)B*nr2dr (2.17)

The line current density ,4(r) is the electric loading per one stator active sur-face in the case of a typical stator winding distributed in slots (double-sidedstator and internal rotor) or electric loading of the whole stator in the case ofan internal drum type or coreless stator.

2.4 Magnetic fluxFor sinusoidal distribution of the magnetic flux density waveform excited

by PMs, the average magneticflux density is

(2 .18)

Since the surface element per pole is 2nrdrl(2p), the magnetic flux excitedby PMs per pole for a nonsinusoidal magnetic flux density waveform Baus :

a;B*n is

Bn n ''t(pa)d.a : -* u *n [i

*",o",] " "

: -]- B*olcos ?r - cos ol : ? u*o7f '71

21 7la iB*n- j rd r : a iB- zp

^np

: onB,.n#@?,,, - R?.)

B a u g :Tr lp - 0 lo"'o

f c l R o u t

l r - |t - l

l t ll ' ) n o "

: I:-oJ

(2.re)

where B*n is the peak value of the magnetic flux density in the air gap, p isthe number of pole pairs, Ro'1 : O.5Dout is the outer radius of the PMs andRh : 0.5D,;n is the inner radius of the PMs.

It is convenient to use the inner-to-outer PM radius or inner-to-outer PMdiameter ratio. i.e.

40 AX]AL FLUX PERMANE]{T MAGNET BRUSHLESS MACHINES

Thus,

o / : o ,B*o ! [ (0 .5D, , ,12 - (0 .5D; , ) ' ] : o , B*n ! DI , ,G - k ' i l Q .2 l l' " ' 2p ' " 6p

The same equation for a cylindrical type machine is [96]

Q r : ?rLiB,no" '77

where r is the pole pitch and Lt, is the effective length of the stack.T,he permeance of the air gap in the d-axis at the radius r is given by d,G n :

uofiatffdr or

, ^ r f R . u r t t ^ . , l r 2 l R " " ' I nGn : * * , ' : I rc t r - #" , ; l ' r l - t to )a i * (n : , , - R7, )" g ' , p J R , " g ' P L z ) a , , g ' t p

: ^n*,+@2,, - R?,) Q.23)

where \s : lro I g' is the permeance per unit surface and g' is the equivalent airgap'

2.5 Electromagnetic torque and EMFThe average electromagnetic torque developed by AFPM motor according

to eqns (2.15) and (2.17) is

d,Td : 2 a im1 I o IY 1k.1 B rnnr dr

If the above equation is integrated from Dou1f 2to Di,f 2 with respect to r, theaverage electromagnetic torque may be written as

, R'in D';,-

Rn,,t Dr'rt

Ta : ),nn

rrloNrk-rB^s(D3.r - D?,)

: )aimrt{&dB^sD'lut0

- k:i)h

(2.20)

(2.22)

(2.24)

where k; is according to eqn (2.20). Putting eqn (2.21) into eqn (2.24) theaverage torque is


T a : 2 L * r N 1 k * 1 Q s I o1T

To obtain the rms torque for sinusoidal current and sinusoidal magnetic fluxdensity, eqn (2.25) should be multiplied by the coefficient

"rDla = 1.11, i.e.

Ta : TlpNtk,te ylo - kTIov'2

where the torque constant

k, : ftrNtk*t{_f

(2.27)

In some publications [84, 218] the electromagnetic force on the rotor is simplycalculated as the product of the magnetic and electric loading BoooA and activesurface of PMs S : n(R\,, - R?,),i.e. F, : rBo,,nA(R\., J Rl.),whereA is the rms line current density at the inner radius R4n. For a double-sidedAFPM machine S : 2tr(R?-", - R?"). Thus, the average electromagnetictorque of a double-sided AFPM machine is

Ta: F*&n:2trBounA(R?""r- R?)Rn, :2trBo,gAR2*(ka - tcl l 1z.zt l

Taking the first derivative of the electromagnetic torque 7a with respect to k4and equating it to zero. the maximum torque is for ,ka = | I /i. lndustrialpractice shows that the maximum torque is for ka I t lt/9.

The EMF at no load can be found by differentiating the first harmonic ofthe magnetic flux waveform iDyr : O/ sinot and multiplying by ly'1k,,1, i.e.

ey : Nlk-14*-! , t :2rf N{c-1Qy cosoltdt

The magnetic flux (D1 is expressed by eqns (2.19) and (2.21). The rms valueis obtained by dividing the peak value 2n f N1k.tQ f of the EMF by y8,, i.e.

Et: nrt f N1k*1Q1: nt[2pNtk-rQfn": kErL" (2.29)

where the EMF constant (armature constant) is

kB : ntf2pNyk-1Qy (2.30)

The same form of eqn (2.29) can be obtained on the basis of the developedtorque Ta : mrElI"l(2trn") in which 74 is according to eqn (2.26). For thedrum type winding the winding factor k-1 :1.

41

(2.2s)

(2.26)


2.6 Losses and efficiency2.6.1 Stator winding losses

The stator (armature) winding resistance per phase for the d.c. current is

R7d.: Nil.-,.,

a,pauosa

where l/1 is the number of armature tums per phase, 11.,,., is the average lengthof turn, c,o is the number of parallel current paths, a- is the number of parallelconductors, o1 is the electric conductivity of the armature conductor at giventemperature (for a copper conductor ot r= 57 x 106 S/m at 20"C and o1 =

47 x 706 S/m at 75"C), and so is the conductor cross section. The averageleneth of the armature turn is

11o,, -- 2Lt + lun ! Iuut (2.32)

in which l1;,-, is the length of the inner end connection and l1ou7 is the lengthof the outer end connection.

For a.c. curuent and stator winding distributed in slots (ferromagnetic core)the stator winding resistance should be divided into the resistance of bars (ra-dial portions of conductors) R16 and resistance of the end connections fir",

Rt : Rn * Rr": ly ' t

(2L;ktn I l tn I luut) x k111R14" Q.33)aosa

where k16 is the skin-effect coefficient for the stator (annature) resistance. Fora double-layer winding and ur.(r) : ,(r') or 13 : 1 [149]:

k t r y , : p r (€ r ) + vr ( { r ) (2.34)

where

t4# -(v.'";)']

(2.31)

(2.3s)

(2.36)

(2.37)

pr(dr) : €rsinh 26r * sirr 2{r

cosh 2{1 cos 2{1

q i n h F ' - s i n F ,i l r , / F , \' r \ \ r / - ' ' c o s h q ,

- c o s { r

7r I F"ot ,0 1 1


nfid m4 is the number of conductors per slot arranged above each other intwo layers (this must be an even number), 7 is the phase angle between thecurrents of the two layers, / is the input frequency, bpon is the width of all theconductors in a slot, b11 is the slot width and h, is the height of a conductor inthe slot. If there arte tT"l conductors side by side at the same height of the slot,they are taken as a single conductor carrying n";-times greater current.

In general, for a three-phase winding ? : 60o and

(2.38)

For a chorded winding (w"(r) < r (r)) and ? : 600

k* xer((r) * l*? ' - - t - 3(r - y ' l r ) -3, . ] v,re, t e.3slL 3 lr i " ' l

The skin-effect coefficient k16 for hollow conductors is given, for example, in

[r4el.

(a) If m"1: 1 and 1 : 0, the skin-effect coefficient kyp : pr({r) (the sameas for a cage winding).

(b) Ifl : 0, the currents in all conductors are equal and

krR :p,(€r) . (4f +)vr(6r)

- 2 - - 1k tn= q \ t ) + - : ! ' _ :V r (€ r )

J(2.40)

For small motors with round armature conductors fed from power frequenciesof 50 or 60H2,

Rt x Rta. (2.4r)

The armature winding losses are

LPw : ruISRr = mlllRla.kyp (2.42)

Since the skin effect is only in this part of the conductor which is located inthe slot - eqn (2.33), the armature winding losses should be multiplied by thecoefficient

kn * lu. I (2Li) * 11"6 I (2L.i)

rather than by k1a.

1 - t lu" l (2L i ) + t t * t l (2L i )(2.43)

44 AXIAL FLUX PERMAI{ENT MAG]VET BRUSHLESS MACHINES

2.6.2 Stator core lossesThe magnetic flux in the stator (armature) core is nonsinusoidal. The rotor

PM excitation system produces atrapezoidal shape of the magnetic flux densitywaveform. The stator windings are fed from switched d.c. sources with PWMor square wave control. The applied voltage thus contains many harmonicswhich are seen in the stator flux.

The eddy current losses can be calculated using the following classical for-mula

, m

LP, ," : "^ "ja 1ztll.n,p.t "' ' le'-,, + *-,,10 P F " n I

- 2 ^ _- ' ;

#f d2p,mp"lB2-,, - B?,,,1q7,

where oF", dF", pp" andlmlle are the electric conductivity, thickness, specificdensity and mass of laminations respectively, n are the odd time harmonics,Brnrn and B,nrn are the harmonic components of the magnetic flux density inthe r (tangential) and z (normal) directions and

(38*"2)'2 + (3B,nA)2

B2r-r, + Blr,

(58 ry ! : \ 2 + ( !F - , i ) 2 + Q .451

D m r T T D m . z 1

(2.44)

(2.46)

is the cofficient o.f distortion of the magnetic fux density. For qa : 1, eqn(2.44) expresses the eddy current losses under sinusoidal magnetic flux density.

In a similar way, the hysteresis losses can be expressed with the aid ofRichter's formula, i.e.

r O OrLPnp" : r] ;r,rp"\rr2lal,", + 82,-",1

I t , t , n _ 1

{t - : - t r r t r , lb ' - , t * I J ' - r1 ) r1 '4

100

where e, :7.2ro2.0mal(]Hkg) foranisotropic laminations with4o/o Si, e : 3.8m4l1H kg) for isotropic laminations with2o/o Si and e : 4.4to 4.8 m4l(H kg)for isotropic siliconless laminations.

Eqns (2.44) and (2.46) exclude the excess losses (due to magnetic anomaly)and losses due to metallurgical and manufacturing processes. There is a poorcorrelation between measured core losses and those calculated using classicalmethods. The losses calculated according to eqns (2.44) and (2.46) are lowerthan those obtained from measurements. The coefficient of additional core

Principles of AFPM machtnes 45

losses ko6 ) 7 can help to obtain a better agreement of predicted and measuredcore losses

LPtp": koa(LP"r" * LP1rp") (2.47)

If the speciJic core losses are known, the stator core losses LPt p" can be cal-culated on the basis of the specific core losses and masses of teeth and yoke,i .e.

LPtp" lko a1 B! 1m 1 1 -t k o,1, Bl om 1 ol (2.48)

where kad.t ), \ and ko6, ) 1 are the factors accounting for the lncrease lnlosses due to metallurgical and manufacturing processes, L11lso is the specificcore loss in Wkg at I T and 50H2,.B11 is the magnetic flux density in a tooth,B1o is the magnetic flux density in the yoke, m11is the mass of the teeth, andm1, isthe mass of the yoke. For teeth ko6 : 1.7 to 2.0 and for the yoke

kod,s : 2 .4 to 4 .0 l l47 l .

2.6.3 Core loss finite element modelThe core losses within the stator and rotor are calculated using a set of finite

element method (FEM) models, assuming constant rotor speed and balancedthree-phase armature currents. The eddy current and hysteresis losses, withinthe cores, in the 2D FEM including distorted flux waveforrns can be expressed

by eqns (2.44) and (2.46).The field distribution at several time intervals in the fundamental current

cycle is needed to create the magnetic flux density waveforms. This is obtainedby rotation of the rotor grid and phase advancement of the stator currents. Froma field solution, for a particular rotor position, the magnetic flux density at eachelement centroid is calculated. Three flux density components in an elementcan be obtained from a single FEM solution.

2.6.4 Losses in permanent magnetsThe electric conductivity of sintered NdFeB magnets is from 0.6 to 0.85 x

106 S/m. The electric conductivity of SmCo magnets is from 1.1 to 1.4 x 106S/m. Since the electric conductivity of rare earth PMs is only 4 to 9 timeslower than that of a copper conductor, the /osses in conductive PMs due tohigher harmonic magnetic fields produced by the stator cannot be neglected.

The most important losses in PMs are generated by the fundamental fre-quency magnetic flux due to the stator slot openings. In practice, those losses

t r , , 4 / 3: ar'z'o (jo)


are only in AFPM machines with slotted stator feromagnetic cores. The fun-damental frequency of the magnetic flux density component due to the statorslot opening is

f s l : s t P n (2.4e)

where s1 is the number of stator slots, p is the number of pole pairs and n isthe rotor speed in rev/s.

The magnetic flux density component due to slot opening is [111]

Bst : ct,11B"1,kgBo,,o (2.s0)

where Boro is the mean magnetic flux density overthe slot pitch - eqn(2.4),kg is Carter coefficient (l.2\ and

o ' : * (o tn

"#* )

s in(1 6nr )

1 \. I/ ; - , t I

v L | t i ' /

h t t

g'

, J r r : 0 5 ( 1 -

(2 .51 )

(2.s2)

(2.s3)l :bt 1

In the above equations (2.51), (2.52) and (2.53) b1a is the stator slot opening,gt : g * hm I ltrr"" is the equivalent air gap, tt is the slot pitch and h,r,r is themagnet thickness per pole.

Assuming that the relative recoil magnetic permeabllity 1.t,.,r,. r 1, thepower losses in PMs can be expressed by the following equation obtained froma 2D electromagnetic field distribution, i.e.

(2.s4)

where ap, is according to eqn (1.16) for u : 1, a : (t + j)k is according toeqn (l.l 1) for u : I, k is according to eqn (1.12) for u : 7, p ts according toeqn (1.6) for u : 7 and oppl is the electric conductivity of PMs. Eqn(2.5a)can also be used to estimate the reactive losses in PMs if ap, is replaced withuy, according to eqn (1.17).

The coefficient for including the circumferential component of currents in-duced in PMs can be found as

I ta t2 ( B , t \2 k ^L P p t r - - i r n , k - . ; t - , - r p n 1z lJ \HUHrr ' ' / oP ' \ ]

where 0.5tr is the induced cuffent loop span and0.5(Do"t - Dn) is the radiallength of the PM - see eqn (1.30). The active surface area of all PMs (single-sided machines) is


&RFe

r u 2 - r t ^

I)ou,t - l)in

SpM : "o nQ3,t

- D7")

where the average pole pitch r is according to eqn (1.9).

l@_.a2p-a2y*

47

(2.ss)

(2.s6)

(2.s7)

2.6.5 Rotor core lossesThe rotor core losses, i.e. losses in backing solid steel discs supporting PMs

are due to the pulsating flux produced by rapid changes in air gap reluctanceas the rotor passes the stator teeth.

The magnetic permeability of a solid steel disc varies with the z axis (normalaxis). To take into account the variable magnetic permeability and hysteresislosses in solid ferromagnetic discs, coefficients a1u, axu according to eqns(1.16) and (1.17) must be replaced by the following coefficients:

_ 1

p' luFl

1

,/,

- tp' l". . . . : l

k2 lI

1

rtaxFe (2.58)

where an: L4 to 1.5, ax :0.8 to 0.9 according to Neyman [184], k" is

according to eqn (1.12) and B is according to eqn (1.6) for u :1.

The power losses in solid ferromagnetic discs can be expressed by a similarequation to eqn (2.54), i.e.

LPzp" : *o*r"*"ry ffi)' *t r. (2.se)

where appu is according to eqn (2.57) for u : 1, c is according to eqn (1.11)

for u : 1, k is according to eqn (1. 1 2) for u : 1, B is according to eqn ( 1.6) foru : l,8"7 is according to eqn (2.50), p, is the relative magnetic permeability

48 AXIAL FLUX PERMANENT MAGNET BRLTSHLESS MACHINES

and op. is the electric conductivity of the solid ferromagnetic disc. The fre-quency in the attenuation coefficient k is according to eqn (2.49). Eqn (2.59)can also be used to estimate the reactive losses in the solid ferromagnetic discif o,pp" is replaced with a;p" according to eqn (2.58). The flux density B.r7is according to eqns (2.50) to (2.53). The coefficient k" is according to eqn(2.55) and the surface of the disc is

sF.: [{n3,, - D?.) (2.60)

2.6.6 Eddy current losses in stator conductorsFor slotted AFPM machines the eddy current losses in the stator winding are

generally ignored as the magnetic flux penetrates through the teeth and yokeand only small leakage flux penetrates through the slot space with conductors.

In slotless and coreless machines, the stator winding is exposed to the air gapmagnetic field. The motion of PMs relative to the stator winding produces analternating field through each conductor and induces eddy currents. In the caseof a coreless AFPM machine with a solid ferromagnetic rotor discs, there isalso a tangential field component B,n, inaddition to the axial field componentBrr". This can lead to serious additional eddy current loss especially at highfrequency. Neglecting the proximity effect, the eddy current loss in the statorwinding may be calculated by using a classical equation similar to eqn (2.44)for calculation of the eddy cunent losses in laminated cores, i.e.

r for round conductors [43]

- 2 * o c

Lp": Titrar-.o,, f rr2lB2^*, + B?,",]

' n :7

: | \ 12a'rn,onlB'^,t + B?,,"r ln\t Q.6l)+ I )

r for rectangular conductors [43]

) (Y)

AP" = ; ^f',r'^.o, I n,2[82,n*, + B?r"r]J P

n - l

2 ^

-1 f'o'*"orlB?rrtL-. + g?'1f- o

3p'r."tl'l'o (.2.62)


where d is the diameter of the conductor, a is the width of the conductor (paral-lel to the stator plane), o is the electric conductiviry p is specific mass densityof the conductar, m"on is the mass of the stator conductors without end con-nections and insulation, / is the stator current frequency, Brr* and Brn" arcthepeak values of tangential and axial components of the magnetic flux density,respectively, andrla is the coefficient of distortion according to eqn (2.45).

2.6.7 Rotational lossesThe rotational or mecltanical losses LProt consist of friction losses APy,

in bearings, windage losses LP*tnd. and ventilation losses LPu.nt (if there isa forced cooling system), i.e.

LPr"t - LPr, * LP,ttrd, * LPo"nt (2.63)

There are many semi-empirical equations for calculating the rotational lossesgiving various degrees of accuracy. The friction losses in bearings of smallmachines can be evaluated usine the followine formula

A,Py, :0.06kya(m, * m"6)n W (2.64)

where kf,, : I to 3 m2ls2, rn, is the mass of the rotor inkg, m"6 is the massof the shaft in kg and n is the speed in rpm.

The Reynolds number for a rotating disc with its outer radius Roul is

2trnpRf;u, (2.6s)

where p is the specific density of the cooling medium, u : 1)r - 2trRo",1n isthe linear velocity at the outer radius Rout, fr is the rotational speed and p isthe dynamic viscosity of the fluid. Most AFPM machines are air cooled. Theair density at I atm and 20"C is 1.2 kg/m3. The dynamic viscosity of the air at1 atm and 20"C is F : 1.8 x 10-5 Pa s.

The cofficient of drag for turbulent flow can be found as

(2.66)

The windage losses for a rotating disc are

R": pRou" :I,L

LP-rnd. : )c

y pQnfit @u.,, - R\n) (2.67)


where fi.r7, is the shaft diameter.AFPM machines are usually designed without a cooling fan so that the ven-

tilation losses AP",unr : 0.

2.6.8 Losses for nonsinusoidal currentHigher time harmonics generated by static converters produce additional

losses. The higher time harmonic frequency in the stator winding is n/ wherefr :5,7,1I, . . . . The armature winding losses, the core losses, andthe straylosses are frequency-dependent. The mechanical losses do not depend on theshape of the input waveform.

If the stator winding and stator core losses have been calculated for funda-mental frequency, the frequency-dependent losses of an invefter-fed motor orgenerator loaded with a rectifier can be found as

o stator (armature) windins losses:

APr., - LPr*,: *tD l inRy,, x m1R16,1L lZ,tt t*, (2.68)r t : l n- l

o stator (armature) core losses

co oo

L,P, r;- f AP, ,-- : lA,P,.-- l--, \-Z - z " ) " - ' / J

n-B'7 (2.69)

where k16,, is the a.c. armature resistance skin effect coefficient for n,f , Io, isthe higher harmonic rms armature current, [r, is the higher harmonic inverteroutput voltage, V1r. is the rated voltage, [APrp.,.]n:l are the stator core lossesfor n : 1 and rated voltase.

2.6.9 EfficiencyThe total power losses of an AFPM machine are

AP : LP:.- * APrr'" * LPzp" + LPzM + LP" -f LProt Q.70)

The fficiency is

Dr olrt (2.71)P,6 * L'P

where Po6 is the mechanical output power for a motor and the electrical outputpower for a generator.

oc

\-z .

/ V t , \ 2t _ l

\V , )


UNDTRIXCITTDGTNERATOR

RC LOADo> Y > -90 '

UNDTREXCITIDMOTOR

RL*gO'>Y >- 180 '

OVER[XCITTDCTNTRATOR

RL LOADo< Y <go'

trod:Io sinY

OVTRIXCITIDMOTOR

p n

9O '<Y <180 '

5 l

-l-

,9ilcrg

Figure 2.1 3. Location of the armature current l" in d-q coordinate system.

2.7 Phasor diagramsThe synchronous reactance of a synchronous machine (sine-wave machine)

is defined as the sum of the armature reaction (mutual) reactance Xo4, Xon andstator (armature) leakage reactance X1, i.e.

r in the d-axis

Xsd, : Xo4 I X1 (2.72)

r in the q-axis

X"q: Xon * Xt (2.13)

When drawing phasor diagrams of synchronous machines, two arrow systemsare used:

(a) generator alrow system, i.e.

E.r : Vr i-IoRt * jloaX"a + jloqx"q


: Vr f I"a(Rt * jX,a) *I"q(R4 * jX"q)

(b) consumer (motor) arrow system, i.e.

Vr : E/ * Io-Rr * jIo6Xr,1+ jloqxr,l

: E / - l T "a(Rt * jX"a) * loq( .R1* . iX"q)

(2 .74)

(2.7s)

and

where

I o - I o 6 , * l 6 q (2.76)

Ioa: Ios in 'U 1oq : 1o cos \! (2.71)

The angle V is between the q-axis and armature current 1o. When the currentarows are in the opposite direction, the phasors Io, l,r,L aadl.aq are reversedby 180". The same applies to the voltage drops. The location of the armaturecurrent Io with respect to the d- and q-axis for generator and motor mode isshown in Fig. 2.13.

Phasor diagrams for synchronous generators are constructed using the gen-erator arrow system. The same system can be used for motors, however, theconsumer arrow system is more convenient. An overexcited generator (Fig.2.I4a) delivers both active and reactive power to the load or utility grid. Anunderexcited motor (Fig. 2.lab) draws both active and reactive power from theline. For example, the load culrent I" (Fig. 2.14b ) lags the voltage phasor V1by the angle $. An overexcited motol consequently, draws a leading currentfrom the circuit and delivers reactive power to it.

In the phasor diagrams according to Fig. 2.141116] the stator core losseshave been neglected. This assumption is justified only for power frequencymachines with unsaturated armature cores.

For an underexcited synchronous motor (Fig. 2.lab) the input voltage Iprojections on the d and q axes are

7 r s i n 6 : I u q X " n - I o a R t

I cos 6 -- E.f t Io6X"4 t IoqRl (2.78)


j l "X,

Figure 2.14. Phasor diagrams ofsalient-pole synchronous machine: (a) overexcited generator(generator arrow system); (b) underexcited motor (consumer arrow system).

) J

(a) jl"a4o<_

i l l"o+--

+

Figure 2 . 1 5 . Equivalent circuit per phase of an AFPM synchronous machine : (a) for generatingmode; (b) for motoring mode. Stator core losses have been neglected.

where d is the load angle between the voltage V1 andEMF Ep (q-axis). For anoverexcited motor

V1 s inS : IonX"n* Io6R1

I/r cos 6 : Ef - IodX"d, * IoqRt (2.7e)

AXI A L F LUX P E RMAN E NT MA GNET B RU SH L E SS M AC H I N E S

The currents of an overexcited motor

, Vr (X"ocosd - Rr s in d ) - E IX" ,t 1' uu

x r6x "ns - R '2 ,

, _ V r ( R 1 c o s 6 + X " 6 s i n d ) - E f R t

' ' t ' l X " 6 X " q - R 2 1

(2.80)

(2 .81 )

are obtained by solving the set of eqns (2.78). The rms armature current as afunction of V1,81, X"d, X",r, d, and R1 is

I*:ffi+lfu-X"aX"q * R?

f(X"n cos 6 - Rtsind) - Ef X,n1' + l(/?r cos rI * X"4 sin 6) - E f Rr]2(2.82)

The phasor diagram can also be used to find the input electric power. For amotor

Pin : mlVylo cos @ - rnlVy(Io,n cos d - 1"a sin d) (2.83)

Thus, the electromagnetic power for a motor mode is

P"Ln :

';;;"ff;;;,ff)&",- x"q)t Lprp. eB4)

On the basis of phasor diagrams (Fig. 2.14), equivalent circuits of a AFPMsynchronous machine can be drawn (Fig. 2.15).

2.8 Sizing equationsThe main dimensions of a double-sided PM brushless motor with internal

disc rotor can be determined using the following assumptions: (a) the electricand magnetic loadings are known, (b) the number of tums per phase per onestator is Nr; (c) the phase armature current in one stator winding is 1o; (d) theback EMF per phase per one stator winding is 81.

The peak line current density at the average radius per one stator is expressedby eqn (2.15) in which the radius may be replaced by an average diameter

Vr


8 0 0 0 01 0 0 0 0 0

Figure 2.16. Outer diameter D6a1 zs a {tnction of the output power Po,1 and parameter ki7for e : 0.9, k-1q cos Q : 0.84, n" - 1000 rpm: 16,67 rev/s and B*nA^ : 26, 000 TA/m.

D :0.5(D^"t + Din) :0.5D^"t(7 -t ka) (2.8s)

where Doul is the outer diameter, Dan is the inner diameter of the stator coreand ka : DinlD^ft (according to eqn (2.20)). Thus,

55

^ A{2mtloNrtant:

"D^,^r + kd)

The EMF induced in the stator winding by the rotor excitation system, ac-cording to eqns (2.29) and(2.21) has the following form

Ef : nrf2n"pN1k.yQ7 : !rtn"Ntk,1B^nD2our$

- n3) e.87)

The apparent electromagnetic power in two stators is

(2.86)

(2.88)

S.r,n : m1(281)1": mtEf (21")_2

: ik-1n"8*sA*DZdG + ki\ - k2d)

For series connection the EMF is equal to 2Ey and for parallel connectionthe current is equal to 2Io. For a multidisc motor the number "2" should bereplaced by the number of stators. Putting

56 AXIAL FLUX PERMANENT MAGNET BRTJSHLESS MACHINES

S elrn : n2 k 11k*1n "B

rng ArnDZut (2.e0)

The apparent electromagnetic power expressed in terms of active output poweris thus

1, t r : r (1 +k, i1-k: i )

the apparent electromagnetic power is

^ Pout\ , f -ee tn t -

, / cos g

where the phase EMF-to-phase voltage ratio is

E yI /v 1

D "t e | m

" ) - -4 t t t L s

(2.8e)

(2.er)

(2.e2)

Formotors e < 1 and for generators e ) 1.In connection with eqns (2.90) and (2.91), the PM outer diameter (equal to

the outer diameter of the stator core) is

r? q3)

The outer diameter of PMs is the most important dimension of disc rotor PMmotors. Since Do,1 o, i/P""t the outer diameter increases rather slowly withthe increase of the output power (Fig. 2.16). This is why small power discmotors have relatively large diameters. The disc-type construction is preferredfor medium and large power motors. Motors with output power over l0 kWhave reasonable diameters. Also, disc construction is recommended for a.c.servo motors fed with high frequency voltage.

The electromagnetic torque is proportional rc D!,r, i.e.

, l c Pout, ,U O U I -

l l o ,

\l r'2 k pk *p, B ̂ nA -r7 cos o

,S"7- cOS V) o n

: T k ok -, D3ou, B ̂ n Arn cos v (2.e4)

where P"1* is the active electromagnetic power and V is the angle between thestator current Io and EMF 81.

Prr'nciples of AFPM nachines 57

2.9 Armature reactionThe magnetic fluxes produced by the stator (armature) can be expressed in

a similar way as the field excitation flux - eqn (2.19), i.e.

r in the d-axis

t - n2 , , R? ,Qod : aB rnod . t "

t Lo l )

7T " " * * ' p 2(2.es)

r in the q axis

(2.e6)

where Bmad1 is the peak value of the first harmonic of the stator (armaturereaction) magnetic flux density in the d-axis and Brno4 is the peak value ofthe first harmonic of the stator magnetic flux density in the q-axis. The statorlinkage fluxes are

r in the d-axis

) a O ' r - R ? nQoq:

} " *on ' , ; ' " t ,

*o: #*tk,oteaa: i*rk-t1B-,"ar| ry e.s7l

r in the q axis

, I ,o : *& k-teos: lNrn-, ,?o*-- , !R?'" ' - R?'

' \/2 v , iBmaqT--*f (2'98)

where l/r is the number of stator turns per phase and k.,1 is the winding factorfor the fundamental space harmonic.

Neglecting the magnetic saturation, the first harmonic of the stator magneticflux density normal components are

r in the d-axis

Bmailr: kydB,ood,: kya\aFoa: kro#*f Yr"o

Q.gg)

58

r

AXTAL FLUX PERMANENT MAGNET BRUSHLESS MACHINES

in the g-axis

B-oqt - k laB-od - k laAqFoo: t r tu*yQ! ! ! , .n (2 .100)qa f tP

, B ^ o d L B - o q lt ' J d -

B ^ o r l " . l Q B n , o q

where rn1 is the number of stator phases and the perrneance per unit surface inthe d- and q-axis are

\ . - \ - l t o/ \ t 1 - / \ 0 -

I

r l'o/ \ q -

ea(2.r0r)

In the above equations (2.99) and (2.100) theformfactors of armature reactionare defined as the ratios of the first harmonic amplitude-to-maximum value ofnormal components of armature reaction magnetic flux density in the rJ- andq-axis respectively, i.e.

(2.r02)

The equivalent air gaps in the d- and q-axis for surface configuration of PMsare

r for a stator with ferromasnetic core

g' : qkckrot I (2 .1 03)

g 'n : skck "a tq lhx l l (2.104)

r for a coreless stator

nM

tt--

e' :2 [{n * o.tr-; . H)

9n : 2l(g + 0.51,,) -t h'vl

(2. l os)

Q.ra6)

where f,., is the stator winding axial thickness, h1,1 is the axial height of the PMand p,rr"" is the relative recoil permeability of the PM. To take into account the

Principles oJ'AFPM machines 59

effect of slots, the air gap (mechanical clearance) for a slotted ferromagneticcore is increased by Carter coefficient kc > l according to eqn (1.2). Thesaturation of the magnetic circuit can be included with the aid of saturationfactors k"ot ) 1 in the d-axis and k"o4 ) 1 in the g-axis. For a corelessstator the effect of magnetic saturation of the rotor ferromagnetic discs (core)is negligible.

The MMFs fo4 and fon in the d-axis and q-axis are

m t t / ' l 1\ 1K61 ,r a d - t a d'1T p

l i r r tTn1 V Z 1 \1K ,1 t r1

Tu aq ' aq- 1 f p

(2.101)

(2.108)

where Io6 and Ion are the d- and q-axis stator (armature) currents respectively.The armature reaction (mutual) inductance is calculated as

r in the d-axis

, vd. 1L a d : m r p o -

l ad 7 f

\trq 1TnILLO-

laQ 7T

(Yy)'@58-r,, (2toe)

r in the o-axis

T -"aq

For p,,ec = 1 and surface configuration of PMs (kf a : kf n : 1), the d- andg-axis armature reaction inductances are equal, i.e.

(:F)' (R3*:, R?,) r,n (2 110)

r _ r _ r l / l / r / c - r \L a : L a d - I L a e - m t q \ i \

, /

' (n3,, - R?,)(2 .1 l 1 )

For surface configuration of PMs kfa: kfn : I 196]. For other configura-tions, equations for MMFs in the d- and q-axis will contain reaction factorskya* k fq196 l .

The armature reaction EMFs in the d- and q-axis are

Ead,: nt/2f Nrk*rQoa (2.112)


Table 2.1. Armature reaction equations for cvlindrical and disc-tvoe machines

Quantity Disc-type machine

Armature reactionmagnetic flux

in the d-axisAmature reactlonmagnetic flux

in the q-axis

Pemeanceofthe air gap

in the d-axisPermeanceofthe air gap

in the q-axis

Permeance of theair gap per surfaceofone pole

in the d-axisPermeance of theair gap per surfacearea of one pole

in the q-axis

Armature reactionfeactance

in the d-axis

Amature reactlon

reactance

in the q-axis

Armature reaction

inductance

in the d-axis

Armature reactron

inductance

in the q-axis

oua: lB,noat f f (R\ , , - R7, , )

Q ou : ? Bn,unt f i(R|*t - R7,,)

^o: #*f i (RZ-, - R?^)

R?")1 L s 2 r 1 p 2

T o ' r " ' " u '

\ , l/J)

\ - c.9sit

Y , - E o a

I a , t

: 2 m t p , o f Nr Au, r z R 2 . .k.r a

Y - E a q" , o a

:2mt t t , t f ( { * . t ) 'Wo, ,

f "u : H

- m.rpo+/ A ' r A . , r \ 2 R f , , , - R 7 , , t . ,\ r , I o t " t a

r '! n.o

Cylindrical machine

Q o 4 : 1 B - o 4 1 r L i

Qo, : z Brrru,r l rL i

A, , , : E9ZrL ,' g T

A - l , o 2 - r' 9 ; , n

\ ' - D", lt r " r t -

t a

, ( N r k , " t \ 2 r I '4,n , t rn lU#r# t ' , , ,

X,"r : 1-, o q

\ 2

r - V o , tuod -

I,n-

- 2 n r r r , r 0 4 d ' t ' , , k r , t- ' r ' D . l '

-'2rrrrl,.uJ*{?f .,,, : nL1 lr(r+( ' ' , , ') 'Wr,,

where the armature fluxes Q o6 and Q on are according to eqns (2.9 5) and (2.96) .The armature reaction reactances can be calculated by dividing EMFs .tr"a

arrd E aq according to eqns (2.1 12) and (2.1 I 3) by currents I o4 and I on, i.e.

r in the d-axis

Xad. :2t r fLoa


r in the q-axis

Eoq : nt/2f N1k*1@,o

- 2m, u^, ( Ntkn\2' ' " " \ p /

(R3,, - R?,) ,-d

*Id

Xaq:2 t r fL "n

:2mr un, ( Nft-r\2- ' - "

\ p /

(R2,, - R7) ,- . - K f n

g;

- Eo,l,

I od.

61

(2.rr3)

(2.1t4)

: Eon

Jas

(2.rts)

Table 2.1compares the armature reaction equations between conventionalcylindrical machines and disc-type machines.

2.10 AFPM motor2.10.1 Sine-wave motor

The three-phase stator winding with distributed parameters produces sinu-soidal or quasi-sinusoidal distribution of the MMF. In the case of inverter op-eration all three solid state switches conduct current at any instant of time. Theshape of the stator winding waveforms is shown in Fig. 1.3b. The sine-wavemotor works as a PM synchronous motor.

For a sinusoidal excitation (synchronous machine) the excitation flux can befound on the basis of eqn (2.19) or (2.21), the EMF per phase induced by PMrotor can be found on the basis of eqn (2.29) and the electromagnetic torqueon the basis of eqn (2.26). The EMF constant kB and torque constant k7 areexpressed by eqns (2.30) and (2.27) respectively.

62 AXIAL FLUX PERMANE]{T MAGNET BRUSHLESS MACHINES

2.10.2 Square-wave motorPM d.c. brushless motors with square-wave stator current (Fig.. 1..3a) are

predominantly designed with large eflective pole-arc coefficients, a)"q,, where*f,"n' : br,(r) I r (r) . Sometimes concentrated stator windings and salient statorpoles are used. For the Y-connected windings, as in Fig. 2.1 7 , only two of thethree motor phase windings conduct at the same time, i.e. i"as (TlT4), ioAC(T1T6), i"s6 (T3T6), i"pn (T3T2), i"sa (T5T2), i,,sB (T5T4), etc. Atthe on-time interval (120") for the phase windings A and B, the solid stateswitches T1 and T4 conduct (Fig.2.l7a). when Tl switches offthe currentfreewheels through diode D2. For the off-time interval both switches Tl andT4 are turned-offand the diodes D2 and D3 conduct the armature current whichcharges the capacitor c. If the solid state devices are switched at relativelyhigh frequency, the winding inductance keeps the on-off rectangular cunentwaveforms smooth.

For d.c. current excitation ur * 0, eqn (2.75) is similar to that describing asteady state condition of a d.c. commutator motor, i.e.

V4.: Elr r ]_2RrIGo) (2.r16)

where 2fi1 is the sum of two-phase resistances in series (for Y-connected phasewindings), and Eyr-t is the sum of two phase EMFs in series, V;" is thed.c. input voltage supplying the invefter and I["q) is the flat-topped value ofthe square-wave cur:rent equal to the inverter input curent. The solid switchvoltage drops have been neglected in eqn (2.116). The phasor analysis doesnot apply to this type of operation since the armature current is nonsinusoidal.

For a rectangular distribution of Brns : const with the pole shoe widthbp { , being included, the excitation flux is

*fn) : ol"d u,*n#(R3,, - R?.) (2.117)

For a square-wave excitation the EMF induced in a single turn (two conduc-tors) is 2B*nLiu : ApnB,noL;r. Includingbo and fringing flux, the EMF for

Nrk*t turns e.1 : 4pnNrk.urc'l"q)B,ns+,(R|,,, - R7) : 4pnN1k-yQt7'q).For the Y-connection of the armature windings, as in Fig. 2.l7,two phases- areconducting at the same time. The line-to,line EMF of a Y-connected square-wave motor is

Eyr-L : 2ef : 8pl/rk.r al'q) B,,n(n l2p)(R3*, - n?,)"

: BpNlk-1Ffn', : k E,t.t t, ( 2 . 1 1 8 )

III T

II

II

l r "Il - .>

Cdc

-

* o . -' t f r .f " U

+ t lt l

F, CI!I

u z l. l

I__)

\ T\

' 4 I o, , il]lfy . , ' \\ '.1 ""

(a)


Figure 2.17. Inverter currents in the stator winding ofa PM brushless motor: (a) currents ln

phases A and B for on*time and off-time intervals, (b) on-offrectangular current waveform.

63

where the EMF constant or armature constant ks4" is

k*d.: lPN1k-1Q\fq)

The electromagnetic torque developed by the motor is

P"t* Eyur,I["q)

2rn, 2nn

,1 ,= lply'r k-rotfn'If"o) : kra"I|"n)

7f

where the torque constant of a square-wave motor is

kTd" : * : lnn lv r t - ro fn )

(2.rre)

(2.r20)

(2.121)


and I;"'f is the flat-top value of the phase current.The ratio Ta of a square-wave motor-to-Ta qf a sinewave motor is

Assuming the same motor (*l"n' : ct6) and, the same values of air gap mag-netic flux densities, the ratio of the square*wave motor flux to sinewave motorflux is

, : " ' : !C! i ! [ 'o ' -^cefq) r ;q)z . - ; r ta f I "

= ' ' o * , L

Q7 : @yr : aikSB,nn*rrO3,, - R?,)

5(-sa) ^("q) o t - |- J _ q i u f r lq t t , lQdl(R\" , - R?,) 1 ,^ . ̂ ^ .oi - f f i :1 t , t t ' t z r )

(2.t22)

(2.124)

where [96]

and

r, : *.u,(i.)

fl . Io . T,l: t - t -

no Insh Td"t

(2.r2s)

on the basis of eqns (2.118) and (2]20) the torque*speed characteristic canbe expressed in the following simplified form

(2.126)

where the no-load speed, locked rotor armature current and stall torque arerespectively

Trlrt: kr6.Io"h (2.r27)

For half-wave operation i? : Rr while for full-wave operation R : 2Rt.Note that eqn (2.126) neglects the armature reaction, rotational and switchinglosses.

The torque-speed characteristics are shown in Fig. 2.18. Eqns (2.126) and,(2.127) are very approximate and cannot be used in calculation of performancecharacteristics of practical PM d.c. brushless motors. Theoretical torque-speedcharacteristics (Fig. 2.18a) differ from practical characteristics (Fig. 2.18b).The continuous torque line is set by the maximum rated temperature of the

W,. vd,no- kE

I " "n - i


mT

65

(a)()f

Y

ofg"

cont.stall

torque

cont.rated

torque

_ peak stall torque

peak rated torque

raled speed speed

Figure 2.18. Torque-speed characteristics ofa PM brushless motor: (a) theoretical, (b) prac-

tical.

motor. The intermittent duty operation zone is bounded by the peak torque

line and the maximum input voltage.The rms stator current of a d.c. brushless motor for a 120o square wave

(T : 2r lw) is

T -L O . - /fotlzot

- r(ss)- t o , (2.t28)

2.ll AFPM synchronous generator

2.ll.l Performance characteristics of a stand alonegenerator

An AFPM machine driven by a prime mover and connected to an electric

load operates as a stand alone synchronous generator. For the same syn-

chronous reactances in the d'and g-axis Xsd. : X"q : X" : aL", and

load impedance per phase

? l::;"

.l

Zr , :R r * jwLp - i ^u a C

speed

iz(t)dt:+ 1,"'"1 r ' \6 ; )

(2.tze)

66 AXIAL FLUX PERMANENT MAGNET BRT]SHLESS MACHINES

the input current in the stator (armature) winding is

, - E I

The voltage across the output terminals is

,r:r"W

(2. l 30)

(2.r3r)

characteristics of EMF per phase t;, phase voltage vt, stator (load) cur-rent Io, output power Po6, inpttt power P;,r, efficiency q and power factorpf : cosl versus speed n ofa stand alone AFPM synchronous generator forinductive loadZy : Rr * jaLr are plotted inFtg.2.l9.

2.11.2 Synchronization with utility gridAn AFPM synchronous generator can be synchronized directly (connected

in parallel) with the utility grid. The number of pole pairs is usually mini-mum2p: 6, so that to synchronize a 6-pole generator with a 50Hz powersystem (infinite bus), the speed of the prime mover must be n : 60(f lp) :60(50/3) : 1000 rpm. For 2p : 72 and the same frequency, the speed willdrop to n : 500 rpm. In general, direct paralleling of AFPM generators re-quires low speed prime movers. Before connecting the generator to the infinitebus, the incoming generator and the infinite bus must have the same:

r voltage

r frequency

r phase sequence

r phase

In power plants, those conditions are checked using a synchroscope.AFPM synchronous generators have recently been used in distributed gen-

erator systems as microturbine- driven high speed self-excited generators. Amicroturbine is a small, single shaft gas turbine of which the rotor is integratedwith a high speed electric generator (up to 200 000 rpm), typically rated from30 to 200 kW. If an AFPM generator is driven by a microturbine, in most casesthe speed exceeds 20 000 rpm. The high frequency current of the generatormust first be rectified and then inverted to obtain the same frequency as thatof the power system. To minimize the higher harmonic contents in the statorwindings, an active rather than passive rectifier is used (Fig. 2.20).


t-

(b)

l 1

(c)

Port

P,n

Figure 2 . 1 9 . Characteristics of a stand alone AFPM synchronous generator for inductive load

Zr, : Rr,l juLt (a) EMF .try perphase andphase voltage l/r versus speed n, (b) load cunent

1o versus speed n, (c) output power Pout andinput power P;, versus speed n, (d) efficiency 4

and power factor pf: cos @ versus speed z.

67

(a,

Ef

v1

active rectifier

c l+

Figure 2.20. Power circuit of a microturbine driven AFPM generator.

68 AXIAL FLUX PERMANEI,IT MAGNET BRUSHLESS MACHTNES

Numerical example 2.1Find the armature current, torque, electromagnetic power and winding loss-

es of the S802F AFPM d.c. brushless servo motor (Table 1 . 1) at n : 2500 rpmand input voltage 230 V (line-to-line).

Solution

The line to line EMF is

L.s t -L : t /Jk 'ea"n : f i * : t^^" +P : 2p,24Yl(X)t) ttO

because the EMF constant kEd.. : 42 V 11000 rpm is for the phase EMF.Assuming that the d.c. bus voltage is approximately equal to the input volt-

age, the amature current at2500 rpm is

T G q ) -r o230, 278.24: 7.74 A

2 x 0.76

because the resistance per phase is 0.76 0.The shaft torque at2500 rpm is

T : kra"I lss) : 0.64 x 7.74: 4.95 Nnr

because the torque constant is k76": 0.64 NmiA.The electromagnetic power (only two phases conduct current at the same

time) is

PeIm: E1r. r l f , " ' ) :218.24 x 7.74 t 1689 W

The windine losses for 2 x 0.76 O line-to-line resistance are

LP,J : (2 x 0.76) x 7.742 - 91 W

Numerical example 2.2A three phase, Y-connected, 2p : 6 pole, AFPM brushless motor has the

surface PM of inner radius Rtn : 0.06 m, outer radius Rout : 0.11 m andthe pole shoe width-to-pole pitch ratio a.i : 0.84, the number of turns perphase -Aft : 222, the winding factor k-1 : 0.926 and the peak value of theair gap magnetic flux density Bms :0.65 T. Neglecting the armature reaction,find approximate values of the EMF, electromagnetic torque developed by themotor and electromagnetic power at n : 1200 rym andrms current Io : 73.6A for:


(a) sinewave operation (V : 0o)

(b) 120" square wave operation

Solution

(a) sinewave operation at V : 0o

The speed in rev/s

1200n :

6 0 : 2 0 l r e v l s

The form factor of the excitation field

r, : lsinff : !,, i"9+ll : 1.233The excitation flux according to eqn (2.19) is

2oy: o ; r :1 r 1 .238 x 0 .6b x ! x e . I f -0 .062) :0 .00114Wb

7 t b

where B,nsl : kf B*n.The EMF constant according to eqn (2.30) is

kn : npt/iN1k,,o1Ly : 7T x g x \/, x 222 x0.96 x 0.00114 : 6.452 Vs

The EMF per phase according to eqn (2.29) is

Ef : knn :0 .6 .452 x 20 :129V

The line-to-line EMF for Y connection is

E1r,-L : JSnt : rt x L29 : 223.5Y

The torque constants according to eqn (2.27) is

k r : \ p N t k - t @ ! : + x 3 x 2 2 2 x 0 . 9 6 x 0 . 0 0 1 1 4 : 3 . 0 8 N m / A\/2- \/2

The electromagnetic torque developed at 14 A according to eqn (2.25) is

Ta: k r lo : 3 .08 x 13 .6 : 41 .9 Nm

The electromagnetic power is

Perrn : mlBylacosV : 3 x 729 x 13.6 x 1 : 5264.5W

7O AXIAL FLUX PERMANENT MAGNET BRUSHLESS MACHII,{ES

where iU is the angle between the EMF Ey and stator current Io.

(b) 120" square-wave oPeration

The flat-topped value of the phase current according to eqn (2.128) is

t; r;If,"o) : ,,1|r": /U t te.e : 16.66 A

The excitation flux according to eqn (2.1 17) is

ofn) : 0.84 x 0.65 x 6n" x (0.tt2 - 0.062) : 0.00122 wb

The ratio of the square-wave flux to sinewave flux

*fn) : o.oor22:1.02o; 0 .00114

Note that it has been assumed that ai : 2ln : 0'6366 for sinewave mode and

al"q) - 0.84 for square wave mode, For the s€rrne oi the flux ratio is equal to

! l k t .The EMF constant according to eqn (2.119) is

kE, t " :BpN1k-1* fn ' : B x 3 x 222x0 '96 x 0 '00122:L2 '43Ys

The line-to-line EMF (two phases in series) according to eqn (2.1 l8) is

1200Ey t-L: l '2.43 x

f f : 248.6 V

The torque constant according to eqn (2.121) is

krd,: r :0"

:12'43 - 1.g7g Nm/A2 n 2 r

The electromagnetic torque at ltss) : 16'66 A according to eqn (2'120) is

Ta : kra"Il"q) : 1'978 x 16'66 : 32'95 Nm


Petm: Ett-r l f , "q) :248'6 x 16'66 : 4140'6 W

Principles of AFPM machines 7l

Numerical example 2.3Find the main dimensions, approximate number of turns per phase and approx-imate cross section of the stator slot for a three-phase, double-sided, double-stator disc rotor PM brushless motor with a laminated stator core rated at:Po't : 75 kW VrL :460 V (Y connection), .f : 100 Hz, n" : 1500 rpm.The stator windings are connected in series.

Solution

For / : 100 Hz andn": 1500 lpm : 25 revls the number of poles is 2p : g.

Assuming ka : Dn/Dout : IlJ7 the parameter kT,l according to eqn (2.89)is

k D : : 0 .131

, phase current for seriesFor a 75 kW motor the product q cos $ xconnected stator windings is

f -r a -P^rt 75 000 : 104.6 A

m1(2Vgr1cos$ 3x 265.6 x 0.9

where 2V1 : 4601\/3 : 265.6 V. The electromagnetic loading canbe as-sumed as Brnn: 0.65 T and Arn: 40,000 A/m. The ratio e : Et lVr x 0.9and the stator winding factor has been assumed k,,:r : 0.96. Thus, the statorouter diameter according to eqn (2.93) is

D o u t :0.9 x 75 000 :0 .452 rn

a'2 x 0.131 x 0.96 x 25 x 0.65 x 40 000 x 0.9

The inner diameter according to eqns (2.20) rs

0.452D i n : : 0 . 261m,

The magnetic flux according to eqrr (2.21\ is

) r ^ / 1 \Q r : o

x 0 . 6 5 x - - l ' x 0 . 4 5 2 2 ( t - ^ I : 0 . 0 0 5 5 5 W b' r E x 4 \ ( r / J ) ' /

The number of stator turns per phase per stator calculated on the basis of linecurrent density according to eqn (2.86) is

n , _ nD* t ( t + ka)A* _ 7 r x0 .453 x 1 t + t l r t )x 40000 _ * ," , - 4 * r r f 2 h 4 y f f i ^ 1 g 4 3

- " '

( * ) ' ]

0.9. The

:('.#) ['-

D<vut

\/3 Jz

72 AX]AL FLUX PERMANENT MAGNET BRUSHLESS MACHINES

The number of stator turns per phase per stator calculated on the basis of eqn(2.87) and (2.92) is

nt/1 x100 x 0.96 x 0.00555=50

A double layer winding can be located, say, in 16 slots per phase, i.e. s1 - 4gslots for a three phase machine. The number of tums should be rounded to48. This is an approximate number of turns which can be calculated exactlyonly after performing detailed electromagnetic and thermal calculations of themachine.

The number of slots per pole per phase according to eqn (2.2) is

s 1 4 8- : ' )' ' - 2 p . r B x 3 - '

The number of stator coils (double-layer winding) is the same as the numberof slots, i.e. 2pq1my: B x 2 x 3 :48. If the stator winding is made of fourparallel conductors au : 4, the number of conductors in a single coil for oneparallel current path ar: 1 according to eqn (2.$ is

o , , , lV r 4 x 48A / - 1 . )" ' ' -

W,r ) -

14gJg7 ' '

The current density in the stator conductor can be assumed J, x 4.5 > 106A/m2 (totally enclosed a.c. machines rated up to 100 kW). The cross sectionarea ofthe stator conductor is

104.6 ).: D . 6 I 1 m n ] -D O -

^r eVt" r{2f k",1Q I

0.9 x 265.612

t'^i'n : ry

: -f: o'0171 m : 17'1 rrrur

Io

aru Jo. 4x4 .5

The stator winding of a 75 kW machine is made of a copper conductor ofrectangular cross section. The slot fill factor for rectangular conductors andlow voltage machines can be assumed to be 0.6. The cross section of the statorslot should, approximately, be

5 . 8 1 1 x 1 2 x 2= 233 mm2

where the number of conductors in a sinsle slot is 12 x 2 : 24. The minimumstator slot pitch is

0.6

Principles oJ AFPM machines 73

The stator slot width can be chosen to be ll.9 mm; this means that the sta-tor slot depth is 23311L.9 = 20 mm, and the stator narrowest tooth width iscrrnin : 17.1 - 11.9 : 5.2 mm. Magnetic flux density in the narrowest partof the stator tooth is

B7tuno ' - B*s t r * in - 0 '65-x 17 '1 :2 ' I4T

CImin 5 . 'Z

This is a permissible value for the narrowest part of the tooth and silicon elec-trical steel with saturation masnetic flux densitv of 2.2 T. The maximum statorslot pitch is

TDert r x 0.453t r ,no , :

; :

48 : 0 .0296 m: 29 .6 mm

The magnetic flux density in the widest part of the stator tooth is

B7t'ni' = B*nt"no' - 0'65 x 29'6

: 1'09 T' -

"rrr"*

- 29.6 - 1l-9

- r 'ur r

Numerical example 2.4A 7.5-kg cylindrical core is wound of isotropic silicon steel ribbon. It can

be assumed that the magnetic field inside the core is uniform and the vectorof the magnetic flux density is parallel to steel laminations. The magnitudesof magnetic flux density time harmonics are: BrnL - 1 .7 T, B,n3 : 0.25 T,Brns : 0.20 T and B-7 : 0.05 T. Harmonics n, > 7 are negligible. Theelectric conductivity of laminations is op" : 3.3 x 106 S/m, specific massdensity pFe :7600 kg/m3, thickness dF" :0.5 mm and Richter's coefficientof hysteresis losses e : 3.8. Find the core losses at 50 Hz.

Solution

Eddy-current losses

The coefficient of distortion of the magnetic flux density according to eqn(2.45\ is

: 1 .258

The eddy current losses according to eqn (2.44) arc

r specific losses at sinusoidal magnetic flux density

0.25 \ 2

L ? )0 .20 \ 2

L 7 )0.05 \

2

r . t /

Lp""i , : +

^=# x 502 x 0.0005 x 1.72 : \ .29w/kg

74 AXIAL FLIJX PERMANEI{T MAGNET BRUSHLESS MACHINES

r specific losses at nonsinusoidal magnetic flux density

Lp.: LP""i,n x n3:7'29 x 7'2582 :2'04w/kg

r losses at sinusoidal magnetic flux density

LP"r i .n - Lp"" inrr tFe:1.29 x 7.5 : 9.68 W

r losses at nonsinusoidal magnetic flux density

LP" : Ap"*Fu : 2.04 x 7.5 : 15.32 W

Hysteresis losses

The hysteresis losses may be calculated according to eqn (2.46), in whichRichter's coefficient of hysteresis losses e : 3.8

r specific losses at sinusoidal magnetic flux density

Lryh,tn: 3'8 x # " 502 x 1'72: 5'49wlkg

r specific losses at nonsinusoidal magnetic flux density

LPn: LPlr in x 11]:5 '49 x L2582: 8'69 Wlkg

r losses at sinusoidal magnetic flux density

LPn"m: Lph" tnmp" , :5 .49 x 7 .5 : 41 .18 W

r losses at nonsinusoidal magnetic flux density

L P h : L q n m p . : 8 . 6 9 x 7 . 5 : 6 5 . 1 9 W

Specific eddy current and hysteresis losses plotted against frequency are showninF ig .2 .2 I .

Total losses

The eddy cun:ent and hysteresis losses at sinusoidal magnetic flux densityare calculated as


AP "rin(0

Ap .(t)

_ip ii"ttr

_^r_{0

S . 0 l0

0

I

50Ii /

- : ' . / ', t '

r l / */ ? '

: / . / . - /- / . r ' '/ /

' : ; - " ' - " , :

" " " ' "

*'- .....,-.

//

75

. - t 6t o

t 4

l 2

l 0

R

o

4

2

100

r00

Figure 2.21. Specific eddy-currentandhysteresis losses versus frequency. Numerical example2.4.

APF""I^ : LP""tn -l LPn"tn: 9.68 + 41.18 : 50.86 W

The eddy curent and hysteresis losses at nonsinusoidal magnetic flux densityafe

LPp.: LP. * LP': 15.32 + 65.19 : 80.51 W

The ratio of hysteresis*to-total losses is the same for both sinusoidal and non-sinusoidal magnetic flux densiry i.e.

41.18 65 .19: 0 .8150.86 80.51

Numerical example 2.5Find the power losses in PMs and solid rotor backing steel disc of a single-

sided AFPM with slotted stator at ambient temperature of 20oC. The innerdiameter of PMs is D,;n: 0.14 m, the outer diameter of PMs is Doul : 0.242m, number of poles 2p : 8, magnet width-to-pole pitch ratio is at : 0.75,height of surface permanent magnet is hxy : 6 mm, air gap thickness g : 1.2mm, number of slots 5t : 36 and speed n : 3000 rpm. Assume the peakvalue ofthe air gap magnetic flux density Bms :0.71 conductivity of NdFeBPMs op- : 0.8 x 106 S/m at20oC, its relative recoil magnetic permeability

Frrec:1.05, conductivity of solid disc op" : 4.5 x 106 S/m at20oC and itsrelative recoil magnetic permeability 1tr: 300.

76 AXIAL FLUX PERMANEI,{T MAGNET BRUSHLESS MACHTNES

Solution

The average magnetic flux density is Born : (2lr)B*n : (2ln) x 0.7 :0.4661the average diameter D :0.5(Dout I D,n) :0.5(0.242 + 0.14) :0.191 m, the average pole pitch is r : nD lQp) : r0.Igll}: 0.075 m, theaverage slot pitch h : rDlsl : 7T0.191136 :0.017 m. The frequency ofthe fundamental harmonic of the slot component of the magnetic flux densityaccording to eqn (2.49) is

f "t : stpn: 36 x 4 t

3# : 72oo Hz.

The corresponding angular frequency is c,r"l : 217200: 45 238.9 radls.The equivalent air gap in the d-axis for kct : 1 according to eqn (2.103) is

st :0.0012+ q q0=6 : 0.006914rn1 . 0 5

The parameters rc : 0.434, 0a:0.041, | : 0.18 anda,"1 : 0.546 have beenfound on the basis of eqns (2.53), (2.52) and (2.51) respectively. The Carlercoefficient is k6 :1.012 - eqns (1.2) and (1.3). Thus, eqn (2.50) gives themagnetic ffux density component due to slot opening as

B s r : 0 . 5 4 6 x 0 . 0 4 1 x 1 . 0 1 2 x 0 . 4 4 6 : 0 . 0 1 0 1 8 T

The parameters k : 139.283 l /m for prrec:1.05, A : \ lk - 0.0072m,o : 1 3 9 . 2 8 3 + j 1 3 9 . 2 8 3 1 l m , 0 : r l Q . S t t ) : r l ( 0 . 5 x 0 . 0 1 7 ) : 3 7 7 . 2 4 1llm, n - 386.668 + j50.962 llm, as, - 2.733 and aa, : 0.366 for u : 1.have been found on the basis ofeqns (1.12), (1.11), (1.6), (1.12), (1.16) and(1.17) respectively. The transverse edge effect coefficient k" according to eqn(2.55) is

0 . 5 x 0 . 0 1 7A ' z : r * o l q z

l l q l ' u 6 l

The active surface area of PMs according to eqn (2.56) is

Sp*r :035r x l (0.5 x 0.242)2 - (0.5 x o.ta)21 : 0.023 rn2

The active losses in PMs according to eqn (2.51is

L P p v :1

t x 2.733x r .ost x () '

21139.283 + j139.2831

377.24r

0.01018" ( 0.4tr x 10 6 x 1.05) '

, , -139?!t x 0.023 : 1r8.2 w


The reactive power losses in PMs can be estimated as

LQpm - aX' A,Pp1u : 3* x 118.2 : 15.8/VAr

aR, 2.733

For calculation of power losses in the solid steel disc of the rotor, the magneticflux density component due to slot openings B"t : 0.01018 T is the same. Therelative magnetic permeability F, : 300 and conductivity of the disc op" :

4.5 x 106 S/m are different, so that the attenuation factor (1.12) calculated forthese values will be k : 6194.6 1/m. The coefficients aRFe : 1.451 andaxFe -- 0.849 are calculated using eqns (2.57) and (2.58) for 471 - 1.45 and(trx : 0.85. The remaining field parameters, i.e. a : 8982 -t j5265 llm,

13 : n I (0.5tt) : r I (0.5 x 0.017 : 377.241 llm andrc : 8988 * j5362 llmhave been found from eqns (1.1 1), (1.6) and (1.12) respectively.

The surface area of the rotor disc according to eqn (2.60) is

SF": \ x (0.2a22 - 0.742): 0.031 m24 '

The active power losses in the rotor disc according to eqn (2.59) is

LPr.z:1' 1.4b1 x 1.081 x ffgYi4Tlf)'2 \ ZrZ.z+1 )

1 0 .0101s \2 6194 .6,. (o.4;ffi) " *;lou x o'031 : l8"t w

The coefficients k, : 1.081 is the same as for calculation of losses in PMs.The reactive power losses in the rotor disc can be estimated as

L Q P . z - a x F e ' ^ n 0 ' 8 4 q

ffitor.z: lfr x 118.2 : 10.8 VAr

Numerical example 2.6Find the rotational loss of a 3000 rpm disc type machine with outer radius

of the rotor Rout : 0.2 m, radius of shaft behind the rotor core ,R"7, : 0.025m, mass of the rotor m, : 2.72 kg and mass of the shaft. m"7, : I.49 kg. Themachine is naturally cooled with air. The ambient temperature is 20" C. Thecoefficient of bearing friction is ky6 : 1.5.

Solution

The bearing friction losses according to eqn (2.64) are

77

300060

L,P1, :0.06 x 1.5 x \2.72 + 1.49) 18.96 W


The Reynolds number according to eqn (2.65) is

R e : 1 . 2 , 2 n 3 o o o

, r-5|';r

x ;;

x 0.22 : 8.378 x 105

where the air density is p : 1.2 kglm2 and dynamic viscosity of the air is

/l : 1.8 x 10-5 Pa s. The coefficient of drag according to eqn (2.66) is

3 .87

" / :75=ff i* :4.228x10*3The windage losses according to eqn (2.67) ue

1 / 3000\ -L P * ; , d - ; x 4 . 2 2 8 x 1 0 - 3 x l . 2 x ( Z n x = ) ( 0 . 2 5 - 0 . 0 2 5 t ) : 2 5 . 1 7 W

2 \ 6 U l

The rotational losses are thus

LP""t : 18.96 + 25.17 : 44.13 W

Chapter 3

MATERIALS AND FABRICATION

3.1 Stator cores

Stator cores of AFPM brushless machines are made of laminated steels orsoft magnetic powder materials. Soft magnetic powders simplify the manufac-turing process and reduce the cost of AFPM machines.

3.1.1 Nonorientedelectricalsteels

Most laminated cores for stators of AFPM brushless machines are made ofnonoriented (isotropic) silicon steel rlbbons with standard thickne ss from 0.12to 0.64 mm. Nonoriented steels are Fe-Si alloys with a random orientation ofcrystal cubes. Magnetic properties are practically the same in any direction inthe plane of the sheet or ribbon. A secondary recrystallization process is notneeded and high temperature annealing is not essential. Nonoriented gradescontain between 0.5oh and3.25yo Si with up to 0.5% Al addition to increasethe resistivity and lower the temperature of the primary recrystallization.

Nonoriented electrical steels are available asbothfully processed and semi-processed products. Fully processed nonoriented electrical steels are com-pletely processed by the steel manufacturer, ready for use without any ad-ditional processing required to achieve the desired magnetic quality. Semi-processed nonoriented electrotechnical steels are those which have not beengiven the full annealing treatment by the steel producer. In some cases, usersprefer to develop the final magnetic quality and achieve relief of fabricatingstresses in laminations or assembled cores for small machines.

The most universally accepted grading of electrical steels by core losses isthe American Iron and Steel lndustry (AISI) system (Table 3.1), the so called"M-grading". For small and medium power electrical machines (output power


Table 3.1. The most important silicon steel designations specified by different standards

EuroperB.c 404-8-4

(r e86)

U.S.AAISI

JapanJIS 2552( l 986)

RussiaGOST 21427

a-75250-35-A5270-3s-A5300-3s-A5330-35-A52"10-50-45290-50-A53 t 0-50-45330-50-45350-50-A5400-s0-A5470-50-A5530-50-A.5600-50-A5700-50-A5800-50-A5350-65-A5400-65-A5470-65-A5530-65-As600-65-A5700-65-A5800-65-A51000-65-A5

35425035/'21035A300

501.270504290504310

50A3s050A400501'470

50A60050A70050A800

65A800654.1000

M - 1 5M-19M-22M-36

M- l5M-19M-27M-36M43

l + 1 5

L + I L

24t1

24131 A 1 a

2411231223112 2 1 22112

2111

M-45

M-4'7

M-19M-27M-43

M-452 3 1 2221222112u2

less that 75 kW), the following grades can be used: M-27, M-36, M-43,M-45and M-47.

Laminating a magnetic core is ineffective in keeping excessive eddy currentsfiom circulating within the entire core unless the surfaces of laminations areadequately insulated. Types of surface insulation include the natural oxidesurface, inorganic insulation, enamel, vamish or chemically treated surface.The thickness of the insulation is expressed with the aid of the stackingfactor:

t - _

d+2L( 3 .1 )

g'here d is the thickness of bare lamination and A is the thickness of the in-sulation layer measured on one side. The stacking factor ki is typically from0.94 to 0.97.

Mate rials and fa bricatio n

Table 3.2. Specific core losses of Armco DI-MAX nonoriented electrical steels M-27, M-36and M-43 at 60 Hz

81

Magneticflux

densityI

Specific core losseswkg

0.36 mm I o.+r mm I o.o+ mmM-27 1M-36 1 M-27 1M-36 I M -43 1 M-27 1M-36 1 M-43

).201.50).701.00t .30t .50t .60t .701 .80

0.090.470 .811.462.393 .374.00

4.95

0 . 1 00.520.89r . 6 12 .583 .574 . t 94.74s . 1 4

0 .100.530.921.6"/2 . 6 /

3.684.304.855.23

0 .1 I0.560.971 . 7 52.803 .86A < 1

5.085.48

0 .1 10.591.031 .872.994.09A 1 a

5 .335.79

0 . 1 20.62t . 1 l2.06-) - -)z+

4.565.345.996.52

0 .120.641 . 1 42 . 1 23.464.705.486 . 1 56.68

0 . 1 30.66t . t 72 . t 93.564.835.606.286.84

Magnetic fluxdensity

T M-27 1

Magnetic field intensityA/mM-36 I M-43

0.200.400.70r .00r .201 .501 .601 .701 .802.002 .102.20

365074

1 1 6175859

2 1 8 847598785

26 97764 93s

t37 203

4 15'l80

1 1 9t74785

210947278722

26 0226s 492

t36 9'77

4'16489

1 3 0187777

198145928682

26 81866 925

t37 075

Table 3.3. Magnetization curves of fully processed Armco DI-MAX nonoriented electricalsteels M-27, M-36 and M-43

Core loss curves of Armco DI-MAX nonoriented electrical steels M-27, M-36 and M-43 tested at 60 Hz are given in Table 3.2. Core losses when testedat 50 Hz would be approximate$ A.79 times the core loss at 60 Hz. Magneti-zation curves of the same electrical steels are given in Table 3.3. The specific

82 A XIA L F L UX P E RMA NE NT M AGNE T B RU SH LE SS MAC HINE S

Table 3.4. Specific core losses and d.c. rnagnetization curve ofnonoriented thin eiectricalsteels manufactured by Cogent Power Ltd., Newport, U.K.

mass density of DI-MAX M-27.M-36 and M-43 is 7650. 7700 and 77 50kg/m3respectively. The stacking factor is k; : 0.95 to 0.96. The prefix DI-MAX,e.g. DI-MAX M27, designates a registered trademark with a special strip-annealed process that maximizes punchability. DI-MAX grades have superiorpemeability at high magnetic flux density, low core losses and good gaugeuniformity. A smooth surface, excellent flatness and high stacking factor isobtained as a result of cold finishing and strip annealing.

For frequencies exceeding the power frequency of 50 or 60 Hz nonorientedlaminations thinner than 0.2 mm must be used. Table 3.4 shows magnetizationand specific core losses of nonorientedgradesNO 12, NO l8 andNO 20 ca-pable of operating up to 2.5 kHz (Cogent Power ltd , Newport, UK). Typicalchemical composition is 3.0 % Si, 0.4 o A1,96.6 % Fe. The standard thicknessof an inorganic phosphate based insulation is 1 pm (one side). The maximumcontinuous operating temperature in the air is 230"C, maximum intermittent

Magn.flux

dens.T

NO 120.12 mnr

so l+oo l 2 .5H z l H z l k I l z

Specific core losseswkg

NO 180 .18 mm

50 laoo l 2 .sI l z l L I z l k H z

NO 200.2 mm

50 1400 I 2 . sH z l H z l k H z

Magn.field

SffCN.

kA/m

0 . 1 00.200.300.400.500.600.'700.800.901.001 . t 01 .201 .30t .401 .501.601 .701 .80

0.020.080 .160.260.370.480.620.760.321 .09L311 .561 .892.292.743 . 1 43.493 .78

0 . 1 60.'711 . 5 52.573.755.056.498.099.841 1 . 814.116.719.924.028.5

1 .656.8315.22.543'1.752.066 .183. I103 .0156

0.020.080 . 1 60.260.360.470.610.750.901 .071 .281 .521 .842.23z . o /

3.063.403.69

0 . 1 80.731 .502.543 .865.226.778.4710.412.314.91 8 . 121.625.630.0

2 . t 81 0 . 61 9 . 13t .745.96 1 . 58 1 . 1104.01 6 1 . 0198.0

0.020.070 . t40.230.320420.540.660.800.951 . 1 4I . J O

1.652.002.402.753.06) . J Z

0 . r70.721.492.503.805 . 1 76.708.3610 .312.214.817.921.425.329.7

2.7910 .624.440.458.478.4103 .0133 .0205.0253,0

0.0250.0320.0390.0440.0510.0570.0640.0730.0840.0990.1240.1600.2480.4701.2903 .550'1.070

I J

Materisls and fabrication

Table 3.5. Physical properties of iron based METGLAS amorphous alloy ribbons (Honeywell,Morristown, NJ. U.S.A.)

2605SA1

83

2605CO

Saturation magnetic fluxdensity, T

Specific core lossesat 5OHz and I T, Wkg

Specificdensity, kg/m3

Electric conductivity, S/m

Hardness inVicker's scale

E las t ic i t y rnodu lus , GNrm2

Stacking factor

Crystallizationtemperature, "C

Curie temperature, "C

Maximum servicef p n n a r o f . ' r p o f

1 . 8

less than 0.28

7 560

0.813 r 106 S/m

8 1 0

100 . . . 1 10

less than 0.75

430

4ts

125

1.59 annealed1.57 cast

about 0.125

7200 annealed7190 cast

0.769 x 10b S/m

900

100 . . . 1 10

less than 0.79

507

392

1 5 0

operating temperature in an inert gas is 850oC, hardness 180 HV and density7650 kg/m3.

3.1.2 Amorphous ferromagnetic alloysTo minimize core losses at high frequencies, nonoriented electrotechnical

steels should be replaced with amorphous magnetic alloys (Tables 3.5 and3.6). Amoryhors fenomagnetic alloys, in comparison with electrical steelswith crystal structure, do not have arranged in order, regular inner crystal struc-ture (lattice).

Amorphous alloy ribbons based on alloys of iron, nickel and cobalt are pro-duced by rapid solidification of molten metals at cooling rates of about 10tr

"C/s. The alloys solidify before the atoms have a chanc€ to segregate or crystal-


Table 3.6. Specific core losses of iron based METGLAS amorphous alloy ribbons (.Honeyu*ell,Morristown. NJ. U.S.A.)

lize. The result is a metal alloy with a glass-like structure, i.e. a non-crystallinefrozen liquid.

Application of amorphous alloy ribbons to the mass production of electri-cal machines is limited by hardness, up to 1100 in Vicker's scale. Standardcutting methods like a guillotine or blank die are not suitable. The mechan-ically stressed amorphous material cracks. Laser and electro-discharge ma-chining (EDM) cutting methods melt the amorphous material and cause un-desirable crystallization. In addition, these methods make electrical contactsbetween laminations which contribute to the increased eddy-current and addi-tional losses. In the early 1980s chemical methods were used in General Elec-tric to cut amorphous materials but these methods were very slow and expen-sive ll76]. The problem of cutting hard amorphous ribbons can be overcomeby using a liquid 1et 12201. This method makes it possible to cut amorphousmaterials in ambient temperature without cracking, melting, crystallization andelectric contacts between isolated ribbons.

3.1.3 Soft magnetic powder compositesPowder metallurgy is used in the production of ferromagnetic cores of small

electrical machines or feromagnetic cores with complicated shapes. The com-ponents of soft magnetic powder composites are iron powder, dielectric (epoxyresin) and filler (glass or carbon fibers) for mechanical strengthening. Powdercomposites for ferromagnetic cores of electrical machines and apparatus canbe divided into 1236):

dielectromagnetics and magnetodielectrics,

magnetic sinters.

Magnetic flux density, BT

Specific core2605CO

50 Hz I 60Hz

losses, Ap, Wkg2605SA1

50 Hz | 60Hz0.050 . 100.200.400.600.801 .00

0.00240.00710.0240.0634.12s0 .1960.274

0.0030.0090.0300.0800 . 160.250.35

0.00090.00270.00630 .0160.0320.0630.125

0.00120.00350.0080.020.040.080 . l 6

M(tterials and fabr icatio n

Table 3.7. Magnetization and specific core loss characteristics ofnon-sintered Accucore (TSCFe rr i te I nter n a tional, Wadsworth, IL, U. S.A. )

Dielectromagnetics and magnetodielectrics are names referring to materialsconsisting of the same basic components: ferromagnetic (mostly iron pow-der) and dielectric (mostly epoxy resin) material12361. The main tasks of thedielectric material is insulation and binding of ferromagnetic particles. In prac-tice, composites containing up to 2o/o (of their mass) of dielectric materials areconsidered as dielectromagnetics. Those with a higher content of dielectricmaterial are considered as magnetodielectrics f236).

TSC International, Wadsworth, IL, U.S.A., has developed a new soft pow-der material , Accltcore, which is competitive to traditional steel laminations[4]. The magnetization curve and specific core loss curves of the non-sinteredAccucore are given in Table 3.7. When sintered, Accucore has higher satura-tion magnetic flux density than the non-sintered material. The specific densityis 7550 to 7700 kg/m3.

Hdgancis, Hogands, Sweden, manufactures soft magnetic composite (SMC)powders that are surface-coated metal powders with excellent compressibility

85

MagnrMagnetic flux

density, BT

lzatlon curveMagnetic field

intensity, 11A/m

60Hzwkg

ipecific core loss

100 Hzwkg

curves

400 Hzwkg

0 . r 00.200.300.400.500.600.700.800.901 .001 . 1 01.201 .301.401 .501 .601 .701 . 7 5

152L J . )

312400498o t J

7499091107135'7t677210126873525476365639035r0,146

0 .1 320.4t90.7721 . 2 1 21.7422.3152.9543.6604.4315.2476.1297.0337 .9818.9299.965

10.86911.707t2.125

0.2420.6831.3232.4722.9763.9685.0716.3057.6509.039

r 0.58212.2r413.84515 .56517.39419.04820.63s21.407

1 .0s83.2636 .2 t79 . 8 1 1

14.08818.85024.29530.49037.34644.48952.9r161.37770.1 5 179 .16890.30299.671

r09.880

86 AXIAL FLUX PERMANENT MAG}{ET BRUSHLESS MACHINES

Table 3.8. Specific core losses of Somaloy?A{500 +0.S% Kenolube, 800 MPa, treated at500"C for 30 min in the air, Hriganas, Hriganiis, Sweden

Table 3.9. Magnetization curves of Sornaloy?^t500 +0.5% Kenolube, treaied at 500"C for30 min in the air, Hdganai, Hrigands, Sweden

Magneticfield intensityHA/m

Bat density

6690 kg/m3T

D

at density7l 00 kgAn"

T

Bat density

7180 kg/m''T

Magnetic fluxl ^ - ^ : + - .ug[D rLyr

A/mSpecific losses

wkg50Hz I l00Hz | 300H2 | soog, | 700H2 l000Hz

0.40 .50.60.81 . 02.0

1 . 51 . 92.14.66 .830

33 .6

61 01 650

t2t /

2 l) z

48170

l 82'7.)+

52ii0

270

27405592

140400

456090

t20180570

I 5003 2004 0006 00010 00015 00020 00040 00060 00080 000100 000

0.70.80 .911 .011 . 1 2t .241 .321 .52r .651 . 7 51 .82

0.831 . 1 31 .221 . 3 21 .42t .521 .591 .781 .89t .972.02

0.871 . 1 9t .281 .38l 5 ll 6 t1 .691 . 8 7t .972.052 . t 0

1216). SontaloyTLI500 (Tables 3.8, 3.9) has been developed for 3D magneticcircuits of electrical machines, transformers, ignition systems and sensors.

Mater ials and Jitbricatio n

Figure 3.1. Stator core segment formed from lamination strip: 1- lamination strip, 2groove, 3 - folding,4 compressed segment,5 - finished segment.

3,1.4 Fabrication of stator cores

Fabrication of laminated stator cores

Normally, the stator cores are wound from electrotechnical steel strips andthe slots are machined by shaping or planing. An altemative method is firstto punch the slots with variable distances between them and then to wind thesteel strip into the form of the slotted toroidal core (R & D Institute of ElectricalMachines V(IES in Brno, Republic of Czech). In addition, this manufacturingprocess allows for making skewed slots to minimize the cogging torque andthe effect of slot harmonics. Each stator core has skewed slots in oppositedirections. It is recommended that a wave stator winding should be made toobtain shorter end connections and more space for the shaft. An odd numberof slots, e.g. 25 instead of 24 can help to reduce the cogging torque ([/UESBrno).

Another technique is to form the stator core using trapezoidal segments

[228]. Each segment corresponds to one slot pitch (Fig. 3.1). The lamina-tion strip of constant width is folded at distances proportional to the radius. Tomake folding easy, the strip has transverse grooves on opposite sides of the al-ternative steps. The zigzag laminated segment is finally compressed and fixedusing a tape or thennosetting, as shown in Fig. 3.T 12281.

Fabrication of soft magnetic powder stator cores

The laminated cores of axial flux machines are much more difficult to fab-ricate than those of radial flux machines. SMC powders simplify the manufac-turing process of stator cores with complicated shapes, in general, 3D cores.

8l

88 AXIAL FLUX PERMANEIVT MAGNET BRUSHLESS MACHINES

450 500 550 600 650 700 750 800

compacting pressure, MPa

Figure 3.2. The effect of compacting pressure on the specific mass density of Hoganiis softmagnetic composite powders.

Mass production of AFPM machines is much more cost effective if soft mag-netic powder composites are used as materials for stator cores.

Using SMC powders the stator core of an AFPM machine can be made asa slotted core, slotless cylindrical core and salient pole uore with one coil perpole.

The slotted and slotless cylindrical cores for AFPM machines can be madein a powder metallurgy process using a ferromagnetic powder with a smallamount of lubricants or binders. The powder metallurgy process generallyconsists of four basic steps, namely: (1) powder manufacture, (2) mixing orblending, (3) compacting and (4) sintering. Most compacting is done withmechanical, hydraulic or pneumatic presses and rigid tools. Compacting pres-sures generally range between 70 to 800 MPa with 150 to 500 MPa being themost common. The outer diameter of the core is limited by the press capabil-ity. Frequently, the stator core must be divided into smaller segments. Mostpowder metallurgy products must have cross sections of less than 2000 mm2.If the press capacity is sufficient, sections up to 6500 mm2 can be pressed.Figure 3.2 shows the effect of compacting pressure on the density of HdgandsSMC powders.

For SomaloyTMS00 the heat treatment temperature (sintering) is typically500"C for 30 min. After heat treatment the compacted powder has much lessmechanical strength than solid steel.

The thermal expansion of conductors within the stator slots creates thermalexpansion stresses in the stator teeth. The magnitude of these stresses dependsupon the difference in the temperature of the winding and core, difference in

6800 r400

Materials and fabricatio n

Figure 3.3. Slotted stators for small single-sided disc-type motors [236].

Figure j.4. Powder salient pole stators for small single-sided AFPM motors. Courtesy of MliTechnologies, ZZC, West Lebanon, NH, U.S.A.

coefficients of thermal expansion of both materials and slot filI factor. Thisproblem is more important in powder cores than in laminated cores since thetensile stress of powder cores is at least 25 times lower and their modulus ofelasticity is less than 100 GPa (versus 200 GPa for steel laminations).

Slotted stators for small disc-type motors fabricated from SMC powdersare shown in Fig. 3.3 [148, 236]. SMC powder salient-pole stators for smallsingle-sided AFPM motors manufacturedby Mii kchnologies, LLC, Lebanon,NH, U.S.A. are shown in Fig. 3.4. The three-phase stator has 9 poles. A singleSMC powder salient pole manufactured by Htiganris is shown in Fig. 3.5.

89


(a)

Figtre 3.5, SMC powder salient pole for small single-sided AFPM motors: (a) single SMC

pole; (b) double-sided AFPM motor. Courlesy of Hdganris, Hoganiis, Sweden.

3.2 Rotor magnetic circuitsMagnetic circuits of rotors consist of PMs and mild steel backing rings or

discs. Since the air gap is somewhat larger that that in similar RIPM counter-parls, high energy density PMs should be used.

Normally, surface magnets are glued to smooth backing rings or rings withcavities of the same shape as magnets without any additional mechanical pro-tection against normal attractive forces. Epoxy, acrylic or silicon based ad-hesives are used for gluing between magnets and backing rings or betweenmagnets. The minimum required shearing strength of adhesives is 20 x 106Pa. There were attempts to develop interior PM rotor for AFPM machines.According to [201], rotor poles can only be fabricated by using soft magneticpowders [201]. The main advantage of this configuration is the improved fluxweakening performance. However, the complexity and high cost of the rotorstructure discourage fuither commercializing development.

3.2.1 PM materialsA PM can produce magnetic flux in an air gap with no exciting winding and

no dissipation of electric power. As any other ferromagnetic material, a PM canbe described by its B-H hysteresis loop. PMs are also called hard magneticmaterials, which means ferromagnetic materials with a wide hysteresis loop.

The basis for the evaluation of a PM is the portion of its hysteresis looplocated in the upper left-hand'quadrant, called the demagnetization cunte (Fig.3.6). If reverse magnetic field intensity is applied to a previously magnetized,

say, toroidal specimen, the magnetic flux density drops down to the magnitudedetermined by the point K. When the reversal magnetic flux density is re-moved, the flux density returns to the point tr according to a minor hysteresisloop. Thus, the application of a reverse field has reduced the remanence, ot

Mate rials and fabricatio n

BsaF r

r \ - * * * * - - - - * * ;

. K{afi )*ur)

w,H

& r**

Figure 3.6. Demagnetization curve, recoil loop, energy of a PM, and recoil magnetic pcrme-ability.

remanent magnetism. Reapplying magnetic field intensity will again reducethe flux density, completing the minor hysteresis loop by retuming the core toapproximately the same value of ffux densify at the point K as before. Theminor hysteresis loop may usually be replaced with little error by a straightline called the recoil line. This line has a slope called the recoil permeabilitylJr er.'

As long as the negative value of applied magnetic field intensity does notexceed the maximum value corresponding to the point K, the PM may beregarded as being reasonably permanent. If, however, greater negative fieldintensity fI is applied, the magnetic flux density will be reduced to a valuelower than that at point 1(. On the removal of H, a new and lower recoil linewill be established.

Remanent magnetic.flux density B,-, or remanence, is the magnetic flux den-sity corresponding to zero magnetic field intensity.

Coercive.field strength Hr, or coercivily, is the value of demagnetizing fieldintensity necessary to bring the magnetic flux density to zero in a materialpreviously magnetized.

Both B" and H" decrease as the magnet temperature increases, i.e.

91

- A B*aE

B,:B,2olr* f f i@pM_ 20) l

Hc : Hczotl + ffi (t9 v,x1 - 2o)l

(3 .2)

(3.3)

92 AX]AL FLUX PERMANENT MAGNET BRUSHLESS MACHINES

-1200 -1000 -800

",

-uo*0o,. -400 -20o 0

Figure 3.7. Comparison of B-H and Be-H demagnetization curves and their variations

with the temperature for sintered N48M NdFeB PMs. Courtesy of ShinEtstt, Takefu-shi, Fukui

Prefecture, Japan.

where Spm is the temperature of PM, Br2o and Ha2g are the remanent mag-

netic flux density and coercive force at 20oC and ap ( 0 and all <1 0 ate

temperature coefficients for B, and Hcino/ol"C respectively. Thus, demagne-

tization curves are sensitive to the temperature (Fig. 3.7).lntrinsic demagnetization cuwe (Fig. 3.7) is the portion of the Bt. : f (H)

hysteresis loop located in the upper left-hand quadrant, where Bt : B - FoH.For f1 : 0 the intrinsic magnetic flux density Bt: Br.

Intrinsic coerciviQ iH. is the magnetic field strength required to bring to

zero the intrinsic magnetic flux density B; of a magnetic material described by

the Bi : f (H) curve. For PM materials tH, ) H..

saturation magneticflur density B5a1 conesponds to high values of the mag-

netic field intensiry when an increase in the applied magnetic field produces no

further effect on the magnetic flux density. In the saturation region the align-

ment of all the magnetic moments of domains is in the direction of the externalapplied magnetic field.

Recoil magnetic permeability l1,..is the ratio of the magnetic flux density-

to-magnetic field intensity at any point on the demagnetization curve, i.e.

F

- 0 .8dl

0.6

ABI - t rec

- l to lLrcec

- A 1,:,H

(3.4)

Materials andJitbrication 93

where the relative recoil permeability ltrrrer: - 1 . . .4.5.Maximum magnetic energy per unit produced by a PM in the external space

is equal to the maximum magnetic energy density per volume, i.e.

(3 .5)

where the product (BH),-", corresponds to the maximum energy densitypoint on the demagnetization curve with coordinates B,no* and H,no, (Fig.3 .6 ) .

Form factor oJ'the demagnetizcttion curve characterizes the concave shapeof the demasnetization curve. i.e.

(BH) *o , , , ; tun,or

2 ,J lm-

(BH)n,o*' l : BrH,

:

for a square demagnetization curve 1 :

B*orH,no^,

B,H"(3.6)

I and for a straisht line (rare-earthP M s ) 7 : 0 . 2 5 .

The leakage flux causes the magnetic flux to be distributed nonuniformlyalong the height 2lt.y of a PM, where h,y1 is the height per pole. As a result,the MMF produced by the PM is not constant. The magnetic flux is higher inthe neutral cross section and lower at the ends, but the behavior of the MMFdistribution is the opposite [96].

The PM surface is not equipotential. The magnetic potential at each pointon the surface is a function of the distance to the neutral zone. To simplifythe calculation, the magnetic flux which is a function of the MMF distributionalong the height hy per pole is replaced by an equivalent flux. This equivalentflux goes through the whole height hy and exits from the surface of the poles.To find the equivalent leakage flux and the whole flux of a PM, the equivalentmagnetic field intensity needs to be found, i.e.

1 r h vH: j l H ,d r

nnr Jr:fvrh,nr

(3.7)

where 11" is the magnetic field intensity at a distance r from the neutral crosssection and f tr is the MMF of the PM per pole (MMF : 2Fru per pole pair).

The equivalent magnetic field intensity (3.7) allows the equivalent leakageflux of the PM to be found. i.e.

Qu$ : Qm - Qo (3.8)

where Ona is the full equivalent flux of the PM and On is the air gap magneticflux. The cofficient of leakageflux of the PM,

94 AXIAL FLUX PERMANENT MAGNET BRUSHLESS MACHII\trES

simply allows the air gap magnetic flux to be expressed as (Dn : Q ru lotu.The following leakage perrneance expressed in the flux O*MMF coordinate

system corresponds to the equivalent leakage flux of the PM:

(Dn, Q, n ,otnt : -! | + -+:1 > l

Qs Qs

Gmr-y.r A,t

(3.e)

(3 . l0)

(3 .11 )

(3.r2)

An accurate estimation of the leakage permeance G61 is the most difficulttask in analytical calculation of magnetic circuits with PMs. Using the fieldapproach, e.g. the FEM, the leakage permeance can be found fairly accurately.

The average equivalent magnetic flux and equivalent MMF mean that themagnetic flux density and magnetic field intensity are assumed to be the samein the whole volume of a PM. The full energy produced by the magnet in theouter space is

where I/,y is the volume of the PM or a system of PMs.For a PM circuit with a rectangular cross section, single PM and two mild

steel pole shoes, the magnetic flux density Bn in a given air gap volume 7n :gumlu is directly proportional to the square root of the magnetic energy prod-uct(B1yHx4) [96], i.e.

w:Tv* r

Bs : trroHs :

u,$av1n*,v q

where 11p" is the magnetic field intensity in the mild steel yoke, fI, is themagnetic field intensity in the ak gap, VA,r : 2hpywxal7,1 is the magnet vol-utae, LUlyl is the PM width, 1,11 is the PM length and2lp". is the length of themagnetic flux path in two mild steel pole shoes. Following the trend to smallerpackaging, smaller mass and higher efficiency, the material research in the fieldof PMs has focused on finding materials with high values of the maximum en-ergy product (BH),n"".

The air gap magnetic flux density Bn can be estimated analytically on thebasis of the demagnetization curve, air gap and leakage perrneance lines and

Materia ls and fab rication 95

recoil lines [96]. Approximately, it can be found on the basis of the balance ofthe magnetic voltage drops, i.e.

B ' h t r t : L r t 1 1 + B ' J t

where F,, " " ls,n.,.,""111i1,* "*rri, li r*pM (,";;". rec oil permeabil ity).Hence,

B,hm 1)l ) y

Bo=3" :" h l l - H r , " . 9 1+ y , ' , , " g l hn

(3 .13 )

The air gap magnetic flux density is proporlional to the remanent magneticflux density B, and decreases as the air gap g increases. Eqn (3.13) can onlybe used for preliminary calculations.

For rare-earth PMs the approximation of the demagnetization curve is sim-ple due to practically linear demagnetization curve, i.e.

B(H): u, (r - #) ( 3 . 1 4 )

The approximation of more complicated demagnetizations cules (Alnico orferrites) is given e.g. in [96].

The intersection point of the above demagnetization curve (3.14) and thefollowing line representing the perrneance of the air gap

B(H): 1,oL!!s (3. l s)

gives a point called the operating point. This point conesponds to the air gapmagnetic flux density Bn multiplied by the leakage coefficient olM accordingto eqn (3.9).

3.2.2 Characteristics of PM materialsThere are three classes of PMs currently used for electric motors:

r Alnicos (Al, Ni, Co, Fe);

r Ceramics (fenites), e.g. barium ferrite BaOx6FezO3 and strontium ferriteSrO x 6Fe2O3;

r Rare-earth materials, i.e. samarium-cobalt SmCo and neodymium-iron-boron NdFeB.

The demagnetization cuwes of the above three types of permanent magnetmaterials are given in Fig. 3.8.


\ ' ^^ :^\ J = l V L

t l

NEODYMIUM-IRON IB0R0Nl*>/

' l

\LNICO

(rorl*,u"1-

COBALT

*ttrERRrr2

1 4

1 , 0

I

" tTl0,6

0,4

0,2

0900 800 700 600 500 400 300 200 100

-*- -H [xelm]

Figure 3.8. Demagnetization curyes for diflerent PM materials.

Alnico

Alnico magnets dominated the PM motor market in the range from a fewwatts to 150 kW between the mid 1940s and the late 1960s. The main advan-tages of Alnico are its high magnetic remanent flux density and low tempera-ture coefficients (Table 3. 1 0). The temperature coefficient of B, is -0.02oh l" Cand maximum service temperature is 520"C. Unfoftunately, the coercive forceis very low and the demagnetization curve is extremely non-linear. Therefore,it is very easy not only to magnetize but also to demagnetize Alnico. Alnicohas been used in PM d.c. commutator motors of the disc type with relativelylarge air gaps. This results in a negligible armature reaction magnetic fluxacting on the PMs. Sometimes, Alnico PMs are protected ffom the armatureflux, and consequently from demagnetization, using additional mild steel poleshoes.

Ferrites

Barium and strontium ferrites produced by powder metallurgy were in-vented in the 1950s. Their chemical formulation may be expressed as MOx6(Fe2O3), where M is Ba, Sr, or Pb. Fer:rite magnets are available in isotropicand anis otropic grades.

A ferrite has a higher coercive force than Alnico, but at the same time hasa lower remanent magnetic flux density (Table 3.10). Temperature coefficientsare relatively high, i.e. the coefficient of B,- is -0.20%loc and the coefficientof H. is *0.27 to -0.4ohf"C. The maximum service temperature is 450"C.The main advantages of ferrites are their low cost and very high electric re-

Materials and fab ricatictn

Tsble 3.10. Physical properties of a representative selection of PM materials for small motorsofferedby Magnaquench GnBH, Essen, Germany

9'7

PropertyAlnicosintered

Koerzit 500

Hard fenitebonded

Koercxl2l22p

Hard ferritesintered

Koerox 350Remanent flux density, -B", TCoercivity, H.,kAlmIntrinsic coercivity, i H,,, k A/m(B H)-,o,,kJlm3Relative recoilmagnetic permeability

Temperature coefficient o sof 8,, at 20 to 100"c, %/"cTemperature coeffi cient a ;.rrof iH,. at20 to t00"c,o f cCurie temperature, "CMaximum continuousservice temperature, "CThermal conductivity, W(m "C)

Specific mass density, ppv,kglmsElectric conductiviry S/mCoefficient of thermal expanslonat20 to 100"c , x10 6 / "c

Specific heat, J "C/kg

1.245 l

4t.4

3 to 4.5

-0.02

*0.03 to -0.07850

50010 to 100

73001.4 to 2.5 x 10o

1 1 r o 1 3350 to 500

0.26r 8 0225

l . l

-0.2

+0.44s0

100 to 200

3400< 0.0001

20 to 50

0.392703 1 030

1 . 1

-0.2

+0.3450

2004

4800< 0.0001I 2 parallel8 vertical

800

sistance, which means practically no eddy-current losses in the PM volume.Ferrite magnets are most economical in fractional horsepower motors. Bariumferrite PMs are commonly used in small d.c. commutator motors for automo-biles (blowers, fans, windscreen wipers, pumps, etc.) and electric toys.

Rare-earth permanent magnets

The first generation of rare-earth permanent mognets, i.e. alloys based onthe composition of SmCo5 has been commercially produced since the early1970s (invented in the 1960s). SmCo5 has the advantage of a high remanentflux densiry high coercive force, high energy product, a linear demagnetiza-tion curve and a Iow temperature coemcient (Table 3.11). The temperaturecoemcient of B, is 0.02 to -0.045%l"C and the temperature coemcient of11" is -0.14 to -0.40%loC. Maximum service temperature is 300 to 350oC.It is suitable for motors with low volumes and motors operating at increasedtemperatures, e.g. brushless generators for microturbines. Both Sm and Co arerelatively expensive due to their supply restrictions.


Table 3. I l. Physical properlies of Vacomax sintered SmzCorz PM materials at room temper-ature 20"C manufactured by Vacuumschmelze GmhH, Hanau. Germanv

PropertyVacomax240 HR

Vacomax225 HR

Vacomax240

Remanent flux density, -B"., TCoercivity, H.,kAlmIntrinsic coercivity, i H., kAlm(BH)- .^ " ,k I lm3Relative recoilmagnetic permeability

Temperature coefficient clBof B ,. at 20 to 100" c , o/ol" cTemperature coeffi cient a;r1of i,H,. at 20 to 100" c, o/ol" cTemperature coeffrcient orof B" at 20to 150"C.,o/of'cTemperature coefficient o;sof i H ,, at 20 to 1 50" C, o/ol" CCurie temperature, "CMaximum continuousservice temperature,''CThermal conductiviry W/(m "C)Specific mass density, pntt,kglm3

, ^ f

Electnc conductivi ty, , | 0" S/mCoeff i cient ol thermal expansionat20 to 100 'c , x10-6 / "cYoung's modulus, x 106 MPaBending stress, MPaVcker's hardness

1 .03 to 1 .10720 to 820

1590 ro 2070190 to 225

I .06 to 1.34

-0.030

-0 .18

-0.035

-0 .19

approximately 800

350approximately 12

84001 .18 to 1 .33

100 .1 50

90 to 150approximately 640

1 .05 to 1 .12600 ro 730640 to 800200 to 240

1.22 to 1.39

0 . 1 5

-0 .16

300

0.98 to 1.05580 to 720640 to 800180 to 210

1 .16 to 1 .34

-0 .15

-0 .16

300

With the discovery in the recent years of a second generation of rare-earthmagnets on the basis of inexpensive neodymium (1.{d), remarkable progresswith regard to lowering raw material costs has been achieved. The new gener-ation of rare-earth PMs based on inexpensive neodymium (Nd) was announcedby Sumitomo Special Metals,Iapan, in 1983 atthe29th Annual Conference ofMagnetism and Magnetic Materials held in Pittsburgh, PA, U.S.A. The Nd is amuch more abundant rare-earth element than Sm. NdFeB magnets, which arenow produced in increasing quantities have better magnetic properties (Table3.12)thanthose of SmCo, but unfortunately only at room temperature. The de-magnetization curves, especially the coercive force, are strongly temperaturedependent. The temperature coefficient of B, is -0.09 to -0.15o/ol"C and thetemperature coefficient of fI" is -0.40 to -0.80%1"C. The maximum service

Materials and fabrication 99

temperature is 250oC and Curie temperature is 350oC. The NdFeB is also sus-ceptible to corrosion. NdFeB magnets have great potential for considerablyimproving the performance-to cost ratio for many applications. For this rea-son they will have a major impact on the development and application of PMmachines in the future.

Chemical reactivity of rare-earth magnets is similar to that of alkaline earthmetals, e.g. magnesium. The reaction is accelerated at increased tempera-ture and humidity. The NdFeB alloy if exposed to hydrogen gas, usually ata slightly elevated temperature and/or elevated pressure, becomes brittle andwith very little effort, it can be crushed. Diffusion of hydrogen into the alloycauses it literally to fall apart.

Corrosion protective coatings can be divided into metallic and organic. Formetallic coatings, e.g. nickel and tin, galvanic processes are used as a rule.Organic coatings include powder coatings applied electrostatically, varnishesand resins.

Nowadays, for the industrial production of rare-eafth PMs the powder met-allurgical route is mainly used 1194]. Apart from some material specific pa-rameters, this processing technology is, in general, the same for all rare-earthmagnet materials. The alloys are produced by vacuum induction melting orby a calciothetmic reduction of the oxides. The material is then size-reducedby crushing and milling to a single crystalline powder with particle sizes lessthan 10 trrm. In order to obtain anisotropic PMs with the highest possible(BH)-", value, the powders are then aligned in an external magnetic field,pressed and densified to nearly theoretical density by sintering. The most eco-nomical method for mass production of simply shaped parts like blocks, rings

or arc segments is die pressing of the powders in approximately the final shape.Researchers at General Motors, U.S.A., developed a fabrication method

based on the melt-spinning casting system originally invented for the produc-tion of amorphous metal alloys. In this technology a molten stream of NdFe-CoB material is first formed into ribbons 30 to 50-pm thick by rapid quench-ing, then cold pressed, extruded and hot pressed into bulk. Hot pressing andhot working are carried out while maintaining the fine grain to provide a high

density close to 100% which eliminates the possibility of internal corrosion.The standard electro-deposited epoxy resin coating provides excellent corro-sion resistance.

The prices of NdFeB magnets ordered in large quantities are now belowUS$20 per kg. Owing to a large supply of NdFeB magnets from China it isexpected that the prices will fall further.

3.2.3 OperatingdiagramThe energy ofa PM in the external space only exists ifthe reluctance ofthe

extemal magnetic circuit is higher Ihan zero. If a previously magnetized PM


Table 3.1 2. Physical properlies of Hicorex-Super sintered NdFeB PM materials at room tem-perature 20"C manufactured by Hitachi Metals,ltd, Tokyo, Japan

PropertyHicorex-Super

HS-38AVHicorex-Super

HS-25EVHicorex-Super

HS-47AHRemanent flux densiry .B., TCoercivity, H",kAlmIntrinsic coercivity, i, H,,, kNm(BH) , , ,o* ,kJ lm3Relative recoilmagnetic permeabilityTemperature coe{ficient asof 8,. at20 to l00"C,okl"CTemperature coefficient otrof i ,H,. at20 to 100"c,yol"cCurie temperature, "CMaximum continuoussewice temperafure, "CThermal conductivity, W(m" C)Speciflc mass dens., pp M,kglmsElectric conductivity, x 106 S/mCoefficient of thermal expanslonat20 to 100"c , x10 6 / "c

Young's modulus, x 106 MPaBending stress, MPaVicker's hardnessFeatures

1.20 to 1.30875 to 1035min . 1114278 to 319

High energyproduct

0.98 to 1.087 16 to 844min. 1989183 to 223

1.03 to 1.06

-0.1 I to -0. l3

0.65 to -0.72r 3 1 0

180

7500x 0,67

* 1 . 50 .1 50260

= 600High

temperature

1.35 to 1.431018 to I 123min. 1 I 14342 to 390

Super highperformance

140160

is placed inside a closed ideal fenomagnetic circuit, i.e. toroid, this PM doesnot show any magnetic properties in the external space, in spite of the fact thatthere is the masnetic flux

Q r : B r S 7 4 : B r w x 4 l p 1 (3 .1 6)

coffesponding to the remanent flux density E, inside the PM.A PM previously magnetized and placed alone in an open space, as in Fig.

3.9a, generates a magnetic field. To sustain a magnetic flux in the externalopen space, an MMF developed by the magnet is necessary. The state of thePM is characterized by the point K on the demagnetization cule (Fig. 3.10).The location of the point K is at the intersection of the demagnetization curvewith a straight line representing the peffneance of the external magnetic circuit(open space):

Materials and fabrication

Figure 3.9. Stabilization of a PM: (a) PM alone, (b) PM with pole shoes, (c) PM inside anexternal magnetic circuit, (d) PM with a complete extemal amature system.

r0r

G"r t : Y ,J-K

Q r c l Q ,r

- ( : , r c- v e l r o rtan G"r; :

FxlF"(3. l 7)

(3 .1e)

The permeance Gs.r1 coffesponds to the flux O-MMF coordinate system andis referred to as MMF at the ends of the PM. In the O-MMF coordinatesystem the remanent flux O" is according to eqn (3.16) and the MMF corre-sponding to the coercivity FI" is

f . : H .hM ( 3 . 1 8 )

The magnetic energy per unit produced by the PM in the extemal space isrDK : BKHK 12. This energy is proporlional to the rectangle limited by thecoordinate system and lines perpendicular to the @ and f coordinates pro-jected from the point 1{. It is obvious that the maximum magnetic energy isfor B1a : Brno, and for HK : Hrnor.

If the poles are furnished with pole shoes (Fig. 3.9b) the permeance of theexternal space increases. The point which characterizes a new state of the PMin Fig. 3.10 moves along the recoil line from the point K to the point A. Therecoil line KGu is the same as the intemal permeance of the PM, i.e.

w t t l t r t . S n l\ t 1 y 1 : 1 1 r e c F t " . ,

rLNl nL,l

The point A is the intersection of the recoil line KGm and the straight lineOGa representing the leakage permeance of the PM with pole shoes, i.e.

GA: y! ,J-A

Ftana4 - ,o

*(3.20)

102 AXIAL FLUX PERMANENT MAGIVET BRUSHLESS MACHINES

The energy produced by the PM in the external space decreases as comparedwith the previous case, i.e. utl: ffogo1r.

The next stage is to place the PM in an extemal ferromagnetic circuit asshown in Fig. 3.9c. The resultant perneance of this system is

6 -Gp: i ! ,

{ P

Ftanap -

" , * ,

(3.2r)

which meets the condition G p > G n ) G."t. For an external magnetic circuitwithout any electric circuit carrying the armature current, the magnetic state ofthe PM is characterizedby the point P (Fig. 3.10), i.e. the intersection of therecoil line K G u and the perrneance line OG p .

When the external magnetic circuit is furnished with an armature windingand when this winding is fed with a current which produces an MMF magne-tizing the PM (Fig. 3.9d), the magnetic flux in the PM increases to the valueO1,'. The d-axis }l4MF FL.r of the external (armature) field acting directly onthe PM corresponds to O1,'. The magnetic state of the PM is described by thepoint l/ located on the recoil line on the right-hand side of the origin of thecoordinate system. To obtain this point it is necessary to lay off the distanceOf'"aandto draw aline G p from the point ft"6 inclined by the angle ap to theF-axis. The intersection of the recoil line and the perrneance line Gp gives thepoint l/. If the exciting current inthe external armature winding is increasedfurther, the point lt/ will move further along the recoil line to the right, up tothe saturation of the PM.

Figure 3.1 0. Diagram of a PM for finding the origin of the recoil line and operating point


When the excitation current is reversed, the external atmature magnetic fieldwill demagnetize the PM. In this case it is necessary to lay off the distanceOf'"ofrom the origin of the coordinate system to the left (Fig. 3.10). The lineGp drawn from the point, ftro with the slope rr p intersects the demagnetizationcurve at the point K' . This point can be above or below the point K (for thePM alone in the open space). The point K/ is the origin of a new recoil lineK'G'n.Now if the armature exciting cur:rent decreases, the operating pointwill move along the new recoil line K'G'y to the right. If the armature currentdrops down to zero, the operating point takes the position P'(intersection ofthe new recoil line K'G'n with the permeance line Gp drawn from the originof the coordinate system).

On the basis ofFig. 3.10 the energies lDpr : Bp, Hp, f2, u)p : BpHp f2,zndusp, I wp. The location of the origin of the recoil line, as well as thelocation of the operating point, determine the level of utilization of the energyproduced by the PM. A PM behaves dffirently than a d.c. electromagnet: lheenergy of a PM is not constant if the perrneance and exciting current of theexternal ar:rnature changes.

The location of the origin of the recoil line is determined by the minimumvalue of the permeance of the external magnetic circuit or the demagnetizationaction ofthe external field.

To obtain the properties of PMs more independent of the external magneticfields, PMs need to be stabilized. Stabilization means the PM is demagnetizedup to a value which is slightly higher than the most dangerous demagnetizationfield during the operation of a system where the PM is installed. In magneticcircuits with stabilized PMs the operating point describing the state of the PMis located on the recoil line.

More details about how to find the operating point of a PM graphically andanalytically can be found in [96].

3.2.4 Permeances for main and leakage fluxesPermeances of air gaps and permeances for leakage fluxes can be found

analytically by dividing the magnetic field into simple solids. Petmeances ofsimple solids shown in Fig. 3.1 1 can be found using the following fonnulae:

(a) Rectangular prism (Fig. 3. 1 I a)

G: LnYYy H (3.22)

104 AX]AL FLUX PERMAAIENT MAGNET BRUSHLESS MACHINES

,r,M]

o' N

r lw r l s { * r f --'-l {;{;f E

Figure 3.11. Simple solids: (a) rectanguiar prism, (b) cylindeq (c) half-cylinder, (d) one-quarter of a cylinder, (e) half-ring, (0 one-quarter of a ring, (g) one-quarter of a sphere, (h)one-eighth ofa sphere, (i) one-quarter ofa shell, O one-eighth ofa shell.


(b) Cylinder (Fig. 3.1Ib)

105

(c) Half-cylinder (Fig. 3.1 1c)

G :0.26p,olnr (3.24)

where the average air gap gau : 1.229 and, the surface wmltw should bereplaced by 0.322glLr ll3)

(d) One-quarter of a cylinder (Fig. 3.1 1d)

G :0.52p,o1u (3.2s)

(e) Half-ring (Fig. 3.1 le)

Lr l-Lt)r(gl tuM * 7)

(3.26)

G : l r o *

For g { 3tuy,

G: ^Vm(t + '** \7 T \ . 9 /

(f) One-quarter of a ring (Fig. 3. I 10

r ' : l ' t on@1"+w

2lm

(3.23)

(3.27)

(3.28)

For g < 3c,

G : po2tM r" (r + 9) e.2s)7T \ g /

(g) One-quarter of a sphere (Fig. 3. I I g)

G : 0.077|,tog (3.30)


(h) One-eighth of a sphere (Fig. 3.I th)

G : 0.308pr,og

(i) One-quarter of a shell (Fig. 3.1 1i)

G : p o ;

fi) One-eighth of a shell (Fig. 3.1lj)

( 3 .31 )

(3.33)

Fig. 3 .12 shows a model of a flat electrical machine with smooth armature core(without slots) and surface PM excitation system. The armature is of steellaminations. The PMs are fixed to the mild steel yoke.

The pole pitch is r, the width of each PM is w16, and its length is /7yr. In anAFPM machine

lu :0 .5 (Dout - Dm) (3 .34)

The space between the pole face and the armature core is divided into a prism(l), four quarters ofcylinders (2 and 4), four quarters ofrings (3 and 5), fourpieces of 1/8 of a sphere (6) and four pieces of 1/B of a shell (7). Formulaefor the perneance calculations have been found on the assumption that theperrneance of a solid is equal to its average cross section area to the averagelength of the flux line. If we ignore the fringing flux, the permeance of arectangular air gap per pole (prism I in Fig. 3.12) is

Ggt: prYf f (3.3s)

The equivalent air gap g' is only equal to the nonmagnetic gap (mechani-cal clearance) g for a slotless and unsaturated armature. To take into ac-count slots (if they exist) and magnetic saturation, the air gap g is increasedto gt - gkck"ot, where kc > 7 is Carter's coefficient taking into account slots(1.2), and k"at )> 1 is the saturation factor of the magnetic circuit defined as

G: t "o ;

Mq terials and Jbb rication

1 ll s l +1 l1 lf t "

(b)

,,i.,!-------i-------T;I

t07

(c)

'1 0

x4

;+i t

l m

Figure 3.1 2. Electrical machine with flat slotless armature and flat PM excitation system -

division of the space occupied by the magnetic field into simple solids: (a) longitudinal section,(b) air gap field, (c) leakage ficld (between the PM and steel yoke).

the ratio of the MMF per pole pair to the air gap magnetic voltage drop (MVD)taken twice 1961.

To take into account the fringing flux it is necessary to include all paths forthe magnetic flux coming from the excitation system through the air gap to thearmature system (Fig. 3.l2), i.e.

Gn : G6 * 2(Gsz * Gsz * Gsa -t Gss) * 4(Gsa + Gsz) (3.36)

where Go1 is the air gap permeance according to eqn (3.35) and G sz to G szare the atr gap perrneances for fringing fluxes. The permeances G sz to G n5 canbe found using eqns (3 .25), (3 .28), (3.3 I ) and (3 .32).

In a similar way the resultant perrneance for the leakage flux of the PM canbe found. i.e.

GLu :2(GB * Grc) * AGns (3.37)

where GB, Grc (one-quafter of a cylinder) and G110 (one-eight of a sphere) arethe permeances for leakage fluxes between the PM and rotor yoke accordingto Fig. 3.12c - eqns (3.25) and (3.31).

3.2.5 Calculation of magnetic circuits with PMsThe equivalent magnetic circuit of a PM system with armature is shown in

Fig. 3.13. The reluctances of pole shoes (mild steel) and armature stack (elec-trotechnical laminated steel) are much smaller than those of the air gap and

I t ll s t l gI t iI t l

108 AXIAL FLUX PERMANENT MAG]\IET BRUSHLESS MACHINES

R,'m

Figure 3. I 3. Equivalent circuit (in the d-axis) of a PM system with armature.

PM and have been neglected. The "open circuit" MMF acting along the inter-nal magnet permeance G M : T lftpnt is Tmo : H Nrohx,L the d-axis armaturereaction MMF is f oy,the total magnetic flux of the PM is @,y1, the leakage fluxof the PM is Q17,1, the useful air gap magnetic flux is On, the leakage flux of the

external armature system is (01o, the flux in the d-axis produced by the atma-

ture is Ooa (demagnetizing or magnetizing), the reluctance for the PM leakage

flux is sf4,r.r : LlGtm,the airgapreluctance is Sr, :7lGg, andthe exter-

nal armature leakage reluctance is S,ro - llGgn.The following Kirchhoff'sequations can be written on the basis of the equivalent circuit shown in Fig.3 . l 3

( D , r 1 : Q 1 g 1 l Q s

Q I o :+ F ,!! o,o,

Vl1,,ta

Tuo * QnlWpr4 - Q11qTlp17r : 0

QtmTltt r - Q nBrn T To,t : 0

The solution to the above equation system yields the air gap magnetic flux:

GnG't

Gn*Gtu *Gy r

GnG*Gt lGy r

I Gn (Gg + GtM)(Gar + Gt^r)lQ g : l f t t " T f a c t n

L -s*Ga, I GnGtu Ior

' tprg

Gt(Gnr * Gttr

l*,, *n-n,t

.fi' 0 0

' ' i r ta

- drAIO t f od, GnGn'r

(3.38)

Mnterials and fabrication

Figure 3.14. Shapes of PM rotors of disc-type machines: (a) trapezoidal, (b) circular, (c)semicircular.

where the total resultant perrneance G1 for the flux of the PM is

109

Gt: Gs I Gw : ot11Gs

and the direct-axis armature MMF acting directly on the PM is

F[a - ,"ocjb; : ro,t (' _,_ +) -'

: {-uo' l t * U r n t \ G , ) o t r r

The upper sign in eqn (3.38) is for the demagnetizing armature ffuxlower sign is for the magnetizing armature flux.

The coefficient of the PM leakage flux (3.9) can also be expressedof permeances, i.e.

(3.3e)

(3.40)

and the

in terms

(3 .41 ), o l , r i , Gt t to l M : ,

%

3.2.6 Fabrication of rotor magnetic circuitsMagnetic circuits of rotors of AFPM brushless machines provide the exci-

tation flux and are designed as:

r PMs glued to a ferromagnetic ring or disc which seryes as a backing mag-netic circuit (yoke);

r PMs arranged into Halbach array without any ferromagnetic core.

Shapes of PMs are usually trapezoidal, circular or semicircular (Fig. 3.14).The shape of PMs affects the distribution of the air gap magnetic field andcontents of higher space harmonics. The output voltage quality (harmonics of


Table 3.13. Magnetization cur.res of solid ferromagnetic materials: I - carbon steel(0.27%C).2 - cast iron

Magnetic flux densiry B

T

Magnetic field intensity, 11Mild carbon steel 0.27o/o C

A/urCast iron

A/m0.20.40.60.81 . 01 . 21 .41 . 51 . 61 . 7

190280320450900I 50030001 5006600

r I ,000

900I 60030005 1509s0018,00028,000

the EMF) of AFPM generators depends on the PM geometry (circular, semi-circular, trapezoidal) and distance between adjacent magnets [75].

Since the magnetic flux in the rotor magnetic circuit is stationary mild steel(carbon steel) backing rings can be used. Rings can be cut from 4 to 6 mmmild steel sheets. Table 3.13 shows magnetizalion characteristics B-11 of amild carbon steel and cast iron. Electrical conductivities of carbon steels arefrom 4.5 r 106 to 7.0 x 106 Stm ar 20oC.

Halbach array

Twin rotors of double-sided coreless AFPM machines (Fig. l.ad) may usePMs arrange d in Halbach array I I 04- 1 06] . The key concept of Halbach arrayis that the magnetization vector of PMs should rotate as a function of distance

I t + I

Figure 3.15. Cartesian Halbach array

Materials andfabrication l1 1

along the array (Fig. 3.15) [04-106]. Halbach anay has the following advan-tages:

r the fundamental field is stronger by a factor of 1.4 than in a conventionalPM array, and thus the power efficiency of the machine is doubled;

r the amay of PMs does not require any backing steel magnetic circuit andPMs can be bonded directly to a non-ferromagnetic suppofiing structure(aluminum, plastics);

r the magnetic field is more sinusoidal than that of a conventional PM array;

r Halbach array has very low back-side fields.

The peak value of the magnetic flux density at the active surface of Halbacharray is

(3.42)

where B," is the remanent magnetic flux density of the magnet, 13 :2rlI" -

see also eqn (1.6), lo is the spatial period (wavelength) of the arcay andnylis the number of PM pieces per wavelength. For the array shown in Fig. 3.15nM : 4. For example, assuming B, : 1.25 T, hat : 6 mm, lo : 24 mm,Dm : 4 (rectangular PMs), the peak magnetic flux density at the surface ofHalbach anay B1q6: 0.891 T.

The tangential B, and normal B, components of Halbach arliay at the dis-tance z from the surface of PMs are

Bmo - B,l7 - exp(-ljhl,)l ,rjp

B"(r, z) : B,nocos(l3r)erp( l3t)

B "(r,

z) : B,nosi.n(Pr)erp( - P z)

(3 .43)

(3.44)

For a double-sided configuration of Halbach arrays, i.e. twin disc externalrotors, the tangential and normal component of the magnetic flux density dis-tribution in the snace between discs are

B,(r, ")

: B-.oicos(0r)-- ^Lsinh(pz) (3.45)

B "(r, z) : B^osin( e") Ai0r,cosh(Pz)(3.46)

t12 AXIAL FLUX PERMAAIENT MAGNET BRUSHLESS MACHINES

where B,ns is according to eqn (3.42) and I is magnet-to-magnet distancebetween two halves of the disc. The origin of the \ry z coordinate system is asin F ig . 1 .8 .

3.3 Windings3.3.1 Conductors

Stator (armature) windings of electric motors are made of solid copper con-ductor wires with round or rectangular cross sections.

The electric conductiviQ at20oC of copper wires is 57 x 106 ) ozo ) 56 x106 S/m. For aluminum wires o2o x 33 x 106 Sim. The electric conductivityis temperature dependent and for 0 - 20" < 150"C can be expressed as

o20(3.41)

l +a (d -20 " )

where a is the temperature coefficient of electric resistance. For copper wiresa : 0.00393 1/"C and for aluminum wires o : 0.00403 l/"C. For I - 20" >150oC eqn(3.47) contains two temperature coefficients cr and p of the electricresistance. i.e.

o20(3.48)

1 * a(t9 - 2A) + p(0 - 20")2

The maximum temperature rise for the windings of electrical machines is de-termined by the temperature limits of insulating materials. The maximum tem-perature rise in Table 3.14 assumes that the temperature of the cooling medium8. < 40"C. The maximum temperature of windings is actually

S r n o * : 8 . + L 8 (3.4e)

where Ari is the maximum allowable temperature rise according to Table 3.14.A polyester-imide and polyamide-imide coat can provide an operating tem-perature of 200"C. The highest operating temperatures (over 600oC) can beachieved asing nickel clad copper or palladium-silver conductor wires and ce-ramic insulation.

3.3.2 Fabrication of slotted windingsStator windings are usually made of insulated copper conductors. The cross

section of conductors can be circular or rectangular. For large AFPM machinesa direct water cooling system and consequently hollow conductors can be con-sidered.

It is difficult to make and form stator coils if the round conductor is thickerthan 1.5 mm. If the current density is too high, parallel conductor wires of

Mate rials and fabrication 113

Table 3.14. Maximum temperature rise Arl for armature windings of electrical machines ac-cording to IEC and NEMA (based on 40"C ambient temperature)

Rated power ofmachines,length of coreand voltage

Insulation classA E B F H"C "C "C OC "C

IECa.c. machines < 5000 kVA(resistance method) 60 75 80 100 125IECa.c. machines > 5000 kVAor length ofcore ) I m 60 70 80 100 125(embedded detector method)NEMAa.c. machines < 1500 hp 70 90 1 15 140(embedded detector method)NEMAa.c. machines > 1500 hp and < 7 kV(embedded detector method) 65 85 I 10 135

smaller diameter are recommended rather than one thicker wire. Stator wind-ings can also have parallel current paths.

The anrrature windings can be either single-layer or double layer (Seclion2.2). Af\er coils are wound, they must be secured in place, somehow, so asto avoid conductor movement. Two standard methods are used to secure theconductors of electrical machines in place:

t dipping the whole component into a varnish-like material, and then bakingoff its solvent,

t trickle impregnation method, which uses heat to cure a catalyzed resinwhich is dripped onto the component.

Polyester, epoxy or silicon resins are used most often as impregnating materialsfor treatment of stator windings. Silicon resins of high thermal endurance areable to withstand $n,', ) 225"C.

Recently, a new method of conductor securing that does not require any ad-ditional material, and uses very low energy input, has emerged [63]. The solidconductor wire (usually copper) is coated with a heat and/or solvent activatedadhesive. The adhesive which is usually a polyvinyl butyral, utilizes a low tem-perature thermoplastic resin [163]. This means that the bonded adhesive cancome aparl after a certain minimum temperature is reached, or it again comesin contact with the solvent. Norrnally this temperature is much lower than the

tt4 AXIAL FLUX PERMANENT MAGNET BRUSHLESS MACHINES

Figure 3.16. Disc-type coreless winding assembled of coils of the same shape according toU.S. Patent No. 5 744 896 !391: (a) single coil; (b) three adjacent coils. I - coil side, 2 -

inner offsetting bend, 3 - outer offsetting bend.

thermal rating of the base insulation layer. The adhesive is activated by eitherpassing the wire through a solvent while winding or heating the finished coilas a result ofpassing electric current through it.

The conductor wire with a heat activated adhesive overcoat costs more thanthe same class of non-bondable conductor. However, a less than two secondculrent pulse is required to bond the heat activated adhesive layer and bondingmachinery costs about half as much as trickle impregnation machinery [63].

3.3.3 Fabrication of coreless windingsStator coreless windings of AFPM machines are fabricated as uniformly

distributed coils on a disc-type cylindrical supporting structure (hub) made ofnonmagnetic and nonconductive material. There are two types of windings:

(a) winding comprised of multi-turn coils wound with turns of insulated con-ductor ofround or rectangular cross section;

(b) printed winding also calledy'lm coil winding.

Coils are connected in groups to form the phase windings typically connectedin star or delta. Coils or groups of coils of the same phase can be connected inparallel to form parallel paths.

To assemble the winding of the same coils and obtain high density packing,coils should be formed with offsetting bends, as shown in Fig. 3. I 6. The spacebetween two sides of the same coil is filled with coil sides from each of theadjacent coils.

Coils can be placed in a slotted structure of the mould (Fig. 3.17). With allthe coils in position, the winding (often with a supporting structure or hub) is


(a)

Figure 3.17. Moulds for positioning the coils: (a) mould with guide slots; (b) mould withguide pins.

Figure j.18. Film coils for AFPM micromotors. Courtesy of EMbest, Soeul, Korea

moulded into a mixture of epoxy resin and hardener and then cured in a heatedoven. Because of the difficulty of releasing the cured stator from the slottedstructure of the mould (Fig. 3. l7a), each spacing block that forms a guide slotconsists of several removable pins of different size (Fig. 3.17b).

For very small AFPM machines and micromachines printed circuit core-less windings allow for automation of production. Printed circuit windings for

I l 5

I16 AXIAL FLUX PERMAAIENT MAGNET BRUSHLESS MACHINES

AFPM brushless machines fabricated in a similar way as printed circuit boardshave not been commercialized due to poor performance. A better perfotmancehas been achieved using film coil windings made through the same process asflexible printed circuits [85]. The coil pattern is formed by etching two copperfilms that are then attached to both sides of a board made of insulating mate-rials (Fig. 3.18). Compact coil patterns are made possible by connecting bothsides ofcoil patterns through holes [85].

Numerical example 3.1A simple stationarymagnetic circuit is shown in Fig. 3.19. There are two

Vacomax 240 HR SmCo PMs (Table 3.1 1) with B, : 7.10T, H, : 680 kA/m,

temperafure coefficients ()B : -0.03%l"C and as : -0.15o/ol"C aI 20 I'Bpm { 100"C. The height of the PM per pole is hy : 6 mm and the air gap

thickness g : 7 mm. The U-shaped and I-shaped (top) ferromagnetic coresare made of a laminated electrotechnical steel. The width of the magnets andcores is 17 mm. Calculate the air gap magnetic flux density, air gap magneticfield strength, the useful energy of PMs and normal attractive force per twopoles at: (a) 8pu: 20oC and (b) ,5ptr :100oC' The MVD in the laminated

core, leakage and fringing magnetic flux can be neglected.

Solution:

(a) Magnet temperature I pm : 20"C

The relative recoil magnetic permeability according to eqn (3.4) for a straight

line demasnetization curve is

1 1 .10 -0M; Y 104 680,0U0 - 0

1ABItrrrec:

tto, LH : x L .29

The air gap magnetic flux density according to eqn (3.13) is

1 .10 : 0.906 TD -u g -L+ I . 29 x 1 .0 /6 .0

The air gap magnetic field strength according to eqn (3.14) in which H : Hsand B: Bg is

/ 8 .Ho: H.l t "u' ,) : ouu x ro3 (r

' r : , t1) r20.r2 x r03 A/rn

The useful energy per magnet volume according to eqn (3.5) is

- , : u-p :W#e:54 3e5.8 J/m3

M ate rial s and.fa bric atio n

r .074

117

1 7

mffi

Figure 3.19. A simple stationary magnetic circuit with PMs and air gap. Numerical example3.1 .

The useful energy per pole pair is

W g : w g V I V : 5 4 , 3 9 5 . 8 ( 2 x 6 x 1 5 x 1 7 x 1 0 n ) : 0 . 1 6 6 J

The normal attractive force per 2 poles is

Bl I o€\a'2, - ,fr(2s.lr)

(b) Magnet temperature ,3pnt -- 100oC

The remanent magnetic flux density and coercivity at l00oC according to eqns(.3.2) and (3.3) is

B,: r ro [r. +#(roo-,o)] ror4r

r/" : 680 x tor fr + **troo - 20)l : 5e8.4 x 103 A/mL 1 0 0 j

At'B p u : 100"C the demagnetization curve is nonlinear. lts linear part is onlybetween 0.5 T and B, parallel to the demagnetization curve at 20oC. Thus, therelative recoil magnetic permeabthty 1.t,.,,.. and air gap magnetic field strengthHo at l00oC are approximately the same as those at room temperature.

The air gap magnetic flux density according to (3.13) is

Bs*7+7 .29 x 1 .0 /6 .0

: 0.884 T


The useful energy per magnet volume is

0.884 x 720,120: 53 090.3 Um3u g x

The useful energy per pole pair is

Wg:53 090 .3 (2 x 6 x 15 x 17 x 10 e ) : 0 .162 J

The normal attractive force per 2 poles is

Numerical example 3.2A single-sided, 8-pole AFPM machine with slotted ferromagnetic stator has

the PM outer diameter Do6 : 0.22 m and inner diametet Din : 0.12 m.

The air gap including the effect of slotting (Carter coefficient) is I : 1.9

mm. Trapezoidal sintered NdFeB magnets have B,: 1.15 T and /1. : 900

kA/m at 20oC. The temperature coefficient for B" is as : *0.15 o/o l"C and

the temperature coefficient for H.t's as: -0'64 o/o l"C' The coefficient of

PM leakage flux is otv,r : 1.15 and pole width-to-pole pitch coefficient is

a ; : 0 . 7 2 'Find PM dimensions to obtain the air gap magnetic flux densitY Bs : 0.64

T at no-load and temperature 8pv : B0oC. Sketch operating diagrams in the

B-H and O-I,t M F coordinate system at no load. Assume that the magnetic

circuit is unsaturated.

Solution:

The remanence and coercivity at Spxn : 80"C according to eqns (3.2) and(3.3) is

B,: r . tb [ r

. *# ( f pm *ro) ] 1.046 r

H. : eooft * *9(dp.,rr - 2o)l : bb4.4kAlnL r u u I

Approximation of demagnetizationcurves according to eqn (3'14) at 20oC and

B0"C respectively

N RR42r :

*f f i (r5 x 17 x to 6) : 158.6 N

/ H \Bto(H) - r . r i [ , -

oo*oo ]/H \

B (H) :1 .046 t1 - - l

" 554 4001

Materials and fabrication 1 19

The relative recoil magnetic permeability according to eqn (3.a) is

1 .046lf,,ec: g4r. ,a 1g-o * ttn n*

: -t' ir

The axial height ofthe PM perpole according to eqn (3.13) is

, o t A I B n l . l $ v n A , ahtr : !,,." Ufff ire: t.S**ff ia0.0019 - 0.0068m

The equivalent air gap is

s"q: e - # :

l 'e I L : :6 '4mrn

The average diameter, pole pitch (1.9), length (3.34) and width of the magnetare respectively

D : 0. 'o(0.22 + 0.72): 0.17m " : y:: ry

: 0.0668 m

I ,r.r - 0.5(0.22-0.I2): 0.05 m ux,1 : crir :0.72x0.0668 : 0.048 m

The permeance of the air gap according to eqn (2.23) is

Go:1ro iY\o i , , - D?, )o 8 n

: 0.4n10-6--1- 0'72r

rc.222 - 0.122): 1.59 x 10-6 HU.00198x4 \ " ' " "

OI

t L ' 7 1 1 1 7 4 . ^ 6 0 . 0 4 8 x 0 . 0 5Cu - t-ro::L - 0.4 x n'10 bffi - 1.59 x tu 6 H

The total penneance for magnetic flux including leakage permeances is

G 1 : o y n G g : 1 . 1 5 x 1 . 5 9 x 1 0 6 : 1 . 8 2 8 x 1 0 6 H

Approximation of the total perneance (air gap and leakage) line can be ex-pressed as a linear function of 1{

h , , . ^ 6 0 . 0 0 6 9\ t (H) - r , f f iH : t .B2E x ro ood; ; ;G H :b.146 v io 6H

The magnetic field intensity corresponding to the operating point of the magnetis calculated as

I2O AXIAL FLUX PERMANENT MAGNET BRUSHLESS MACHINES

(a ) , )l l

l

uzo ( l t ) 0 .8

B(H) 0 .6

lrr*,0.4

0.2

I

(b)o.ot) l o ool

0.0025

o( F) o.oo2O . ( F )' 0 .00 t5

-Ty" oool

5 ro-'

1 o u 8 . 1 0 '1000000

6 . 1 0 ' -4 .t 0- - 2 . 1 { ) '

-4000 -3s00 -3000 -2500 -2000 -r500 -r000 -500 0

0- 4000

Figure 3.20. Operating diagram of PM at no load: (a) in B-H coordinate system; (b) in O-I,I L,I F coordinate system. Numerical example 3.2.

H M -Gfty1f Qt1rtru) * B,lH.

B,

- 1 '046 - : 148 795 Alrn5.146 x 10-6 + 7.0461554,400

" ' - ' "-

The air gap magnetic flux density as obtained from the operating diagram (Fig.

3.20a) is

h n , - 0 . 0 0 6 8B - : G ^ _ ! ! ! L 1 1 n , : 1 . 5 9 r l 0 6 _ - l _ " " " ! - - l 4 B 7 g b : 0 . 6 6 6 Te - Y w ; r l ; r

0 . 0 4 8 x 0 . 0 5

To plot the operating diagram in the Q-M M F coordinate system, eqns (3.16)and (3.18) are used to find the magnetic flux O, correspondingto Br and theMMF -A per pole correspondingto H", i.e.

O, : 1.046 x 0.048 x 0.05 : 0.00252 Wb

Materials and fabricatio n

f , : 554 400 x U.0068 : 3750.6 A

Approximation of the magnetic flux line is

t2l

:ooo252(r-#)

Bmo:1.2511 * exp(-130.e x 0.006)1"#P: 0.62 T

, , \O (F ) :O -11 - :, \ T 1

\ r c /

The MMF F11 coffesponding to the operating point of the magnet in the O-M M F coordinate system (Fig. 3.20b) is

F " . * 0.00252Gt I Q,lf" 1.828 x 10-6 + 0.002521375A.6

: 1006.6 A

The air gap flux line (Fig. 3.20b) is

O q ( . F ) : G g F : 1 . 5 9 > 1 0 6 F

The total flux line (Fig. 3.20b) is

O r ( f ) - G L f : L B 2 B x 1 0 - 6 f

The air gap magnetic flux conesponding to the operating point is Qs(FM) :0.0016 Wb. The air gap magnetic flux density is Bn : 0.0016/(0.048 x0.011) : 0.666 T.

Numerical example 3.3The magnetic field in the air gap of an AFPM machine with coreless stator

is excited by sintered NdFeB magnets arranged in Halbach array. The extemaltwin rotors do not have any backing steel discs (Fig. l.ad). The remanentmagnetic flux density is B, - 7.25 T, the height of the PM is hxn : 6 mm,the wavelength at the average diameter is lo - 2r : 48 mm and the magnet-to-magnet distance is f - 10 mm.

Find the distribution of the magnetic flux density in the space between mag-nets for the 90-degree Halbach array, i.e. nNr :4. Estimate, how the numbern11 of PMs per wavelength affects the magnetic flux density at the active sur-face of PMs.

Solution

The peak value of the magnetic flux density at the active surface of Halbacharray according to eqn (3.42) is

o_

122 AXIAL FLLTX PERMANENT MAGNET BRUSHLESS MACHINES

( a ) 0 8

e *x,:j.

roo"7 " rr'[ ' ; j

0.8

0 .8

0.6

0.4

0.2

- 0.2

- 0.4

- 0.6

- 0.80

0(b ) , ) ) r

0.80 .6

0 4B x(0 ,2) 100 0 .2

----7 , 0

B - l 0 . 2 5 I ̂ " z l

*0.4

-0.6

o 8 -o.s-0.004

TFigure 3.2L Distribution of B* and B,tion. Numerical example 3.3.

0.040.030.020.01

-0.002 0 0.002 0.004

z g

;

components: (a) in the z direction; (b) in the z direc-

where 0 : 2 x r 10.048 : 130.9 lim.The distribution of the tangential component B, in the space between mag-

nets is described by eqn (3.45) and the distribution of the normal componentB, is described by eqn (3.46). Both components B" and Bz are plotted in Fig.3.2r .

0.80 .8

0 .6

0.4

0.2

0

B m0lim

s ,oo(n N4 )re

02

2

8 1 0 t 2 1 4 1 6

n M 1 6

Figw'e 3.22. Peak value of magnetic flux density 8,,, as a function of number n,ry of PMs per

wavelength. Numerical example 3. 3.


For the 90-degree Halbach array (ny1 : 4) the peak value of the magneticflux density at the active surface of PMs is -8,r,6 : 0.42 T. Similarly, using eqn(.3.42), the peak value B-s can be calculated for other Halbach configurations.For 60-degree Halbach arcay (n,y : 6) B-o : 0.649 T and for 45-degreeHalbach array (nx1 : B) B-o : 0.663 T. In general,

,#T"" Brno: B,l1-exP(1 - \h'm)1ry#

: 1 .25 [1 -exp(130.9 x 0 .006) ] x 1 : 0 .68T

since lim"*ssinrf r : 1. The peak value Br,rg ?s a function of number n,yof PMs per wavelength is shown inFig.3.22.

Chapter 4

AFPM MACHINES WITH IRON CORES

In Chapter 2, principles of operation, topologies and fundamental equationsof a broad family of AFPM machines were discussed. In this chapter, the focusis on those types of AFPM machines that make use of the stator and rotor fer-romagnetic cores. The AFPM machines with ferromagnetic cores are designedboth as single-sided and double-sided. The stator core can be fabricated usingeither laminated steels or SMC powders. General equations given in Chapter 2for the performance calculations will be developed further and adjusted to theconstruction of AFPM machines with ferromagnetic cores. Application of theFEM analysis to performance calculations is also emphasized.

4,1 GeometriesSingle-sided AFPM machines with stator ferromagnetic cores have a single

PM rotor disc opposite to a single stator unit consisting of a polyphase windingand ferromagnetic core (Fig. 2.1). The stator ferromagnetic cores can be slottedor slotless. The stator winding is always made of flat wound coils (Fig. 2.8).The PMs can be mounted on the surface of the rotor or embedded (buried) inthe rotor disc. In the case of a slotless stator the magnets are almost alwayssurface mounted, while in the case of a slotted stator with a small air gapbetween the rotor and stator core, the magnets can be either surface mountedon the disc (Fig. 2.1) or buried in the rotor disc {Fig.2.6). Large axial magneticforces on bearings are the main drawback of single-sided AFPM machines withferromagnetic stator cores.

ln double-sided AFPM machines with ideal mechanical and magnetic sym-metry the axial magnetic forces are balanced. Double-sided AFPM machineswith stator ferromagnetic cores have either a single PM rotor disc with iron-cored stators on both sides of the disc (Figs l.4c and 2.3) or outer PM rotordiscs with iron-cored stator fixed in the middle (Figs 2.4,2.5 and2.6'). As with

126 AXIAL FLUX PERMANENT MAGNET BRUSHLESS MACHTNES

single-sided AFPM machines the stator ferromagnetic cores can be slotted orslotless, and the rotor magnets can be surface mounted, embedded or buried(Fig. 2.6). Again, in the case of a slotless stator with a large air gap betweenthe rotor and stator core the magnets are almost always surface mounted. Thestator windings of double-sided AFPM machines can be flat wound (slotted orslotless) as shown in Fig. 2.8 or toroidally wound (normally slotless) as shownin Fig. 2.9.

4.2 Commercial AFPM machines with statorferromagnetic cores

An example of a commercial double-sided AFPM servo motor with fer-romagnetic core is shown in Figs.4.1 and 4.2. Extemal stators have slottedring-shaped cores made of nonoriented electrotechnical steel ribbon. The in-ner rotor does not have any ferromagnetic material. PMs are mounted on anonmagnetic rotating disc.

Figure 4. I . Double-sided AFPM brushless servo motor with the stator f'erromagnetic core andbuilt-in brake. Courtesy of Mavilor Motors, 5.A., Barcelona, Spain.

Fig. 4.3 shows a double-sided AFPM synchronous generator with the statorcore wound of amorphous alloy ribbon manufacturedby LE Incorporated,In-dianapolis, IN, U.S.A. The volume of lE AFPM generators is approximately60o% lower than that of classical synchronous generators of the same rating.

AFPM machines with iron cores r27

Figure 4.2. Longitudinal section of the double-sided AFPM brushless servo motor shown inFig.4.1. Courtesy of Mavilor Motors,,S.l., Barcelona, Spain.

Figure 4.3. Gensrnart:I Lt AFPM synchronous generator with amorphous alloy stator core.Courtesy of LE Incorporated,lndianapolis, IN, U.S.A.

4.3 Some features of iron-cored AFPM machinesIron-cored AFPM machines are distinguished in two ways from coreless

(air-cored) AFPM machines, namely: (i) iron-cored machines have core losseswhile coreless machines do not and (ii) the per unit values of the synchronousreactances of iron-cored machines are much hieher than those of coreless ma-chines.

'v :.*l:::::,::::::,:,:::,,:,&

wlillrlll',.:llllllll:t l


The core losses are functions of amongst other things the frequency anddensity of the magnetic flux in the ferromagnetic core - see eqn (2.a8). Thefrequency of the ffux variation in the core is in turn determined by the speedand number of pole pairs. As AFPM brushless machines tend to have a highnumber ofpoles (minimum 2p : 6), the speeds of iron-cored AFPM machinesare limited to keep the frequency, and hence the core losses of the machine,within limits; unless the machines are designed to have low flux densities inferromagnetic cores. Flux frequencies are normally kept below, say 100 Hz,for laminated ferromagnetic cores. If higher frequencies are required, thensilicon steel laminations with a thickness of less than0.2 mm, amorphous alloyribbons or SMC powders must be used.

The higher synchronous inductance of iron-cored AFPM machines affectsnegatively the voltage regulation of the machine in generator mode, whichmight be considered as a disadvantage. However, for solid-state converter-fedapplications the higher synchronous inductance of iron-cored AFPM motors isan important advantage as it helps reduce the current-ripple due to converterswitching. Thus the relatively low inductance of coreless AFPM machines canbe a significant disadvantage in switched solid state converter applications.

4.4 Magnetic flux density distribution in the air gapAFPM brushless machines with ferromagnetic stator and rotor cores can

produce strong magnetic flux density in the air gap with a minimum volume ofPMs. The distribution of the normal component of the magnetic flux densityin the r-direction (circumferential) excited by PMs without armature reactionat the radius corresponding to the average pole pitch r canbe described by thefollowing equation

1B n Q ) : . B , p u ( r ) * 8 " 1 \ r )

" K 6

where the PM excitation flux density for smooth stator core is

(4 .1 )

and the magnetic flux density component due to stator slots is

(4.3)

The peak values of the higher harmonics of the magnetic flux density distribu-tion of eqn (4.2) arc B*s, : (Bnf o1y)b".

Ba(n): x"@)#B"pnr(r)

AFPM machines with iron cores t29

0 0.02 0.04 0.06 0.08 0.1 0.12 0.14 0.16 0.18 0.2 0.22

0 x 2 . p t

Figure 4.1. Magnetic flux density distribution in the air gap of an AFPM machine with ironslotted core obtained on the basis of eqn (4.1) forp : 3, s1 : 18, r : 36.7 mm, a; : 0.78,b p : d t r , B , : 1 . 2 T , p , , . " : 1 . 0 6 1 , g : 1 . 5 m m , b r a : 3 . 5 m m , h , x 1 : 5 m m , o : 0 a n do t v : 1 . ! 5 .

In the above equations (4.1), (4.2) and(4.3) kc is Cafier's coefficient ac-cording to eqn (1.2), b, is according to eqn (1.8) usually for a : 0, r is theaverage pole pitch according to eqn (1.9), g' is the equivalent air gap in the d-axis according to eqn (2.103), Bo is the flat-topped value of the magnetic flux

1 . 0 t

0.8

0.6

0.4

B J9 o.z

B - ' ( x)" '

-0_2

-0.4

-0.6

-0.8

- 1 o - t

- 3 . l 0 j3 . 1 0 )

s2.5 10-

52 .10 "

p , ( x ) t . s t 0 5

l ' 1 0 '

5 ' 10 '

00 0.02 0.04 0.06 0.08 0.1 0.12 0.14 0.16 0.18 0.2 0.22

0 x 2 . p . r

Figure 4.5. Magnetic pressure distribution in an AFPM machine with iron slotted core ob-tained onthebasis ofeqn (4.7) forp : 3, s1 - 18, r : 36.7 mm, ar : 0.78, b, : a.r,B , : 7 .2T, p1 , , " , , : 1 .061, g : 7 .5mm, b1a : 3 .5 mm, hm : 5mm, a : 0 andotu : 1 .15 .


density according to eqn (3.13), o1x1is the coefficient of the PM leakage fluxaccording to eqn (3.9) and .\"t is the relative slot leakage perrneance given by

/ 2 r \l u x l\ t r /

(4.4)

in which the average slot pitch h : 2prls1, s1 is the number of stator slotsand the amplitude of slot harmonics as derived by W. Weber 164, I 1 I I is

B l n ) l 4 ( ^ . u 2 l 2 \au : t to 'n," ' , ; (O.s + ' iB _tFpj s in( t .6utrr) (4.5)

The remaining quantities 0(n), rc and I are expressed by the following equa-tions:

13(")bu1

2

/ I \t - l I

\ - \E -E ) '

7 Bo ( t ) ' 2Hzy* , -

2 l r l

9 * h u / t t , , , . 'f - = ( 4 6 )

1:1

The distribution of the magnetic flux density in the air gap obtained on thebasis of eqn (4.1) is shown in Fig. 4.4. The magnetic pressure on the stator androtor active surfaces can be found on the basis of the normal component (4.1)of the magnetic flux density distribution in the air gap, i.e.

(4.7)

The distribution of the magnetic pressure (.7) is visualized in Fig. 4.5. Themagnetic pressure resolved into Fourier series yields harmonics of magneticforces acting on the stator. It is necessary to calculate those harmonics, e.g. inthe noise analysis of electromagnetic origin radiated by the AFPM machine.

4.5 Calculation of reactances4.5.1 Synchronous and armature reaction reactances

Calculations of the stator current, other machine parameters and charac-teristics require knowledge of the synchronous reactance per phase which isexpressed by eqns (2.12) and (2.73). The synchronous reactance X"4 and X",is the sum of the armature reaction (mutual) reactance X,rd, Xoq and the statorwinding leakage reactance X1 . The atmature reaction reactances Xod", Xoqand armature reaction inductances Lod,, Loq can be calculated with the aid ofequations given in Section 2.9 and Table 2.1. The analytical approach to cal-culation of the stator leakage reactance X1 is discussed in Section 4.5.2.

AFPM machines with irutn crtres 131

h

h . "

frtz

fl,,.,

(b)

h,,oh .^n' ' 1 2

h' ' 1 1

: nnf ,.tJ#(Ar"krx +

(c)

h" 1 4

firah"12

h , ,

1ii,, . Iro..,t ,

t^,. , , * i ; ^,," ' ,r * )ra)

' 1 1 - 1 1 O r = 9 p

Figure 4.6. Stator slots of AFPM brushless machines: (a) rectangular semi-open slot; (b)rectangular open slot; (c) oval semi-open slot.

4.5.2 Stator leakage reactanceThe armature leakage reactance is the sum of the slot leakage reactance

X1.r, the end connection leakage reactance Xp, and the differential leakagereactance X14 (for higher space harmonics), i.e.

X t : X t " I X r c * l r a

where l/1 is the number of turns per phase, k1;; is the skin-effect coefficientfor leakage reactance, p is the number of pole pairs. q1 :

"tl(2prn,1) is the

number of stator slots s1 per pole per phase (2.2),11i" is the length of the statorwinding inner end connection, l1,,rr1is the length of the stator winding outer endconnection, )r" is the coefficient of the slot leakage penneance (slot-specificpermeance) , \r",in is the coefficient of the leakage perrneance of the inner endconnection, \reout is the coefficient of the leakage perneance of the outer endconnection and )1,7 is the coefficient of the differential leakage.

The coefficients of leakage perrneances of the slots shown in Fig. 4.6 are:

r for a rectangular semi-open slot (Fig. 4.6a):

(4.8)

, h 1 h n 2 l t t : r h t +A t ^ -

3 b r r b r r b l l * b 1 1 b r t(4.e)

132 AXIAL FLTIX PERMANEAIT MAGNET BRUSHLESS MACHINES

r for a rectangular open slot (Fig. 4.6b):

r for an oval semi-open slot (Fig.4.6c):

) r . = 0. t4241 l f * ! ' ' t +0.5arcs in lJb r r bn +t# (4.1r)

u 1 4

The coefficients of leakage pelmeances for other shapes of slots than thoseshown in Fig. 4.6 are given, e.g. in [147]. The above specific-slot penneances(4.9), (4.10) and (4.11) are for single-layer windings. To obtain the specificperrneances of slots containing double-layer windings, it is necessary to mul-tiply eqns (4.9), (4.10) and (4. I l) by the factor

30+t

r outer end connection

, h t t h n * h ' m * h Mi l ' t - -

,J o i I O t I

)k i , , x 0 .77q1A - :W)

)1oo,1 =0.17q1O - i f f ; l

(4 .10)

(4.r2)

<{3<

(4 .13)

4

where p is according to eqn (2.7). Such an approach is justified if 2131 . 0 .

The specific perrneance of the end connection (overhang) is estimated on thebasis of experiments. For double-layer, low-vo1tage, small and medium-powermachines the specific permeances of the inner and outer end connections are:

r inner end connection

(4.14)

where l1;'-, is the length of the inner end connection, l1ou1, is the length of theouter end connection, ul",;r. is the inner coil span, and u).orr1 is the outer coilspan. The speciflc peffneance of two end connections is a sum of permeances(4.13) and (4.14), i .e.

(bulbn)2)

AFPM machines with iron cores

r outer end connection

133

)1u : )10,i,, * )l"ort : 0.34qt (t - lt 'u"i ' Ibut * tu"outlrin\

\ ?r hinlbu,t ) @'15)

For wrir, : ucout : 'tltc &fid lyin - lrou,t - 1i1" the speciflc permeance (see

eqn (4,15)) of two end connections has the same form as that for a cylindricalstator. i.e.

) r . :o .34qr ( r -?g)\ 7 1 ' l f , , /

A7"in x 0.27q11_ ?ffi lni,

(4.r6)

Putting ut.fl1" : 0.64, eqn (4.16) also gives satisfactory results for single-layer windings, i.e. the specific perrneance of two end connections becomes

)1" ru 0.2q1 (4 .17)

For double-layer, high-voltage windings the specific perneances of the innerand outer end connections are:

. inner end connection

(4 .18)

(4.re)

where the stator winding factor k-1 for the fundamental space hatmonic z : 1is according to eqn (2.10). The specific perneance of two end connections

) r " : ) r , in r ) t t ou t : o .azq1 ( t l a t ' \ tL l } l r ' t ! t \

n t , (4 .20)\ n l l i n t l o u t /

In general, the following approximate relation may be used for most of thewindinss:

t reour = o .21q1r t - :# rn ' - ,

) 1 " = 0 . 3 q 1 (4.21)

134 AXIAL FLUX PERMANENT MAGNET BRUSHLESS MACHTNES

The specific penneance of the differential leakage flux is

where g/ is the equivalent air gap according to eqns (2.103) or (2.104) and krolis the saturation factor of the masnetic circuit. The differential leakase factorTdr is

, m tq t r k ' | , , tA t d : * T a t

T'9 ' Ksat

ra t -J - f1 l - r1zb ' t I' " t r t l yS\

Str=ffi

(4.22)

(4.24)

(4.2s)

(4.23)

The curves ofthe differential leakage factor 16 are given inpublications deal-ing with design of induction motors, e.g. 196, | 11 , 1471.

In practical calculations it is convenient to use the following formula

n2(toql + z)t o t -

The specific perrneance between the heads of teeth:

27. /30 ' \

s l l r l - l - 1\ Q r l

should be added to the differential specific peffneance )1a of slotted statorwindings.

4.6 Performancecharacteristics

Specifications of Mavilor AFPM motors (Figs. 4.1 and 4.2) are shown inTable 4.1. Torque-speed characteristics of Mavilor AFPM motors are plottedin Fig. 4.7. AFPM servo motors MA-3 to MA-30 are designed with Class Finsulation and IP-65 protection. Table 4.2 shows specifications of brakes forMA-3 to MA-30 servo motors.

Table 4.3 shows specifications of GenSmartTM AFPM synchronous gen-erators with amorphous alloy stator cores manufacturedby LE Incorporated,Indianopolis, IN, U.S.A. GenSmar{M AFPM synchronous generators can beused both as stationary and mobile generators.


Tnrqur iNmi

l r !

141 !1 *sfi47.fi

tul4-![

MA.-30

_ MA-1fi

.MK.E

- MA"3

135

18

0 5flf 1 nflfi 'l 5flfi ?0fifl 25*fi '}*{Jt} 35fl CI 4Dnfl$peecl irpnti

Figure 4.7. Torque-speed curves of AFPM brushless servo motors manufactured by Mavilor,Barcelona, Spain.

Table 4.1. AFPM brushless servomotors manufactured bv Mcrvilor. Barcelona" Spain

MA-3 MA-6 MA-10 MA.2O MA-30Maximum speed, rpmStall torque, NmStall current, APeak torque, NmTorque density, Nm/kgEMF constant, Vs/radTorque constant, Nm/ACogging torque, NmWinding resistance, {)Winding inductance, mHRotor moment of inertia, kgm2 x 10-3Mechanical time constant, msE,lectrical time constant, msThermal time constant, sThermal resistance, "C/WMass, kgRadial load, N

9000 6000 60001 .3 3 .6 5 .82.2 4.2 6.85.2 28.5 40.70.1 0.8 L l0 .3 0.5 0.50.6 0.9 0.9

< 0 .2 < 0 .1 < 0 .110.2 5.3 2.225 .0 11 .6 0 .40.04 0.30 2.102 .0 3 .8 3 .62.5 2.2 7.51500 1500 18001 .1 0 .6 0 .5

2r8 225 225

6000 600010 .0 16 .010 .3 16 .569.8 96.01 . 2 1 . 60.6 0.61 . 0 1 . 0

< 0.2 < 0.31 .4 0 .57.0 4.00.80 1.602 . 1 1 . 65.0 7.5

1500 15000.4 0.434 36390 390

r36 AXIAL FLUX PERMAI{ENT MAGNET BRUSHLESS MACHINES

Table 4.2. Speciflcations of built-in brakes for AFPM brushless seryomotors manufactured byMavilor, Barcelona, Spain

MA-3 MA6 MA-10 MA-20 Ma-30Holding torque, Nmd.c. voltage, VInput power, WMomentof inertia, kgm2 x 10-3Disengagement response time, msEngagement response time, msMass, kg

I4 .85

0.0875

0.3

424220.3307

0.8

424220.3307

0.8

8 81 1 1 /

22 220.3 0.330 307 7

0.u 0.8

Table 4.3. GenSmartT ̂r AFPM synchronous generators manufactured by LE, Inc., Indianop-ol is. IN. U.S.A.

28-G22 90-G32 t20-G49Rated output poweq kWRated speed, rpmMaximum speed, rpmVoltage, VStator insulationEfficiency, ToFrame extemal diameter, mmFrame extemal length, mmStator core materialCoolingAmbient temperature, "CMaximum allowabietemperature, "CEnclosureMountingOvertemperature controlMass, kgPower densiry kWkg

28 9036004240

480 or 208Class H

94.93 1 5186

Amorphous alloyliquid or air cooled

-50 to 60

125 (rise from 40"C)Totally enclosedFlange or foot

Embedded thermistor44

2.045

t202s003000

95.3485200

92.2216150

I . J J J

1 1 51.043

4.7 Performance calculation4.7.1 Sine-wave AFPM machine

The electromagnetic power of a sine-wave (synchronous) AFPM motorexpressed by eqn (2.84) which can also be brought to the following form:

is


Perr, : mllloE lcos rll + * (t", - X,n)I?,sin 2V]J 2 \

Hence, the developed torque is

t37

(4.26)

P"l^, [ s :' ^

2nn "

: t# l l r r 1ku,1o 1Io< os v * ) t r "o

- L"s) I : , in zv l @.271

For buried and interior PM rotors X",t t X"n and L",t ) ,L"n, which im-plies that an additional reluctance power and torque component is developedby the machine. For surface PM rotors the reluctance dependent componentsof power and torque are almost not existent as X"a = Xsa and L",1. = L"n. Ineqn (4.26) the EMF E y canbe calculated by means of eqn (2.29). The currentIo and angle V in eqns (4.26) and (4.27) are either specified, or determinedaccording to Section 2.7 using voltage phasor V1 projections on the d, and qaxes. The reactances and inductances are calculated as described in Sections2.9 and 4.5.2. Hence, with all the parameters known, the performance of theAFPM brushless motor in terms of the electromagnetic power and developedtorque can be calculated. Note that, for the generating mode, the second term ineqns (4.26) and (4.27) (dependent on the difference between the d- and q-axissynchronous inductances) is written with the minus ( ) sign.

The electric power available, after losses, of an AFPM machine with thestator ferromagnetic core is calculated as

r the input power for motoring mode

Pr.n: P.t,n * LPt- * LPrp" * LPzp" * APppy + AP" (4.28)

r the output power for generating mode

Pout : P"t^ - LPu, - LPtt"", LPzp" * A.Ppm - LP", (4.29)

where P"1^ is according to eqn (4.26), LPr, are the stator winding lossesaccording to eqn (2.42), LPtpu are the stator core losses according to eqn(2.47), LPzp" are the rotor core losses according to eqn (2.59), LPpyl are

138 AXIAL FLUX PERMANENT MAGNET BRL]SHLESS MACHINES

the losses in the PMs according to eqn (2.54) and AP" are the eddy currentlosses in the stator conductors according to eqns (2.61) or (2.62) (only forslotless stators). The shaft power P"7.. (input power Pi, for generators, outputpower Po6 for motors) is calculated by adding to the electromagnetic powerP"1- (generators) or subtracting from the electromagnetic power (motors) therotational losses LProt according to eqn (2.63).

The shaft torque is

r for a motor (developed by the motor itself)

(4.30)

r for a generator (developed by the prime mover)

(4.3r), , - P , L_

", _

27r, ,

and the efficiency is

Por,tt ,- sn

2 rn

PL O U f' t p

t 1,n,

(4.32)

4.7.2 SynchronousgeneratorThe phasor diagram of a salient pole synchronous generator with RL load is

shown in Fig. 4.8. The input voltage projections on the d and q axes accordingto Fig. 4.8 are

V r s i n 6 : I o n X " n - I o a R t

l/r cos 6 : Ef * IodX",t, * IoqRt (4.33)

14 sin 6 : IoaRr IoqXr

I cos 6 : IonRl * IoaXr G}4)

and

AFPM machines with iron cores 139

j l "oX,

j l"oXL

l"oR,

o

I

Figure 4.8. Phasor diagram of an overexcited salient pole synchronous generator for RL load.

where Zr - Rr * jXr, is the load impedance perphase across the outpultetminals. The d- and q-axis curents are

r from eqns (4.33)

r , -' a d , -E.f X", - Vt(X"qcos d F R1 sind)

t -' a q

X"aX"q * R,'4

Vr (X"a sin d - fir cos d) + tf RtX"aX"q* R?

(4.3s)

(4.36)

r from eqns (4.34)

W(Rr sin d * X; cos d)r , -t q . a -

R2r_ + x2,(4.37)


(4.3e)

Combining eqns (4.33) and (4.34), the d- and q-axis currents are independentof the load angle d, i.e.

r . -L a d -

Ef (X'q a xr)(4.40)

(X"a* x r ) (X"qaxr ) + ( /? r lRr ) '

ES(Rt * Rr , ) (4.4r)"n

- (x"o* xy)(x"n a xr) + (i?r * Rr)2

The angle V between the current Io and g-axis and the angle $ between thecurrent Io and voltage Vy arc respectively,

(4.38)

The load angle 6 between the voltage Vl and EMF Ei can be determined, e.g.from the first eqn (4.33), i.e.

, Vt (.Rr cos li Xl sin d)t o r : W

d : arcsin ( I"dRL - I"qXL\

\ I / r /

irr : arccos (?)- arccos (m)

d: arccos (+): arccos (X)

(4.42)

(4.43)

where I" : I

lia * Iln @ee also eqn (2.82)). The output electrical power onthe basis of phasor diagram (Fig. 4.8) and eqn (a.33) is

Pout : myVllocos @ - m1V1(Ia,rcos d * Ioa sin d)

: mllEylo, - Io6,Ior(X"a - X"q) - I iA,l 6.44)

Including only the stator winding losses, the internal electromagnetic power ofthe eenerator is

Petrn: Pout -f LP:'- : mllEylon - Io6Ion(X"a - X"q)) (4.45)


4.7.3 Square-wave AFPM machine

The square (trapezoidal) wave AFPM brushless machine has already beenintroduced in Section 2.10.2. Square-wave machines are characterized by theirtrapezoidal or quasi-square back EMF waveforms with the conduction anglefrom 100 to 150 electrical degrees, depending on the construction. The trape-zoidal back EMF waveforms can be obtained by proper design of the magneticand electric circuits. Both slofied and slotless AFPM machines can be de-signed so as to obtain sinusoidal or trapezoidal back EMF waveforms, exceptthe toroidal AFPM machine of Figs 2.4 and2.5. The toroidal machine is almostalways designed to have atrapezotdal back EMF waveform. The amplitude ofthe back EMF can be calculated by means of eqn (2.118) for a three phaseY-connected machine with two phase windings active.

The square-wave AFPM machine is always fed by means of a solid stateinverter. The inverter supplies d.c. PWM voltages to the machine phase wind-ings during the conduction intervals. The current square waveforms (see Fig.

1 .3a) are described by the flat-topped value of the current 4"q). The developedtorque Ta of Ihe square-wave AFPM brushless machine can be calculated bymeans of eqn (2.120). Hence, the electromagnetic power Pr1- of the machinecan be found. Using the same loss and power balance equations as for thesine-wave machine, the input and output power can be calculated with the aidof eqn {4.28) and the ouQut power Pottt : Putr, - LProt. Note that LPn,must be calculated by using the true rms value of the current given by eqn(2.t28).

4.8 Finite element calculations

Instead of using analytical or semi-empirical formulae, some of the equiv-alent circuit parameters and losses of the AFPM machine can be calculatedaccurately by means of the FEM analysis. The 2D and 3D FEM electromag-netic software packages are nowadays available at affordable prices and thefield solution time has become attractively short. For example, most of the2D FEM magnetostatic problems can be solved in seconds on today's personalcomputers.

The synchronous inductances -Lr6 and Lrn and the EMF Ef of an AFPMbrushless machine are the critical parameters used in the performance calcula-tions.

The first step is to specify on a 2D plane the outline, dimensions and ma-terials of the AFPM machine. Due to the symmetry of an AFPM machine,it is usually sufficient to model only one pole pitch (or sometimes even halfa pole pitch) of the machine by applying periodic boundary conditions [233].The cross section is taken at the average radius of the active part of the sta-tor winding, i.e. at 0.2s(Dort + D,"). Depending on the machine topology

t4l


Air GapF'lux 0

Density(r)

l g 0 " 9 0 0Rotor angle

l g 0 0

Air (iap

Flux g

Density(r)

0

Figure 4.9. Magnetic flux plot and air gap flux density with only PM excitation of (a) slotlessand (b) slotted disc type machine with surface PMs.

and material propefties, either Neumann or Dirichlet condition may be im-posed on the remaining boundaries. The length of the winding, which is inthe radial direction, is taken as the active length of the stator winding, i.e.Lt: ltr :0.5(Dout Dm) - eqn (3.34). After assigning different materialpropefiies to various regions of the model, the defined structure can then bemeshed.

The second step is to specif,u the phase currents, i.q,,ia andig, in the ma-chine according to the position of the rotor. To calculate the parameter L"4 otL", the phase cuments must be assigned in such a way that the stator MMFcan be aligned with the d-axis or q-axis respectively. In both cases the PMshave to be kept inactive. In the case of calculation of the EMF Ef equal to theno load voltage in generating mode, the phase currents are set to zero and onlyPMs are active.

The third step is to run the FEM solver and obtain for each of the three casesdescribed above a solution for the air gap magnetic flux density in the axialdirection of the machine. The fundamental component of the air gap magnetic

,!

-''\,\

(b)

\ \ - - - : + -

..t--j--___=t' / '-- '--z;:*;

!: t,',";-E=iliilii

\ /- r . ' - - - - - = - 1

/ J ' - - - - .

' \ '

ffi#a+ji)ArAf-,5.$mn ii.ltitif--li| |ii-litiiiilt i l tit[. ; tf-]riltL:l I i ilj i llif -+; {--l

Aluminium

AFPM machines with iron cctres t43

0 . 1MagnetFlux

Density(r) o

-0 .1

l1' * / \ _ ,

\r :7

0.24

MagnetFlux

Density(r)

(b) Rotor angle

Figure 4.10. Magnetic ffux plot and air gap flux density of interior AFPM machine with (a)

only d-axis and (b) only g-axis stator winding excitation.

flux density is determined by Fourier expansion of the axial component of theair gap flux density. Hence, the peak values of the fundamental air gap fluxdensities can be determined for each of the cases above: (1) B,n"at with onlythe d-axis MMF and thus only the d-axis cuffent I"a, (2) Brroql with only theg-axis MMF and the q-axis cunent lor,and(3) Bn,s with only the PMs active.

Step four is to calculate by means of analytical equations the inductancesand induced EMF. With Brnc,,1r and B,nonl known from the FEM analysis, theflux linkages Va and Ilrn can be calculated according to eqns (2.97) and (2.98).The inductances l",y and L"o can be calculated as described in Section 5.4.2.With B-e known from the FEM analysis, the back EMF Ey can be found byfirst calculating the magnetic flux per pole Oy according to eqn (.2.22) and then.O1 according to eqn (2.29).

Fig. 4.9 shows the FEM flux plots and air gap flux densities due to PM ex-citation alone for two single-sided AFPM machine configurations with slottedand slotless stators. Fig. 4.10 shows the FEM flux plots and air gap flux den-

I 80-g 0 0

Rotor angle

ffi=='Ltffi


sities for a single-sided interior AFPM machine with only the d- and q-axisstator winding exci tat ion.

Numerical example 4.1A three-phase, 2.2-kW, 50-Hz, 380-V (line-to-line), Y-connected, 750-rpm,

T : 7870, cos @ : 0.83, double-sided disc PM synchronous motor has thefollowing dimensions of the magnetic circuit: PM outer diameter Dout : 0.28m, PM inner diameter D;r: 0.16 m, thickness of the rotor (PMs) 2h7,1 : gmm, single-sided mechanical clearance g - 1.5 mm. A surface configurationof uniformly distributed PMs has been used. The rotor does not have anysoft ferromagnetic material. The rotor outer and inner diameters correspondto the outer and inner outline of PMs and the stator stack. The dimensions ofrectangular semi-closed slots (Fig. 4.6b) are: hn : 11 mm, hr2 :0.5 mm,hs : 1 mm, hu - 1 mm, bn : 13 mm andbla : 3 mm. The numberof stator slots (one unit) is sr :24, the number of armature tuins of a singlestator per phase is ly'r : 456, the diameter of the stator copper conductor is0.5 mm (without insulation), the number of stator parallel wires is a- : 2 andthe air gap magnetic flux density is B,nn - 0.65 T. The rotational losses areLP,ot: 80 W and the core and PM losses arc L,P1p. + LP1M :0.\5Pout.There are two winding layers in each stator slot. The twin-stator Y-connectedwindings are fed in parallel.

Find the motor performance at the load angle d : 11o. Compare the calcu-lations obtained from the circuital approach with the FEM results.

Solution

The phase voltage is I,z1 : 3801/3 : 220 V. The number of pole pairs isp : f ln: 50 x 601750: 4 and 2p : B. The minimum slot pitch is

, rD,i,n. t m ? , n -

5 1 24,zr x 0.16 : 0.0209 rn = 21 mnr

The width of the slot is b12 : 13 mm, that means the narrowest tooth widthclrnin : trnir, - btz : 2I - 13 : 8 mm. The magnetic ffux density in thenarrowest part of the stator tooth

Brtnro, - B*nt\'ni'

cLrnirt

which is rather low.The average diameter and average pole pitch according to eqn (1.9) are

D :0 .5 (0 .28 + 0 .16) :0 .22 m

0.65 x 21 :7 .7 T

n x 0.22: 0.0864 rn


Because the number of slots per pole per phase (2.2)

s l 24q I

z p - t - g " J I

the winding factor kr,1 : k6kpt: 1 x 1 : 1 as expressedby eqns (2.8), (2.9)and (2 .10) .

The magnetic flux according to eqn (2.22) and EMF induced by the rotorexcitation system according to eqns (2.29) are respectively

)e r : 1 x 0 . 6 b { [ ( 0 . 5 x 0 . 2 q 2 - ( 0 5 x 0 . 1 6 ) 2 ] : 0 . 0 0 2 1 4 5 w b

" T t 8 "

Ef : nt/250 x 456 x 1 x o.oo2r4b : 2rT.z\l

It has been assumed that B,',ny - Brns.Now it is necessary to check the electric loading, current density and fill

(space) factor of the stator slot. For two parallel wires a- : 2,the number ofconductors per coil of a double-layer phase winding according to eqn (2.3) is

Ar o r ly ' r 2 x 456 , , n" " -

( " , l r , , ) -

(2413)

Thus the number of conductors in a single slot l/"1 is equal to the (number oflayers) x (number of conductors per coil N") : 2 x 774 : 228 or accordingto eqn (2.5)

| ' ,2 x 456, \ ' , i : _ _ * - : 2 2 x

The rated input current in a single stator is

- Pout 2200I - " - r . 5 7 _ \

2 m 1 V 1 r 7 c o s @ 2 x 3 x 2 2 0 x 0 . 7 8 > U . 8 3

The stator line current density (peak value) on the basis of eqn (2.86) is

^ 4 r /2 * t loNr 3 \ / r 456 x 2 .s7A- : _r;-- - -- - l-l -152.2 A/rn

t, \uout + Di") 0.0864 x 4

which is rather a low value even for small PM a.c. motors. The cross sectionof the stator (armature) conductor

,^ : ndT - ro'52 : o.1gz mm2o o - , t

- /

-

146 AXIAL FLUX PERMANENT MAGI'{ET BRUSHLESS MACHINES

gives the following current density under rated conditions

2.57, l a

- :6.57 Af nln22 x 0.797

This is an acceptable value of the current density for disc-type a.c. machinesrated from I to l0 kW.

For the class F enamel insulation of the armature conductors, the diameterof the wire with insulation is 0.548 mm. Hence. the total cross sectional areaofall conductors in the stator slot is

^^ . n0 .548 '22s# = 54 mnr2

The cross section area of asingle slot is approximately h nbn : 11 x 13 : 143mm2. The slot fill factor 54f 143 : 0.38 shows that the stator can be easilywound, since the average slot filI factor for low voltage machines with roundstator conductors is about 0.4.

The average length of the stator end connection for a disc rotor a.c. machineis 11" = 0.154 m. The average length of the stator turn according to eqn (2.32)is

l to , , :2(Lt . + l t " ) : 2(0.06 + 0.154) : 0 .428 m

where Lt : O.5(Do,ut - Dn) : 0.5(0.28 - 0.16) : 0.06 m. The statorwinding resistance per phase at a temperature of 75"C (hot motor) accordingto eqn (2.33) is

Rrlfr lrou 456 x 0.428 : 10.57 Oa1n6so, 47 x106 x 2 x 0.1965

Carter's coefficient is calculated on the basis of eqns (1.2) and (l .3), i.e.

r o o - l28.8 - 0 .00526 x

\ 2- I : 1.00417 /

28.8

1 : +[* arctan (#") -'" V[ (--?__,,, *f] : 0 00526

where h : rDlsr : '1T x 0.22124: 0.0288 m: 2B.B mm. The nonfer-romagnetic air gap in calculation of Carter's coefficient is g' = 29 l2h'y :

2 x 7.5 * 8 : 11 mm. Since there are two slotted surfaces of twin stator cores,

Carter's coefficient has been squared.The stator (one unit) leakage reactance has been calculated according to eqn

( 4 . 8 ) i n w h i c h l y ; , A 1 . ; n f L ; - l l r o u t \ t , o u r f L ; = i 1 " ) t " f L , . i . e .


xt - rx 0 .4r v I0 6r , .5ga56 ' t i 'm (o .T7g+ f f io .z ra

+0.2297 + 0 .9322) : 6 .158 CI

where

r the coefficient of slot leakage reactance - eqn (4.9) is

A r " 1 1 o ' 5 2 x 1 l:

3 x 13 + rs + re+g *5 :o ' t tn

r the coefficient of end connection leakage perrneance * eqns (4.16) in whichthe average coil span wc: T is

) r" = 0.34 x t ( t -?*ry) : 0.218\ / f u . t ) + /

r the coefficient of differential leakage perrneance - eqns (4.22) and (4.24) is

)r'r: #i#?##o oe66 :o22e.

r(tr 4t#-,i,,$ _ r o.oe6ei

r the coefficient of tooth-top leakage peflneance - eqn (4.25) is

. 5 x7713Arr :5 *o ; f i -0 .9322

According to eqns (2.114) and (2.115) in which kf a: kf n:1, the armaturereaction reactances for surface tvne PM rotors and unsaturated machines are

X o ' t : f , a a 2 x 3 x 0 . 4 x r x 1 0 6 t s o ( { 9 t 1 ) '\ 4 /

* (o.r x o.zs)2 - (o.s x o. to)2 _ 5.856 CI

1.004 x 0.011

where the air gap, in the denominator, for the armature flux should be equal tog' x 2 x 1.5t8 - 11 ffiffi(F,,.. = 1). The synchronous reactances accordingto eqns (2.12) and (2.73) are


Figure 4.11. Magnetic flux plots in the double sided AFPM motor: (a) zero armature curent,(b) rated armature current. Numerical example 4.1 .

Xsd, : X"q :6 .158 + 5 .856 : 12 .01 O

The armature currents are calculated on the basis of eqns (2.80), (2.81) and(2.82). For d : 11" (cosd : 0.982, sind : 0.191) the current componentszre ' . f o4 : 1 .82 A, 1oq : 1 .88 A and Io :2 .62 A.

The input power absorbed by one stator is expressed by eqn (2.83). Theinput power according to eqn (2.83) absorbed by two stators in parallel is twiceas much, i.e.

P in -2 x 3 x 220(1 .88 x 0 .982 - ( -1 .82)0 .191) : 2892.4W

The input apparent power absorbed by two stators is


(a) I

0.E

0.6Magoetic

nllli, o.n'(r)

0.2

0

*q.2-90'

I(b)

0.8

0.6Magnetic

nll'li, o.r{r)

4.2

0

*o.2-s0q *45" 00

Rntor angle

Figure 4.12. Magnetic flux density distribution along the pole pitch: (a) zero armature cunent,(b) rated armature current. Numerical exa.mnle 4.I .

5;,, : 2 x 3 x 220 x 2.62 : 3458.4 VA

The power factor is

,aa, ,4cosE - ' ;rr*:0.836

The losses in two stator windings according to eqn (2.42), in which kyp rt I,are calculated as

LPt, , : 2 x 3 y 2.622 x 10.57 : 435.2W

The output power assuming that LP1p. + LP.4: 0.05Porr is

7 1Puut - 71 ; (P ; , , - Apr . - Lp ,or ) : . ; - (2g92.4 +J5.2 B0. t t ) = 2264W

r . u i t l . U l r

-450 0" 4$ERotor angl*

150 A,YIAL FLUX PERMANENT MAGNET BRL]SHLESS MACH]NES

I

35

30

25

20

15

10

o

0

*5-154 0, 150

Rotor angle

Figtrre 4. I 3. Torque as a function of the disc rotor position. Numerical example 4. I

Thus

LPrr. + LPPM -- 0.05 x 2264: 113.2 W

The motor efficiency is

2264.0: 0.783 or r l :78 .37o

2892.4

The shaft torque is

))(\A["n -

2o\7,.,1V60) - 28'83 Nm


Petm: P,n- LPt-- LPtr" ' "- LPpm - 2892.4-435.2-713.2 :2344W

The electromagnetic torque developed by the motor is

ry1 , _r d ,

2r x 750160: 29.84 Nm

The results of the FEM analysis are shown in Figs 4.11,4.12 and4.13. TheFEM gives higher values ofthe average developed torque than the analyticalapproach. Eqns (2.114), (2.115) and (a.8) do not give accurate values of X,6,X"n and X1. The electromagnetic torque plotted in Fig. 4.13 against the rotorposition has a significant cogging effect component with the period equal todouble slot pitch, i.e. 30".

TorqueNm

4go304

2344

Reluctance torgue €--Total torque -*-

AFPM machtnes with iron cores l5l

Numerical example 4.2A three-phase, Y-connected, 50 Hz, 5.5-kW AFPM synchronous generator

with slotted stator has the following parameters of the steady-state equivalentcircuit: fir : 0.1 Q, X"d, : 2.3 Q and X"n : 2.2 Q. The generator is loadedwith a resistance of Rt, : 2.2 Q and inductance of L7: 0.0007 H connectedin series. The EMF per phase at no load induced by the rotor PM excitationsystem is Ey : 100 V and rotational losses are LProT: 90 W.

Find the stator currents, electromagnetic powet output power and efficiency.Stator core losses and losses in PMs have been isnored.

Solution

The load reactance and module of load impedance are

X L : 2 t r . f L r : 2 r x 5 0 x 0 . 0 0 0 7 : 0 . 2 2 { )

Z 7 : / 2 2 2 + 0 2 2 2 : 2 . 2 1 1 Q

The stator currents according to eqns (4.40), (4.41) and (2.82) are

, "n

: : 21'2lt A\4 . . r - r 0 .22) (2 .2 + 0 .22) + (0 .1 + 2 .2 )2

L^ - Loo(o' l - 2'2) t{) 2() A'uq 23 -0 .22 ) (2 .2+o .22 ) + (0 .1 + 2 .2 )2

Io: J212b2 + 2020, : 2g.32 A

The terminal voltage (across the load impedance) is

V : IuZr :29.32 x 2.27I :64.82Y

VtL: nEVt : \ /5 64.82 :112.3 V

The power factor, load angle d and angle V according to eqns (4.43), (4.39)and (4.42) respectively are

cos@- zg ' ?? \ - z ' z : 0 .9e5

4 :5 .77 '64.82

v : arccos (ff i) :46.4b"

152 AXIAL FLTJX PERMANENT MAGT)ET BRUSHLESS MACHINES

d : arcsin (27'25 x 2'2-- 20'20 x 0'22 ) : 40.24o

\ 64.82 I

d : V * 4, : 46.450 - 5.77" : 40.740

The electromagnetic power according to eqn (a.45) is

Petrn :31100 x 20.20 2I.25 x 20.20(2.3 - 2.2)l: 5930.3 W

The stator winding losses according to eqn (2.42) is

LP t - * : 3x 29322 x0 .1 : 257 .8W

The output power is

Pou,t : rrllVllecosd - 3 x 64.82 x 29.32 x 0.995 : 5672.5 W

Pout : P"t^ * APw: 5930.3 - 257 '8 :5672.4

The input power is

Pin : P.h, i LProt: 5930.3 * 90 : 6020.3 W

The efficiency is

5672.54 :6020 -3 :o ' 942

Chapter 5

AFPM MACHINES WITHOUT STATOR CORES

5.1 Advantages and disadvantagesDepending on the application and operating environment, stators of AFPM

machines may have ferromagnetic cores or be completely coreless. A corelessstator AFPM machine has an internal stator and twin external PM rotor (Fig.L4d). PMs can be glued to the rotor backing steel discs or nonmagnetic sup-porting structures. In the second case PMs are arranged in Halbach anay (Fig.3.15) and the machine is completely coreless. The electromagnetic torque de-veloped by a coreless AFPM brushless machine is produced by the open spacec urrent-carrying conductor-PM interacti on (Lor entz force theorem).

Coreless configurations eliminate any ferromagnetic material, i.e. steel lam-inations or SMC powders from the stator (armature), thus eliminating the as-sociated eddy current and hysteresis core losses. Because of the absence ofcore losses, a coreless stator AFPM machine can operate at higher efficiencythan conventional machines. On the other hand, owing to the increased non-magnetic ak gap, such a machine uses more PM material than an equivalentmachine with a ferromagnetic stator core.

Typical coil shapes used in the winding of a coreless stator are shown inFigs 3. 1 6 and 3 .17 .

In this chapter AFPM brushless machines with coreless stator and conven-tional PM excitation, i.e. PM fixed to backing steel discs, will be discussed.

5.2 Commercial coreless stator AFPM machinesBodine Electric Company, Chicago, IL, U.S.A. manufactures 178-mm (7-

inch) and 356-mm (I4-inch) diameter e-TORQTM AFPM brushless motorswith coreless stator windings and twin external PM rotors with steel backingdiscs (Fig. 5.1a). The coreless stator design eliminates the so called cogging

t54 AXIAL FLUX PERMANEI{T MAGNET BRUSHLESS MACHINES

Figure 5.1. AFPM brushless e-TORQT\I motor with coreless stator windings: (a) generalview; (b) motor integrated with wheel of a solar powered car. Photo coudesy of Bodine ElectricCo mpa ny, Chicago, IL, USA, www.Bodine-Electric.com.

(detent) torque, improves low speed control, yields linear torque-cunent char-acteristics due to the absence of magnetic saturation and provides peak torqueup to ten times the rated torque. Motors can run smoothly at extremely lowspeeds, even when powered by a standard solid state converler. In addition, thehigh peak torque capability can allow, in certain applications, the eliminationofcostly gearboxes and reduce the risk oflubricant leaks.

The 356-mm diameter e-TORQTM motors have been used successfully bystudents of North Dakota State University for direct propulsion of a solar pow-ered car participating in2003 American Solar Challenge (Fig. 5.lb). A welldesigned solar-powered vehicle needs a very effrcient and very light electricmotor to convert the maximum amount of solar energy into mechanical energyat minimum rolling resistance. Coreless AFPM brushless motors satisfy theserequirements.

Small ironless motors may have printed circuit stator windings or film coilwindings. The film coil stator winding has many coil layers while the printedcircuit winding has one or two coil layers. Fig. 5.2 shows an ironless brushlessmotor with film coil stator winding manufacturedby EmBesl, Soeul, South Ko-rea. This motor has single-sided PM excitation system at one side of the statorand backing steel disc at the other side of the stator. Small film coil motors canbe used in computer peripherals, computer hard disc drives (HDDs) 1128, 129),mobile phones, pagers, flight recorders, card readers, copiers, printers, plotters,micrometers, labeling machines, video recorders and medical equipment.

AFPM MACHTNES WITHOT]T STATOR CORES 155

Figure 5.2. Exploded view of the AFPM brushle ss motor with film coil coreless stator windingand single-sided rotor PM excitation system. Courtesy of Embest, Soeul, South Korea.

5.3 Performance calculation5.3.1 Steady-stateperformance

To calculate the steady-state performance of a coreless stator AFPM brush-less machine it is essential to consider the equivalent circuits.

H 9 d *< ; c | HU g* S . r r. * H A :' U :

, : p ,

6 :w :

3,* v )

b f r gs2 z P +

f 5 H ;

( a ) jl"oX"o jl"oX"o<__

jl"oX"o jl"oX"t<__ <_x1

- +

Figure 5.3. Per phase equivalent circuit ofan AFPM machine with a coreless stator: (a) gen-erator arow system; (b) consumer (motor) arrow system. Eddy current losses are accounted forbv fhc shunt rc5istance n, .

The steady-state per phase eqLdvalent circuit of a coreless stator AFPMbrushless machine may be represented by the circuit shown in Fig. 5.3, whereR1 is the stator resistaoce, X1 is the stator leakage reactance, E1 is the EMF

];,rr :,l,lli' '

" 6- 1

14

+ , lt " ' " {


induced in the stator winding by the rotor PM excitation system, Ei isthe rmsvalue of the internal phase voltage, V1 is the terminal voltage and Io is the rrnsstator current. The shunt resistance -Ru is the stator eddy current loss resistance,which is defined in the same way as the core loss resistance [116] for slottedPM brushless motors.

The stator currents lo,t", Ioq and Io for a given load angle d (corresponding tothe slip s in induction machines) can be calculated on the basis of eqns (2.80),(2.81) and (2.82) respectively. If loa : 0, all the stator current Io : Io,tproduces the electromagnetic torque and the load angle 5 : Q. The angle

/ between the stator current 1o and terminal voltage % is determined by thepower factor cos @.

If we ignore the losses in PMs and losses in rotor backing steel discs, theinput power can then be calculated as follows

r for the motoring mode (electrical power)

Pi,: P"hn * LPt- + LP"-

r for the generating mode (mechanical shaft power)

(s 1)

P i n : P " t * , * L P r o t (.s.21

where P"1,n is the electromagnetic power according to eqn (2.84) in whichLPtr" : 0, LP1, is the stator winding loss according to eqn (2.42), A,P" arethe eddy current losses in the stator conductors according to eqn (2.61) or eqn(2.62) and A,P,o1are the rotational losses according to eqn (2.63).

Similarly, the output power is:

r for the motoring mode (shaft power)

Pou t :Pu ln r -LPro t

r for the generating mode (electrical power)

(s.3 )

Pout: P"I*, - LPt- - LP", (s.4)

The shaft torque is given by eqn (4.30) for motoring mode or eqn (4.31) forgenerating mode, and the efficiency is expressed by eqn (4.32).

AFPM MACHTNES WITHOUT STATOR CORES 157

5.3,2 DynamicperformanceFor a salient pole synchronous machine without any rotor winding the volt-

age equations for the stator circuit are

tba: (L"a* Lv)i"a* ths : L'aioa* 4;f

,!q : (Loq -t Ly)i,"n : L"qioq

(s.7)

(s.B)

ln the above equations (5.5) to (5.8) tr14 and'u1n are d- and q-axis componentsof the terminal voltage, r! S is the maximum flux linkage per phase producedby the excitation system, Br is the armature winding resistance, Lo6, Lon arethe d- and g-axis components of the armature self-inductance, r,r : 2n f isthe angular frequency of the armature current, iod, ioq are the cl- and q-axiscomponents ofthe armature current. The resultant armature inductances Lsd, :

Lo,j I L1 and Lrq : Loq t Ly are referred to as synchronous inductances. Ina three-phase machine Lod : Gl\Lt*,j and Lo, : (3f 2)Lt"q where Ltoo andL'on are self-inductances of a single phase machine. The excitation linkageflux /7 : Lyaly where Lya is the maximum value of the mutual inductancebetween the armature and field winding. In the case of a PM excitation, thefictitious field current is 1; : H.hu.

Putting eqns (5.7) and (5.8) into eqns (5.5) and (5.6), the stator voltage equa-tions in the d and q-axis can be written as

u t d : R t i " o + * - d u qdL

u t q : R 1 i ' o + * * a a dAL

in which the linkage fluxes are defined as

u1,1: R1,io6 * 4#f "o

- aL"niondt

,u1n : R1,ion + *- f"n I aLr6io4 a alt t- o,1;

For the steady state operati on (d I dt) L "d,iacr

: (d I d,t) L "qi"qj l , rq,Yt : Va I jVtq, loy : f2Iod, i ,s.q : f2lo, , u14

(s.s)

(s.6)

(s.e)

(s.10)

: 0 , I o : I o 4 l

- J2Vra, rrn :

r58 AXIAL FLUX PERMANENT MAGNET BRUSHLESS MACHINES

,fiVtn, Ey : wLyalt lt/2 : ,rltf lt/2 [86]. The quantities aL,4 and, uL,,are known as the d- and q-axis synchronous reactances respectively.

The instantaneous power to the motor input terminals is [86, 96]

pi, : [email protected],i.

-l uhioq) (s . 1 1)

The input power of a motor (5.1 1) is equivalent to the output power of a gen-erator. The electromagnetic power of a three-phase machine is [86, 96]

Petrr t : l "bl , t * (L"a - L") i 'oa)zoq $.12)

The electromagnetic torque of a three phase motor with p pole pairs is

ro: p&# :')nltr -t (L"a - L"n)i,oali,on

The relationships between,io4,,ioo and phase currents i,o4, ioB

(s. r 3)

ate

(s.14)

(s. l 5)

14) and

( " ,+/ 2r \l w t l\ 3 /

o

uao, - ,O

' io4cosut * i46 cos * i,og r:os

daA :' io4cos ut - ion sin at

r^^ s in

and'iog

2^\ lT))

2"\ lT))

ns (5.

. 2 l / 2 2 . \ /ioq:

; Lt ,o sinc,: / * io6 sin (r ,

- -3

) | rnr- s in (ut +

The reverse relations, obtained by simultaneous solution of eq(5.15) in conjunction with iot * i 'e t ioc - 0, are

Za,B : ?o4 COS Q'-T)

Q'*T)

/ 2 r \( . ' ' - T)-

/ 2r \[ u f+ i ) -

(5. I 6)

LaC,' : ?,adCOS ri-^ sin

AFPM MACHINES WITHOUT STATORCORES 159

5.4 Calculation of coreless winding inductances

5.4.1 Classical approachThe synchronous inductance L" consists of the atmature reaction (mutual)

inductance Lo and the leakage inductance -L1 . For a machine with magneticasymmetry, i.e. with a difference in reluctances in the d and q axes, the syn-chronous inductances in the d* and q-axis, L

"6 and L

"n, are written as sums

of the armature reaction inductances (mutual inductances), Loa and Lo,,, andleakage inductance t f . i .e.

LsrL : Lo i l * L t L" r r : Lo , * L t (5 . l 7)

The armature reaction inductances are expressed by eqns (2.109), (2.110) and(2.111), in which air gaps in the d- and q-axis are given by eqns (2.105)

and(2.106). The armature reaction reactances are given by eqns Q.fl4) and(2.115). Table 2.1 compares armature reaction equations for cylindrical anddisc-type machines.

The leakage inductance is expressed analytically as a sum of three compo-nents, i.e.

Lt : Lr, * Lt" * Lta : 2LroY()r, + E^r,+

)ra) (s .1 B)

where Lt : O.S(Dout - Dm) is the active length of a coil equal to the radial

length ly of the PM, qr is the number of coil sides per pole per phase (equiv-

alent to the number of slots) according to eqn (2.2), ly" : 0.5(1u,, -f luut)is the average length of the single-sided end connection, Ly" and .\7" are theinductance and specific perrneance for the leakage flux about radial portions ofconductors (corresponding to slot leakage in classical machines) respectively,Lp and.\1s ore the inductance and specific perrneance for the leakage fluxabout the end connections respectively, and L6 and ).y1 are the inductance

and specific perrneance for differential leakage flux (due to higher space har-

monics) respectively.It is difficult to derive an accurate analytical expression for ),1" for a core-

less electrical machine. The specific penneances .\1" and )1" can roughly beestimated from the following semi-analytical equation:

, \ 1 5 ! , \ 1 . = 0 . 3 9 r (s.1e)

The specific permeance for the differential leakage flux can be found in a sim-ilar way as for an induction machine I I I I ], using eqn (4.22) in which ks,,l x I


and gt x 2l(g +0.5t-) +hml. The thickness of the stator winding is f- and thedistance from the stator disc surface to the pM active surface is g (mechanicalclearance). It is not difficult to show that L1a : L,,ray flll).

5.4.2 FEM approachunlike conventional slotted AFPM machines, there is no clear deflnition for

main and leakage inductances in a coreless or slotless machine as discussedin U2,77, 1221. using the 2D FEM analysis both mutual and leakage fluxescan be taken into account. The only remaining part is the end winding leakageflux.

with the 2D finite element solution the magnetic vector potential I t asonly a z component, i.e. A : A@,il.a" where a, is the unit vector inz direction (axial direction). The total stator flux of a phase winding th,sBcthat excludes the end-winding flux leakage can be readily calculated by usingStokes'theorem, i.e.

(s.20)

As an approximation the flux linkage of a phase coil can be calculated byworking out the difference between maximum magnetic vector potential valuesof each coil side. In the case that the coil is not very thin, magnetic vectorpotential varies in the coil cross-section area. Therefore, the average magneticvector potential values should be used. For first-order triangular elements, theflux linkage of a coil with N1 turns, area ,g and length I is given by [133]

(s .21)

where Aii is the nodal value of the magnetic vector potential of the triangularelement j, e : *1 or ( : -1 indicates the direction of integration either intothe plane or out of the plane, A, is the area of the triangular element j, and nis the total number of elements of the in-going and out-going areas of the coil.It follows that for an AFPM machine with only one pole modelled, the totalflux linkage of a phase winding is

aARC- l"E.{s: l"t"A a3-t ' ,A a1

$:N,i? tf * o,,f

(s.22)

where u is the total number of elements of the meshed coil areas of the phase inthe pole region and ao is the number of parallel circuits (parallel cul:rent paths)of the stator windins.

,b.qec:'+y,r [T f.. ̂,,7

AFPM MACHINES WITHOUT STATOR CORES 16I

From a machine design perspective, it is important to find the fundamental

components of the total flux linkages. For a coreless stator AFPM machine

with usually unsaturated rotor yoke, the flux linkage harmonics due to iron

stator slots and magnetic saturation are absent. Owing to the large air gap, the

stator winding MMF space harmonics are negligible in most cases. The most

important harmonics needed to account for are those due to the flat-shaped

PMs.Given these considerations, the ffux linkage wave of an AFPM machine is

nearly sinusoidal, though for a concentrated parameter (non-distributed) wind-

ing, an appreciable 3'd and less significant 5th and Tth harmonics are stillprisent in the total flux linkage waveform. If the 5th, 7Lh and higher harmon-

ics are ignored, the fundamental total phase ffux linkages can be calculated by

using the technique given in [133], i.e.

frl, anc t) = lrl, ancl - lQ aBcs) (s.23)

where the co-phasal 3'd harmonic flux linkage, including the higher order triple

harmonics, can be obtained from:

with the fundamental total phase flux linkages and rotor position known, the d

and q-axis flux linkages are calculated using Park's transformation as follows

[86]:

Itaqol: lKoll,l'asct) (s.2s)

where [86]

tbas: ,!tt : tbcz x |{r,,

* 4;s +,!s)

L'",1,: Loa * L\ : Lod. * L* i Lu

L ' "q : Los t L \ : Lon * L t " I Lu

(s.24)

(s.27)

, I cos I cos(o - !) cos(g + {)Kr-- ; l - ' i "e -s \n( | r -* ) *s in(e+#)

l t 7 t I ,, ,u,With a constant rotor angular velocity cu the angle 0 : wt' In the 2D FEM

model the d-axis and g-axis synchronous inductances do not include the com-ponent due to end connection leakage flux [96], i.e.

(s.28)


The inductances tr'", and Lt"o result from eqns (5.7) and (5.8), i.e.

(s.2e)

The end winding inductance L1" e&n be calculated from numerical evaluationof the energy stored in the end connections 1169] or simply by using an ap-proximate equation resulting from eqn (5.18), i.e.

^ T 2 lr n l Y l [ 1 c .

t r l e : Z p O - A l e

PQT(s.30)

Finally,

L'"d: *# ancl L'"r:

Lsd : Lt"r1 * Lp and Lsd, : L'",7 * Lrc

Vq;"aq

(s.3 1 )

5.5 Performance characteristicsSpecifications of e-TOROTN{ AFptrrt brushless motors manufacture d,by Bo-

dine Electric Company, Chicago,IL, U.S.A. are given in Table 5.1. The EMFconstant, torque constant, winding resistance and winding inductance are line-to-line quantities. Motors are designed for a maximum winding continuoustemperature of 130"c. Steady-state performance characteristics of a 356-mm,l-kW, 170-V e-TORQrra motor are shown in Fig. 5.4.

Fig. 5.5 shows an air-cooled 160-kW AFPM brushless generator with acoreless stator built at the university of Stellenbosch, South Africa 12321. Thestator winding consists of sixty single-layer trapezoidal-shape coils, whichhave the advantage ofbeing easy to fabricate and have relatively short over-hangs (Fig.3.17). The winding coils are held together to form a disc-typestator by using composite material of epoxy resin and hardener. Sintered Nd-FeB PMs with B, = 1.16 T and maximum allowable working temperaturearound 130oC have been used. The detailed design data are given in Table 5.1 .

The output power and phase current at different speeds are shown in Fig.5.6. Owing to very low stator winding inductance per phase, the output voltagevaries almost linearly with the load cunent.

It has been found from both experimental tests and calculations that for atypical sine-wave AFPM machine with a coreless stator, the ratio of the d- andq-axis inductances of the phase winding is near unity, i.e. Lral Lr, = 1. Thus,the analysis of the AFPM brushless machine with a coreless stator may be donein a similar way as that of the three-phase cylindrical machine with surfacedPMs [118, 145] .

AFPM MACHII,IES WITHOUT STATOR CORES 163

Tabte 5.1. Speciflcations of e-TORQTNT AFPM motors with coreless stators manufactured byBodine Electric Companr, Chicaso, IL, U.S.A.

Parameter178-mm AFPM motorLow EMF High EMFconstant constant

356-mm AFPM motorLow EMF High EMFconstant constant

Output power, kWNumber of polesd.c. bus voltage, VSpeed, rymPeak speed, rpmTorque, NmPeak torque, NmCurrent, APeak current, AEfficiency, %Torque constant, Nm/AEMF constant, V/krpmWinding resistance, QWinding inductance, mHViscous friction, Nm/rad/sStatic friction, NmElectrical time constant, msMechanical time constant, msMoment of inerlia, kgm2Mass of active pafts, kgPower density, W/kg

0.78

1703000 15003500 22002.26 2.83

170 300300 70700 40031 .1 33 .9

22.65508 l

0.4859502.2t . 4

0 .578

300

t3.672

10 .575

1.299137t4.310 .5

1 . 0l 6

4.50 .2130.8732.39

0.26l 6

17.780 .2130.878.42

776 .81471343

t52.1 84.41 3 564 t2.5

9.9 x 10-5 0.000190.00728 0.0378a.$64 0.7344.538 4.026

0.00525 0.005256 . 1 7 6 . 1 71 13.5 92.4

842.382491 . 3 33.6 29.4

0.00669 0.0120.02357 0.1442

2.'11 0.684

5.6 Eddy current losses in the stator windings

5.6.1 Eddy current loss resistanceFor an AFPM machine with a coreless stator, associated stator iron losses

are absent. The rotor discs rotate at the same speed as the main magneticfield, thus the core losses in the rotor discs due to the fundamental harmonicof the stator field also do not exist. Howevel the eddy culrent losses in thestator winding are significant due to the fact that the machine is designed with2p > 6 to operate at relatively high frequencies f = pn.

Eddy current losses AP" in stator conductors are calculated according toeqn (2.61) or eqn (2.62). A more detailed method of the eddy current losses

computation is discussed inl234l. Eddy cunent losses in the stator conductors

can be accounted for in the same way as core losses in the stator stack [l16].The eddy-loss cunent Iu and its d- and q-axis components 1",1 and I"n shownin Fig. 5.3 is in phase with the internal phase voltage t7 across the shunt re-


Table 5.2. Specifications of a three-phase, 160-kw, 1950-rpm AFpM brushless synchronousgenerator with ironless stator core built at the (Jniversity ofstellenbosch. South Africa

Output power P,"t, kWSpeed n, rpmNumber of phases m1Rated line voltage, VRated phase current, AFrequency /, HzNumber of stator modulesNumber of pole pairs pNumber of stator coils (3 phases)Number of turns per phaseWire diameter, mmNumber of parailel wires ri,-Axial height of PM per pole h,y, mmAxial thickness of the winding f,,,, mmAir gap (one side) 9, mmAir gap magnetic flux density B-n under load, TCurrent density, Almm2PM outer diameter Dou1., mmka : Dtn/Do,,i r&tioClass of insulationWinding temperature rise, "CCooling systemType of windi le layer trapezoidal

sistance Bu. The internal phase voltage -oi is generated by the resultant airgap flux and usually referred to as the air gap voltage [86]. consequently, theshunt resistance in the equivalent circuit representing the eddy current loss isexpressed as

1601 950

3 (Wye)435 V215 A100I

20605 1

0.421 2

10.7t5.72.750.587 . 17200.69

F56

Selfair-cooled

(s.32)

where

(5 .33)

on the basis of equivalent circuits (Fig. 5.3), the following equations can bewritten in the phasor form:

AFPM MACHINES WITHOI]T STATOR CORES

(a) ;oo

100 150

troque, Nm

(b)

",

0 50 100 150 200 250 300

torque, Nm

Figure5.4. Steadystatecharacteristicsofof356-mm, l-kW 170-v e-ToReTNi AFpMmotor:(a) output power Po.u,1 and speed n versus shaft torque ?"6; (b) phase current and efficiency ver-sus shaft torqueT"6. Data captured at22"C for totally enclosed non-ventilated motor. Courtesvof Bodine Electric Company, Chicago, IL, U.S.A.

r for generators

E"r: Er I jTo6Xo6+ jloqxo,,t (s.34)

165

fi00

33 soo

oIg 4oo

o- 300E

d zoog.

100

80

- 7 0xj

.9

o 5 0{E * '

I ' u : I o * I "

0

(s.3s)

166 AATAL FLUX PERMAI,IENT MAGI{ET BRUSHLESS MACHTNES

Figure 5.5. Air-cooled single-stage synchronous AFPM machine: (a) rotor disc with surfacemounted PM segrnents, (b) coreless stator with busbars, and (c) the assembled machine. Cour-tesy of the University o.f Stellenbosch, South Africa.

0 250 500 750 1 000 1250 1 500 1 750 2000Speed (rpm)

Figure 5.6. Output power and phase current versus speed for generating mode ofa 160-kWAFPM brushless generator. Specifications are given in Table 5.2.


r for motors

t 67

Ef :E1 - jToaXoa- j l oqXoq (5 .36)

I ' o : I o - I . (s.37)

where Il is the stator current with eddy curents being accounted for and Iu isthe stator current with eddy currents being ignored.

5.6.2 Reduction of eddy current lossesIn an AFPM machine with a coreless stator the winding is directly exposed

to the air gap magnetic field (see Fig. 5.7). Motion of PMs over the corelesswinding produces an alternating field through each conductor inducing eddycurrents. The loss due to eddy currents in the conductors depends on both thegeometry of the wire cross section and the amplitude and waveform of the fluxdensity. In order to minimize the eddy current loss in the conductors, the statorwinding should be designed in one of the following ways using:

r parallel wires with smaller cross sections instead of a one thick conductor;

r stranded conductors (Litz wires);

r coils made of copper or aluminum ribbon (foil winding).

In an AFPM machine with an ironless winding alrangement (as shown inFig. 5.7a), in addition to its normal component, the air gap magnetic field hasa tangential component, which can lead to serious additional eddy curent loss(Fig, 5.7b). The existence of a tangential field component in the air gap dis-courages the use of ribbon conductors as a low cost arrangement. Litz wiresallow significant reduction of eddy current 1oss, but they are more expensiveand have fairly poor filling factors.

As a cost effective solution, a bunch of parallel thin wires can be used.However, this may create a new problem, i.e. unless a complete balance ofinduced EMFs among the individual conducting paths is achieved, a circulatingcurent between any of these parallel paths [49, 206,234] may occur as shownin Fig. 5.7c, causing circulating eddy current losses.

When operating at relatively high frequency magnetic fields, these eddy cur-rent effects may cause a significant increase of winding losses, which are in-tensified if there are circulating currents among the parallel circuits. These


Axial Flux

Tangential Flux

Airgap field

Circulating Eddy Losses

(c)

Figwre 5.7. Eddy curents in the coreless stator winding of an AFPM machine: (a) magneticfield distribution in a coreless stator; (b) eddy currents in a conductor; (c) circulating eddycurrents among parallel connected conductors.

losses will deteriorate the performance of the AFPM brushless machine. Pre-dicting the winding eddy current losses with a good accuracy is therefore veryimportant at the early stage of design of such machines.

Eddy current losses may be resistance limited when the flux produced bythe eddy currents has a negligible influence on the total field 1206]. In this casethe conductor dimensions (diameter of thickness) are small when compared tothe equivalent depth of penetration A : I lk" of the electromagnetic field -

eqn (1 .12) .

5.6.3 Reduction of circulating current lossesTo minimise the circulating current in a coil made of parallel conductors,

the normal practice is to twist or transpose the wires in such a fashion that eachparallel conductor occupies all possible layer positions for the same length ofthe coil. The effect is to equalize the induced EMFs in all parallel conduc-tors, and to allow them to be paralleled at the ends without producing eddycirculating currents between the parallel conductors.

Figure 5.8 illustrates the effectiveness of suppressing circulating eddy cur-rent by wire twisting. Four coils are made with the only difference that the par-

(a)

(b) Local Eddy Losses

AFPM MACHINES WITHOUT STATOR CORES t69

(c) Ch 1 : 100 mA/Div 2.5 ms/Div (d) Ch 1 : 100 mA/Div 1 mslDiv

Figure 5.8. Measured circulating cument of (a) non-twisted coii, (b) slightly twisted coil, (c)moderately twisted coil, (d) heavily twisted coil.

allel wires of each coil are: (a) non-twisted, (b) slightly twisted (10 to l5 turnsper metre), (c) moderately twisted (25 to 30 turns per metre), and (d) heavilytwisted (45 to 50 tums per metre) respectively. All the coils have been used toform a portion of an experimental stator, which is placed in the middle of thetwo opposing PM rotor discs. The machine operates at a constant speed (400rpm in this case). The circulating currents between two parallel conductorshave been measured and logged on a storage oscilloscope. It can be seen thatthe induced circulating current is greatly reduced even with a slightly twistedcoil and can generally be ignored in a heavily twisted coil. These twisted wirescan easily be manufactured in a cost effective way.

The fill (space) factors for the non-twisted and the heavily twisted coils areestimated as 0.545 and 0.5 respectively, which is slightly less than that of theLitz wires (typically from 0.55 to 0.6). However, the saving in manufacturingcosts is usually more important.

It should be noted that due to the low impedance of a coreless stator winding,circulating current could also exist among coil groups connected in parallel(parallel current paths) if a perfect symmetry of coils cannot be guaranteed.

(a) Ch 1:2 NDiv 2.5 ms/Div

.i'Ufl ,il(b) Ch 1: 100 mA/Div 2.5 ms/Div

tq" "irl "i l,l : 'n i' lt" ': ! 1 l i l r l : i l t : i l : l, : t t ' l : , ' h ' i l l ' t : , / { ' . h ' ! ! . ' h . .

:_ . l t i . .u ._ : i l . . . , \1 . . , . i l

l t : : : :

'M"I t I

, : - . 1

l ' : "l ; 1,L; ,1

..1-r.

:

I{: i: J

I lur. l. lI

i4;e*

170 AXIAL FLUX PERMANENT MAGNET BRUSHLESS MACH]NES

5.6.4 Measurement of eddy current losses

The resistance limited eddy loss in the stator of an AFPM machine may beexperimentally determined by measuring the difference in input shaft powersof the AFPM machine at the same speed, first with the stator in, and then byreplacing it with a dummy stator (no conductors). The dummy stator has thesame dimensions and surface finish as the real stator and is meant to keep thewindage losses the same.

A schematic representation of the experimental test setup for measuringeddy current losses in stator conductors is shown in Fig. 5.9. The shaft ofthe tested prototype and the shaft of the prime mover (driving machine) arecoupled together via a torque meter. The stator is positioned in the middle ofthe two rotor discs with the outer end ring (see Fig. 5.9a) mounted on the out-side supporting frame. Temperature sensors are also attached to the conductorsin order to take into account temperature factor in the measurement.

Initially, the prototype (with the coreless stator placed in it) was driven bya variable speed motor for a number of different speeds. The correspondingtorque measurements were taken. Replacing the real stator with a dummyone, the tests were repeated for the same speeds. Both the torque and thetemperature values were recorded. The difference of the torques multiplied bythe speed gives the eddy current loss. The eddy losses due to eddy-circulatingcurrent in the windings can also be determined by measuring the difference ofinput shaft powers, first with all the parallel circuits connected and then withdisconnected parallel circuits.

Fig. 5. I 0 shows the measured and calculated resistance limited eddy lossesof the prototype machine. It can be seen that the calculated eddy losses ob-tained by using the standard analytical formula - eqns (2.61) and (2.62) withonly the B-, component taken into account yield underestimated values (43%less). The discrepancy between the measured and calculated results becomeslarge at high speeds. Better accuracy may be achieved by including both thenormal B,n" and tangential B-" components of the magnetic flux density andimplementing eqn (2.61) or eqn (2.62) into the 2D or 3D FEM [235].

5.7 Armature Reaction

The 3-D FEM analysis has been applied to the modelling of a coreless statorAFPM machine in [10]. Both no-load and load operations have been modelled.It has been shown that good accuracy can be expected even when the first orderlinear FEM solution is applied to the AFPM machine if the magnetic circuit isnot saturated (large air gap). It has also been found that the armature reactionfor an AFPM machine with a coreless stator is generally negligible.

Using a 40-pole, 766 Hz coreless stator AFPM machine as an example, thesimulated effects of armature reaction to the air gap flux distribution has been

AFPM MACHINES WITHOUT STATOR CORES 171

(a)

u't' ,"',{lSupplv\ '

q . q . ,

Thermometert,'''_'lHryTf

AFPM Machine

TorqueSensor

Figure 5.9. Laboratory set formeasuring eddy current losses in the statorwinding: (a) spe-cially designed stator; (b) experimental machine; (c) schematic of experimental set-up.

demonstrated in Figs 5.1 I and 5.12. lt can be seen that the plateau of the axialfield plot is somewhat tilted due to the interaction between the flux of the PMsand the armature ffux generated by the rated culrent (Fig. 5.1 1). Similarly, themodified tangential field plot is compared with the original one in Fig. 5.12.As the atmature reaction flux is small in coreless AFPM machines with largeair gaps, the air gap magnetic flux density maintains its maximum value veryclose to that at no load. The influence of the armature reaction on the eddycurrent losses is usually insignificant though it can be easily accounted forwhen the FEM modelling is used. The harmonic contents of the air gap fluxdensity obtained with and without armature reaction are compared in Table 5.3.It is evident that, in this case, the change of the field harmonic composition dueto the armature reaction is negligible.

Speedometer

tr--.. _l

lL : I


600 800 1000 1200

Speed (rpm)

Figure 5.10. Comparison of calculated eddy loss with measurements.

Rotor angle (degrees)

Figure 5.1 I. Air gap axial field component at noload and full load conditions

900

800

700

, 600

E soooI- 4nn

t|J 3oo

200

100

0

0

AFPM MACHINES WTTHOUT STATOR CORES 173

Rotor angle {degrees)

Figure 5. I 2. Air gap tangential field component at no-load and full load conditions.

Table 5.3. Hatmonics content of the axial air-gap flur density with and without armature re-action

Harmonics Rated armature current Zero armature cunent

0 4

0.3

0.2

Fe 0

m

-0.1

-02

-03

-0.4

0 1

- - -o - - - Zero armature current

--+- Rated armature current

I 0.603467840.0374565 10.0409906 I0.035026890.012313970.003045730.005595430.003149080.00083 1 590.00307828

0.602460330.037457590.040705250.035 146090.012300320.002623090.005'797390.00312t790.000868 I 24.00272939

2 r t d

5'',t7'hgtlt

l L t h1 2Lh

t r t h

l 7 t h

l g t h

5.8 Mechanical design featuresIn the mechanical design of an AFPM brushless machine, obtaining a uni-

form air gap between the rotor disc and the stator is important. Therefore, themethods of fixing the rotor discs onto the shaft and the stator onto the enclosure(frame) are very important. Improper methods of fixing, or misalignment in the

t74 AXIAL FLLIX PERMANENT MAGNET BRUSHLESS MACHINES

assembling of the stator and rotor will cause a nonuniform air gap, vibration,noise, torque pulsation and deterioration of electrical performance.

With regard to cooling in an air-cooled AFPM machine, the entry losses ofthe air flow can be quite high if the machine-air-inlet is poorly designed. It isimportant to reduce these losses without weakening the mechanical structurefor better cooling.

To summarise, attention should be paid to the following aspects of the me-chanical design:

r Shaft. The load torque, the first critical speed and the shaft dynamicsshould be taken into account in the shaft design.

r Rotor. (i) The deflection of the rotor disc due to the strong magnetic at-traction force, (ii) the means of mounting and securing the magnets on therotor discs to counteract the strong centrifugal force especially for highspeed applications, and (iii) the balancing of the rotor discs.

r Stator. (i) The strength and rigidity ofthe resin reinforced stator and frame,and (ii) the positioning and spacing of the coils to ensure perfect symmetry.

r Cooling. For air cooled AFPM machines, the air inlet and air flow pathsthrough the machine should be carefully designed in order to ensure a bettermass flow rate and therefore better cooling.

r Assembly. An effective tool to facilitate the assembling and dismantling ofthe machine for maintenance.

5.8.1 MechanicalstrengthanalysisThe deflection of the rotor discs due to the strong magnetic pull may have

the following undesirable efTects on the operation and condition of AFPM ma-chines:

closing the running clearance between the rotor disc and the stator:

loose or broken PMs:

r reducing air-flow discharging area thus deteriorating the cooling capacity;

r nonuniform air gap causing a drift in electrical performance from the opti-mum.

For a double-sided AFPM machine with an internal coreless stator, the rotordiscs account for roughly 50% of the total active mass of an AFPM machine.Hence, the optimal design of the rotor discs is of great importance to realise adesign of high power-to-mass ratio. All these aspects require the mechanicalstress analysis of the rotor disc.

AFPM MACHINES WITHOUT STATOR CORES 175

Attraction force between rotor discsThe attraction force between two parallel rotor discs can be calculated by

usine the virtual work method. i.e.

dW LW Wz-Wtt - '

d z L , z z 2 - z r(5 .38)

where tr4/ is the total magnetic energy stored in the machine and Az is thesmall variation of the air gap length. The accurate prediction of the attractionforce is a prerequisite for the mechanical stress analysis. Hence, the respectivemagnetic stored energies W1 andW2 for air gap lengths z1 and ,z2 are usuallycalculated by using the FEM.

Analytically, the normal attractive force between two parallel discs withPMs can be expressed as

," = ttlLnsr* (s.3e)

where the active area of PMs is according to eqn (2.56).

Optimum design of rotor discs

The structure of the rotor steel discs may be optimised with the aid of anFEM structural program. It is important that the deflection of the rotor steeldiscs, due to the axial magnetic pull force, is not too dangerous for small run-ning clearance between the coreless stator and PMs. Two important constraintsshould be considered, i.e. (i) the maximum allowable deflection, and (ii) themaximum mechanical strength of the material used to fabricate the disc.

When choosing allowable deflection, one needs to make sure that the PMsdo not experience any excessive forces due to bending of the disc that canpotentially peel them off from the backing steel disc. Owing to the cyclicalsymmetry of the disc structures, it is sufficient to model only a section of thedisc with symmetry boundary conditions applied. In the FEM analysis theaxial magnetic force can be applied in the form of a constant pressure loadover the total area that the PMs occupy. Usually, the axial-symmetric elementsare preferred for modelling a relatively thick disc. However, it has been shownin [167] that the FEM modelling of rotor discs using both axial-symmetric-elements and shell-elements gives very close results.

Fig. 5.13 shows the finite element model of the analysed rotor disc using 4-node shell-elements, with symmetrical boundary conditions applied. The axialmagnetic attraction force has been calculated as 14.7 kN and applied in theform of a constant 69.8 kPa pressure load. Specification of the investigatedAFPM machine are given in Table 5.2. The stiffness provided by the magnets

r76 AXTAL FLUX PERMANENT MAGNET BRUSHLESS MACHINES

has not been included, to keep the design on the conservative side. As the rotordiscs are mounted on the centre support hub, additional boundary constraintshave been defined so that there is no axial displacement in the vicinity of themounting bolts and contact area.

To find the suitable thickness of the rotor disc, which satisfies the criticalstrength requirements of the rotor disc with a 1ow steel content, the linear FEMstatic analysis was performed for different thicknesses of the rotor disc.

Figtre 5. I j. FEM model for analysing the mechanical stress of the rotor disc.

Based on the analysis, the rotor disc thickness was chosen as 17 mm with amaximum deflection of 0.145 mm. Fig. 5.14 shows the deffection (blown-up)and the von Mises stress distribution of the laboratory prototype of the 17-mmthick disc. The maximum stress of 35.6 MPa is much lower than the typi-cal yield strength of mild steel, that is in the region of 300 MPa. It has beenshown in literature ]67lthat the bending of the rotor disc decreases towardsits outer periphery. The rotor disc may be machined in such a way that thedisc becomes thinner towards the outer periphery. As shown in Table 5.4, thetapered disc uses approximately l0o/o less steel than the straight disc. The max-imum deflection increases by only 0.021 mm with the tapered disc, which isnegligible. This can effectively reduce the active mass of the machine withoutcompromising the mechanical shength, but does not bring down the cost of thesteel.

If manufacturing costs are taken into account for small production volumes,it is better to use a steel disc with uniform thickness. Obviouslv. a uniform disc

kPa masnetic force

Support boundary conditions

AFPM MACHINES WITHOUT STATOR CORAS

Output Set: MSCA,IASTRAN Case IDeibmed [0. 166]: Total TranslationContour: Plate Top VonMises Stress

Tip deflection resulting fi'om 1 47 I 5Nmagnetic force : 0. 166 mm

177

re35.58 m

3327 w

30.95',(z

28.64 ,

26 .33 ' l

24o1Ji217 | 1,

1 e 3 e I In o T J1476 i :

12.45 1 |t :

1 0 1 3 1

7 8 1 8 w

5504m3 1 e 1 u

zI

X

Figure 5.14, Deflection (blown-up) and von Mises stress distribution of the rotor disc.

means a heavier rotor disc. It can, howevel be argued that the extra machiningwork needed for producing a tapered rotor disc may be too costly to justifii theprofit due to improvement in the dynamic perfomance. As long as the addedmass can be tolerated, this option is viable for small production volumes andfor laboratory prototypes.

Table 5.4. Comparison of different designs of rotor disc

Parameter Straight disc Tapered disc

Mass, kg

Maximum deflection, mm

Maximum von Mises stress, MPa

39. l 84

0 .1 45

35.6

31.296

0 .1 66

33.4

5.8.2 Imtlalanced axial force on the statorAs a result of the interaction of alternating currents in conductors and the

tangential component of the magnetic field, there is an axial magnetic force f "on each half of the coil as shown in Fis. 5.15. When the stator is located in the

r78 AXIAL FLUX PERMANENT MAGNET BRUSHLESS MACHINES

Figure 5.15. Schematic diagram showing the axial force exerted on stator.

Electrical angle (degrees)

Fisure 5.16. Unbalanced axial force exerted on the stator.

middle of the air gap, the forces on each side of the stator should cancel eachother.

Assuming that the coreless stator of the AFPM machine is slightly off cen-tre, the axial forces on each side of the stator (/1 and f2) as shown in Fig. 5.16will not be the same, resulting in an unbalanced force, A,f : lh - fzl,be-ing exerted on the stator. This unbalanced force may cause extra vibration andthus have an adverse effect on the mechanical strength of the epoxy reinforcedstator.

z. zv

9

F o3< -zv

as

AFPM MACHINES WITHOIJT STATOR CORES 179

5.9 Thermal problemsOwing to the excessive heat generated in the stator winding and the resul-

tant thermal expansion, an epoxy encapsulated stator is subject to certain de-formation. When the deformation is significant, it may cause physical contactbetween the stator and the magnets resulting in serious damage to the statorwinding and the magnets.

) 40 60 80 100

Temperature (degree C)

Figure 5.17. Thermal expansion of the stator for different temperatures.

Fig.5.l7 shows the thermal expansion of the stator at different tempera-tures. The rated current (16 A) has been conducted through a coil in the epoxyencapsulated stator. A thermal coupler and a roundout meter have been usedto measure the coil temperature and surface deformation respectively. lt hasbeen found that the relationship between the stator deformation and its tem-perature is almost linear. On average, the deflection of the stator surface isabout 0.0056 mm/oC, resulting in a 0.5 mm deffection at the temperature ofI77"C. The remaining air contents in the epoxy can also contribute to the heattransfer deterioration and temperature increase. To solve this problem, a morededicated production process is suggested. The running clearance between thestator and the rotor should be kept reasonably large.

Numerical example 5.1A three-phase, Y-connected, 3000 rpm PM disc motor has a coreless stator

and twin external rotor with surface PMs and backing steel discs. SinteredNdFeB PMs with B, : 7.2 T and prrec: 1.045 have been used. The non-magnetic distance between opposite PMs is t - 1.1mm, the winding thicknessis f- : B mm and the height of PMs (in axial direction) is h71 : 6 mm.

0.6

0.5ts

E oa. 9 ^ .( E - -

g 0 2oo

0 .1


The outer diameter of PMs equal to the outer diameter of the stator conduc-tors is Dort : 0.22 m and the parameter ka : 71J5. The number of polesis 2yt : 6, the number of single layer coil sides (equivalent to the number ofslots) is sr : 54, the number of turns per phase is I'I1 : 234,the number ofparallel conductors au : 2, the diameter of wire d- : 0.912 mm (AWG 19)and the coil pitch is ur" : 7 coil sides.

Find the motor steady state performance, i.e. output power, torque, effi-ciency and power factor assuming that the total armature current Io : 8.2 Ais torque producing (Ioa:0). The saturation factor of the magnetic circuit isksc,t : 1.02, the motor is fed with sinusoidal voltage, the mass of the twin rotorTrLy :3.4 kg, the mass of shaft Tilsh:0.64 kg, the radius of shaft ftsh : 15mm, the conductivity of copper conductors o : 47 x 106 S/m at 75"C, thespecific density of copper conductors p : 8800 kg/m3, the density of PMsppttr : 7700kg1m3, the air density p : 1.2 kg/m3, the dynamic viscosityof air pr,: 1.8 x 10-s Pa s, the coefficient of bearing friction kfu = 1.5 andthe coefficient of distortion of the magnetic flux density \a:1.15. Losses inPMs, losses in steel rotor discs and the tangential component of the magneticflux density in the air gap are negligible.

Solution

The number of coils per phase for a single layer winding is n" : s t I (2rnt): 54lQ x 3) : 9. The number of tums per coil is ly'., : l{tln, : 23419 :26. The number of coil sides per pole per phase (equivalent to the number ofslots per pole per phase) qt : stl(2p*t) : 5 l$ x 3) : 3.

The air gap (mechanical clearance) is 9 : 0.5(t - t-) :0.5(11 - B) : 1.Smm and the pole pitch measured in coil sides is rr : sl f (2p) : 5416 : L

The input frequency at 3000 rpm is

x 3 : 1 5 0 H 2

The magnetic voltage drop equation per pole pair is

. 3000r - , ! s y -

6 0

nffin^u : nB# l#+ (o + |'-) n"")Hence

Brng7 I Ut,,."(g + 0.5t",) f hulk"o,

7 .2I + f1.045(1.5 +0.5 x s) /01 x I .02

: 0.607 T


The magnetic flux according to eqn (2.21) is

o, : 1 ?[o.oor x 0.222[r - f+) ' l : o ooru32 wb, B rJ - ' - t - \V : , t ]

The winding factor according to eqns (2.8), (2.9) and (2.10) is

, s i n r l Q x 3 ) ^ 1 t ) " Trr,_ff i_ 0.ebe8: O__T_,

1 r / t \kor : sin ( O r / : 0.9397 kut : 0.9598 x 0.9397 : 0.9019

The EMF constant according to eqn (2.30) and torque constant according toeqn (2.27) are respectively

kn : n t /2x3x234x0.9019x0.001632: 4.b9rV/( rev/s) : 0 .0765 V/rprn

kr : kr3: 4.b91;1 :2.192Nm/A'27T 2r

The EMF at 3000 rpm is

E f : k a n : 0 . 0 7 6 5 x 3 0 0 0 - 2 2 9 . 5 V

The electromagnetic torque at Io, :1oq : 8.2 A is

T a : k r l u : 2 . 1 9 2 x 8 . 2 : 1 7 . 9 7 N m


Petm : 2rrtT,1. : 2n-9 x \7.97: 5646.8 W* 6 0

The inner diameter D.i, : Doutll! : 0.221\n : 0.127 m, the averagediameter D :0.5(Dout* Dm) :0.5(0.22+0.727): 0.1735 m, the averagepole pitch r : z-0.173516 :0.091 m, the length of conductor (equal to theradial length ly1 of the PM) Li : Iy : 0.5(Do6 * Dm) : 0.5(0.22 -0.I27) : 0.0465 m, the length of shorler end connection without inner bendsI7e.-in : w. f r,,)x D n I Qp) : (7 I 9)n x 0.727 I 6 : 0.052 m and the length ofthe longer end connection without outer bends l7".rno, : 0.052 x 0.2210.727 :0.0896 m.

t 8 l

182 AXIAL FLUX PEKMANENT MAGNET BRI.]SHLESS MACH]NES

The average length of the stator turn with 15-mm bends (Fig. 3.16) is

lroo x 2Lt * h"rnin * l t "rno*+ 4 x 0.015

:2 x 0.0465 + 0.052 + 0.0896 + 0.06 : 0.2943 m

The stator winding resistance at75oC according to eqn (2.33) is

234 x 0.2943 1 l t r oD ,r r I -

47 x106 x2x r x ( 0 .912 x70 s )214

The maximum width of the coil at the diameter Dinisluw : rD;rf s1 :

n0.I27 154 : 0.0074 m : 7.4 mm. The thickness of the coil is fr, : 8 mm.

The number of conductors per coil is Af : &y x l{6 : 2 x 26 : 52. Themaximum value of the coil packing factor is at Din, i.e.

klrri, : tt?- x N" :o o}?l:r" :0.732q -

t - u * 8x7 .4

The stator current density is

t " : =-J l - :6 '28 Af nm22 x n0.912214

The stator winding losses according to eqn (2.42) are

A,P1u, : 3 x 8 .22 x I . I22 : 226.2W

The eddy curent losses in stator round conductors according to eqn (2.61) ate

n2 4T x 106L p " : ; # 1 b 0 2 x 0 . 0 0 0 9 1 2 2 x 0 . 2 5 x 0 . C 0 7 2 x 1 . 1 5 2 : 9 0 . 2 W

where the mass of stator conductors (radial parts) is

mcon : p6uTrllau, N1 ( *\ Ot,,\ 4 1

: 8800 x 3 x 2 . zz+(4 !0991'2)

rr,, 0.0465) : 0.75ks\ 4 /

The friction losses in bearings according to eqn (2.64) are

LPy, :0 .06 x 1 .5 (3 .4 + 0 .64)# : 18 .2 W

AFPM MACHII{ES WITHOUT STATOR CORES 183

The windage losses according to eqn (2.67) are

. 1 . / 300{ ) \ : lA P , , . i n , l : l 7 . 8 5 3 x l 0 " x 1 . 2 ( r " : : ) l t o . s x 0 . l 1 5 ) s - ( 0 5 x 0 . 0 1 b ) 5 1z \ 6u /

r2 .8W

where

R'o,,t, x 0.5Do6 + 0.005 : 0.5 x 0.22 + 0.005 : 0.115 m

R": L22:(:oo?!60=) x 0.11b2 :2.77 x ror'1 . 8 x 1 0 - b

" r : - , - j . L . :2 .353 x 1o-3' J2.77 x 7os

The rotational (mechanical) losses according to eqn (2.63) are

LP,ot: IB.2 * 2.8 : 21 W

The output power is

Pout : P". tr , - LProt: 5646.8 - 21 :5625.8W

The shaft torque is

T"r. : 5625'8

: 17.g1 Nm" n - 2 r x 3 0 0 0 / 6 0

The input power is

Pin : P"hn * LP.LP": 5646.8 + 226.2 + 90.2 : 5963.2 W

The efficiency is

5625.8' l :

sg6:,2: o '943

The leakage reactance can be approximately calculated taking into account theradial part ofconductors, end connection and differential leakage fluxes, i.e.

) r n = 0 . 3 q 1 : 0 . 3 x 3 : 0 . 9 ) r " r y ) r " : 0 . 9

I84 AXIAL FLUX PERMANENT MAGNET BRUSHLESS MACHINES

, 3x3x0 .091 x0 .90192)r,l :

where according to eqn (4.23), the differential leakage factor 16: 0.0059 for5 1 u < 9 9 7 .

The stator leakage reactance is

xr :4trx0.4nx 10 6,. ,rn?L|$out (o n Jr|ul , x 0.e - 0.m6)

: 1 .543 0

where the average length of one end connection is 11" : 0.5(h",n;.r*lt.,no*) :0 .5(0.052 + 0.0896) : 0 .071 m.

The equivalent air gap in the d axis according to eqn (2.105) is

. te ' : 21 (1 .5 + 0 .5 x 8 )1 .02 * . : l : 22 .7 rnm" L.

/ 1 .0451

The equivalent air gap in the g axis according to eqn (2.106) is

sL :21 (1 .5 l * 0 .5 x s ) + 6 l : 23 r r rn

Armature reaction reactances according to eqns (2.114) and (2.115) are

xo , t : 2 x 3 x 0 .4x t r x 10 -6 x15 - / 234 x 0 ' 9019 \2 1' f : ) otnn

x [(0.5 x 0.22f - (0.5 x 0.727)2): 1.e8e ()

) ) 7Xaq X",t

' , , .n: 1.963 o

where kf a: kf n : 1 for surface configuration of PMs [96].

Synchronous reactances according to eqns (2.72) and(2.73) are respectively

X", t , :1 .543 + 1.989 : 3 .532 o

x "q :1 .543 + 1 .963 : 3 .506 f )


The input phase voltage is

V t : J @ t - r I o R l \ 2 + 1 I " X , n 1 z

: I (229.5 * 8.2 x 7.722)2 + (8.2 x 3.500)2 :240.by

The line-to-line voltage Vtr,-r : J3 x 240.b: 416.5 V.

The power factor is

E1 I IoRr 229.5 + 8.2 x 1.122cos@: T :

- 2405

:0 .993 = 1 .0

Numerical example 5.2For the coreless stator AFPM brushless motor described in Numerical ex-

ample -I. 1 find the rotor moment of inefiia, mechanical and electromagnetictime constants and axial magnetic attractive force between the backing steeldiscs of the twin rotor.

Solution

The following input data and results of calculation of Numerical example5.I arc necessary:

r input phase voltage V : 240.5Y

r input frequency f : 750 Hz

r aft gap magnetic flux density Brrs : 0.607 T

r Stator winding resistance per phase Rt : I.I22 Q

r d-axis synchronousreactance Xscl:3.532 Q

: q-axis synchronous reactance f sa 3.500 0

r torque constant kr :2.792 Nm/A

r Electromagnetic torque 7a : 19.97 Nm

. speed n : 3000 rpm

r power factor cos d : 0.993

r PM outer diameter Do6 : 0.22 m

r PM inner diameter Din :0.727 m

r85

I86 AXIAL FLUX PERMANENT MAG]{ET BRLTSHLESS MACHINES

r shaft diameter D"h - 2R"h :0.03 m

r number ofpole pairsp : 3

r pole width to-pole pi tch rat io o ; :2lr

r axial height of PM (one pole) h,u :6 mm

r mass of twin rotor without shaft m, : 3.4k9

r mass of shaft wlsh : 0.64 kg

r specific mass density of PMs {)pL,t : 7700 kglms

r specific mass density of mild steel pp" : 7850 kg/m3

1. Rotor moment of inertia

The active surface area of PMs (one side) according to eqn (2.56) is

spv : ?!p.zz2 - 0.1,27\: 0.01614 m21 T 4

The mass of all PMs is

' t tLp1,1 :2 x 7700 x 0.01614 x 0.006 : 1.49 kg

The mass of backing steel discs is

mFe: mr - TnPA, f :3 .4 - I .49 - 1 .91 kg

The shaft moment of inefiia is

J"h : * *+ : 0 .640 ' :3 ' : o .o72x 1o-3 kgm2

The moment of inertia of PMs is

- D7 , , , + D?^ ^ . ^0 .222 - 0 .1272JPnr : * rn,"# , nnT : o 'ot2 ksm2

The moment of inertia of backing steel discs is

D2 t D2, 0.222 -r 0.032JF, ' ' r 'o t# : t '91f f o 'o l l ' kgur2

The resultant moment of inertia of the rotor is

J, : J"h I Jv'p1 I Jpo, : 0.072x 10-3 + 0.012 + 0.0118 : 0.02386 kgni2

AFPM MACHINES WITHOL]T STATOR CORES

2. Mechanical and electromagnetic time constants

187

Since the d-axis current f ad. : 0, the angle between the q axis and statorcuffent t! : 0. For the power factor cosd : 0.993 the angle between statorcurrent and terminal voltage d : 6.78". The load angle is

6 : d - , $ : 6 . 7 8 _ 0 : 6 . 7 8 "

At the first instant of starling the EMF Ef : 0. Assuming the load angle atstarting is the same as for nominal operation, the stator current according toeqns (2.80), (2.81) and (2.82) is

r - -r 0 s h d . -240.5(3.506 x 0.993 - 7 . I22 x 0.118) - 0 x 3.506

" t ,3 . 5 3 2 x 3 . 5 0 6 + L 1 2 2 2

- r J '59.04 A

240.5(1.r22 x 0.993 + 3.532 x 0.118) - 0 x 7.122n v Aa t n

r' o s n qasnq- 3 .532 x 3 .b06+ r .1 ,222

1,,"r , : /bgn|, nP :64.g2 L

where sin/ : 0.118 (cosd : 0.993). The electromagnetic starting torqueaccording to eqn (2.26) is

TrJrt : kr lo"t"s : 2.192 x 27.A: 59.2 Nm

The no load speed assuming linear torque-speed curve according to eqn (2.126)is

3000ns -

I _ I'LW l*g2 : 4526.9 rplrl : 75.44 rev f s

The mechanical time constant is

T-,,h r,'rU: 0.02386'"Jl#: o. [9] s

The d- and q-axis synchronous inductances are

Lsd - -4t -:r.bil22r7bo: o.oo375 Ht1T .I

- x"-L"q

2 ; i 3 .50 f '2n150 = 0 .00372 H

188 ANAL FLUX PERMANENT MAGNET BRUSHLESS MACHINES

The electromagnetic time constant of the stator winding is

T, L"d' 0'00375 : o.oo334 sz l n : 6

: I n 2

The mechanical-to-electromagnetic time constant ratio is

T*" "h - 0 .191 - b7 . .2T.t,n 0.00334

3. Axial attractive force tretween backing steel discs of the twin rotor

Assuming that the two twin backing steel discs are perfectly parallel, the

axial magnetic attractive force between them can be found on the basis of eqn(s.39)

0 FtOGzF" - " ' " - " 0 .01614 - - 2365.5 N' 2uo

The magnetic pressure is

F, 2365.5r ) . : - - 146 601.2 Pa = 146.6 kPa

S p t t 0 ' 0 1 6 1 4

The backing steel disc thickness is

, TfLFed -v r ' l -

2pp, r(D!,, D?") 14

1 .910.0033 m 3.3 rnm

2 x 7850r(0.22'2 - 0.7272) I 4

and outer diameter Dout : 0.22 m can provide adequate stiffness of the disc

under the action of 146.6 kPa magnetic pressure in the axial direction.

Chapter 6

AFPM MACHINES WITHOUT STATORAND ROTOR CORES

6.1 Advantages and disadvantages

With the availability of high energy magnets the stators and rotors of AFPMbrushless machines can be fabricated without ferromagnetic cores 197, 138,139, 2031. A completely coreless design re duce s the mass and increases the ef-ficiency of the machine as compared with a conventional design. Besides this,a coreless AFPM brushless machine does not produce any normal attractiveforce between the stator and rotor. It also does not produce torque pulsationsat zero current state.

There is a limit to the increase of the electromagnetic torque that can beachieved by enlarging the machine diameter. Factors limiting the single discdesign are listed in Section 2.1.6. A reasonable solution for larger torques aredouble or triple-disc machines.

The disc-type PM brushless machines without stator and rotor cores werefirst manufactured commercially in the late 1990s for servo mechanisms andindustrial electromechanical drives [138], solar powered electrical vehicles

1203] as well as micromotors for computer peripherals and vibration motorsfor mobile phones [85].

6.2 Topology and constructionThe AFPM brushless machine without any ferromagnetic core is shown in

Fig. 6.1. The machine consists of a twin rotor (3) with rare earth PMs (2) andnonmagnetic supporting structure. The steel-free stator (armature) winding (1)is located between two identical parts of the rotor. The stator polyphase wind-ing fixed to the frame (6) is assembled as "flower petals" (Fig. 3.16) !391.Multi-turn coils are arranged in overlapping layers around the shaft-axis ofthe machine. The whole windine is then embedded in a hich mechanical in-


Figure 6.1 . Disc type coreless PM brushless machine: I - coreless stator (armature) winding,2-PMs,3 tw in ro to r ,4 -shaf t ,5 bear ing ,6- f rame.

Figure 6.2. Segmental constntction of a disc type coreless PM brushless machine: (a) singlemodule (segment), (b) three-module assembly.

tegrity plastic or resin. Since the topology shown in Fig 6.1 does not use anyferuomagnetic core with slots, the machine is free of cogging (detent) torqueand core losses. The only eddy current losses are losses in the stator windingconductors and metallic parts (if they exist) that reinforce the stator corelesswinding.

AFPM machines without stqtor and rotor cores 191

(a)

Figure 6.3. Construction of a three-phase, 8-pole AFPMranged in Halbach array: (a) PM ring; (b) stator winding;stator winding and complete twin rotor.

brushless machines with PMs ar-(c) one half ol the twin rotor; (d)

,ffi

Figure 6.1. 3D magnetic flux density distribution excited by an 8-po1e twin rotor with PMs

arranged in Halbach array.

The coreless machine designed as a segmental (modular) machine is shownin Fig. 6.2. The output shaft power can easily be adjusted to desired level byaddins more modules.


{ a }900

(c) 45o

Figure 6.5. Arrangement of the twin rotor PMs in 90", 60", and 4b" Halbach array.

To obtain a high power (or high torque) density motor, the magnetic fluxdensity in the air gap should be as high as possible. This can be achievedby using PMs arranged in "Halbach array" (Figs 3.15, 6.3 and, Fig 6.4). Themagnetic flux density distribution excited by Halbach arrays is described byeqns (3.42) to (3.46).ln practice, the angle between magnetization vectors ofadjacent magnets is 90", 60" or 45o (Fig. 6.5).

6.3 Air gap magnetic flux densityFig. 6.6 shows the results of the 2D FEM modelling of the magnetic field

in the air gap of a coreless AFPM brushless machine. NdFeB magnets withremanent flux density B, :7.2 T and coercivity H.: 950 kA/m have beenconsidered. The thickness of each PM has been assumed 6 mm, the corelessstator winding thickness is l0 mm and one-sided air gap thickness equals to 1mm.

With the aid of Halbach anay a high peak value (over 0.6 T) of the nor-mal component of the magnetic flux density has been excited. This value issufficient to obtain a high electromagnetic torque. The peak value of the fluxdensity can be even higher for the optimized magnetic circuit of an AFpM ma-

(b)

AFPM machines without stator and rotor cores

(b)

193

t 5

F

Figure 6.6. Normal and tangential components of the magnetic flux density in the centre of

the air gap of a double-sided coreless AFPM brushelss machine excited by Halbach arrays of

PMs: (a) 90"; (b) 45".

chine. In pmctice, 60" and 45" Halbach arrays produce similar peak magneticflux density (Fig.3.22). The peak value of the nolmal component of the mag-netic flux density is higher than that in a standard arangement of surface PMs.The backing ferromagnetic discs added to the double-sided PM structure withaTarge nonmagnetic gap do not increase the flux density as much as Halbacharray excitation does.

6.4 Electromagnetic torque and EMFThe electromagnetic torque of a coreless AFPM brushless machines with

Halbach array PM excitation can be calculated on the basis of eqns (2.25),(2.26), (2.27), (2.120) and (2.121). Similarly, the EMF can be calculated ac-cording to eqns (2.29), (2.30), (2. I 1 8) and (2.1 19).

1 , m

,^-Nonlal

+'fancenl

6

II \

q

\

\\ 1

E d


Figure 6.7. Exploded view of the SEMA AFPM brushless machine. Courtesy of Lynx MotionTechnologlt, Greenville, IN, U.S.A.

6.5 Commercial coreless AFPM motorsCoreless AFPM machine architecture known as segmented electro-magnetic

array (SEMA) has been proposedby Lynx Motion Technology, Greenville, IN,U.S.A. for electric motor, actuator and generator applications requiring highpower density and high efficiency !a01. Applications that require an elec-tromechanical drive with high power density, high efficiency and low torqueripple include precision motion control, naval propulsion systems and acous-tically sensitive applications. SEMA technology may also find applications indistributed generation systems and energy storage systems, such as flywheelmotor generator systems. Motors with high torque and efficiency are de-manded for gearless electromechanical drives. The use of direct drive motorswithout speed reducers eliminates gear noise, oil leaks, positioning errors frombacklash and lack oftorsional stiffness.

The stator coreless and toothless design (Fig. 6.7) not only eliminates thecogging torque but also increases the area available for conductors. It alsoboosts peak torque capability and allows PMs to be more effectively utilizedlla0l. The stator coils are fully potted in high-strength, thermally conductiveepoxy resin. Such construction gives the machine structural integrity and effec-tively damps the high frequency vibration when the motor is PWM inverted-fed. Machines with coreless stator winding perform excellently at constantspeed, variable speed and at reversals.


Figure 6.8. In-wheel motor, PM ring and stator winding of a coreless AFPM btushless motor

for solar-powered vehicles. Courtesy of CSIRO, Lindfield, NSW, Australia.

Figure 6.9. Exploded view of the AFPM brushless motor with film coil coreless stator winding

and twin PM rotor. Courtesv of EmBest^ Soeul, South Korea.

195

,; 5l s

s g E4 : &s . i q

! ' i3 : .

r 3

. ,

6

,4.

o tt 9a z{.1g:

196 AXTAL FLUX PERMAI,{ENT MAGNET BRUSHLESS MACHINES

Table 6.L Design data and parameters of a three-phase, 10-kw, 750-rpm disc type AFpMbrushless machine with ironless stator core

Design dataOutput power Pot,WSpeed n, rpm

10,000'7 50

3 (Wye)28.410028

24100 (one module)

I slot6 x 7 . 2

61 01

0.584.175t r , 1 6t / y J

3600.6575

naturalf

Number of phases m1Input current 1, AInput frequency f ,HzNumber of stators (modules)Number of pole pairs pNumber of coils (3 phases)Number of turns per phaseCoil pitchWire diameter, mmAxial thickness of PM hx1 ,mmAxial thickness of the winding f-, mmAir gap (one side) g, mmAir gap magnetic flux density B,,n under load, TCurrent densiry Almmzka,: D,;, ,1Do"1 rat io [5]Rotor outer diameter ,o1lr, mmWinding packing factor at r :0.SD.tnWinding temperature, oC

Cooling systemClass of insulation

CSIRO klecommunications and Industrial Physics, Lindfield, NSW, Aus-tralia manufactures in-wheel coreless AFPM brushless motors for solar pow-ered vehicles 1203]. solar-powered vehicles compete in the world Solar chal-lenge solar car race organized every two years in Australia between Darwinand Adelaide, which has become a well-known intemational event.

cslRo provides in-wheel AFPM brushless motors both with surface pMsglued to steel discs and with PMs arranged in Halbach array. The motor struc-ture, PM disc and stator winding are shown in Fig. 6.8 [203].

Fig. 6.9 shows a coreless brushless motor with film coil stator winding andtwin PM rotor manufactured by EmBest, Soeul, South Korea. The corelessstator has a foil winding at both sides. The 8-pole PM rotor is designed as atwin extemal rotor.

AFPM machines without stqtor and rotor cores 197

(a) aoo 4oo

T , 6 ( 1 )r00

.1. tf"',\p u(l) 2oo

i ly" 'A P 1 0 0

l 0

I

| ( l )- 0.9

_'1l

0.8

0.75

0 1 0 2 0 1 0 4 0

0 1 4 0

current. A

(b)

l . 0 i

o l r o z o r o 4 00 1 4 0

cunent. A

Figure 6.10. Calculated performance characteristics of a 10 kW coreless AFPM brushlessmotor according to Table 6.1: (a) shaft torque 7"1, line-to-line voltage [7., winding lossesAP,,, ,addit ional losses LPoaa,andmechanical lossesAP",,versusstatorcurrentatn:750rpm - const; (b) efficiency 4 and power factor pJ versus stato. cunent at n : 75A rpm : const.

6.6 Case study: low-speed AFPM coreless brushless motorA low speed, three-phase, Y-connected AFPM brushless motor rated at 10

kW 750 rpm, 28.5 A has been designed and investigated. The rotor does nothave any ferromagnetic core and consists of trapezoidal coils embedded in ahigh mechanical integrity resin. Average quality sintered NdFeB PMs withB, : I.2 T and H, : 950 kA/m have been used. The double-disc con-struction is similar to that shown in Fig. 6.2b. The design data and calculatedparameters are given in Table 6.1. All parameters except the air gap magneticflux density B-n and synchronous reactance X"d : Xsq X, have beencalculated analytically. The magnetic flux density and synchronous reactancehas been calculated using the 2D FEM. The resistance R1 : 0.175 0 andsynchronous reactance X" : 0.609 O perphase are for two stator modulesconnected electrically in series. The EMF constant kB : 5.013 Vs and torqueconstant kr : 2.394 Nm/A have been calculated for one stator segment.

6.6.1 Performance characteristicsThe current density 4.175 Almm2 in the stator winding at rated load is low

and a totally enclosed motor can even operate without any forced air cooling.The recommended cuffent density for enclosed a.c. motors with class F ofinsulation rated up to l0 kW is from 4.5 to'/ R/mm2 [63].

The calculated characteristics are shown in Figs. 6.10 and 6.11. It canbe seen from Fig. 6.11 that the maximum-to-rated current ratio for torque-speed characteristic is 1.3. In Fig. 6.11 the voltage increases linearly up toapproximately rated speed and then is kept constant.

198 AXIAL FLI]X PERMANENT MAGNET BRUSHLESS MACHTNES

z

116Gp)

r0il;i;;

200 200

1 5 0

1 0 0

50

0 2 4 6 8 l 0 t 2 . 1 40 n k 1 4

speed, rev/s

Figure 6. I L Shaft torque, cuffent and phase voltage versus speed of a 1 0 kW coreless AFPM

brushless motor according to Table 6.1.

6.6,2 Cost analysisThe cost model has been presented in [96]. Average prices of materials for

electrical machine construction are as follows (in US dollars: $): silicon sheetsteel cp" : 1.25 $/kg, isolated copper conductor (magnet wire) c6, : 5.51$/kg, sintered NdFeB PMs cp,y : t5 $/kg and steel bar for the shaft cste,et :

2.6 $/kg. The active materials are conductors, sheet steel and PMs. The totalvolume of the steel bar to the volume of shaft is 1.94. The coefficient takinginto account the cost of machining of the shaft is 2.15. The cost of labourinvolved in the assembly of active parts has not been estimated.

Table 6.2. Mass and cost of components of a disc type coreless PM brushless motor rated at

10-kW.750-mrn

ltem Mass, kg Cost, $

1v 1

WindingStator plastic materialPMsShaftFrame, end bells, and bearingsComponents independent of the machine shapeTotal

10 .1 31 . 0 112 .385.48

22.51 (active parts)

55.847.09

185.6659.4s165.00140.00613 .05

AFPM machines without stator and rotor cores t99

Table 6.3. Mass and cost of components of a cylindrical PM brushless motor with laminatedcore rated at 10-kW 750-rpm

Item Mass, kg Cost, $WindingCorePMsShaftFrame, end bells, and bearingsComponents independent of the machine shapeTotal

8 . 5 130.981 .575.12

41.06 (active parts)

46.972.4923 .5562.07i 65.00r40.005 10.0 1

Table 6.2lists the mass and cost of components of the 10 kW 750 rpm core-less motor of disc construction. Table 6.3 lists the mass and cost of componentsof the equivalent cylindrical motor with laminated stator and rotor cores. Com-ponents independent of the machine shape are the encoder, terminal leads, ter-minal board, and name plate. The 10 kW coreless AFPM brushless motor costs$6 I 3.05 (PMs cost $ 1 85.66) while a classical PM brushless motor of cylindri-cal construction with the same ratings costs only $510.01 (PMs cost $23.55).The contribution of PMs to the total costs of a coreless motor is predominant.

6.6.3 Comparison with cylindrical motor with laminatedstator and rotor cores

Table 6.4 compares the design data and perfomance of a l0 kW, 750 rpmcoreless AFPM brushless motor and the equivalent 10 kW, 750 rpm PM brush-less motor with laminated stator and rotor cylindrical cores. In both motors thenumber of phases is 3, number of poles is2yt:16, and input frequency is 100Hz.

The analysis and the FEM simulation have shown the advantages of thecoreless disc type PM brushless motors in terms of performance and mass ofactive materials. They have higher efficiency and power density when com-pared with conventional PM machines with laminated cores.

The efficiency of the l0-kW AFPM brushless motor is l.2o/o higher (0.925versus 0.914) and power density (output power to mass of active materials)is 82o/o higher (444.25 Wkg versus 243.55 Wkg) because the mass of activematerials is 45o/o lower than that of an equivalent PM brushless motor withcylindrical ferromagnetic core . Atzerc current state the normal forces betweenthe stator and rotor do not exist. However. the normal forces between the rotorPM discs are large.

200 AXIAL FLLTX PERMANENT MAGNET BRT]SHLESS MACHINES

Table 6.4. Comparison of parameters and performance of 10-kW, 750-rpm PM brushless mo-tOIS

ParameterCorelessdisc type

Cylindricalwith laminated core

Input voltage (line-to-line), V 22',7.61 3 192.s0.9910.5 8

4 . 1 7 50.1 '730.609t2.3822.51444.25613 .05

220.013391.40.960.78

I 1 A a

0.0370.75u1 . 5 741.06243.555 l 0.01

Shaft torque, NmEfficiency, %Power factorAir gap magnetic flux density, TStator winding current density, Nmm2Stator winding resistance per phase at 75"C, QSynchronous reactance, QMass of PMs, kgMass of active rnaterials, kgPower density (only active materials), W&gCost excluding labour, U.S.$

These new types of machines are cogging torque free. Owing to the lack offerromagnetic cores the hysteresis and eddy cunent losses in those parts do notexist.

The cost of materials and components of the disc tlpe l0 kW coreless motoris 20oh higher than that of a cylindrical motor with laminated core. On theother hand, the cost of tooling will be much lower as a coreless motor does notrequire stamping and stacking tools.

The high cost of PMs limits commercial applications of coreless AFPMbrushless motors to small size machines, special servo drives, airborne appara-tus (lightweight construction) and electromechanical drives where the coggingtorque ripple and normal forces must be reduced to zero.

6.7 Case study: low-speed coreless AFPM brushlessgenerator

The AFPM brushless machine (Table 6.1) has been analysed as a stand alonea.c. generator. The open circuit characteristic, i.e. EMF (line-to-line) as afunction of speed is shown in Fig. 6.12. This characteristic is linear.

The AFPM generator has been connected to the inductive load Zr : R,r *j Xr : 7 + j0.628 O. The curent-speed characteristic for generating mode isshown in Fig. 6.13.

The line voltage versus speed is shown in Fig.6.14, output and input activepower in Fig. 6.15, and efficiency and power factor in Fig. 6.16. The voltage is


200

150n n ( n J

100

t 5

0 n i 1 5speed, rev/s

Figure 6.12. Open circuit characteristic: line-to-line E,MF versus speed.

201

250

l 0

- t

o t

50

t",, ( ' ') |

l 0

l 5

u

.oeed::v/s

r)

Figure 6.13. Current versus speed for generating mode.

a nonlinear function of speed and depends on the value of the load impedancezl and power factor. For inductive load (RL) the power factor decreases asthe speed increases.

6.8 Characteristics of coreless AFPM machinesTable 6.5 shows specifications of coreless AFPM brushless motors for solar

powered vehicles with surface PMs glued to a steel yoke and PMs arrangedin Halbach anay (CSIRO, Australia) respectively. The steady-stare efficiencycuryes for surface PMs and Halbach array are plotted in Fig. 6.17. The maxi-

202 AXIAL FLI]X PERMANEI:IT MAGNET BRUSHLESS MACHINES

1 s 0

\ |iJ I roo

I

50

5 l 0

I

speed, rev/s

l 5

1 5

. t - ,9 ^ l v _ , r n

Figure 6.14. Line voltage versus speed for generating mode.

1 . 1 0 4I 0000

8000

Pgo,, (ni)

l-r",)' g t n

o n i

speed, rym

l 5

l 5

Figure 6.15. Output power Psout. and input power Psn, for generating mode.

mum efficiency is obtained when the inverter applies a sinusoidal voltage syn-chronized to the rotor position. The inductance of the stator winding is lowand most inverlers require additional series inductance.

The 8225 coreless AFPM motor (Table 6.6) has been developed by LynxMotion kchnology, Greenville, IN, U.S.A. for air-handling applications, inwhich system efficiency is a high priority. The family of Lynx 225-mm diam-eter motor designs offers a broad range of possible system configurations forspeed and position servo applications requiring both high efficiency and hightorque. Performance ratings of theE225 motor are based on air-cooled 105"Cwinding at25oC ambient airtemperature. The EB13 coreless AFPM machines

e,

l 0

, " r /

,/

,/

/


r .05

r ts(n i )

0.5prg (n i )

203

o

F

5 l 0

nI

speed, rpm

l 5

1 5

Figure 6. I 6. Efficiency 4n and power factor pf n for generating mode.

0 200 400 *t ::,'r,i;fi"],'ff

1400 1600 1800 2000

Figure 6.17. Efficiency as a function ofoutput power ofa 3-phase, 1.8-kW coreless AFPMbrushless motors for solar-powered vehicles: (a) rotor with surface PMs; (b) rotor with PMsarranged in Halbach array. Courtesy of CSIRO, Lindfleld, NSW, Australia.

has been designed for power generation applications (distributed generationsystems) where high efficiency of the system is important. Performance rat-ings of the E813 machine are based on 130"C winding at 40oC ambient airtemperature. Both 8225 and E8l3 machines have extremely linear torque con-stant k7 independent of speed. Other applications of Lynx coreless machinesinclude servo applications, precision robotics, marine propulsion, generatorsand weapons tunets.

;e

'o

I


Table 6.5. Comparison of three-phase 1.8-kW coreless AFPM brushless motors with surfaceand Halbach PM excitation manufactured bv CSIRO. Australia

ParameterSurface PMs

and steel yokeHalbach

arfayOutput power, WEfficiency, %Number of polesNominal speed, rpmMaximum speed, rpmNominal torque, NmMaximum continuous torqueat 1060 rpm and maximumwinding temperature, NmAbsolute maximum torque, NmTorque constant per phaseat sinusoidal excitatir:nNominal phase EMF, VEMF constant per phaseat sinusoidal current, Vs/radNominal phase current, AWinding losses, WEddy current losses in thestator winding, WWindage losses, WTotal losses, WWinding temperature rise, "COverload winding temperature rise, "CMaximum winding temperature, oC

Air gap at each side, mmResistance per phase, QMass of complete motor, kgMass of frameless motor, kg

I 80097.440

l 060286s16.2

J I

50.2

0.39* J

0.3913 .943.9

2.62 . 148.622641 1 02

0.0757to .z

r0.7

1 80098.240

1 060286516.2

39s0.2

0.5662

0.569.627.6

2 .72 . 132.41 4401 1 02

0.0997t J . z

7.7

When coupled with a three-phase H-bridge inverler, Lynx motors offer ahighly efficient electromechanical drive with the high peak torque capabilityrequired for the most demanding high-transient applications, e.g. fuel-cell aircompressors.

Numerical example 6.1The coreless AFPM motor with the same dimensions as that described in

Numerical Example 5.1 has been redesigned to obtain the speed of 1000 rpmzt Io : 8.2 A (I"d : 0). The number of pole pairs has been increased to

AFPM machines without stator and rotor cores 205

Table 6.6. Specifications of coreless AFPM motors manufactured by L1,nx Motion kchnologt,Greenville" IN" U.S.A.

Parameter E225 AFPM motor 8813 AFPM motorNumber of poles

d.c. bus voltage, VTerminal voltage, V

Speed, rpmTorque, NmPeak torque, NmCurrent, APeak curent, AOutput power, kWTorque constant, Nm/AEMF constant per phase, V/krpmElectrical time constant, /rsWinding resistance at 100"C, f,)Winding inductance, g,HRotor momenl of inenia. kgm2Mass of motor, kgExternal diameter, m

l 21 5 5t17

rms phase voltageH-bridge

60009.997.41 8 . 71806.20.53l 9

0.3480.204

7 10.0184

8.40.225

28851)571

peak line-to-line

2750450900l l 92381303.782091 .66

0.026544

9 . 1 6295

0 .813

p : 12, the number of coil sides to st : 72 and PMs have been arrangedin 90o Halbach affay with nLr : 4 PM pieces per wavelength. The numberof stator winding turns per phase is l,h : 240, the number of parallel wireson, : B, the diameter of wire d* : 0.455 mm (AWG 25) and the coil pitchmeasured in coils sides a'. - 3. Since both stator and rotor do not have anysteel magnetic circuit, the magnetic saturation does not exist and ksat : 1. Allother parameters and assumptions are the same as those in Numerical example5 .1 .

Find the motor steady state performance, i.e. output power, torque and effi-ciency at rated current Io : Iorr: 8.2 A.

Solution

The following calculated parameters are the same as those in Numerical ex-ample 5.1: g: 1.5 r t f i11, Di,n:0.727 f f i , D -- 0.1735 r ' rr , Li : Iat :46.5

mm, Rtorrl: 0.115 m (for windage losses), R"h : 0.015 m and n'LcorL : 0.75kg.


The number of coils per phase for a single layer windingis n,.. : stl(2rn):72lQx3) : 12. The numberofturnspercoi l is Af, , : Nt ln, :240172 :20. The number of coil sides per pole per phase (equivalent to the number ofslots per pole per phase) qt : stl(2p*t') - 721Q4 x 3) - 1. The pole pitchmeasured in coil sides is r, : slf (2p) : 72124: 3 and the average polepitch r : nD I Qp) : r0.7735 124 : 0.023 m

The input frequency at 1000 rpm

" 1000f : n"p:

60 x 12 - 200}J2

The wavelength Io at the average diameter and constant p for Halbach array is

l o :2 r :2 x0 .023 : 0 .046 m IJ :+ : ] I - : 138.3 1 /m1,,, 0.046

The magnetic flux density in the air gap according to eqn (3.42) is

B, ,g N Bmo:1 .21r *exp( -138.3 x 0 .006) ]s rn( t l4 : 0 .609 T7T / 4

The magnetic flux according to eqn (.2.21) is

o, : 1 ?lr uro x 0222[r - (a) I : o oo,,nr rru' B r12 L \ /3 / l " " " - '

The winding factor according to eqns (2.8), (2.9) and(2.10) is

k d 1 : ; s i n n / ( 2 x 3 ) 1 n u J c , 7

t s inn / (2 x 3 x 1 ) : l i ' :

i . : g

kpr :s i ' (3 ; ) : r k ,o r :1 x 1 :1

The EMF constant according to eqn (2.30) and torque constant according toeqn (2.27) is

kn :nJ2x12x240 x r x 0 .00041 -b .24 , y1$ev l s ) : 0 . 0BZ3V / rpm

kr : k /+ : b .24! :2 .5 Nm/A'Z7T 'zir

The EMF at 1000 rpm is

Ef : kan, : 0 .0873 x 1000 : 87.34 V


The electromagnetic torque Lt Io - Ioq : 8.2 A is

201

Ta : kr lo : 2.5 x 8.2 : 20.5 Nm


Put,n : 2rn "7,1:

,o t99o

x 20.5 : 2148.6 wtt0

The length of the stator shorter end connection without inner bends lr.min :

(w"f r.)rDi"l(2p) - (313)r x0.127 124: 0.017 m and the length of the sta-tor longer end connection without outerbends lk^or: 0.017 x0.22f 0.I27 :

0.0288 m (Fig. 3.16).

The average length of the stator turn with 15-mm bends is

l looN2Lt ' * l l " rn ' i , lL l . r ro , +4 x 0 '015

:2 x 0 .0465 + 0 .017 + 0 .0288 + 0 .06 : 0 .1984 m

The stator winding resistance at 75"C according to eqn (2.33) is

240 x 0.1984 : 0.7963 Ot)f L l -

47 x 706 x B x n- x (0.45 * t}-s1'z 14

The maximum width of the coil at the diameter D;' is uuu: : rDinf sy :

10.127172: 0.0055 m: 7.4 mm. The thickness of the coi l is l - : B mm.Thenumberof conductorspercoi l is Al , : r t ry x l {s1: 8 x 20: 160. The

maximum value of the coil packing factor is at Din, i.e.

k1'nin: '4*: n nui. l lon : o '731

l , , , L D , u 6 x C . D

The stator cur:rent density is

J r , , : B x n0.452 l4:6.45 Af mm2


AP,, : 3 x 8.22 x 0.7963 : 160.6 W

The eddy cuffent losses in stator round conductors according to eqn (2.61) are

A,p. : n2 47 ̂ 106

20G x0.000452 x 0.75 x 0.60g2 x 1.152: 3g.3 Wa r r - 4 S f t o o

8.2

208 AXIAL FLUX PERMANENT MAG]{ET BRLISHLESS MACHINES

The friction losses in bearings according to eqn (2.64) arc

LPy,:0.06 x 1.5(3.4 + 0.0+1400 : 6.1 \ [ 'tlu

The windage losses according to eqn (2.67) are

1 r 1 O O O r 3L P , i n d - - 0 . 0 1 3 r 1 . 2 ( z o ' " 1 1 1 f r o . s x 0 . i l 5 ) 5 - ( o . s x 0 . 0 1 5 ) 5 12 \ 6 0 /

L \

r 0.18 \ [ r

where

n": r.2ffffi x 0.1152: e.233 x 1oa

3.87' f : ,,/g.2',r,.Iff:0'013

The rotational (mechanical) losses according to eqn {2.63) are

LPro t : 6 .1 * 0 .18 : 6 .28 W

The output power is

Pout : P.trn - LProt : 2748.6 * 6.28 : 2742.3W

The shaft torque is

T"r" : 2142'3

: 20.40 Nm" n - 2 r x 1 0 0 0 / 6 0

The input power is

Pi, : P.t^ * LP* * LP":2148.6 + 160.6 + 39.3 : 2348.5 W

The efficiency is

2142.3n : 234&s:

o '912

AFPM machines without stator and rotor cores 209

Numerical example 6.2A three-phase, 15-kW, 3600-rpm coreless AFPM motor with Halbach array

PM twin rotor has the stator winding resistance per phase Rr - 0.24 f), statorwinding leakage reactance X1 : 0.92 O and armature reaction reactancesXod. : Xoq : 0.BB O. The input phase voltage is [ : 220V, power factorcos 4! : 0.96, angle between the stator current and q axis \F : 5", EMFconstant kr : 3.363 V/(rev/s), eddy current losses in stator conductors LPe, :184 W and rotational losses LP,ot: 79 W.

Find the internal voltage fl excited by the resultant air gap flux and thestator d- and q-axis current adjusted for eddy current losses.

Solution

The phasor diagram showing the EMFs Ey and E; is drawn in Fig. 6.18.The EMF E7 excited by the rotor magnetic flux

HI : ke , :3 .363 t #

:210 .78 V

The synchronous reactance is

Xsd,: Xsq: Xoa * Xt : Xo,t * Xr : 0.BB + 0.92 : 1.8 0

The angle between the stator current and input voltage r/ - arcsin 0.96 :16.26". The load angle between the voltage and EMF Ey is 6 : rf W :76.26 - 5 : 7I.26". The stator currents according to eqns (2.80), (2.81) and(2.82\ are:

r . -' a d -220(I.Bcos 11.260 - 0.24sin 11.26o) - 201.78 x 1.8

: 4 . 5 A

r -' a q

1 .8 x 1 .8 +0 .242

220(1.8 cos 11.260 * 1 .8 s in IL26") - 20L78 x 0.24:24 .5 A1 .8 x 1 .8 +0 .242

Io: 1 /Lb2 + Al r2 :24.g A


LPt', : 3 x 24.92 x 0.24 :445'6 W

The input power is

Pin : rnlVlIacos@ - 3 x 220 x 24.9 x 0.96 : 15 763.0 W

210 ANAL FLUX PERMANENT MAGNET BRUSHLESS MACHINES

blgure 6.18. Phasor diagram of u .o..t.r, AFPM synchronous motor (eddy current 1" is inphase with the intemal voltage Ei). Numerical example 6.2.

The electromagnetic power according to eqn (5.1) is

Pet rn :15 763 445 '6 184 : 15 133.3 W

The output power according to eqn (5.3) is

Pout : 15 133.3 - 79 : 15 054.3 W

The efficiency is

15 054.3? : 15 z63J

: o '955

The internal voltage E; excited by the resultant air gap flux according to thephasor diagram (Fig. 6.18) is

En:@

: 1f QOt.fA * 4.5 x 0.88)2 + (24.5 x 0.88)2 : 206.87 V

AFPM machines without stator and rotor cores 2Il

The angle d; between the EMF Ei and g-axis is

d; : ar"r ",,(o!;i*",) - arcr,n (ro, 24 si*%*) - , or"

\ f . t t t o 4 A o d / ,

The eddy current shunt resistance according to eqn (5.32) is

)nG R72R" :3? -6e7 .75Q

The current in the vertical branch of the equivalent circuit (Fig. 5.3) found onthe basis of the phasor diagram (Fig. 6.18)

. E i . c 2 0 6 . 8 7I "a : - ts ind ; : -

r r , ^s in5 .97" : -0 .031A

t", : *cos

d,. : # rryrcos 5.97" : 0.295 A

(-0.031)2 + 0.2952 : 0.296 A

I . ' E i 246 '8T= ft : ,* ^cos 5.97" : 0.296 A

The stator current adjusted for eddy current losses found on the basis of thephasor diagram (Fig. 6.18)

IL.a :

206.87 cos 5.972

Ezcos6i - Ef Eis inSt

Xo,] R"-

- 201.78 206.87 s in 5.972r 4 .5A

' a q

0.88

E; cos dr _R"

206.8T sin 5.972

697.75

206.87 cos 5.972= 24.8 A

E; sin d;v -

A a e

ro , -

O.BB 697.75

tlo+ t!,n

(I'"a), + (IL)2 : \f Lb2 +rLB2 x 25.2 A

Chapter 7

CONTROL

In the previous chapters it was shown that there is a direct relationship be-tween the rotor speed and the frequency of the phase voltages and curentsof the AFPM machine, It was also shown that the magnitude of the inducedphase voltages is directly related to the frequency and hence the rotor-speedof the AFPM machine. Therefore, for variable speed operation of the AFPMmachine both the frequency and magnitude of the supply voltage must be ad-justable. This requires a solid-state convefter to be used between the flxed a.c.or d.c. supply and the terminals of the AFPM machine as shown in Fig. 7.1. Tohave good position andlor speed control of the converter-fed AFPM machinedrive, the torque and therefore the current of the machine must be controlled.For current control, information of the phase curent as well as the position ofthe rotor is necessary. Thus, both the current and rotor position of the AFPMmachine is sensed and fed back to the controller as shown in Fig. 7.1. Thecontroller in its turn controls the supply voltage and frequency of the AFPMmachine via the solid-state convefier (inverter).

This chapter focuses on all the control aspects of the AFPM machine driveof Fig. 7.1. The control of the two types of AFPM machines considered inprevious chapters, namely the ttapezoidal and sinusoidal AFPM machines, isdealt with separately. Finally, position sensorless control is briefly discussedand some numerical examples are given.

7.1 Control of trapezoidal AFPM machineTrapezoidal AFPM machines are surface-mounted PM machines and are

characterised by their trapezoidal or quasi-square EMF waveforms. Exampleof these EMF waveforns are shown in Figs 7.2a and7.2b,which are the opencircuit phase voltage waveforms induced by PM flux of a small 1 kW, slottedtrapezoidal AFPM machine at half and rated speed respectively. It can be ob-

214

Fixed

AC or DC

supply

AXIAL FLUX PERMAIVENT MAGNET BRUSHLESS MACH]NES

Figure 7.1. Converter-fed AFPM machine drive.

served, firstly, that at rated speed the frequency and the magnitude of the EMFare double what they are at half rated speed. Secondly, and very important, itcan be seen that the shape of the EMF waveforrn is not sinusoidal, but trape-zoidal with a flat-topped voltage of about 120 electrical degrees. It is duringthis period of 120 electrical degrees that the phase is excited by means of thesolid-state converter. This period is therefore called the conduction period, ascunent is flowing in that phase during that period as shown in Fig. 7.2c. Notethat the time of conduction or the time of occurrence of the flat-topped voltageis directly related to the position of the rotor; the time of conduction can thusexactly be determined by means of a simple, low resolution position sensor.

During the conduction period one can consider the induced back-EMF phasevoltage as a d.c. quantity due to the flat voltage waveform. With a three-phasemachine the phase voltages are 120 electrical degrees out of phase, which im-plies that the conduction periods of two phases are always overlapping (seeFig. 7 .2) and that two phases are always active. In the case of AFPM machinedrives with 180 electrical degree conduction periods, e.g. [31], then all threephases are active. A different convefier should be used in this case. In thissection only those trapezoidal AFPM machine drives that have 120 electricaldegree conduction periods are considered as they are commonly used.

7,1.1 VoltageequationsWith two phases of the Y-connected three-phase machine always active (the

third phase is switched off by means of the solid-state converter), the powercircuit of the trapezoidal AFPM brushless machine can be represented by theelectric circuit of Fig. 7.3a. Here, phases A and B are active and phase C isswitched off(shown in dotted lines). In this circuit R1 and L" are respectivelythe phase resistance and phase synchronous inductance. The synchronous in-ductances in the d and q-axis are equal, i.e. L"4 - L.sq - L". The voltagesefA, efB and eyc are the EMFs per phase. As phases A and B are in theirconduction periods, both e 1e and e y s are at their flat-topped values. Hence,

Solid-State Converter(SSC)

Control 215

20

1 5

1 0

o d

:- 1 0

-20

(a)40

30

20

> 1 6

=s -10

-24

-30

40

0.008 0012 0.0'16 0.02 0.024

Time (s)

0.016 a.a2 0.024Time (s)

0.028 0.032

Figure 7.2. Open-circuit induced phase voltage waveforms of a l-kW trapezoidal AFPM ma-chine obtained from measurements: (a) at half speed (30 Hz); (b) at rated speed (60 Hz); (c:)theoretical EMF and phase current waveforms.

efA: El!'' unaeJB : -Ef') where nl!'l t" the flat-toppedvalue of thetrapezoidal voltage waveform(fig. Z.Zc1. Combining the resistances, induc-tances and induced voltages of Fig. 7.3a results in the equivalent circuit of Fig.7.3b inwhich Eyr-r is taken as a d.c. voltage equal to E1r,-L : 2Ef'),R.p : 2R1, Lo : 2L", ia : ioA - -ioB and uo : urL-L. The dynamicvoltage equation of this circuit is

0.008 0.012

(b)

(c)

216 AXIAL FLUX PERMANENT MAG]{ET BRUSHLESS MACHINES

" ll-l.

Figure 7. j. Trapezoidal AFPM machine connected to the solid-state converter with two phasesactive: (a) electrical circuit; (b) combined equivalent circuit for the analysis.

u,p 2R1ioa + 2L"q9!a[

+2Ey')

(7 .1 )

Applying a d.c. voltage up : V, across terminals A and B by means of thesolid-state converter will imply that ideally in the steady state, a d.c. current

io : IL"q) will flow through the two phase windings according to the followingsteady-state voltage equation derived from eqn (7.1'), i.e.

Vp: R'pIL"q) + Eyr-r (7.2)

The induced voltage E y r-L is given by eqn (2.I l8), the electromagnetic power

of the machine is P.1,rn : E f r, ;I["q) andthe developed torque is given by eqn

(2.120). Note that da: I\sq) and Eyr I are instant quantities that can changewith time, similar to a brush-type d.c. machine.

7.1.2 Solid-stateconverterThe complete power circuit connected to the three-phase trapezoidal AFPM

brushless machine is shown in Fig. 7.4. In this circuit the fixed three-phasea.c. supply is first rectified by means of a three-phase diode rectifier to obtaina fixed d.c. voltage. The d.c. voltage is then inverted to a three-phase a.c.trapezoidal voltage. With the diode rectifier no power can flow back to thefixed a.c. supply if the AFPM machine is operating in generator mode. Thismeans that any generated power from the machine must be dissipated at thed.c. link of the converter. This is done by switching a braking resistance at thed.c. link as shown in Fig. 7.4. lf it is required that the generated power must

: Rp io I L r+ r L l t - t' - o , t

Control 217

flow back to the fixed a.c. supply, then use must be made of a so-called activerectifier. In the rest of this section only the switching and control of the d.c. toa.c. inverter of Fig. 7.4 is studied, assuming a fixed d.c.-link voltage.

ACsupply

Command feedback

Figure 7.4. Solid-state a.c.-a.c. converter and equivalent three-phase AFPM machine connec-tion.

The three-phase invefter of Fig. 7 .4 has six power electronic transistor swi-tches. Nowadays Insulated-Gate Bipolar Transistors (IGBTs) or MoS fieldeffect transistors (MoSFETs) are very popular for use as switches for the in-verter. The power transistor switches are switched on and off at a relativelyhigh switching frequency (typically from I to 20kHz or even higher). Eitherthe top transistor of an inverter-leg is switched on and the bottom transistoris switched off, or vice versa, or both transistors are switched off. It was ex-plained in the previous sections that only two phases of the converter-fed trape-zoidal AFPM machine drive are active at any time. The third phase is switchedoff by switching offthe top and bottom transistors of the inverter-leg connectedto that phase winding. The three-phase inverter of Fig. 7.4 also has six anti-parallel diodes to make current flow possible when a switch is turned off (thisis due to inductive stored energy) and also to make the generator (braking)operation of the drive possible.

The circuit diagrams of Figs 7.3 and 7.4 show that the trapezoidal AFPMmachine drive can be analysed by considering only the two active phases ofthe machine and the two active switching legs of the inverter. The circuit thenreduces to the general circuit of Fig. 7.5.

One method of controlling the power semiconductor switches of the inverlershown in Fig. 7.5 is explained as follows. consider in the forward speed di-rection that the voltage Eyr*r and the average current io@us) : I[uq) arepositive, then the average supply voltage up@rg) also has to be positive accord-ing to the steady-state equation, eqn (7.2), i.e. up(ood : Vp ) Eyr_r. Apositive average supply voltage can be obtained by switching on transistor Tu

SSC

,,-l+ *:-)

la

V,

" - ]

2t8 AXIAL FLUX PERMAI{ENT MAGI{ET BRUSHLESS MACHINES

Figure 7.5. Equivalent circuit ofconverter-fed trapezoidal AFPM machine (two phases active)

and pulse-width-switching (PWM-switching) transistors Tu and 7l of Fig. 7.5at duty cycles D and (1 D) respectively, such that in the steady-state

DV4: up(ous) (7.3)

where

+ f- c o n . t s (7.4)

andto,. is the switching-on time, f" is the switching period and, f " is the switch-

ing frequency of the transistors. This switching and the switching waveformof the supply voltage ?rp across the terminals of the two phases of the machineare shown in Fig. 7.6(a). As is shown up@,g) is the switching period averageof the volta1e up. Note that in Fig. 7.6 the drive is not in the steady-state as

the instant average current io@us) and the average voltage up@u!t) change with

time. Also note that the drive system only reacts on the average of the supply

voltage and not on the high frequency components thereof, as the switchingfrequency is relatively high and the time constant of the mechanical system isrelatively large.

Let us consider next the flow of cuffent in the converter and the machinein motoring mode. When transistors Tu and To of Fig. 7.5 ate switched on,

cuffent flows from the d.c. supply through Tu andthrough the machine winding

andTr, and then back to the supply. If ?l, and T, arc switched on, the curent

then free-wheels through diode D, and through the machine andTr. In this

case no current is flowing from or to the d.c. supply. An example of the phase

D:bLts

Control 2t9

winding and d.c.-link current waveforms in motoring mode is shown in Fig.7.6a. As mentioned before io@r,fi is the instant average of the phase curenti , o.

In generating (braking) mode with E I r L positive, the duty cycle D of eqn(7.3 ) is adj usted in such a way that u pGo g) < E y r _ L to allow i o@,ry) to becomenegative as shown in Fig. 7.6b. ln this case Do is always conducting and thecurrent either flows through 71, when switched on, or through D, to the supplywhen switched off. An example of the d.c.-link curent waveform in generatingmode is shown in Fig. 7.6b.

When operating the machine in the reverse speed direction, in which caseEyr,L is negative with respect to the polarity given in Fig. 7.5, transistor 2,, isswitched on during the conduction cycle and transistors I and T, are pWM-switched. In this case the supply voltage un(auo) is negative and the curent canbe controlled again to be positive or negative in the same way as in the forwardspeed mode.

The advantage of the above switching method is that only one inverter-legis switched at a high frequency at any time, keeping the switching losses ofthe invefier low Which inverter-leg of Fig. 7.5 should be selected to be PWM-switched is simply a logic decision that depends on the sign (positive or neg-ative) of the supply voltage u,@,s). Note that l)p(ouil is controlled directly bythe controller of the drive (Fig. 7.1).

7.1.3 Current controlFor good speed control of any drtve a.fast torque control is necessary. Ac-

cording to eqn (2.120) the torque of the trapezoidal AFPM machine drive canbe controlled directly by controlling the stator current io and hence the in-stant average current io@oti explained in Fig. 7.6. Close examination of thecurrents of Fig. 7.6 reveals that the required information regarding the cur-tent 'io1oon1 is also present in the average d.c.-link current i,I1ors1, i.e. if thesample-measurement of current i,4 is at the right instant. The current of all thephases of the machine can be controlled by just controlling the d.c.-link currenti46us1.Thus, only one current sensor is necessary. One aspect of this methodof current sensing, however, must be kept in mind. If the machine is operating,e.g. in forward motoring mode or reverse motoring mode, then in both casesthe cument i,t1o,,s1 will be positive. This creates a problem from a control pointof view as the reference current io,(,r,,s)* will be, say, positive for forward mo-toring mode, but negative for reverse motoring mode. Howeveq this problemcan easily be solved in the controller by always multiplying the d.c.-link cur-rent signal with the sign (positive or negative) of the controlied supply voltageup(oug)* signal.

A block diagram of the single sensor current controller is shown in Fig.7 .7 . The current controller acts on the comparison between the desired current


t,

'o ',

l

D" i- - -1T :

I p(^9,

vd

(a) (b)

Figure 7.6. Voltage and cuffent waveforrns of a converter-fed trapezoidal AFPM machine: (a)

motoring mode; (b) generating mode (see Fig. 7.5).

io1oud* and the measured d.c.-link cuffent i,J(aua), and then controls the supplyou@ut voltage by controlling the signal uolorsy*. The PWM generator outputsthe PWM signal in terms of a logic I or 0 to the programmable logic device(PLD). The sign (positive or negative) of up6,,s)* is also an logic input (1 or0) to the logic device. Three logic position signals sn, s6 arrd sc are also inputsto the PLD. These three signals are received from three Hall-effect sensorsmounted in the machine. The signals supply information about which twophases must be active according to the rotor position. The outputs of the PLDdirectly control the switching of the six power semiconductor switches.

lo

0

Id

0

Control

Two aspects in the block diagram of Fig. 7 .7 have not been referred to yet.The first is that a speed voltage signal is added to the output of the cuffentregulator. This is to decouple the current regulator from the effects of speedvariation. The gain, 1{i, represents the gain of the solid-state invefter. Thesecond aspect is that the d.c.-link current is sampled at certain times to get theaverage valte'i61oon) as shown in Fig. 7.6.

Figure 7.7. Block diagram of single sensor current controller for trapezoidal AFPM.

To determine the parameters of the current regulator the transfer functionof the current control system must be obtained. According to Fig. 7.3b andeqn (7.1), the dynamic voltage equation of the machine in terms of averagecomponents is

221

n,up(oud : Rpioloos) * L,

, l t i , t ' ,6 * E7t-r (7.s)

where up : up(o"-g) * Itr,'io : io(oug) i i,r., and u, and i," are the ripple voltageand ripple current respectively (see Fig. 7.6). ln Laplace transform eqn (7.5)becomes

up(at,s;(s) : (Eo * Lrs)i.o1ouel(s) + Eyr-r(s) (1.6)

With the use of the decoupling speed voltage signal in the current controlsystem of Fig. 7.7, the speed voltage term E f r r(s) of eqn (7.6) has no effecton the current regulator's response. Hence, the control block diagram of thecurrent control system can be represented by the block diagram shown in Fig.7.8. In this block diagram the current regulator can be, e.g. a gain or a PI-regulator. The gain 1{,; represents the voltage gain of the solid-state converter


(inverter) as mentioned before. The transfer function of the current control sys-tem can be determined from the block diagram of Fig. 7.8 and the parametersofthe current regulator can be designed according to classical control systemmethods.

Figure 7.8. Block diagram of decoupled cuffent control system.

7.1.4 Speed controlWith the cuffent control system in place, as explained in section 7.1 .3, a

speed control loop can be applied around the current control loop. The electri-cal and mechanical torque balance equations for the system are as follows:

Talou s1ft) : k7,1.io1ore; (s)

Ta lous ; ( r ) - f r ( " ) : (B+ J .s )c , : (s )

(7."1)

(7.8)

where ";(s)

is the load torque, B is the equivalent total damping ofthe system,J is the equivalent total moment of inertia of the system and a is the rotorspeed in radls. For a two-pole machine the angular mechanical speed is equalto the angular frequency of the stator currents. Note that eqns (7.7) and (7.8)refer to the instant average components of current, torque and speed, and notto the high frequency ripple components due to the inverter switching. Fromequations (7.7) and (7.8) and from Fig. 7.8, the speed control block diagram ofthe system can be represented as in Fig. 7.9. Hence, the transfer function of thespeed system can be determined and the parameters of the speed regulator canbe designed to obtain a certain speed response. A speed signal can be obtainedelectronically from the signals of the three Hall-effect position sensors installedin the machine.

7.1.5 High speed operationEquations (2.118), (7.2) and (7.3) show that as the speed of the machine

increases, the EMF Eyr-t, the voltage urdorlt) and the duty cycle D will in-

Control zz)

Figure 7.9. Block diagram of speed control system.

crease till the speed is reached where D becomes unity. The speed where ,becomes unity is simultaneously the speed where the output voltage of the con-verter (inverter) reaches a maximum. This speed is often called the base speedof the drive. Field or flux weakening in the high speed region of the machineto keep E y t,- r : constant is not possible with high-energy-product surfacemounted PMs. Therefore, at speeds higher than the base speed, Eyr-r ) V,t,and control of the current and torque of the machine is lost. In fact, the currentand torque rapidly drop to zero at speeds slightly above the base speed. Thisimplies that the speed-range of the trapezoidal AFPM machine using surfacemounted PMs is very limited. Techniques to increase the speed substantiallybeyond base speed are: (a) change smoothly from a 120" current conductionperiod, as discussed earlier in this chapter, to a 1B0o six-step conduction pe-riod [17, 89, 208] and (b) advance the current wave with respect to the EMFwave [125]; note that during sub-base speed operation the current wave is con-trolled to be in-phase with the EMF waveform as shown in Fig. "1.2c. Thedisadvantages of these techniques may be the following: (i) an increase in ma-chine torque ripple, (ii) danger of converter switches being exposed to highDC-1ink voltages if for some reason the converter switches are switched-offat high speeds (at this condition the high EMFs are rectified by the six diodesof the inverter to a high d.c.-link voltage) and (iii) a higher resolution positionsensor is necessary for the smooth advancing of the current wave as the speedincreases.

A technique to obtain high speed operation that avoid the disadvantages ofthe above techniques and obtain true flux weakening is to increase mechani-cally the air gap of the AFPM machine with increase in speed; this techniqueis not possible in commercial RFPM machines. However, it is questionable ifthis technique is economically viable.

7.2 Control of sinusoidal AFPM machineSinusoidal AFPM machines are designed to have sinusoidal or near sinu-

soidal EMF waveforms. Therefore, in variable speed drive applications where

224 AXIAL FLUX PERMANENT MAGNET BRT]SHLESS MACHINES

a solid-state converter is used to supply the machine (Fig. 7.i), the output volt-age of the converter must be sinusoidal or sinusoidal PWM modulated. Hence,the current in the machine is sinusoidal or else the current regulators of thedrive will force the phase currents to be sinusoidal.

This section focuses on the control aspects of the sinusoidal AFPM machinedrive. First, the modelling and equivalent circuits of the sinusoidal AFPMmachine are described. Secondly, the current and speed regulators of the driveare dealt with. Finally, the hardware of the sinusoidal AFPM machine drive isconsidered.

7.2.1 Mathematical model and dg equivalent circuitsThe phase voltage equations of any three-phase a.c. electrical machine can

be written as

. . , ,u l A B ( ' : n I t a A B C , d t

(7.e)

where tb.qsc is the total stator magnetic flux linkage of phase A, B or C * eqn(5.20). Eqn (7.9) is expressed in the so-called ABC stationary reference framewhere the circuit variables (voltage, current and flux linkage) are expressedin a reference frame that is fixed to the stationary stator. For synchronousmachines, like the AFPM machine, it is very convenient to kansform or referthe stationary stator variables to a reference frame that is fixed to the rotor.In this transformation the stationary ABC stator windings of the machine arereplaced by fictitious dgO windings that rotate with the rotor.

To explain this, let us consider the cross-section of a two-pole AFPM ma-chine as shown in Fig.7.10a (side view) and Fig. 7.10b (front view). Fig.7.10a shows that the PMs are embedded into the rotor steel yoke, but the mag-nets in the sinusoidal AFPM machine may also be on the surface of the yokelike in atrapezoidal AFPM machine. With the magnets embedded, the AFPMmachine is not a pure PM machine anymore, but a combined PM-reluctancemachine because the electromagnetic torque has two components: PM syn-chronous torque and reluctance torque.

Fig. 7.10 explains the ABC and dq winding layout of the machine. Therotating d and q-axis windings are in quadrature of each other and their mag-netic axes are aligned with the d and q-axis of the rotor. In this case thed-axis of the rotor is chosen to be aligned with the centre lines of the PMs andthe g-axis between the magnets. The position of the rotor and dg-windingswith respect to the stationary ABC windings is defined in Fig. 7.10 as the an-gle between the rotating d-axis and the phase , -axis. Note, that in Fig. 7.10bthe direction of the flux (O) is into (or out ofl the paper (z*direction), whilethe current is in the ry-plane.

Control

o, --"t,iru--{a/

nttt '

iotr .'

(b)

Figure 7.10. Stationary ABC androtating dq windings of a simple two-pole AFPM machine:(a) side view; (b) front view (PMs are shown in dotted lines).

To transfer the circuit variablesto the dqO reference frame, or vice

from the stationary ABC refercnce frame

225

IL

versa, the Park transformation

: lKpllf ascl

d - axis

lfano) (7. l 0)


and inverse Park transformation

lf anc) : lKp) t

lfonol (7 . l l )

are used [86], where llfpl is according to eqn {5.26) and lkpl-i is the inversematrix of lKp). In the above eqns (7.10) and (7.11), faqo and f asg are thedq} and ABC vanables of voltage, current or flux linkage respectively. Ineqn (5.26) the angle 0 is the electrical angle defined in Fig. 7.10. With a con-stant rotor angular velocity cu the angle 0 : at. For a balanced three-phaseAFPM machine it is only necessary to consider the d and q-axis circuits asthe zero-sequence circuit is playing no role in the performance of the machine.Applying eqn (7.10) to the voltage eqn (7.9) leads to the dq voltage equations(5.5) and (5.6) of the balanced AFPM machine (omitting the zero-sequencecomponent). In eqns (5.5) and (5.6) u is the electrical speed of the rotor, andtlta and tftn arc the d and q-axis flux linkages. Let us consider the followingthree cases of operating conditions of the AFPM machine:

(I) The first case is when the machine is open circuit and is mechanicallydriven at a certain speed cu. The dq stator currents, thus, are zero andonly the magnets are active. From Fig. 7.10 rt is clear that the magnetflux will only link the d-axis winding and not the q-axis winding. In thiscase tf,tn: 0 and rha : tbf , and from eqns (5.5) and (5.6) ura : 0 andu 4 : a $ 1 '

(ff The second case is when both the magnets and the d-axis winding arenot active, but d.c. (steady-state) current is flowing in the q-axis statorwinding. The dq stator windings and the rotor are at a rotating speed of u.,.Clearly with no magnets and no d-axis current, lba : 0. With positive d.c.q-axis current, i.e. ion: t/2loq, then ,ltn: t/lL"nloowhere ;,", is theq-axis winding synchronous inductance. Note that the relation between$q and ion is nonlinear due to magnetic saturation; L"o wlll thus vary withsaturation. From eqns (5.9) and (5.10) it follows in this case that ,rn :Rfi,r,, and u1g : -wL"ndor,

(III) In the third case only the d-axis winding is active in terms of a positived.c.currentflowing of io,1 : uEloa. Therefore rlrq:0asthemagnetsarenot active and don : 0, and da - J2L

"41o,1 where.L"4 is the synchronous

inductance of the d-axis winding. Again, the relation between da and i,oais nonlinear and L"4 will vary with saturation. In this case from eqn (5.9)and (5.10) u1n : aLr4'io4 and u6 : Rliod.

If the magnets and the dq stator windings are active, then the above threecases can be summarized.by eqns (5.7) and (5.8). From eqns (5.5) to (5.10) itfollows that the electromagnetic power of a three-phase machine is given by

Control 227

(7.r2)Perrn : |O"nrr1to

ioaw'{q) : }r(.rbo'i"n

- |)qi"a)

The factor 3l2has been explained in Section 5.13. The developed torque ofthe machine is expressed by eqn (5.13). The first term in eqn (5.13) expressesthe torque component due to PM excitation, while the second term expressesthe reluctance torque component. For surface mounted AFPM machines it canbe assumed that L"6: L"q, hence the torque is directly proportionalto ior.In the case of an embedded AFPM machine like in Fig. 7.10a it is clear thatL"d 1 -L"n, which implies that i,o4 in eqn (5.13) must be negative in order togenerate a positive reluctance torque. Fig. 7.1 la shows the phasor diagrams ofthe motor for i,o4: 0 while Fig. 7.1 lb shows the phasor diagram of the motorat unity power factor.

- aL,riu,

(a) (b)

Figure 7.1 L Phasor diagrams of and overexcited AFPM motor: (a) for i."a : 0; (b) at unitypower factor.

The inductances in the d and q-axis windings are expressed by eqns (5.17)and the magnet flux linkage T/1 is further expressed as

4' t : L"ai f (7.13)

where Lo4is the armature reaction (mutual) inductance in the d-axis and zy isa fictitious magnetising current representing the PM excitation.

The flux linkage and mutual inductance between the d-axis winding andthe fictitious permanent magnet (field) winding need further explanation. For

q-axls q-4"\rs


the d-axis winding we have the following equation (ignoring cross couplingeffects with the q-axis winding and ignoring any stator slotting effects):

dr!adt

, dio,l , , dlt: Lsd--- l l - t Lfd ," - d l " ' d l

(7 .14)

: (Lr I Loa)4: ,0 * t ,o*dt d,r

where Loa is given by eqn (2.109) and L1 is a leakage inductance. 17 is thefictitious magnet (field) winding current. L y4is the mutual inductance betweenthe d-axis winding and the fictitious magnet (field) winding given by

(7.1 s)

where k-f NJ and fo.rl/r are the effective turns in series of the fictitiousmagnet-field and d-axis windings respectively. o4,r and @ya are the propor-tions of flux produced by the d*axis and magnet-field windings respectivelythat link with the opposite winding. Note that in this case o/d is equal to oyof eqn (2.19). From eqn (7.15) the flux linkage of the d*axis winding due tothe field winding, Ty';, is given by

$f : k-t l/rOfa : Lyaly (7 .1 6 )

However, this flux linkage is also expressed by eqn (7. l3) and is represented inthe d-axis equivalent circuit of Fig. 7 .12b. Hence, from eqns (i .13) and(7.16i)

L , ,i r - , ' " I I ( 7 . 1 7 1" Lod.

Furthermore, the d-axis inductance Lo4 is given by eqn (2.109) as

r. , *ua,o -k.*1N1Qu,1

(7 . r 8)

where Qo4 is the d-axis flux passing the air gap, linking the rotor. The totalflux of the d-axis winding, (D4, is given by

iDa : Ol -f Qod, (7.1e)

where Q7 is the leakage flux. Now, if O;i of eqn (7 .15) [this is the proportion ofthe flux produced by the d-axis winding that links the field windingl is equal

r . * k , 1 N y Q a 1 _ k , r N 1 O l a" J d - I *

- t ,

Ioa

Control 229

to kQo6, i.e. @ay : kQad,where 0 < k < 1 (i.e. not all the d-axis flux linkingthe rotor necessarily links the fictitious magnet-field winding), then from eqns(7.15) and (7 .l8) it follows that

Lad:l##fr)',,and fuilhermore from eqn (7 .17) that

(7.20)

(7.21)

Hence, if the effective turns of the d-axis and field windings are the same andk : l, then Loa is equal to L y a and i, 1 is equal to Iy.

Using eqns (5.7), (5.8) and (7 .13) and assuming z 1 is not varying with time,eqns (5.5) and (5.6) can be written as

. l k * 1 N y k l -' r : | 1rf f i l t r

r tv l - Rf io4 + (Lr * t"o)T - a(Lt I Loq)ioq (7.22')

uvn : Rf io, * (Lt + L")* * u(h I Lo,1)zoa - l aLoaiy (7.23)

On the basis of eqns (1 .22) and (7 .23) the complete dq equivalent circuits ofthe sinusoidal AFPM machine can be drawn as shown in Fig. 7.12. It shouldbe noted that the modelling according to eqns (7.22) and (1.23) is based onassumptions that

(a) there are no core losses;

(b) the magnetic circuit is linear, i.e. there is no saturation of the magneticcircuit;

(c) there is no cross magnetisation or mutual coupling between the d- andq-axis circuits;

(d) there are no stator slotting effects (smooth stator core).

7.2.2 Current controlThe equivalent circuits of the sinusoidal AFPM machine shown inFig. T .I2

can be used to design the current regulators for controlling the d and g-axiscurrents of the machine. Applying the principle of speed voltage decoupling,

230 AXIAL FLUX PERMANENT MAGAIET BRUSHLESS MACHINES

(a) (b)

Figure 7.1 2. The d and q-axis equivale nt circuits of the sinusoidal AFPM brushless machine.

as for the trapezoidal AFPM machine (section 7.1.3), the dq culrent controlsystem of the sinusoidal AFPM machine can be represented by the block dia-gram of Fig . 7 .13. Here, the d arrd q-axis current regulators act on the enorsbetween the desired and actual dq currents of the machine. The speed voltageterms are added (or subtracted) to the outputs of the regulators to determine thedg machine voltages. Within the machine model the speed voltages are sub-tracted (or added) again, hence the regulators act only on the RL*parts of theequivalent circuits. The block diagrams of the decoupled current controllerscan therefore be simplified to those shown in Fig. 7.14. With the equivalentcircuit parameters of the machine known, the transfer functions of the d andq-axis cuffent controllers can be determined and the d and q-axis current reg-ulators canbe designed accordinglyto obtaintherequired dqcurrentresponse.

7.2.3 Speed controlIt is always good in terms of efficiency to control the drive at maximum

torque per ampere. For the surface mounted (nonsalient) AFPM machine,where it can be taken that Lsd, : L"n, it is clear from eqn (5.l3) that maximumtorque per ampere for this machine is obtained by keeping iod : 0. However,for embedded (salient-pole) AFPM machines where L"a * -L"n, maximumtorque per ampere is obtained by making io,1 negative, that is by controllingthe current phasor at some current angle V as shown in Fig. 7.15 (see alsoFig. 7.11b). Note from Fig. 7.15 that negative torque is obtained by keepingboth'ir,1, and 'ion negative, or in the case of the nonsalient machine, only ,io,

is negative. In the sub base speed region (a < ,) of the drive, where thereis enough voltage available so that the current regulators do not saturate, themachine is controlled to operate at maximum torque per ampere. For the non-salient AFPM machine this implies that the current angle V : 0, while for thesalient-pole machine iF : Vo (see Fig. 7.15), which is an (average) optimumangle for all load conditions.

Control 231

dq Cument controller

Lu,l i +

-t@L,qiq

aLri,,

Figure 7.13. Block diagram ofd and q-axis current control system ofthe AFPM drive irnple-menting speed voltage decoupling.

(b)

Figure 7.14. Decoupled d and q-axis cuffent control systems

However, in the high speed region (a > wu), the EMF voltage wLo4i,y :

at!y of eqn (7.23) (see also Fig. 7.11b) becomes larger than the possible out-put voltage of the inverter. The current regulators therefore start to saturate,

R, + lus

232 AXIAL FLUX PERMANENT MAGNET BRUSHLESS MACHI],{ES

culrent control is lost and the torque of the machine rapidly drops as the speedincreases. To avoid this torque decrease and to ensure a wider high-speed re-gion one has to deviate from the maximum torque per ampere control and startto inject a larger negative d*axis current to reduce the g*axis terminal voltage(Fig. 7.1 lb) as the speed increases. This implies that the current angle v mustbe increased as shown in Fig. 7.15, keeping the current amplitude equal or lessthan the rated curent amplitude depending on the load. At a maximum currentangle, V-, the speed range can be extended much more if the current angle isheld constant at tlr : v- and the amplitude of the phase current is reduced asshown in Fig. 7.15. Note from Fig. 7.1lb that as the curent angle rlr increasesthe apparent power of the machine decreases and the power factor improves.

The above current control strategy can be used for both salient and non-salient AFPM machines. It must be noted, however, that the speed range ob-tained with the above control method depends very much on the value of thestator phase inductance of the machine (see Numerical example 7.2). If thephase inductance is relatively small (this implies a low per unit stator phasereactance), as is the case with slotless and air-cored AFPM machines, the highspeed range of the machine is very limited.

From above, thus, the current of the machine can be controlled by control-ling the magnitude of the current and keeping the current angle constant at anoptimum value, and advancing the current angle at higher speeds. To simplifzthis control method, the current angle \Ir is defined as a positive angle between0 to 90". The current angle is also taken as a function of the absolute value ofthe speed, lo'1. Furlhermore, a current i7 is defined, which controls the torqueof the machine and is proporlional to the current amplitude of the machine.Hence.

i o,t : - l17'l sin tl.t

iaq ri7 cos V for iI/ > 0 ('7.24)

Substituting eqn (7.24) into eqn (5.13) and noting that Lra{L"o, the electro-magnetic torque is

Ta - 3ptb f i7 cos(V) + f,nQ"n

- L",t)ir.lirl sirr(2V) (7.2s)

It can be seen from the first term of eqn (7.25) that there is a linear relationbetween the PM torque component and the cument i7 for a given current angleV. The second term of eqn (7 .25) is the reluctance component of the torque.It is found for reluctance machines [32] that the inductance difference A,L :Lsct L"a is not a constant at a ceftain current angle, but varies inverselywith load current z7 due to saturation and cross magnetization. The cross

Control a 1 a

Figure 7.15. Current phasor control ofthe AFPM drive in the low and high speed regions ofthe machine.

magnetization or cross coupling is the magnetic coupling between the fictitiousd and q-axis windings of the machine. It is thus a fairly good approximationto assume for this component of the torque a linear relation between reluctancetorque and current i7 for a given cuffent angle V [134]. Thus, eqn (7.25) canbe simplified as

Ta x kyli,y * k7y.1i7 x k7i1. fbr V : consta?Lt (7.26)

where lryl and k7r"1 zte the PM torque and reluctance torque constants, re-spectively, and k7 : krf * kr,d. Note from eqn (7.26) that to generatea negative torque, ri7 must be negative; V is taken in the control as a posi-tive quantity between 0 to 90". ln the case where V : 0, then k7r.1 : Q,kr : Kr f : 3prl, r 12 and, i,7 - ias.

With the current control strategy in place and with the torque as a functionof current as given by eqn (7.26), a speed controller for the AFPM machinedrive can be implemented around the current controller as shown in Fig. 7.16.


The block diagram of Fig. 7.16 describes the basic principle of the current andspeed control of the AFPM machine drive. The speed regulator acts on theerror between the desired and measured speed of the system and controls thecurrent i7 of eqn (7 .26). The maximum curuent of the machine is limited bythe limiter as shown in Fig. 7.16. The current angle V is, as a positive quantity,a function of the absolute value of the speed of the machine, lu.'1. as shown inFig. 7.16. In the low speed region the angle IF is kept constant. In the speedregion above the base speed (a > ai the angle V is increased with speed.In the very high speed region the angle I[ is kept constant again. With thecurrent and curuent angle V known, the desired dq cunents, ,io,1* and ior* , aredetermined by eqn (7 .24). With the measured speed and measured dq currentsas the other inputs, the current controller outputs the necessary dq voltagesaccording to the block diagram of Fig. 7.13. These voltages are transformedto ABC voltages using the inverse transformation given by eqn (7.11), andare then put through the PWM generator to control the inverter and hence theterminal voltages of the machine.

It must be noted that the speed control method of Fig. 7.16 is only one wayof controlling the speed of the PM brushless motor and is recognized as a basicmethod. Several other techniques and algorithms for wide-range speed controlofPM motor drives have been proposed 122,53,126, 152,164,249J and canbe applied to the speed control of the sinusoidal AFPM brushless motor drive.The important aspect is the prevention of saturation of the dq cunerftregulatorsin the high speed region of the motor.

To design the speed regulator of the system of Fig. 7 .16 a few approxima-tions can be made to simplifz the model of the speed control drive. Firstly,the mechanical time constant of drive systems is in general much longer thanthe electrical time constant of the drive so that the latter can be ignored. To-gether with this, a good approximation is to assume that the current controllersare forcing the actual currents equal to the command (desired) curents, i.e.iod" : iod*, ioq : ioq*, and iy : i,r*. Applying further eqn (7.26), the speedcontrol system can be simplified to that shown in Fig. 7.17. From the simplifiedcontrol system the approximate transfer function of the system can be deter-mined and the speed regulator can be designed to obtain the required speedresponse.

7.2.4 Hardware of sinusoidal AFPM machine driveFor the sinusoidal AFPM brushless motor the same solid-state converter as

for the trapezoidal AFPM brushless motor can be used (Fig. 7.4). A more de-tailed diagram of the hardware of the sinusoidal AFPM brushless drive systemis shown in Fig. 7.18. The fixed a.c. supply voltage is rectified by means ofa diode rectifier or voltage-source controlled (active) PWM rectifier to obtaina fixed d.c. voltage. The d.c. voltage is then inverted by means of a voltage-

235Control

L Rs ;

. i :

ili fll- f ^ia >:-

236 AXIAL FLUX PERMAI,IENT MAGNET BRUSHLESS MACHINES

Figure 7.17. Biock diagram of simplified speed control system.

source PWM inverter to a three-phase a.c. voltage of variable frequency andmagnitude. The difference between the trapezoidal and sinusoidal drives liesin the PWM switching-control of the inverler bridge. In the case of the trape-zoidal AFPM motor drive, quasi-square PWM voltages are applied, whereasin the case of the sinusoidal AFPM motor drive, sinusoidal PWM voltagesare applied and the phase currents of the stator are sinusoidally regulated asdescribed in the previous sections.

The peak value of the fundamental frequency voltage component of theinvefter-legs of Fig. 7.18 with respect to the neutral point l/ is clearly jV6. nsthe fundamental frequency voltage components of the inverter-legs are 120"out of phase, the maximlrm rrns line-to-line voltage of the inverter at the fun-damental frequency with sinusoidal PWM is

VrL-L^o" : 0 .612Va (7.27)

This result shows the limitation on the maximum rms output voltage of theinverter. This affects, amongst other things, the maximum speed at which ratedtorque can be delivered by the drive (see Numerical example 7.2).

The currents in the three phases of the AFPM machine drive are sinusoidallyregulated. There is, however, a ripple in the phase currents due to the PWMswitching. It can be shown that the peak-to-peak ripple in the phase curent,L,'ip-p, is directly proportional to

'/5vo: - -Jt2

L i r - , - =Vo,t rh ls

('7.28)

where /" is the switching frequency of the inverter and Ly,nthetotal load induc-tance per phase ofthe inverter. The ripple current is thus inversely proportionalto Lon and, f ,. Note that Lph can be increased by the addition of an extemalinductor in series with the stator (armature) of the AFPM machine as shown

Control a f ?L J I

in Fig. 7.18. Careful consideration should be given to the selection of Lrt" and

"f". As the air gaps of AFPM machines, specifically those AFPM machineswith coreless and slotless iron-cored stators, are relatively large, the internalphase inductancas of these machines are relatively small. Thus to keep theripple current in these machines within limits, the switching frequency /" isrequired to be high. With power MOSFETs the switching frequency can bemade high (say /" < 50 kHz), but with IGBTs in the medium-to-large powerrange the switching frequency is very much limited to l, < 10 kHz. In such acase the phase inductance must be increased. The high ripple current that canoccur in most of the AFPM machine drives is often overlooked. A high ripplecurrent has serious consequences on the curent rating ofthe inverter and theefficiency, stator winding temperature, torque quality and acoustic noise of theAFPM brushless motor.

For rotor position feedback of the sinusoidal AFPM drive a position sensorwith high resolution is necessary. Resolvers are often used for this as they arerobust and can be used in harsh environments. Integrated and analog circuitryare necessary to interface the resolver with the digital controller (see Fig. 7.18).Digital interface outputs of up to 16 bit resolution are possible. Normally 12bit resolution gives more than enough accuracy for position feedback.

A11 the measured information of voltage, current and rotor position are fedto the digital controller as shown in Fig. 7.18. The controller outputs PWMsignals via fibre optic links to the inverter bridge. Digital signal processors(DSPs) are nowadays frequently used as drive controllers [227]. Examplesof dedicated fixed point DSPs from kxes Instruments include TMS320F240(20 MHz), TMS320LF2407A (40 MHz), TMS320F2B12 (150 MHz). TheseDSPs have 12 or 16 PWM channels, 16 A/D channels ( l0 or l2 bit resolution)and operate at frequencies of between20 to 150 MHz. ln another recent de-velopment on drive controllers International Rectifier introduced their motioncontrol chipset IRACO2l0 [99]. This chipset uses a high speed configurablefield programmable gate array (FPGA), tightly coupled to gate driver and cur-rent sense interface chips. In this way flexible drive control algorithms areimplemented in FPGA hardware, rather than in software,

7.3 Sensorless position controlIt is obvious that information of the rotor position of the AFPM brushless

motor is absolutely necessary for proper cuffent and speed control. For trape-zoidal AFPM motors a low resolution position sensor may be used, but forsinusoidal AFPM motors a high resolution position sensor is necessary. Theuse of a position sensor that is mechanically connected to the machine and elec-trically connected to the controller reduces the electromechanical drive systemreliability and increases its cost. Moteover, in some applications insufficientspace may make the use of a position sensor difficult. Sensorless po,sition con-

Ivd

I{

238 AXIAL FLLIX PERMANENT MAGNET BRUSHLESS MACHINES

Figure 7.18. Hardware of sinusoidal AFPM drive system.

trol techntques, in which an accurate information of the rotor position can beobtained without the need of a mechanical sensor, are superior.

Various methods and techniques have been proposed the last two decades forthe sensorless position control of PM brushless motors. Most of these methodsare based on the measurement of the voltage andlor current of the machine.Thus, instead of using a mechanical sensor, electrical sensors (not mounted inthe machine but placed at the solid-state converter) are used to obtain the rotorposition signal. ln this way, the position of the rotor is determined indirectly,as measured electrical quantities together with the model of the machine areused. State observers, filters and other calculations are used to estimate themechanical position of the rotor.

The methods of sensorless control can be classified into two types: (i) meth-ods that are based on the back EMF estimation l2l, 82,242f, and (ii) methodsthat make use of the magnetic saliency present in the machine ll27 , 154, 155,209]. The EMF measurement is not suitable for low and zero speed operationof the motor as the induced voltage is proportional to the rotor speed. At standstill, the induced voltage is zero and there is no position-information anymorein the stator quantities. The second method, which makes use of the mag-netic saliency, is more suitable for the detection of the rotor position at lowspeeds and standstill. With this method either test voltage pulses are appliedto the machine or additional high-frequency signals superimposed on the fun-damental voltages (or cunents) are injected. The injection of the revolvinghigh-frequency voltage vector is commonly used. All these methods can beused successfully for the position sensorless control of AFPM motor drives

Control 239

[187]. However, it is still questionable if the high-frequency injection sensor-less control method can be applied to coreless type AFPM brushless motors asthese machines have practically no magnetic saliency.

Fig.7 .19 explains the basic principle of the high frequency voltage injectionsensorless position control technique. High frequency voltage signals are in-jected to the system by adding them to the dq voltage signals u14 and u1,7 ofthe drive. The current response of the drive system to these voltage signals ismonitored by band pass filtering (BPF) the dq cut:rents, so as to obtain the highfrequency current components i,o41, and ion7r. These high frequency currentcomponents contain information about the rotor position as they are affectedby the magnetic saliency of the machine. These currents, together with thehigh frequency injected signals are used by an observer or position estimatorto estimate the rotor position 0^. A low pass filter (LPF) is furthermore used toextract from the dq currents the fundamental current components ios and ion,which are necessary for the fundamental current controller of the drive (Fig.7.13). The frequency of the injected voltage signals must be much higher thanthe fundamental frequency, but also much lower than the switching frequencyof the inverter, and is typically between 500 Hz and2k}{z.

High liequency vof tag ",rr1""t

on -j

rotor position cstirnaior

Fipre 7.19. High frequency voltage injection sensoriess position control.

Numerical example 7.1A small, 35-W 4300 r/min, 12 pole, Y-connected air-cored, trapezoidal

AFPM brushless motor is used as part of a reaction wheel for a micro-satellite(see Fig. 7.20). Reaction or momentum wheels are used on satellites to keepthe satellite steady and to orientate it. Orientation control is necessary as, e.g.the photovoltaic panels must be pointed at all times to the sun for maximum

240 AXIAL FLUX PERMANENT MAGI{ET BRUSHLESS MACHINES

power generation. The motor has a stator phase inductance of -L" : 3.2 Lr,H anda phase resistance of fi1 : 22 rn0. The motor is fed by a 3-phase MOSFETinverter withVa: 14 V and is under square-wave cufrent control as describedin Section 7.1.3. Assuming the voltage drop across a MOSFET switch duringswitching-on as I V, calculate:

(a) the switching frequency /" of the invefter;

(b) the extemal phase inductance required for a maximum peak-to*peak ripplecurrent less than 0.5 A if f" :40kHz.

Figure 7.20. Small coreless AFPM brushless motor. Photo courtesy of the Lrniversib, of Stel-lenbosch, South Africa. Numerical example 7.l.

Solution

First, an approximate equation for the maximum peak-to-peak phase cur-rent ripple of the motor must be derived. For the circuit shown in Fig. 7.5during switching-on, i.e. with the transistors fl, and Q switched on, assum-ing ideal transistor switches and assuming the drive is in the steady-state, thevoltage equation (7.l) canbe written as

v4 : RrIu - R,pi, + tod',i - E.rt L- d,t

(7.2e)

where the phase current 'io : Io + ir, Io is the steady-state average current andz, is the ripple current. Putting eqn (7.3) and neglecting the voltage drop Rri,,eqn (7 .29) can be brought to

, di,"P ,rt

Va - DVa rt (7.30)

Control

From eqns (7.4) and (7.30) the peak to-peak ripple current Ai, is

241

The maximum peak-to-peak ripple curent will occur at a duty cycle of D0.5, hence

n ; _ V a ( l - D ) f o r , _ V a ( l

- D ) DA a , -' Lo LrI"

Li,^o, = J!-4LPJ

"

( 7 . 3 1 )

(7.32)

(a) Switching frequency. Using eqn (7 .32) and taking into account the voltagedrop across the transistor switches, the switching frequency for a maximumripple current of 0.5 A is

" w -2+ NJs - ;-; *- -

4L pl \zrmox

t 4 -24 . x ( 2 x 3 . 2 x 1 0 6 ) x 0 . 5

: 937.5 k}fz

(b) External inductance. Eqn(7.32) gives the following additional phase induc-tance required to keep the ripple current less than 0.5 A at f u : 40 kHz:

_ 1Lph(atid) x

,

Va-2f _

1 4 - 24f ,Li,,,o" 4 x 40 000 x 0.5

-3.2x10-o : 71.8 pH

(7.33)

These results show the low phase inductance problem of coreless AFPMbrushless motors when fed from solid-state invefters. Either the switching fre-quency of the inverter must be high or relatively large extemal inductors mustbe added in series with the phase windings of the machine to keep the ripplecurrent within limits. Usually, external inductors are used, as a high switchingfrequency causes the power losses in the inverter to be high.

Numerical example 7.2Consider a 75-kW, 460-V,105-A, Y-connected, 700-H2,1500 r/min, 8-pole

AFPM motor with single PM rotor disc and double slotted stators connectedin series. The equivalent circuit parameters and flux linkage of this machineare: R1: 0.034 d), L"d - Lsq : 2.13 mH,'$f : 0.538 Wb. The machine isunder dq cunent control by using, amongst other things, a three-phase IGBTvoltage-source inverter with d.c.-link voltage Va - 755 V. Find:

(a) the maximum speed and the developed power of the drive with the machineat rated current and the machine controlled at maximum torque per ampere;

1 A aL A L AXIAL FLUX P ERMANENT MAGNET B RUSHLE SS MACHINES

(b) the per unit high speed of the drive developing the same power as in (a)with the drive at rated current, rated voltage and using an advanced cuffentangle.

Solution

(a) Maximum speed and electromagnetic power

With a surface-mounted AFPM machine maximum torque per ampere isobtained with i,oa: 0 A. Thus, at rated stator current ioq : t/2 x 105 : 148.5A. To obtain maximum speed the output voltage of the invefier must be at amaximum, i.e. from eqn(1.27)therms phase voltageVl :0.612x 7551\/3 :

266.8 V. Thus, the peak phase voltage, V1,, : 1/1 x 266.8 : 377.3 V andT

note that Vr^ : tluu2 I ,to'. By considering the drive in the steady statev

and ignoring the resistive voltage drop, from eqn (7.22), eqn (7.23) and Fig.7.11 we have

u1-d" : Vrrnsin d = -a L"nion (1.34)

u1n: Vlpcos6 x wtf ;y (7.3s)

From this

. u b o t t l oL a n d = 'v.f

- 2 .13x10*3x148 .5

0.538

377.2 v s in ( -30 .45)

and d = -30.45"

: 604.5 racl/s

Using eqn (7 .34) the angular frequency is

V1- sirr dw - _

- L s q x , q -2 .73 x 10 - ' x 148 .5

and the mechanical speed O : S\alptr : 7443 rpm. The maximum speedwith maximum torque per ampere control is thus just less than the rated speedof 1500 r/min of the machine. Using eqn (7.34), an approximate equation forthe steady-state electromagnetic power (7 .I2) can be found as follows:

P,r* era Iu1 o;"n=irW)sind

x sin(-30.45) r 72.45 kW

(7.36)

.)Z

243

which is also just less than the rated power of 75 kW of the machine.

(b) Per unit high speed

The speed of the AFPM brushless motor can be increased beyond base speedby increasing the current angle !I, as shown in Fig. 7.1l(b), keeping the peakvalue of the sinusoidal phase current Io : consto,nt. Note that lorn :

f . ) . . tV L a d ' + L a q ' .

At rated conditions lorn :148.5 A andVlr, : 377.i|V. The same power asin (a), i.e. 72.45 kW must be obtained. Hence, it is clear from eqn (.7.36) thatd will be the same as in (a), i.e. d : -30.45". With the machine considered as100% efficient, the electromagnetic power is equal to the input power, i.e.

P,L,n x |Vrn,In- "or 6

where

c o s @ !72 450

(3 l z )x377 .3x148 .5

The q-axis current i:on can now be calculated as

ioq : Io,ncos(ldl + 4) * cos(30.45 + 30.45) : 72.2 A

Using eqn (7.35) that is still valid, the angular frequency is

: 0.862 and Q x 30.45" (leading)

377.3 x sin(*30.45): 1243 radls-2 .73 x 10 -3 x72 .27r- sin d

, r aY -- L sqlaq

and the mechanical speed O : S\alptr : 2967 rpm. Taking the mechanicalspeed of 1443 rpm in (a) as the base speed, the per unit speed ts 297211443 :2.0 p.u. Hence, the same power can be developed by the drive at two timesbase speed by advancing the current angle V frorn zero to almost 610. It mustbe noted that this increase in speed is very much dependent on the q-axis syn-chronous inductance Lrn as can be seen clearly from all the equations usedabove. If .L"n becomes relatively smal1, the speed increase will be much less.The per unit phase reactance of the above iron-cored, slotted AFPM machineis r" - 0.53 p.u. For slotless and coreless AFPM machines the per unit phasereactance is much less (typically 0.1 p.u.) and the speed increase will be little.

Numerical example 7.3Simulate the dq and ABC current response ofthe drive system of l{umerical

example 7.2. Assume that


.tf-U

I

IJ

R

-

; i " , 1r

fi\+

* - ?

k

s;1" ,1t- r'-l'

4 ^. E 6

BTO d

o r

Control 245

(a) the speed is constant at 1000 rlmin1'

(b) the drive is operating at maximum torque per ampere;

(c) the switching frequency of the inverter is 1.5 kHz;

(d) the dq current regulators consist only of a proportional gain K": 3 ViA.

SolutionVarious software, such as PSpice and Simplorer, can be used for simulating

converler-fed electrical machine drives. Assuming the switching ofthe inverteras ideal, Matlab-Simulink has been used in this example to simulate the curentresponse of the drive.

200

1 5 0

1 0 0

50

0

-50

-1 00

-200

g

o

(a) Time (s)

200

I

E

175

1 5 0

125

100

75

50

25

0

d-axis -

0 Y 0.0052 5 +

.50 l

(b)

Figure 7.22. Simulated current response for step input in the q-axis current ioo: (a) phasecurrents i.A,iatj andi,,c:; (b) dq currents iaa andi,,r. Numerical example 7.1.


A block diagram of the simulation set-up is shown in Fig. 7.21. The simu-lation is done as "continuous", i.e. without any sampling and so forlh like ina digital control system. The current control is done inthe dq reference frameusing the current controller of Fig. 7.13. For both the d and q-axis regulatorsof Fig. 7 .13 a gain K" is used as shown in Fig. 7 .21. The decoupling is done asshown in Fig. 7.13 with the actual dq currents and speed as inputs. For simula-tion of the invefter, the drl voltages are transformedto ABC voltages by usingeqn (7.1 1). To generate the PWM phase voltages, the ABC vollages are com-pared with a 1.5 kHz triangle wave (amplitude of Val2), by using a subtractor(sum) and comparator (relay). The relay outputs +V,t 12. The generated PWMvoltages, uABCN, are with respect to the d.c.-link midpoint l/ of the invefier(see Fig. 7.18), and have to be converted to true phase voltages, u7165r",, withrespect to the floating neutral point n, of the machine as follows:

u A n : ] { r r o r

u B N u c N )

nlln : '5{rr"*

uC,^/ - uA-^/)

lJc,n - t5lrr"

** u/.^\r - uB,^r)

(7.37)

The next step is to either solve the machine equations inthe ABC or in the dqreference frame. Using the dq reference frame, the true PWM phase voltagesmust be converted back to dq voltages as shown in Fig. 7.21. Using the ma-chine model of Fig. 7.13, the 'i6,4 an:d z,rn currents can be determined and fedback to be compared with the input command currents as shown. To obtain in-formation of the actual phase currents, the ioy and io,n cunents are transformedto ABC currents.

The whole block diagram of Fig. 7.21 can be set up in Matlab-Simulinkusing the Simulink blocks. For the machine model, eqns (7.22) and (7.23)can directly be set-up in Simulink using integrators. To simulate the inverterswitching, the relay block can be used. Al1 the other source and mathematicalfunction blocks are available in Simulink. The simulated results can be outputin various ways, in this case to the Matlab workspace.

All the machine parameters are known from Numerical example 7.2. Themechanical speed is taken as constant at 4I9 radls (1000 rpm). For maximumtorque per ampere the dq command currents 'iod.* : 0 and'ioo* : 148.5 Aare given as step inputs to the system (Fig. 7.21). The d,q and ABC ct;rrerf.responses of the drive for a step input in i,or* are shown in Fig. 7.22. Theeffect of the switching of the inverter on the current waveforms is clear. In thiscase, the q-axis cur:rent builds up to the rated cument in less than 5 ms. Thisdepends amongst others on the value of the proporlional gain I{". The effect

Control 247

of the decoupling on the current response can be self-studied by removing thedecoupling signals in the simulation.

Chapter 8

COOLING AND HEAT TRANSFER

8.1 Importance of thermal analysis

During the operation of an electrical machine, heat is generated due to powerlosses in electric and magnetic circuits and mechanical (rotational) losses. Toensure a long operational life for the machine, these losses must be removed asfar as possible from the machine so that the temperature limitations establishedfor the machine materials, such as insulating materials, lubricants and pMs arecomplied with. In addition to the consideration of the machine's operationallife, a lower operating temperature reduces extra winding losses introduced bythe temperature coefficient of the electric resistance - eqn (3.47).

whereas extensive research has been devoted to the thermal studies of con-ventional electrical machines, AFPM machines have received very little atten-tion f 118,279,231,2321. Owing to the fact that AFPM machines possess arelatively large air gap volume and quite often have multi-gaps, the generalperception is that AFPM machines have better ventilation capacity than theirradial field counterparts [48, 96].

Since the external diameter increases rather slowly with the increase of out-put power, i.e. Do,,1 x iE""t 196], the existing heat dissipation capacity maybe insufficient to cope with excessive heat at certain power ratings, so thatmore effective means of cooling have to be enforced. Thus, quantitative stud-ies of the heat dissipation potential of AFPM machines with vastly differenttopologies is important.

8.2 lleat transfer modes

Heat transfer is a complex phenomenon presenting formidable analyticaldifficulties. Heat is removed from an electrical machine by a combination

250 AXIAL FLUX PERMANENT MAGNET BRLTSHLESS MACHINES

of condttction, radiation and convection processes to the ambient air and sur-roundings.

8.2.1 ConductionWhen a temperature gradient exists in a solid body, such as in the copper,

steel, PMs or the insulation of an electrical machine, heat is transferred fromthe hightemperature region of temperature 86o7 to the low-temperature regionof temperature 8"o6 according to Fourier's law,which is given as:

LP": -nou#: Y (onot - 8"om) ( 8 . 1 )

where AP" is the rate of heat conduction, A is the area of the flow path, I is thelength of the flow path and ,k is the thermal conductivity of the material. Thelatter is experimentally determined and is relatively insensitive to temperaturechanges. Thermal properties of typical materials used for AFPM machines aregiven in Table B.l .

Table 8.1. Selected thermal properties of materials

Material

(20"c)

Grade p

Kg/m"

c.p

Ji(kg "C)

k

W(m "C)

Air

Water

Mica

Epoxy resin

Copper

Aluminum

Steel

Permanent magnet

Pure

Alloy (cast)

1% Carbon

Silicon

Sintered NdFeB

1.1 '77

1 000

3000

1400

8950

2700

2790

7850

7700

7600 to 7"100

0.0267

0.63

0.33

0.5

360

z ) l

168

52

20-30

9

1005

4184

8 1 3

1700

380

903

883

450

490

420

8.2.2 RadiationThe net radiant energy interchange between two surfaces with a temperature

difference is a function of the absolute temperature, the emissivity and thegeometry of each surface. If heat is transferred by radiation between two gray

surfaces of finite size, 41 and 42, and temperature, t?1 and tSz (in Celsiusdegree), the rate of heat transfer, A,Pr, may be written as

Cooling and Heat Transfer 251

(8.2)( t 9 , + ) 7? t1 ( , 9 . , ) 7 ' l \ 4

^ D _ \ v t L t a t \ u 2 - . t o )

4 r r - u -' I € l I l - ' .! - 3. t A t ' A t F t z ' e z A z

where o is the stefan-Boltzmann constant, F12 is the shape factor which takesinto account the relative orientation of the two surfaces and e 1 and, e 2 are theirrespective emissivities which depend on the surfaces and their treatment. Someselected emissivities related to AFPM machines are siven in Table g.2.

Table 8.2. Selected emissivities relevant to AFPM machines

Material Surface condition Ernissivity, a

Copper

Epoxy

Mild steel

Cast iron

Stainless steel

Permanent magnet, NdFeB

Polished

Black

White

Oxidized

Uncoated

0.025

0.87

0. u5

0.2-0.3

0.57

0.2-0.7

0.9

8.2.3 Convectionconvection is the term describing heat transfer from a surface to a moving

fluid. The rate of convective heat transfer, APr, is given accordingto Newton'slaw of cooling as:

LP,, : hA(9 7,o1 - 8,r,rd,) (8 .3)

where /z is the convection heat transfer coefficient, which is a rather complexfunction of the surface finish and orientation, fluid properties, velocity andtemperature, and is usually experimentally determined. The coefficient h in-creases with the velocity of the cooling medium relative to the cooled surface.For a surface with forced ventilation, the following empirical relation may beused [147], i .e.

hy : h,"(l * r:6.y61 (8.4)

where h'y and. h,,, are the coefficients of heat transfer for the forced and naturalconvection respectively, t' is the linear velocity of cooling medium and cp. x0.5 to 1.3 is an empirical coefficient.

252 AXIAL T'LUX PERMANENT MAGNET BRUSHLESS MACHINES

Some important formulae for evaluating convective heat transfer coefficientsof AFPM machines are discussed in the followins sections.

Convection heat transfer in disc systems

The rotating disc system plays a major role in the cooling and ventilationof the AFPM machine. Accurately determining the convection heat transfercoefficients needs thorough theoretical and experimental investigation becauseof the complexity of ffow regimes.

In this section the convection heat transfer coefficients in different parts ofthe AFPM machine are evaluated, exploiting a number of existing models.

laminar lent

laminar

(a) (b)

Figure 8.1. Free rotating disc: (a) in laminar flow, (b) transition from laminar to turbulentflow

Free rotating disc

The average heat transfer coefficient at the outside surface of a rotating discmay be evaluated using the formula developed for a free rotating disc [241],i .e.

(8.s)

where -R is the radius of the disc and the average Nusselt number ly'u is givenaccording to the different flow conditions as follows:

(i) For combined effects of free convection and rotation in laminar flow (Fig.8.ta) [241]

turbu

/

k -h - : N u


(8.6)

(8.7)

) ^ l

A/u : r { n " . *G r l a

,_r, - u2

where fie is the Reynolds number according to eqn (2.65), p is the coemcientof thermal expansion, z is the kinematic viscosity of the fluid and Atl is thetemperature difference between the disc surface and surrounding air.

(ii) For a combination of laminar and turbulent flow with the transition at aradius r" (Fig. 8.lb) [241]

" 00(!!Ply 'u :0 .0 l5Res - t .R , (8 .8)

where

r . : ( 2 .5x105u1Q) r / 2 (8.e)

The angular speed Q : 2trn when n is the rotational speed in rev/s. It is in-structive to compare the heat transfer capabilities between a rotation disc and astationary disc. If we consider a steel disc, which has a diameter of 0.4 m androtates at 1260 rpm., the convection heat transfer coefficient may be calculatedas 41 W/(m' "C), which is about ten times that of the same disc at standstill.Altematively, one can say that the effective heat dissipation area of the samedisc can be increased by a factor of 10 when the disc rotates at the specificspeed.

Rotor radial peripheral edge

The heat transfer conelations for the radial periphery of the rotor disc aresimilar to those of a rotating cylinder in air. In this case the average heattransfer coefficient is given as

he: (.kf D",)t{u (8.1 0)

where Do6 is the outer diameter of the rotor disc, the average Nusselt numberis given by

, ) / a

1v u : 0 .133 ReTr P r t /3 ( 8 . i l )

254 AXIAL FLUX PERMANEI{T MAGNET BRUSHLESS MACHIAIES

and Reynolds number at the disc periphery is

Re71 : QDf;,rlu (8 .12 )

Note that a uniform temperature distribution in the cylinder is normally as-sumed when eqn (8.10) is used. Since Do is proportional to the angular speed0, it may be concluded that the rotor periphery plays an increasingly importantrole in the heat dissipation as f,) increases.

Rotor-stator system

As seen in Fig. 8.2, an AFPM machine consists of a number of rotating andstationary discs. The heat transfer relations between a rotating and a stationarydisc are of paramount importance in the thermal calculations. Due to centrifu-gal effects, there is a forced flow between the two discs, which increases thelocal heat transfer rate compared with that of a free disc. The relative increasewill depend on the gap ratio, G : g I R, where g is the clearance between therotor and the stator and -R is the radius of the disc, the mass flow rate and therotational speed of the system [91].

Having radial channels and thick impellers, an air-cooled AFPM machinemay be regarded as a poorly designed fan from a fluid flow perspective. Itstangential velocity component is much larger than the radial component. Thus,the heat transfer rate near the rotating disc shows more dependence on therotational Reynolds number, Rer, givenby eqn (2.65).

Owen [89] provided an approximate solution for the flow between a ro-tating and a stationary disc, which relates the average Nusselt number to themoment coefficient of the stator-side rotor face, Cr.o, by the following equa-tion:

l/z: Re,C,nof n

Cn,oRe ' r ' ' : 0 .333) r

where ,\7 is a twrbulence pqrameter given as arate, Q, as follows

A - 4\r : : ; .Rer s

(8 . l 3)

function of volumetric flow

(8 .14 )

By replacing )7 in eqn (8.13) with eqn (8.14), the average Nusselt numberbecomes


(8 .1 5 )n

ly'tr : 0.333 *ruR,

As discussed in [190], it has been shown that for a smail gap ratio (G < 0.1)the flow in the air-gap space between the rotor and stator can be treated as aboundary layer. Whilst it is not absolutely true that the convective heat transfercoefficient from the stator to the air flow is close to that of the air flow to arotating disc, the same heat transfer coefficient may be assumed in the thermalcircuit simulation.

8.3 Cooling of AFpM machinesDepending on the size of the machine and the type of enclosures, different

arrangements for cooling may be used. From a cooling perspective, AFPMmachines may be classified into two categories as follows:t machines with se(-ventilation, in which cooling air is generated by a ro-

tating disc, PM channels or other fan-alike devices incorporated with therotating part of the machine, and

t machines witlt external ventilation, in which the cooling medium is circu_lated with the aid of external devices, for an example, a fan or a pump.

8.3.1 AFPM machines with self-ventilationThe majority of AFpM machines are air-cooled. compared with conven-

tional electrical machines, a pafiicularly advantageous ieature of disc-typeAFPM machines from a cooling perspective is that they possess inherent self-ventilalion capability. Fig. 8.2 shows the layout and active components of atypical AFPM machine. A close examination of the machine structure revealsthat an air stream will be drawn through the air inlet holes into the machineand then forced outwards into the radial channel as the rotor discs rotate. .fhePMs in fact act as impeller blades. The fluid behaviour of the AFpM machineis much like that of a centrifugal fan or compressor.

The ideal radial channel

According to the theory of an ideal impeller, a number of assumptions haveto be made to establish the one-dimensional model of the ideal radial channel[7 1, 207]:

there are no tangential components in the flow through the channel;

the velocity variation across the width or depth of the channel is zero;

the inlet flow is radial, which means that air enters the impeller withoutore-whirl:

(a)

(b)

(c)


2

Figure 8.2. Exploded view of an AFPM machine: 1 - rotor disc, 2 - stator winding, 3PM, and 4 - epoxy core.

(d) the pressure across the blades can be replaced by tangential forces actingon the fluid;

(e) the flow is treated as incompressible and frictionless.

Figure 8.3 shows a radial channel with the velocity triangles drawn at the inletand the outlet. It can be observed that the pressures at the inlet p1 and the outletp2, and friction tri, make no contribution to the sum of the momentum, D Mo.If gravity is ignored, the general representation of conselation of momentumtakes the following forrn 12371:

A r r) l1o = ;L / Q i x u ' )pdVl t | ( r ' * i )p lu ' . r i )dA (8 .16)z J " d t ' J . u '

l r I J , . "

where r- is the position vector from 0 to the elemental control volume dV andu- is the velocity of the element.

For steady-state, one-dimensional air flowing between the entrance and exitof the channel, eqn (8.16) may be simplified as:

Y, Un : To : (Eo,t x u'z)mz - (En, x u*1)rn1 (8.17)

where rn2 : rnt : pQ, ut : QRm andu2 : ARout.The input shaft powerP;r, is then given by:

hn: ToO : pee2(R7,, _ Ri") ( 8 . 1 8 )

Cooling and Heat Transfer

Re-arranging the above equation gives:

257

(8.1 e)

Based on the principle of conservation of energy, the input shaft power may begiven as:

Pin, :,h(P-?# . ry * zz - zr * r;z - u) (8.20)

If the potential (.22 - zl) and internal energy (uz - L[) (friction) are ignored,eqn (8.20) may be written in the same units as eqn (g.19) as:

Pnn- , ^ * \ u | | - u lg

- tU't Ptl r p- 'n- (8 .21)

If equations (8.19) and (8.21) are equated and noting that w1 : ef A1 andw2 : Q f 42, where Ay and 42 arc the cross-section areas of the inlet and outletof the channel respectively, the pressure difference Ap between the entranceand exit of the radial channel (shown in Fig. 8.3) may be expressed as:

258 AXIAL FLUX PERMANENT MAGAIET BRUSHLESS MACHINES

(8.22)

Eqn (8.22) may be termed the ideal equation describing the air flow throughthe radial channel.

Lp - pz - pt : pQ2(R3,, - R?,, |rh #rrr,

,.I{elative etlciy

'..i

->c\;71i':" \-)

' , i , ' ' . . ' l

r , -

i t

, ' / - ; ;

r'f .', '"- ";/r'il '-. ".. ''il

i;..''.';.iii,;-t-':'4

S].j,tz-

i

Figure 8.4. The relative eddy in the PM channel.

The actual radial channel

The actual characteristics of a hydraulic machine differ from the ideal caseowing to two reasons: (i) the uneven spatial distribution of velocities in theblade passages, and (ii) the leakage and recirculation of flow and hydrauliclosses such as friction and shock losses. These are completely different issueslTll and shall be dealt with separately.

Slip factor

As a result of the unbalanced velocity distribution of the leading and trailingedges ofa PM channel and the rotation effects [2A7l,there exists, according toStodola 1182,2471, a relative eddy within the blade passage shown in Fig. 8.3.This results in the reduction of the tangential velocity components and is calleds/rp, which is usually accounted for using a slip factor. For approximatelyradial blades,the Stanitz slip factor k" (B0o < l3z < 90") is

k " : 1 - 0 . 6 3 t r 1 n 1 , (8.23)


where B2 is the blade angle at exit and n6 is the number of the blades. Whenapplying a slip factor, the pressure relation (8.22) becomes

(8.24)

Total flow leakage flow Q/

Figure 8,5. Leakage flow in an AFPM machine (not to scale)

Shock, leakage and friction

Energy losses due to friction, separation ofthe boundary layer (shock loss)and leakage should also be considered in the flow analysis. As illustrated inFig. 8.5, if the total volumetric flow rate through the PM channel is Q1, thepressure difference between the PM exit and the entrance will cause a leakageor recirculation of a volume of fluid Q1, thus reducing the ffow rate at outlet to

Q : Qt-Q1. The Ql is a function of mass flow rate and discharge and leakagepath resistances. The leakage flow reaches its maximum when the main outletflow is shut.

These losses can be accounted for by introducing a pressure loss term A,p1 ineqn (8.24) as follows 12071

Lp : pe2 (k"RZ., - R?,) . irh - hrn'

- hrn'

* Lpt (8 2s)p , I- r

; \ , 12t ^ 1Lp* pQ2(k,R3, , - R?,)

260 AXTAL FLUX PERMANENT MAG]NET BRUSHLESS MACHINES

System losses

As the air passes through the AFPM machine, the system pressure loss dueto friction must be taken into account. The sum of these losses is eiven bv:

where ki and A,; are the loss coefficient and the cross section area of the flowpath e respectively.

D1

@

-1 _:ut

,_)

Elbow

\t \ \+

Round bend

* ] :v l

a f l ILJ

^/-r2 rL LLpr,: +>,+4 . , f l ;

z : l

(8.26)

Abrupt expansion

[=

Short tube

--1@-_l

Tapering enlargement

/;\

Pipe to annulus bend

Figure 8.6. System losses of AFPM machine.

There are a number of sections through which the air flows in the AFpM ma-chine (see Fig. 8.6). They are:

( I ) entry into the rotor air inlet holes;(2) passage through rotation short tube;(3) bending of air from pipe to annulus (90o);(4) round bend air passage (90');


(5) contraction ofair in the tapering passage;(6) bending of air through the 90o elbow;(7) entry to the permanent magnet channels;(8) expansion of air through the tapering enlargement;(9) abrupt expansion ofthe air on the exit ofthe channel;(10) expansion as the air leaves the opening ofthe parallel rotor discs.

The loss coeffrcients associated with each section in eqn (8.26) are given in157 , 173, 1 82]. When the section is not circular, use is made of the hydraulicdiameter to characterise the cross section. The hydraulic diameter is defined asDn : 4Alp where -,4 is the cross-sectional area of the flow path and p is thewetted perimeter.

The loss coefficient for a pipe is given by ),L ld where ,\ is a friction factorobtained as a function of Reynolds number R,e and surface roughness from aMoody diagram [ 1 75]. To facilitate numeric calculations, the Moody diagrammay be represented by [57]:

^ : B{(B/8e)12 + (x + r ; -81-!

X : {2.457 rn{(7lRe)os +o.zr11n}-1}16

Y: {37 f f i rJ lRe}1( ,

(8.27)

^n- r - \where Re : 41f and where 7 is the equivalent sand grain roughness [57].

Characteristics

It is now possible to relate the theoretical prediction obtained from the idealflow model to the actual characteristic by accounting for the various lossesdiscussed above.

Assuming that the AFPM machine (shown in Fig. 8.1) operates at a con-stant speed of 1200 rpm, the ideal developed pressure characteristic for a ra-dial channel is a function described by eqn (8.22) as shown in Fig. 8.6. Afterintroducing the slip factor, the resultant curve is shown as a dotted line as eqn(8.24). It was not possible to obtain a suitable correlation in the literature [222]for the pressure loss due to shock and leakage as was the case for the slip.

The calculated characteristic curve without considering shock and leakagelosses, i.e. eqn (8.24) Apy" shown in Fig. 8.7, is significantly higher than theexperimental one. The shaded area in Fig. 8.7 represents the shock and leakagelosses. It can be seen that at low flow rates the shock and leakage losses aregreater but tend to zero at the maximum flow rate. This has been discussed andexperimentally validated tn [232].

262 AXI A L F LUX P E R MAN E NT MA GN ET B RU S H LE S S MAC H TN E S

500

4tx)

Ap 300lPal

240

0 0.006 t).012 0.{.}18Q (m3ls)

Figure 8.7. Losses and characteristic curves at 1200 rpm

The derived characteristics describes the pressure relations of a single ro-tating PM disc facing a stator. For a double-sided AFPM machine with twoidentical coaxial rotating discs (Fig. 8.2) operating on the same stator, thecharacteristic curve presented in Fig. 8.7 represents only half of the AFPMmachine. The characteristic curve of the whole machine may be obtained byadding flow rate at the same pressure, which is similar to two identical fans inparallel.

Flow and pressure measurements

Due to the nature and complexity of thermofluid analysis, the form of thesystem characteristics curve can at best be established by test. Depending onthe machine topologies and size, the measurements may be taken either at theair inlet or outlet. The AFPM machine under test is normally driven by an-other motor. Fig. 8.8 shows the experimental amangements of the flow mea-surements at the machine outlet, in which a discharge duct is set up to providegood conditions for observing the flow. Along one side of the duct, several tap-ping points were made for measuring the static pressure with a pressule gauge(manometer). Near the outlet of the duct, provision was made for measuringvelocity using a hot-wire anemometer probe.

To vary the flow rate, the test duct was fitted at its outer end with an obstruc-tion. The test was started with no obstruction at the end of the discharse duct.

ideal curve {eqn (S.22))

I {eqn t8 .26 t )

/ .".,.

eqn (8.24)*APy

/' experimrntal crrre


Figure 8.8. The experimental set up. 1 - manometer, 2 * AFPM machine, 3 - dischargeduct, 4 prime mover (drive machine), 5 - pressure tapping point, 6 - wind speed probe.Photo courtesy of the University o/'Stellenboscl, South Africa.

The only resistance was then the duct friction, which was small and could bereadily computed out of results. As the end of the duct was obstructed progres-sively, the ffow was reduced and the static pressure increased to a maximum atzero volumetric flow rate. The static pressure difference Ap is measured as afunction of volumetric flow rate Q : A' u for different motor speeds, where uis the linear speed.

The air flow-rate measurement can also be carried out by measuring inletair pressure difference Ap, which is then used for calculating mass flow-ratern according to the following equation:

;n: , /2pA4t A4 (8 .28)

where ,46 is the cross section area of the inlet duct. Fig. 8.9 shows the setup ofthe flow measurement. A specially designed inlet duct with a bell mouth wasmounted to the inlet (hub) of the AFPM machine. A few tapping points weremade on the inlet duct for pressure measurements. The pressure drop throughthe bell mouth and inlet duct may often be assumed negligible.

264 AXIAL FLUX PERMAINENT MAGNET BRUSHLESS MACHINES

Figure 8.9. Flow measurement at the air intake of AFPM machine. 1 Prime mover (drivemachine), 2 - inlet duct, 3 bell mouth, 4 manometer, and 5 pressure tapping point.Photo courtesy of the University of Stellenbosclr, South Africa.

8.3.2 AFPM machines with external ventilationFor medium to large power AFPM machines, the loss per unit heat dissi-

pation area increases almost linearly with the power ratings. Thus the forced-cooling with the aid of external devices may be necessary. Some commontechniques are described as follows.

air flow direction

AFPM machineair discharge duct with fan

Figure 8.10. AFPM machine with external air cooling

Cooling and Heat Tran.sfer 265

External fans

Large AFPM machines may require a substantial amount of air flow per unittime in order to bring out the heat generated in the stator windings. Dependingon the operation conditions obtained on site, either an air-blast or a suction fanmay be used as shown in Fig. 8.10. In both cases, intake andior discharge ductsare needed to direct and condition the air flow. Since the inlet air temperature,for a given volumetric flow rate, has a significant effect on the machine tem-perature, this cooling arrangement can also help prevent recirculation of hotair should the machine operate in a confined space (e.g. small machine room).For high speed AFPM machines, a shaft-integral fan may be a good option.Fig. 8.11 shows the assembly of a large power AFPM machine developed inthe Departrnent of Electrical and Electronic Engineering at the University ofStellenbosch, South Africa, in which the rotor hub part seryes as both coolingfan and supporling shucture for the rotor discs. It can be seen that the "blades"of the hub are not curved as the machine may operate in both directions ofrotation.

stahn' right rotor disc

Figure 8.1I. Configuration of the AFPM machine with shaft-integral fan.

Heat pipes

The concept ofa passive two-phase heat transfer device capable oftransfer-ring large amount of heat with a minimal temperature drop was introduced byR.S. Gaugler of the General Motors Corporation in 1942. This device receivedlittle attention until 1964, when Grover and his colleagues at Los Alamos Na-tional Laboratory, NM, U.S.A., published the results of an independent inves-tigation and first used the term heat pipe. Since then, heat pipes have beenemployed in many applications ranging from temperature control of the per-mafrost layer under the Alaska pipeline to the thermal control of optical sur-faces in spacecraft.

A typical heat pipe consists of a sealed container with wicking material. Thecontainer is evacuated and filled with just enough liquid to fully saturate thewick. A heat pipe has three different regions, namely (1) an evaporator ot heat

266 AX]AL FLUX PERMANENT MAGNET BRUSHLESS MACH]NES

addition region ofthe container, (ii) a condenser or heat rejection region, and(111) an adiabatic or isothermal region. lf the evaporator region is exposed to ahigh temperature, heat is added and the working fluid in the wicking sffuctureis heated until it evaporates. The high temperature and the corresponding highpressure in this region cause the vapour to flow to the cooler condenser region,where the vapour condenses, dissipating its latent heat of vaporisation. Thecapillary forces existing in the wicking structure then pump the liquid back tothe evaporator. The wick structure thus ensures that the heat pipe can transferheat whether the heat source is below the cooled end or above the cooled end.

Figure 8.12. AFPM machine cooled by heat pipes

A heat pipe presents an alternative means for removing the heat from theAFPM machine. The heat pipe in an AFPM machine may be configured asshown in Fig. 8.12. Heat is transferred into the atmosphere through the finnedsurface. The finned surface is cooled by air moving over the fins. The heat lossremoved by the heat pipe, LPno, is given by 12l0]:

A p ,* _ n pthot - 0,:rrl,L

(8.2e)1 r 1 IE;",,4t^-

-r E..r,t,^""td

* il;il;AI-

where $7ro7 is the average temperature of the elements that surround the heatpipe in the stator, t9.op1is the average temperature of the air cooling the finnedsurface, h6o7 is the convective heat transfer coefficient on the inside wall of theheat pipe in the statoE 46o1 is the exposed area of the heat pipe in the stator,

finned surface


h"o6 is the convection heat transfer coefficient on the inside wall of the heatpipe in the finned area, A.opl is the exposed area of the heat pipe at the flnnedsurface, \f t , is the efficiency of the finned surface, hln is the convection heattransfer coefficient on the surface of the fins and As1n is the total exposed areaofthe finned surface.

Direct water cooling

Depending on the conditions at the site of operation, it is often necessary touse forced water circulation to cool the stator windings directly, especially forlarge power AFPM machines. An external water pump is required for forcingwater circulation. A longitudinal section of a water cooled double-disc motorhas been shown in Fig. 2.7 . For coreless winding AFPM machines, the windingcoils may have a rhomboidal shape so that the space between the two activesides of each coil may be utilised forplacing a cooling water duct [41].

The heat removed through cooling pipes can be calculated by using eqn(8.29). However, the heat transfer coefficients, h,6o1 and h,"o14, are calculatedusing the following relationships:

(i) for laminar flow, i.e. Rea - ff < ZOOO. where u is the flow velocity andd is the diameter of the water'pipe, the Nusselt number may be obtainedusing following empirical relation [114]

where Io is the length of the water pipe, trr, and pt* are the dynamic viscosityof water at inlet and wall temperature respectively.

(ii) for turbulent flow. i.e. Re6 : # , 2000, the Nusselt number may beca lcu la ted as [23 ]

(8.30)

l{ua - 0.02gRe,to'8 Prn (8.3 r )

where

n _ ! 0.4 for heating of the water,

L 0.3 for cooling of the water.

8.4 Lumped parameter thermal modelLumped-parameter circuits, consisting of a network of thermal resistances,

thermal capacitances, nodal temperatures and heat sources, have been used ex-tensively to represent the complex distributed thermal parameters of electricalmachines 17 6, 147, 2191.

IYu,1 : r .B6(Re6Prl l f* l i th)o'n

268 AXIAL FLUX PERMAI,IENT MAGNET BRI]SHLESS MACHINES

8.4.1 Thermal equivalent circuitAthermal equivalent circuit is essentially an analogy of an electrical circuit,

in which the heat (analogous to current) ffowing in each path of the circuit isgiven by a temperature difference (analogous to voltage) divided by a thermalresistance (analogous to electrical resistance). For conduction, the thermal re-sistance depends on the thermal conductivity of the material, k, andthe length,l, and cross-sectional area, A6, of the heat flow path and may be expressed as

nu: | -A d K

Thermal resistances for convection is defined as:

R.:h

(8.32)

(8.33)

(8.34)

where A. is the surface area of convective heat transfer between two regionsand h is the convection coefficient.

The thermal resistance for radiation between two surfaces is

- _ f€ 1 A 1

1 lA t I t >

T€ t A )R, :

o[('sr + 273) + (82 + 273)11("r + 273)2 + (Oz + 273)21

It is seen that the radiation thermal resistance in eqn (8.34) depends on thedifference of the third power of the temperature, the surface spectral propertye and the surface orientation taken into account by a form factor F.

The thermal circuit in the steady state consists of thermal resistances andheat sources connected between motor component nodes. For transient anal-ysis, the thermal capacitances are used additionally to account for the changeof internal energy in the various parts of the machine with time. The heatcapacitance is defined as:

g : p V c t , : m c u (8 .35)

where c., is the heat capacity of the material, p is the density, and V and m,are the volume and mass of the material respectively. Fig. 8.13a shows a sec-tional view of an AFPM machine with a coreless stator. [t can be observedthat the AFPM stator is symmetrical from a heat transfer perspective and eachhalf of the machine from the centre line mirrors the other half. It is thereforereasonable to model only half of the machine as shown in Fig. 8.13b.The heat source tetms AP1- , LP., LPpnt and L,P,ol stand for winding losses(2.42), eddy cur:rent losses in one half of the stator winding (2.61),losses inPMs (2.54) and rotational losses (2.63) per one rotor disc respectively. C",


Figure 8.13. The thermal resistance circuit ofan AFPMtor.

(b)

brushless machine with coreless sta-

C^ and C, are the thermal capacitances of stator, PMs and rotor steel discrespectively. The heat resistances used in the circuit are described in Table 8.3.

Table 8.3. Definition of thermal resistances

I

(a)

tr

Symbols DefinitionR.t11 c2

R.zRu.t

Rcs

R.a

Rrt

R,Z

/i,:R"tRat

Convection resistance from stator end-winding to open airConvection resistance frorn stator to air-gapConvection resistance from air-gap to permanent magnetsConvection resistance from air-gap to rotor disc plateConvection resistance from rotor disc to open airConvection resistance from rotor radial periphery to open airRadiation resistance from stator end-winding to environmentRadiation resistance from stator to permanent magnetsRadiation resistance from stator to rotor discRadiation resistance from rotor radial periphery to environmentConduction resistance from PMs to rotor disc

8.4.2 Conservation of energyIf conservation of energy is applied, the rate of internal energy change in

each part of a machine (also called control volume) may be written as follows:


(8.36)

where L/ is the internal energy, riz is the mass flow rate and z is the enthalpyand C is the thermal capacitance of a control volume.

For steady-state conditionr, # : 0 and therefore,

0 : L1,. - LPout *'rit,in:iin, - it,o,,1io,,t (8.37)

These equations are applied to each part (the statoq air gap, PM and rotor disc)of the AFPM machine to obtain a set of equations with the temperatures of theparls being the only unknowns. This set of equations is rather complex but isreadily solved using for example, the Gauss-Seidel iteration It should be notedthat the tenn (m,iriin-rnouyior,7) in the above equations represents internal heatremoved due to the air flow pumped through the machine. This air flow is ofparamount importance to the cooling of the machine. The determination of theair gap temperature in the thermal equivalent circuit is only possible if the massflow rate through the air gap can be somehow predicted, hence the necessity ofusing the fluid-ffow model described in section 8.3.1.

8.5 Machine dutiesDepending on the load conditions, there are mainly three types of duties or

operation modes for all the electrical machines, i.e. continuous duty, short-timeduty and intermittent duty.

8.5.1 Continuous dutyWhen an electrical machine operates for a long period so that the temper-

atures of various parls of the machine reach steady-state at a given ambienttemperature, this operation mode is called continuous due. Due to the dif-ferent physical properties, the final stablised temperatures in various parts ofthe machine may vary greatly. The machine can be continuously operated foran infinitely long time without exceeding the temperature limits specified foreach component of the machine. When only the solid parts of the machine areconsidered, the air flow term in the eqn (8.36) is ignored. The temperature riseversus time relationship in a control volume of the machine may be derivedbased on the theory of solid body heating as [47]:

8, : LP n(1 - " - i ) + 0o e- l (8 .38)

where B is the thermal resistance, r : RC is the thermal time constant, C isthe thermal capacitance, AP is the heat loss flow, and 8o is the initial temper-

L I - C4o : A ,P, , LPour I m;n i ; , - t i tou l io , l

Af


ature rise of the control volume. In a case where t?. : 0" the above equation issimply:

d . : A P R ( l - " - ! )

(8.3e)

According to the properties of an exponential function, the final temperaturerise r9.; : A,P . /?. Fig. 8.14a shows the typical transient temperature responseof an AFPM machine operated continuously.

S , + 9 0

Figure 8.14. Characteristic temperature curves of AFPM machines for different operationmodes: (a) continuous duty, (b) intermittent duty, (c) shorl{ime duty.

8.5.2 Short-time dutyShort-time duty means that machine operates only within a short specified

period followed by a long period of rest or no-load condition. The operationtime is so short that the machine does not attain its steady-state temperature,and the machine practically retulxs to its cold state after a long period of rest.Given the operation time f", the temperature rise of the machine can be foundby using eqn (8.39) as

I(b)

272 AXIAL FLUX PERMANENT MAGI{ET BRUSHLESS MACHINES

f " : AP R( .1 - e + ) :8q ( .1 - " -? )

(8.40)

Compared with continuous duty, it is obvious that,r9.. < 8.f .This impliesthat the permissible load for the same machine in short time duty can be 1l 0 -

"-?1 ti*", greater than that in continuous duty. Fig. 8.14c shows the typical

temperature rise curve for short time duty machines.

8.5.3 Intermittent dutyThe intermittent duty is characterised by shorl-time operations alternated

with shorl-time pause intervals. Suppose a machine operates for a shofi periodof tonandthenstopsforaperiod of toyy,thecyclel" , isthen tqt: ton*tof f .The duty cycle d"o may be defined as:

nt .c,q -

L o n t t o f J(8 .41 )

The temperafure rise of the machine r9i during the to,n period can be calcu-lated by using eqn (8.38) provided that thermal time constant and the steady-state temperature rise for continuous operation duty are known. During thetosy period, the machine loss AP : 0 and the machine's temperature de-creases according to an exponential function, i.e. r?;e t,,tt l' 6s1s1e the secondcycle sets in.

After many subsequent cycles, the machine's temperature variation becomesuniform and tends to be within a ceftain limited range (see Fig. 8.14b). Underthe same load and cooling condition, the maximum stablised temperature of amachine in intermittent operation duty is smaller than that in continuous duty.Hence, similar to shorl{ime operation duty, a machine operated in intermittentduty has overload capacity.

Numerical example 8.1A self-cooled 8-pole, 16-kW AFPM generator with an ironless stator as

shown in Fig. 8.2 will be considered. The outer diameter is Do6 : 0.4 mand the inner diameter is Din - 0.23 m. The magnet width*to-pole pitchratio a.4 : 0.8 and thickness of a rotor disc d : 0.014 m. The measured flowcharacteristic culves are shown in Fig. B.15. At rated speed 1260 rpm, the totalIosses are 1569 W, of which (i) rotational losses LP,ot : 106 W; (ii) eddycurrent losses in the stator A.Pr, : 23 W; (iii) stator winding losses (rated)LPru:7440 W. Find:

(a) Convective heat transfer coefficients of the disc system

(b) Steady-state temperatures at different parts of the machine.

tuon,

Cooling and Heat Transfer Z I J

Solution

(a) Convective heat transfer coefficients ofthe disc system

The dynamic viscosity, density and thermal conductivity of air are assumed tobe p : 1 .8467 x [U- ; Pa s . p : L777 kg / rn3 and k :0 .02624 W/(m "C)respectively in the following convective coefficients calculations.

Convection coefficient: outside rotor disc surface

At rated speed, the Reynolds number according to eqn (2.65) is

o D 2R e p - - - - o u r : 1 . 1 7 7 x

4p

2nx1260160x0 .424 x 1 . 8 4 6 x 1 0 - 5

: 336384.7

According to eqn (8.9) the transition between laminar and turbulent flow takesplace at

The average Nusselt number of the disc according to eqn (8.8) is

ly 'u : 0.0t5 x R, i - 100 x ( ? fUout

: 0 .015 x 336384 .7* - 100 * (2 '=0 ,172 ) ' : r x .n\ t J . 4 /

The average heat transfer coefficient at the outer surface of the disc accordingto eqn (8.5) is

; k o 0)614h r - : - x l y ' u : : x 3 2 1 . 9 : 4 2 . 2 W / ( m ' z o C )-r ' | Doa 12 0.412

Convection coefficient: rotor disc peripheral edge

The Prandtl number is taken as Pr :0.7 (Atmospheric pressure, 25 oC). TheReynolds number at disc periphery according to eqn (8.12) is

nZuL 2n x 1260 I t a2ReD -t " :

, , , -- fr , s : 134553u.d

The average Nusselt number according to eqn (8.11) is

,^y'u : 0.133 x Rer? x pr*: 0.133 x 1345538.8? x O.7i : 1439.3

274 AXIAL FLUX PERMANENT MAGIVET BRUSHLESS MACHINES

l{1{} rpn.r.llX.l rprn{i(0 rptn8fii.) rynn

1iii}t} rprr120il rpm14{}0 qxrr

The average heat transfer coemcient around the radial periphery according toeqn (8.10) is

, k - no'rain|Er:

i * x N, x 1439.3 :94.4W/(m2 "C)

1?0

1{}l

8{l

f ] ,( t , l )

t l t r

4{l

21)

{ ,

+.J

A{}

i { 1 r ' '

t l l . " o

-______________ __,: l I

Figure 8.15. Measured characteristic curves of the AFPM machine. Numerical example 8.1.

Convection coefficient: rotor-stator system

The volumetric flow rate of the machine at rated speed can be looked up fiomFig. 8.15. Assuming equal flow on both sides of stator, the equivalent flow rateis taken as Q : 0.013 m3/s. The average Nusselt number according to eqn( 8 . 1 5 ) i s

,,r,u - o ss:r ,;m: 0 333 x

The average heat transfer coefficient between two discs according to eqn (8.5)is

; 2k Nu :2 x 0.02624

x 440 - bT.T w/(m2 "c;n'": Dn*. 0.4

0.013n1 .566x10 5xQ.a l2 ) : 440


(b) Steady-state temperatures at different parts of the machine

If the radiation from the rotor disc to ambient, the convection from the sta-tor overhang to air flow, and the conduction resistance between magnets androtor are ignored, the generic thermal equivalent circuit given in Fig. 8.13 issimplified as shown in Fig. 8.16.

R .hg,sou,

+fr

,/half stator

' .'"'

rotor disc

Figure 8. I 6. Simplified thermal equivaient circuit. Numerical example [l.I

Controlvolume | (hal.f of the stator)

The convection heat transfer resistance between the stator and air flow in theair gap is

R c 1 . :E, "x [ (D ! . r -D?n) /o7 .7xXQ.+ ' -0 .232):0.223 "C/W

The radiation heat transfer resistance between the stator and rotor discs is

Erl :l - r ' 1 1- + - . - + -e t A t ' A t F t z ' e z A z

of(dr + 273) + (82 + 273))i('9r + 2nY + (82 + 27:t)21

in which the areas of both discs can be taken as the same, i.e. A1 - Az :

i@2", D?") - 0.084 m2, the shape factor Fp - 1, the Stefan-Boltzmannconstant o :5.67 x 10-8 W lQn2 K4),the emissivity of epoxy encapsulated


stator e 1 : 0.85. Since part of the rotor disc is covered with PMs, the emissiv-ity of the rotor disc is defined based on the proporlion of different materials,i .e .

€2 : € fea , i I € .y . - (1 - t , ) : 0 .3 x 0 .8+0.9 x (1 - 0 .8 ) : 9 .42

Apparently Rrr is a function of r91 and 82, &n iterative approach has to be usedto solve R"1 for different temperatures.According to conservation ofenergy, the steady-state energy equation for con-trol volume 1 can be written as

I r9 ' r9. ' t9 ' ,9.; ( A P r . I A P . ) - 1 ' n " " " ' = " ' = 0 ( 8 . 4 2 )'2 ll"r R,t

Control volume 2 (.air gap)

The convection heat transfer resistance from air gap to the rotor disc may betaken as the same as that from stator to air gap, i.e. R"2 : R.c7.The mass flowrate ir, : pQ : 7.177 x 0.013 : 0.0153 kg. Assume that the air temperatureat the machine inlet is ambient temperature,i.e. 8;, : 8o and the air gapaverage temperature '82 : j($out * t\;r). The heat dissipated due to the airflow is

houtiout - rnin'iin: h cp (.$out - 0.-) :2rn c, (02 - 8a)

: 2 x0 .0153 x 1005 x ( r l z - 20)

The steady-state energy equation for control volume 2 is

8 t - 8 z 8 z * r 1 z

T - 2 x 0 ' 0 1 5 3 x 1 0 0 5 x ( 8 2 - 2 0 ) : 0 ( 8 ' 4 3 )

Controlvolurme 3 (rotor disc)

The convection heat transfer resistance at the outside surface ofthe disc is

Rd - : -1- :0.1877 "C/Wrt lrrDoul2 42.4x n x0.4'2

The convection heat transfer resistance at the periphery ofthe disc is

_11R*P:

i , "

D. r t :

g44 , n v g4 v g1y4: o '602 oc/w

Cooling and Heat Transfer

The steady-state energy equation for control volume 3 is

'Bs - ,9u, 8 s - 8 o

Rc:lp

277

n (8.44)b#.Wni^*.,-Rct)

Having established the energy equations (8.42), (8.43) and (8.44) for each partof the machine, the steady-state temperatures can be found by solving theseequations. Due to the temperature dependency of Rr1, a simple computer pro-gram using Gauss Seidel iteration has been created to find the solutions of theequations. The results are given in Table 8.4.

Table 8.4. Predicted temperature rises

Machine parts Temperature rise, "C

Stator windingRotor discAir-gap flow

114.918.3221.35

Numerical example 8.2A totally enclosed AFPM brushless machine has a power loss of 2500 w in thestator winding at continuous duty. The machine's outer and inner diameters areDout : 0.72 m and D;n: 0.5 m respectively. To remove the heat from thestator, use is made of heat pipes for direct cooling of the motor as shown inFig. 8.12. The convection heat transfer coefficients on the inside wall of heatpipes in the stator and in the finned area are assumed to be 1000 W/(m2 "C).The average convective heat transfer coefficient on the fin surface is taken as50 W/(m2 "C). The finned surface has an overall area of 1.8 m2 and anefficiency of g2%. The length of heat pipe embedded in the finned surface isly , in :1 .5 m. F ind :

(a) Steady-state temperature of the stator winding if the heat pipe with a diam-eter D1,r,: 9 mm is placed along the average radius of the stator

(b) Steady-state temperatures of the stator winding if the heat pipe is replacedby a 9 mm water cooling pipe, in which water (with an average temperatureof 60"C) ffows at 0.5 m/s.


Solution

(a) Steady-state temperature of the stator winding if the heat pipe with a diam-eter DTro: 9 rnnt is placed along the average radius of the stator

Assuming the outside wall of the heat pipe is in full contact with the statorwinding and finned surface, the exposed area of the heat pipe in the stator willbe

A7ro1 : rD1rr.,r(Dout + Dm) : 0.009n x

n(0.72 + 0.5):0.0542 rrz

The exposed area of the heat pipe embedded in the finned surface will be

Acold.: rD6plf in: 0 '0092 x 1'5 : 0 '0424m2

Assuming the temperature of cooling air over the finned area to be 8ro6 :

30"C, the steady-state temperature of the stator may be obtained by using eqn(8.29)

f statc,,r: fcord+ LPr"e(h#t,.t* ,#;* Ty;,hyaAym

: 30*2500. ( r*#o*r+moo*olCIa**x* ,. *)

: 165'3 oc

(b) Steady-state temperatures of the stator winding if the heat pipe is replacedby a water cooling pipe of diameter d : I mm, in which water flows at0.5 rn/s.

The Reynolds number is first calculated to determine the flow regime. Theproperties of water at 60"C ?r€ p : 983.3 kg/mt. ro :4179 J/(kg "C),F : 4 .7 x 10-a pas , k : 0 .654W(m"C) , p r : l t cp lk : 4 .7 x 10 a x417910.654:3 , Red: pud l (2St ) : 983.3 x 0 .5 x 0 .00914.7 x 10- r :

9474,5 > 2000, so that the flow is turbulent. Thus, the Nusselt number for theheating of the water is

Nu61, : 0. \BRel '8 Pr0'4 :0.023 x 9414.50'8 x 30 4 : 53.9

while the Nusselt number for the cooling of the water is

IVn"6" - 0.023Re0u'8 P"0 3 - 0.023 x 9474.50'8 "

30 ::t : 48.3

The convection heat transfer coefficients of the water pipe inside the stator h7.,o1,and in the finned area h,,,r,1r1, are calculated as


, k Nu61, 0.654 x 53.9h'hot: -f : -ffi : 3916'7 w/(m2 "c)

, k Nu,1. 0.654 x 48.3hcoLd, : -

f : -ffi : 3509'8 w/(m2 "C)

The steady-state temperature in the stator can be calculated as in (a) with theexception that the heat transfer coefficients are different

,gstator : Scotd + LPheG-++ --], + --,L, )" n ' h h o t A h o t h . o 4 A . o l d , 0 f , i n h f . i , r t A . f m '

:30+25oox ( r + 1 )' 39 16.7 x 0.0542 3509.8 x 0.0424 0.92 x 50 x 1.8 '

: BB,B "C

Chapter 9

APPLICATIONS

9.1 Power generation

Brushless PM electrical machines are the primary generators for distributedgeneration systems. They are compact, high efficient and reliable self-excitedgenerators. The distributed generation is any electric power production tech-nology that is integrated within a distribution system. Distributed generationtechnologies are categorized as renewable andnonrenewable. Renewable tech-nologies include sola1 photovoltaic, thermal, wind, geothermal and ocean assources of energy. Nonrenewable technologies include internal combustionengines, combined cycles, combustion turbines, microturbines and fuel cells.

AFPM brushless generators can be used both as high speed and low speedgenerators. Their advantages are high power density, modular construction,high efficiency and easy integration with other mechanical components liketurbine rotors or flywheels. The output power is usually rectified and theninverted to match the utility grid frequency or only rectified.

9.1.1 High speed generators

Although the minimization of windage losses of high speed generators re-quires rotors with small diameters, a multidisc design has the advantages ofmodular and compact construction, low synchronous reactance, good voltageregulation and very high efficiency in the case of coreless stators.

A multidisc AFPM high speed generator is usually driven by a gas micro-turbine. The turbine rotor and PM rotors are mounted on the same shaft. Sucha generator has compact construction, low mass and very high efficiency.

According to TurboGenset Company, U.K., a 100-kW, 60 000 rpm multidiscgenerator has an outer diameter of 180 mm, length of 300 mm and weighs only

282 AXIAL FLLTX PERMANEI{T MAGNET BRUSHLESS MACHINES

Figure 9. L I 00-kW 8-disc AFPM synchronous generator. Courtesy of Zr.r rhoGen'set, London,

U.K.

l2kg (Fig. 9.t)r. the high frequency output is rectified to d.c. and then in-verted to 50, 60 or 400 Hz a.c. (Fig.2.20). The generator is totally air cooled.

Armed forces are interested in applications of microturbine driven PM syn-chronous generators to battery chargers for soldiers. The low energy densityof portable bagpack batteries imposes a major constraint and challenge to fu-ture infantry operations. With recent advancement in PM brushless machinetechnologies, a lightweightminiature generator set can minimize the mass of

heavy batteries and charge them during field operations. A miniature gener-

ator can deliver electric power for a long period of time limited only by thefuel availability. Easy and rapid refueling can be done in the field by using,e.g. kerosene. Fig. 9.2 shows a tiny microturbine integrated with a miniatureAFPM synchronous generator. At speed 150 000 to 250 000 rpm and outerdiameter of PM ring Do,rl = 50 mm, the generator can deliver about I kW

electric power.

9.1.2 Low speed generatorsA low speed AFPM generator is usually driven by a wind turbine. Wilh

wind power rapidly becoming one of the most desirable alternative energysources world-wide, AFPM generators offer the ultimate low cost solution as

compared with e.g. solar panels. Table 9.1 shows specifications of five-phase

lULEV-TAP Newsletter, No. 2, 2000, wwwulev-tap.org

Applications 283

AFPM synchronous generators manufacturedby Kestrel Wind Turbines (Pty)Ltd, Garteng, South Africa. A1l three types of Kestrel generators use lami-nated cores. The Kestrel 2000 is a double-sided AFPM generator with twinrotors. The Kestrel 600 generator rated at 400 W is in fact capable of deliv-

Figure 9.2. High speed AFPM synchronous generator integrated with the rotor of a microtur-bine. 1 SmCo PM, 2 - backing steel ring, 3 - rotor of microturbine,4 - nonmagneticretaining ring, 5 - stator winding, 6 stator core.

_cL

-z:....

iI..........

N b

Figure 9.3. Output power versus wind speed ofKestrel AFPM synchronous generators. Cour-tesy of Kestrel fiiind Turbines. South Africa.

3 ,root

uJ3I rooooo

o


Table 9.1. Specifications offive phase Kestrel AFPM synchronous generators

Type ofgenerator Kestrel 600 Kestrel 800 Kestrel 2000Rated power, WMaximum poweq WNumber of poles 2pGeneration stepsRated wind speed, m/sCut in wind speed, m/sRated rotational speed, rpmRotor diameter, mNumber of bladesType ofbladeTower top weight, kgLateral thrust, NSpeed controlStandard rectified d.c. voltage, VProtection

400 at 12.5m/s 800 at 11.5m/s 2000 at 10.5m/s600 at 14.5m/s 850 at 12mls 2200 at I lm/s

48 48 2002 2 4

t2 .52 .5

1 1001 .2o

Basic aerofoil

232s0

Self stall12,24, 36, 48

1 1 . 52 .51 0 1 0_/.. I

3Full aerofoil

3 5300

IP55

Dynamic tail48

10,52.29253 .63

80450

ffiFigure 9.4. Stator and rotor of a medium power AFPM generator with inner coreless statorand twin external rotor: (a) stator coils, (b) rotor disc with NdFeB PMs.

ering power in excess of 600 W. Controlled by a shunt regulator the maxrmumcharging culrent is 50 A tnto a 12 V d.c. battery bank. At wind speeds of 52.2km/h, which translates into 14.5 mls (28.2 knots) and rotational speed of I100rpm, the power output is 600 W (Fig. 9.3).

Applications 285

speed, rpm

Figure 9.5. Steady-state performance characteristics of a 10-kW AFPM generator shown inFig. 9.4.

Fig.9.4 shows a medium-power AFPM generator with twin external rotorand inner coreless stator for a 5-m blade diameter wind turbine. The statorsystem consists of l5 coils, one coil per phase. The thickness of coil is 12mm and diameter of wire 0.6 mm. Each coil is individually rectified to d.c.to reduce the cogging effect and provide better control over the voltage. Therotor has 2p: 16 poles. Perfonnance characteristics are shown in Fig. 9.5.

9.2 Electric vehiclesElectric vehicles are divided into two general categories: hybrid electric ve-

hicles (HEYs) and battery electric vehicles (EVs). The switch from gasoline toHEVs and EVs would reduce the total primary energy consumed for personaltransportation. Traction electric motors for HEVs and EVs should meet thefollowing requirements :

r power rating: high instant power, high power density;

torque-speed characteristics: high torque at low speed for starling andclimbing, high speed at low torque for cruising, wide speed range includingconstant torque region and constant power region, fast torque response;

high efficiency over wide speed and torque ranges;

'1 t0

1 0 0

to3g s o

5

j 6 0

o4 " "

5

o';

"nc " 'o

ti 20=u

1 0

0

286 AXIAL FLUX PERMANENT MAGNET BRUSHLESS MACHT],,IES

Figure 9.6. Hybrid electric gasoline car: I - gasoline combustion engine, 2 - integrated motor-generator, 3 - cranking clutch, 4 - gearbox, 5 - inverter, 6 - battery.

700

600

500

! aooat

5 300

200

1 0 0

02000 3000 4000

speed, rpm

Figure9.7. Torque-speedcharacteristicsofanelectricmotorandgasolineengine. Theelectricmotor assists the gasoline engine at low speeds.

r high reliability and robustness under various operating conditions, e.g. athigh and low temperature, rain, snow, vibration, etc.;

r low cost.

electric molor to.que---t-**-F"-*engine torque . s

Applications 287

9.2.1 Hybrid electric vehiclesHEVs are now at the forefront of transportation technology development.

HEVs combine the internal combustion engine of a conventional vehicle withthe electric motor of an EV, resulting in twice the fuel economy of conven-tional vehicles. The electric motor/generator is usually located between thecombustion engine and gear box. One end of the rotor shaft of the electric mo-tor/generator is bolted to the combustion engine crankshaft, while the oppositeend can be bolted to the flywheel or gearbox via the clutch (Fig. 9.6). Theelectric motor serves a number of functions. i.e.:

assisting in vehicle propulsion when needed, allowing the use of a smallerinternal combustion engine;

operating as a generator, allowing excess energy (during braking) to be usedto recharge the battery;

replacing the conventional alternator, providing energy that ultimately feedsthe conventional low voltage, e.g. 12 V electrical system;

starting the internal combustion engine very quickly and quietly. This al-lows the internal combustion engine to be tumed offwhen not needed, with-out anv delav in restartins on demand:

r damping crankshaft speed variations, leading to smoother idle.

In a hybrid electric gasoline car the electric motor assists the gasoline engine inthe low speed range by utilizing the high torque of the electric motor, as shownin Fig. 9.7. Currently manufactured hybrid electric gasoline cars (Fig. 9.6) areequipped either with cage induction motors or PM brushless motors. A PMbrushless motor can increase the overall torque by more than 500/o. In mostapplications, the rated power of electric motors is from l0 to 75 kW. Becauseof limited space between the combustion engine and gear box as well as theneed to increase the flywheel effect, electric motors for HEVs are shorl andhave large diameters. AFPM brushless machines are pancaketype high torquedensity motors and fit perfectly the HEV requirements. An AFPM brushlessmachine can be liquid cooled and integrated with a power electronics converter.

In the HEV shown in Fig. 9.8 the energy is stored in a fl).rnrheel integratedwith the AFPM machine. The vehicle may operate without an electrochem-ical battery. lf the electromagnetic conversion process is included within theflywheel, there is no external shaft end, because the power flow to and fromthe machine is via electric connections to the stationary armature [3]. Thus,complex vacuum seals are avoided.


Figure 9.8. HEV with flywheel energy storage: I - gasoline combustion engine, 2 - brush-less generator, 3 - integrated flywheel-motor generator, 4 solid state convertet 5 d.c.bus, 6 - electrical motorized wheel.

The moment of inertia and tensile stress are respectively

r for a rotatins disc

r for a rotating ring

t : f ,m@?,+ RZ,,) ,

pQ2 RZut (e .1)J : T,^Rf,,,,

{a?,

d.c. bus

I R,inR66 + R?",r) (:9.2)

Applications 289

where p is the specific mass density of the rotating body, m is the mass, f) :

2trn is the angular speed, Ro,1 is the outer radius and Ri, is the inner radius.The kinetic energy is

r for a rotating disc

nr: f,lrf

: n3 prlRt,tn2 J (e 3)


Er: 13 pd(Rt t Rt,)r, ' (e.4)

where d is the thickness of the flywheel (disc or ring).Combining together pairs of eqns (9.1), (9.3) and (9.2), (9.4), the stored

energy density in a flywheel can be expressed as

r for a rotating disc


8 7 . 3 o€ 1 r : - ' : a - J l k g

m + p

_ 3 R7,,, + R?o,,, o- 4 R7.* R;nRo6 * R7,, p

(e.s)

J/ke (e.6)R,

rrL

For a very high strength steel, e.g. alloy steel (3% CrMoC) with o ry 1000 MPaand p :7800 kglm:r [3], the stored energy density of a disctype flywheel isep : 96.I kJ/m3. If we need to store a kinetic energy En : 500 kJ, the massof the disc will be 5.2kg.

9.2.2 Battery electric vehiclesBattery EVs are vehicles that use secondary batteries (rechargeable batteries

or storage batteries) as their only source of energy. An EV power train canconved energy stored in a battery into vehicle motion and it can also reversedirection and convert the kinetic energy of the vehicle back into the storagebattery through regenerative braking.


Figure 9.9. Single-sided AFPM brushless motor fitted to spoked wheel ll95l.

AFPM brushless motors are used in EVs as in-wheel motors (Figs 6.8 and9.9) [ 95,2031. The pancake shape of an AFPM motor allows for designing acompact motorized wheel.

With the aid ofthe AFPM brushless motorthe differential mechanism can bereplaced by an electronic differential system [92]. The configuration shown inFig. 9. I 0a illustrates the use of a pair of electric motors mounted on the chassisto drive a pair of wheels through drive shafts which incorporate constant ve-locity joints. In the configuration shown in Fig. 9.10b, the motors forming theelectronic differential are mounted directly in the wheels of the vehicle. Theelectromechanical drive system is considerably simplified, when the motor ismounted in the wheel, because the drive shafts and constant velocity jointsare now no longer needed. However, the resultant "unsprung" wheel mass ofthe vehicle is increased by the mass of the motor. Wheel motors of this di-rect drive configuration also suffer overloading because the speed ofthe rotoris lower than would be the case with a geared alrangement. This leads to anincrease of the active materials volume required in the motor.

The disadvantages of conventional wheel motors can be overcome by usingthe arrangement shown in Fig. 9.1 1. The two stators are directly attached tothe vehicle body whilst the PM rotor is free to move in radial directions. It canbe observed that in this case the wheel and disc rotor form the unsprung mass,whilst the stators of the motor become sprung mass supported on the chassisfq? tL " l '

Applications

t0 l

Figure 9.1(). Alternative forms of "electronic differential" drive schemes: (a) onboard motor,ft) wheel mounted motor.

, ' l

Figure 9.11. Schematic representation of the disc-type machine with lower unsprung mass:-wheel, 2 discrotor, 3 -stator, 4 shaft, 5 damper, 6-spring, 7 chassis.

9.3 Ship propulsion9.3.1 Large AFPM motors

Stators of large AFPM brushless motors with disc type rotors usually havethree basic parts [44]:

r aluminum cold plate;

r bolted ferromagnetic core;

r polyphase winding.

291

292 AXIAL FLUX PERMANENT MAGNET BRI]SHLESS MACHTNES

131rl 1s

t 6I

Figure 9.1 2. Large power double disc AFPM brushless motor. 1 - pMs, 2 - stator assembly,3 -housing,4 shock snubbeq 5 -shockmount,6-rotorshaft, T-rotordisc clanrp, gshaft seal assembly, 9 - bearing retainer, 10 - stator segment, 1 l centre frame housing,12 - spacer housing, 13 rotor disc, 14 - bearing assembly, 15 - rotor seal runner, 16rotor seal assembly. Courtesy of Kaman Aerospace, EDC. Hudson. MA, U.S.A.

The cold plate is a part of the frame and transfers heat from the stator to theheat exchange surface. The slots are machined into a laminated core wound ofsteel ribbon in a continuous spiral in the circumferential direction. The copperwinding, frequently aLitzwke, is placed in slots and then impregnated with apotting compound. The construction of a double disc AFpM motor developedby Kaman Aerospace, EDC, Hudson, MA, U.S.A. is shown in Fig. 9.121441.Specifications of large axial flux motors manufacturedby Kaman are given inTable 9.2.

9.3.2 Propulsion of unmanned submarinesAn electric propulsion system for submarines requires high output power,

high efficiency, very salient and compact motors [59, 180]. Disctype brushlessmotors can meet these requirements and run for over 100 000 h without afailure, cooled only by ambient sea water. These motors are virtually silentand operate with minimum vibration level. The output power at rated operatingconditions can exceed 2.2kwlkg and torque density 5.5 Nm/kg. The typicalrotor linear speed of large marine propulsion motors is 20 to 30 m/s [lS0].

9.3.3 Counterrotating rotor marine propulsion systemAn AFPM brushless motor can be designed with the counterrotation of two

rotors [35]. This machine topology can find applications in marine propulsion

Applications 293

Table 9.2. Design data of large poweq three phase AFPM brushless motors manufactured byKaman Aerospace, EDC, Hudson, MA, U.S.A.

Quantity PA44-5W-002 PA44-5W-001 PA57-2W-001

Number of poles, 2pNumber of windings per phaseOutput power P",r, kWPeak phase voltage, VRated speed, rpmMaximum speed, rpmEfficiencyat rated speedTorqueat rated speed, NmStall torque, NmContinuous cunent(six step waveform), AMaximum current, APeak EMF constantper phase, V/rpmWinding resistanceperphase at 500 Hz, 0Winding inductanceper phase at 500 Hz, pHMoment of inertia, kgm2CoolingMaximum allowablemotor temperature, "CMass, kgPower densiry kWkgTorque density, Nm/kgDiameter of frame, mLength of frame, m

Application

28 282

336 445700 5302860 s2003600 6000

0.95

t t 2 01621

370500

0.24

0.044

1200.9

1951.7235.7430.6480.224

0.96

822I 288

36

74673s

36004000

0.96

r 98027 12

0.20

0.030

1002.065

3402.194s.8230.7870.259

Generalpurpose

370 290500 365

0 . 10

0.022

600.9

Water and glycol mixture

150195

2.2824.2150.6480.224

Traction,Drilling indushy

systems which use an additional counter-rotating propeller in order to recoverenergy from the rotational flow of the main propeller stream. In this case theuse of an AFPM motor having counter-rotating rotors allows the eliminationof the motion reversal epicyclical gear.

The stator winding coils have a rectangular shape which depends on thecross section of the toroidal core [35] (also see Fig.2.q. Each coil has two


Figure 9.1 3. Exploded view of the axial flux PM motor with counter-rotating rotor: I - mainpropeller,2-counter-rotat ingpropeller,3-radialbearing,4-outershaft,5-PMroto16

motor bearing, 7 - assembly ring, 8 - stator, 9 inner shaft.

Table 9.3. EMALS requirements [72]

End speed, m/sMarimum peak-to-mean thrust force ratioCycle time, sEnd speed variation, m/sMaximum acceleration, m/s2Launch energy, MJMaximum thrust, MNMaximum poweq MW

3volume, m-

Mass, kg

1031 .05451 . 556r22l . J

133< 425< 225 000

active surfaces and each coil surface interacts with the facing PM rotor. Inorder to achieve the opposite motion of the two rotors, the stator winding coilshave to be arranged in such a manner that counter-rotating magnetic fields areproduced in the machine's annular air gaps. The stator is positioned betweentwo rotors which consist of mild steel discs and axially magnetized NdFeBPMs. The magnets are mounted on the disc's surface from the stator sides.Each rotor has its own shaft which drives a propeller, i.e. the motor has twocoaxial shafts which are separated by a radial bearing. The anangement isshown in Fig. 9.13 [35].

Applications

9.4 Electromagnetic aircraft launch systemMilitary aircrafts are catapulted from the decks of aircraft carriers with the

aid of steam catapults. A steam catapult uses two parallel rows of slotted cylin-ders with pistons connected to the shuttle that tows the aircraft. The pistonsunder the steam pressure accelerate the shuttle until the aircraft will takeoff.Steam catapults have many drawbacks 172], i.e.:

r operation without feedback control;

r large volume (over 1100 m3; and mass (up to 500 t);

r occupation of the "prime" real estate on the canier and negative effect onthe stability of the ship;

r low efficiency (4 to 6%);

r operational energy limit, approximately 95 MJ;

r need for frequent maintenance.

The electromagnetic aircraft launch system (EMALS) is free of the draw-backs listed above. The EMALS technology employs linear induction or syn-chronous motors fed from disc-type altemators through cycloconverters. Theelectrical energy obtained from the carrier power plant is stored kinetically in

Figure 9.14. AFPM synchronous machine for EMALS. I - PM rotor assembly, 2 stator

assembly,3 -bearing,4-enclosure,5 -mountingflange,6 brake, T-shaftencoder.

295

296 A,Y]AL FLUX PERMANEI{T MAGNET BRUSHLESS MACHINES

Table 9.4. Specifications of AFPM synchronous machine for EMALS [72]

Number of phasesNumber of polesNumber of active stator slotsType of statorNumber ol stator windingsGenerator windingMotor windingMaximum speed, rpmMaximum frequency, HzOuput power at maximum speed, MWMaximum line-to-line EMF for motoring, VMaximum line-to-line peak voltage, VMaximum phase peak current, APower losses, kWEfficiencyResistance per phase, mf)Inductance per phase, pHStator coolingCoolantFlow rate, l/minAverage temperature of winding, "CAverage temperafure of stator core, "CType of PMsRemanence at 40"C, TAir gap magnetic flux density, TTooth magnetic flux density, TMaximum energy storage capacity, MJEnergy density, kJ/kgMass, kg

fl

2'p: 4os\ :24:0

double-sided slotted2

air gap sidebottom of slots

6400213381 .6112217006400127

0.8938,610.4

cold platewater and giycol mixture

1 5 1846 l

sintered NdFeB1 .05

0.9761 . 7t2118 . 16685

the rotors ofAFPM synchronous generators. The energy is then released as afew-second pulses to accelerate and launch an aircraft. The cycloconverterbe-tween the AFPM generator and linear motor raises the voltage and frequency.The EMALS operates in a "real time" closed loop control [72]. The require-ments are given in Table 9.3.

Specifications of the AFPM synchronous machine shown in Fig. 9.74 aregiven in Table 9.4 [721. The EMALS uses four AFPM machines mounted ina torque frame and grouped in counter-rotating pairs to reduce the torque andgyroscopic effect. The rotor of the AFPM machine serves both as the kineticenergy storage when operating as a motor and a field excitation system whenoperating as a generator. The electric power from the on-board generators is

Applications

(a)

297

(b)ll fra l n l

a d i

! ! i Tr,.drrd X

t 1 i n .4 -i4 ill

TOP OFTO{}LJ.ltNT

Figure 9.15. ECI drilling system: (a) general view, (b) power unit with AFPM synchronousmotors, (c) PA-44 Kaman Aerospace AFPM motor. Courtesy of Tesco Corporation, Calgary,Alberta, Canada.

fed to the AFPM machine via rectifier-inverters. There are two separate statorwindings for motoring and generating mode. The motor winding is located atthe bottom of slots to provide better thermal conductivity between the windingand enclosure.

9.5 Motrile drill rigsDrill rigs vary from small electric motor driven tools to large oil field rigs.

The basic elements of an aboveground drill rig are the power unit or motor,pump or air compressor for circulating drilling fluid to the bit and cleaning theborehole, drill head, hoisting drums and cables, derrick, mounting platformor deck and assorted equipment such as hammers for driving and removingcasing, portable mud pit, racks for stacking the drill rods and samples, smalltools for coupling or uncoupling and hoisting the drill string, etc. The powerunit (motor) performs the following functions:

298 AXIAL FLUX PERMANE]VT MAGNET BRUSHLESS MACHINES

Table 9.5. Specifications of ECI drilling systems with AFPM synchronous motors manufac-tured by Tbsco Corporation, Calgary, Alberta, Canada

ECE drilling system 670 1007Drilline unit without swivelMass, kgOperating length, m(including 2.8-m links and elevators)Make-up Torque (lpical), NmBreakout torque, NmMax. Drill Torque, NmMax. Speed, rpm

5,909

4.345 q65

7,5925,098187

6,270

4.349,4901 1 , 3 8 97,860187

Power system (mechanical module)Approximate mass, kgLength, mWidth, m

3,3406.42.3

3,7306.4a . - )

Power system (power module)Approximate mass, kgLength, mwidth, m

1 545

6.35 mm2.311

4 1 ) ( l

6.302.30

r operates a drive weight mechanism for percussion or churn drilling or pro-vides rotary motion to tum augers and coring equipment for rotary drillingoperations;

r operates a winch for raising and lowering the drilling and sampling equip-ment;

r provides downward pressure for pushing boring and sampling equipment,or lifting and dropping a hammer to drive casing or sampling equipment.

For most drilling and sampling operations, the power source is the power take-off from the truck motor on which the drilling machine is mounted or from aseparate engine which is assigned or attached as an integral component of thedrilling rig. It is estimated that approximately 90% of the motors are gasolineor diesel engines and 10oh are compressed air or electric motors. A drive trainwhich consists of gears or hydraulic pumps is used to convert the power sup-ply to speed and torque for hoisting and rotating the drilling equipment. Mostunits have a transmission which allows 4 to B speeds for hoisting and drilling.ln general, the hoisting capacity of the drill rig govems the depth of the bore-hole. A rule of thumb for selecting the power source is that the power whichis required to hoist the drill rods should be about three times the power which

Applications 299

is required to turn the drill string. For high elevations, the power loss is about3oh for each 300 m.

Large power AFPM brushless motors (Table 9.2) are especially suitable forportable drilling equipment because of their compact design, light weight, pre-cise speed control, high efficiency and high reliability.

ln the ECI lightweight top drive drilling system (Fig. 9.15) manufacturedby kscct Corporation, Calgary, Alberta, Canada, the traditional induction orbrush type d.c. motors have been replaced with high performance liquid cooledAFPM synchronous motors. This system is compatible with most 600 V a.c.rig power systems. The product highlights include:

s Kaman PA44 AFPM synchronous motors that (Table 9.2) have been suc-cessfully tested to 609 triaxial loading, making them the ideal choice forrough drilling environments ;

r AFPM synchronous motors which allow a high level of precision in speedand torque control not available with other motors;

r a modular design that allows drilling to continue at reduced power with onemotor;

r direct connection to the rigs a.c. bus and interface with the existing powersupply with minimal degradation to the rig powen

r the entire ECI system can be transpofted in three standard 6-m sea contain-ers.

Specifications of the ECI drilling system are given in Table 9.5.

9.6 ElevatorsThe concept of gearless electromechanical drive Jbr elevators was intro-

duced in 1992 by Kone Corporation in Hyvinkiiii, Finland [103]. With theaid of a disc type low speed compact AFPM brushless motor (Table 9.7'),thepenthouse machinery room can be replaced by a space-saving direct electrome-chanical drive. In comparison with a low speed axial flux cage induction motorof similar diameter, the AFPM brushless motor has a doubled efficiency and athree times higher power factor.

Fig. 9.16a shows the propulsion system of the elevator while Fig. 9.16bshows how the AFPM brushless motor is installed between the guide rails ofthe car and the hoistway wall.

Table 9.6 contains key parameters for the comparison of different hoistingtechnologies [103]. The disc type AFPM brushless motor is a clear winner.

Specifications of single-sided AFPM brushless motors for gearless passen-ger elevators are given in Table 9.7 [103]. Laminated stators have from 96 to

300 AXIAL FLUX PERMANEA|T MAGNET BRUSHLESS MACHINES

Figure 9.16. MonoSpace7nl elevator: (a) elevator propulsion system; (b) EcoDiscTnl motorCourtesy of Kone, Hyvinkziii, Finland.

Figure 9.17. Double-disc AFPM brushless motor for gearless elevators. Courtesy of Kone,Hyvinkdd, Finland.

Applications 301

120 slots with three phase short pitch winding and class F insulation. For ex-ample, the MX05 motor rated at 2.8 kW 280 V 18.7 Hz has the stator windingresistance Er : 3.5 f), stator winding reactance Xt : 10 Q,2p :20, sheavediameter 340 mm and weighs 180 kg.

Tahle 9.6. Comparison ofhoisting technologies for 630 kg elevators [03]

Quantity

Hydraulicelevator

Warm gear

elevatorDirect PM brushless

motor elevator

Elevator speed, m/sMotor shaft power, kWSpeed of motor, rpmMotor fuses, AAnnual energyconsumption, kWhHoisting efficiencyOil requirements, IMass, kgNoise ievel, dB(A)

0.63I 1 .01 50050

72000.3200350

60..65

1 . 05 .5

I 50035

60000.43 .5430

70. . .7 5

1 . 0

95t o

30000.60

t7050. . .55

Table 9.7. Specifications of single-sided AFPM bmshless motors for gearless elevators man-ufactured by Kone, Hy",rinkiiii, Finland

Quantity MXO5 MXO6 MXlO MX18

Rated output power, kWRated torque, NmRated speed, rpmRated current, AEfficiencyPower factorCoolingDiameter of sheave, mElevator load, kgElevator speed, m/s

Location

2 .82401 1 37.7

0.830.9

natural0.34480

I

hoistway

) - t

360961 0

0.850.9

natural0.40630

1

hoistway

o . /

800801 8

0.860 .91

natural0.481000

i

hoistway

46.0l 800I t J

1 3 80.920.92

forced0.651 800

4machine

room

302 AXIAL FLLTX PERMANENT MAGNET BRI]SHLESS MACHIAIES

Table 9.8. Specifications of double-disc AFPM brushless motors manufactured bv Kone,Hyvinkiiri, Finland

Quantity MX32 MX4O MXlOO

Rated output power, kWRated torque, NmRated speed, rpmRated current, AEfficiencyPower factorElevator load, kgElevator speed, m/s

5836001531220.920.93I 600

o

925700153zoz

0.930.932000

8

3 1 514,00021410600.950.964500l 3 .5

r&

Figure 9.18. Penny-motor. Photo courtesy of Mymotctrs & Actuator.s GmbH, Wendelsheim,Germany.

A double disc AFPM brushless motor for gearless elevators is shown in Fig.9.17 [03]. Table 9.8 lists specifications data of double disc AFPM brushlessmotors rated from 58 to 315 kW [03].

9.7 Miniature AFPM brushless motorsUltra-flat PM micromotor, the so called penny-motor is shown in Figs 9.1 8

and 9.19 [ a2]. The thickness is 1.4 to 3.0 mm, outer diameter about 12 mm,torque constant up to 0.4 p,Nm/mA and speed up to 60,000 rym. A 400-pm eight pole PM and a three-strand, 110-pm disc shaped, lithographicallyproduced stator winding have been used [42]. Plastic bound NdFeB mag-nets are a cost effective solution. However, the maximum torque is achievedwith sintered NdFeB masnets. A miniature ball bearins has a diameter of 3

Applications 303

Figure 9.19. Construction ofpenny-motor: 1 - shaft, 2 - soft steel yoke cover, 3 PMring, 4 ball bearing, 5 - stator winding, 6 flange, 7 bottom steel yoke.

Figure 9.20. Two-phase, four-coil, single-sided l5-mm AFPM brushless motor. Photo cour-tesy of Moving Magnet kchnologies,,Sl, Besancon, France.

mm. Penny-motors find applications in miniaturized hard disc drives, cellularphones as vibration motors, mobile scanners and consumer electronics.

Moving Magnet kchnologies (MMf) two or three phase, miniature AFPMbrnshless motors (Fig. 9.20) are well adapted to high volume low cost produc-tion. In order to obtain rigidity the stator coils are overmoulded. The statoris mounted on a single-sided printed circuit board. Each part can be man-ufactured using standard moulding, stamping techniques and automatic coilwinding with a specific design for simple and efficient assembly. Three po-sition sensing methods for the closed-loop control are used: (a) digital Hallprobes located in the stator, (b) EMF signal (sensorless mode) and (c) absoluteanalogue position sensor (position sensor mode).

MMT AFPM miniature rotary actuators (Fig. 9.21) have been designed forautomotive applications to provide an efficient, contactless, direct drive rotarymotion on a limited stroke. Ring, disc and tile shaped PMs have been used.The main features of this family of actuators are:

ffi

304 AXIAL FLUX PERMANENT MAG]VET BRUSHLESS MACHIAIES

Figure 9.21. Miniature two-phase, four-coil, 4-po1e, single-sided AFpM rotary actuator.Photo courlesy of Moving Magnet Technologies. 57, Besancon, France.

r contactless actuation principle;

r constant torque independent of the angular position for a given cunent;

r linear torque*current characteristic;

r two directions of rotation;

r high torque density.

Additional functions, such as a magnetic return spring or analogue contactlessposition sensing can also be implemented. Owing to the linearity of the torque-current characteristic and its independence ofposition, it is possible to operateactuators in an open-loop against a spring or in a simple closed-loop mode byusing a position sensor.

9.8 Vibration motorsAdvances in cellular telecommunication have made mobile phones to be

highly popular communication tool in modern society. Since a mobile phoneis now a gadget as necessary as a watch or wallet, small vibration motors withdiameters from 6 to 14 mm are manufactured in unbelievable large quantities(Fi5.9.22). Thetrends invibrationmotors formobilephones includereductionof mass and size, minimization of energy consumption and guaranteed stablevibration alarming in any circumstances [58].

There are two types of brushless vibration motors for mobile phones: cylin-drical or RFPM motor and coin type or AFPM motor (Fig. 9.23). The unbal-anced excitingforce generated by an eccentric rotor is

F : me{l :2trrnert2 (e.7)

E mobrle Dhone demand A aoplications of vibration motors

Applications

1999 2000 2001 2002 2003 2AA4 2AO5

Figure 9.22. Worldwide demand estimate for mobile phones and vibration motors

(b)

Figure 9.23. Coin type AFPM vibration motor for mobile phones [58]: (a) two coil motor; (b)rnulticoil motor. 1 - phase coil, 2 - PM (mechanically unbalanced system), 3 * ferromag-neticyoke,4 cover, 5-baseplate, 6 shaft, 7-bearing, 8-detentiron [58].

where m, e and n denote the rotor mass, eccentricity and rotational speed re-spectively. The rotational speed is the most effective design parameter to in-crease the unbalanced exciting force [58].

Moving Magnet Technologies single-phase AFPM brushless vibration mo-tors provide a strong vibration feeling and silent alert with a very simple design(Fig. 9.2q. Fabrication of MMT vibration motors is cost effective due to con-tactless design, scalable size and slim shape.

30s

306 AXIAL FLUX PERMANENT MAG},{ET BRUSHLESS MACHINES

Figure 9.24. Cost effective AFPM brushless vibration motor. Photo courtesy of Moving Mag-net kchnologies, Sl, Besancon, France.

9.9 Computer hard disc drivesThe data storage capacity of a computer hard disc drive (HDD) is deter-

mined by the aerial recording density and number of discs. It is expected thatthe aerial density wi l l soon increase from 6 Gb/cm2 - 38.7 Gb/in2 to 15.5Gblcm2 - 100 Gb/in2. The mass of the rotor, moment of inertia and vibrationincrease with the number of discs.

Special design features of computer HDD motors are their high startingtorque, limited current supply, low vibration and noise, physical constraintson volume and shape, protection against contamination and scaling problems.A high starting torque, 10 to 20 times the running torque is required, since thereadlwrite head tends to stick to the disc when not moving. The starling cur-rent is limited by the computer power supply unit, which in turns, can severelylimit the starting torque.

AFPM brushless motors (Fig. 9.25) can develop higher starting torque thantheir radial field counterparts. The additional advantage is zero cogging torque.The drawback of the single-sided AFPM HDD motor shown in Fig. 9.25a isthe high normal attractive force between the stator with ferromagnetic yokeand rotor mounted PMs. In double-sided HDD AFPM motors the stator doesnot have any ferromagnetic core and no normal attractive force is producedat zero-curent state. The stator has a three phase winding with coreless coilsfabricated with the aid of a litographic method. In a typical design, there aretwo coils per phase for 2p: 8 PM poles and three coils per phase for 2'p : 12PM poles. To reduce the air gap and increase the magnetic flux density, theso called pole fingers are created in the lower part of the hub and the rotor

Applications

I o v 1 0

Figure 9.25. Construction of computer HDDs with AFPM brushless motors: (a) single-sidedmotor; (b) double-sided motor. 1 - stator coil, 2 PM, 3 - shalt, 4 -beanng. 5 - hub,6 rotor ferromagnetic yoke, 7 stator feromagnetic yoke, B - base plate, 9 - pole fingers,10 nonmagnetic ring.

magnetic circuit is bended by pressing it towards the stator coil centres (Fig.9.25b). According to [129], for a HDD AFPM brushless motor with a 5l-mmstator outer diameter, r^/r : 180 turns per phase and torque constant k7 -

6.59 x 10-3 Nm/A the current consuption is 0.09 A at 13 900 rpm and no loadcondition.

The acoustic noise of HDD brushless motors with ball bearings is usuallybelow 30 dB(A) and projected mean time between failures MTBF : 100 000hours. HDD spindle motors are now changing from ball bearing to fluid dy-namic bearing (FDB) motors. Contact-free FDBs produce less noise and areserviceable for an extended period of time.

Numerical example 9.1Find the kinetic energy and tensile stress of the ring with dimensions Ro,t :

0.142 m, Rtn - 0.082m, thickness d - 0.022m and density P : 7800 kg/mjlrotating at the speed of 30 000 rym.

307

1

U

308 AXIAL FLUX PERMAI\|IENT MAGNET BRUSHLESS MACHINES

Solution

The mass of the ring is

rn : rpcl(R3,, - R7): n7800 x 0.022(0.1 422 - 0.0822) :7.25kg

The moment of inertia according to eqn (9.2) is

I : rnr.zstl.7422 + 0.0822) : 0.092 kgm2

The rotational speed n : 30 000/60 : 500 rev/s and angular speed O :2tr500: 3141.6 rad/s. Thus the kinetic energy according to eqn (9.a) is

En: n37800 x 0.022(0.1424 - 0.0824) x b002 : 480.74 kJ

The tensile stress according to eqn (9.2) is

7800 x 3141.(2o _ ______J (0.0822 + 0.082 x 0.142 + 0.1.422): 988.6 Mpa

3

The energy density according to eqn (9.6) is

480 740L l i - : 66.3 kJ/kg^ 7.25

The shape factor of the ring [3] is

kst,. - "rI : eo sooff$1su : 0.b23

Numerical example 9.2Find the main dimensions of a three-phase, 1200 W, 4-pole, 200 000 rym

AFPM synchronous generator for a mobile battery charger. The total nonmag-netic air gap including magnet retaining ring (Fig. 9.2) should be g : 2 mm,number of slots sy: 12, air gap magnetic flux density Bs : 0.4 T, line cumentdensity A- : 16 000 A/m, PM inner-to-outer diameter ratio k,1: 0.5, PMtemperature 350"C. Vacomax 225 SmCo PMs (Vaccumschmelze, Hanau, Ger-many) with Br2s : 1.04 T and H" = 760 kAlm at 20"C arc recommended.The temperature coefficient for B, is a6: -0.035 o l"C,leakage flux coef-ficient opv : 1.3, EMF-to-voltage ratio e : 1.3 (Ef > V) and pole shoewidth-to*pole pitch ratio a,; - 0.72

Solution

The winding coefficients (2.8), (2.9) and (2.10) arc k41 : 7, k1t : 1 andk-7 - 1 since qr : 121(4 x 3) : 1. The coefficient kp according to eqn(2.20) is

Applications

t r , :1 (1 + 0 .5 ) (1 - 0 .52) : 0 .1416

The outer diameter of PMs according to eqn (2.93) is

309

1.3 x 1200Dout

r20.74Ix 1 x (200000/60) x 0.4 x 16000 x 0.8 x 0.8: 0.055 m

The remanent magnetic flux density at 350"C according to eqns (3.2) is

I i , : 7 '^ l ' -0'035 2o)l : 0.973 7' t u L r - r

3 5 0 t t u '

l

Since demagnetization curves for different temperatures are parallel lines, therelative recoil magnetic permeability will be approximately the same as for20"C (linear magnetization cule), i.e.

1 .04fL t ' r 'e c

0 . 4 t r x 1 0 6 x 7 6 0 0 0 0 - 1 .089

The PM thickness with the leakage coefficient o1- included, can be calculatedon the basis of eqns (3.13) and (3.9), i.e.

, oI1[B*o 1.3 x 0.4hnr rt F,,"" U;?ffig : 1'08909f3_

1j x 040.002 - 0.0028 rn

The innerdiameterof PMs is Din: k, tDout: 0.5 x 55:27.5 mm, radiallength of PM l,r,r : 0.5(55.0 - 25.0) : 1"3.7 mm, average diameter of PMsD : 0.5(55 .0 + 27 .5) : 41 mm, average pole pi tch r : r4l l4: 32.3 andaverage PM circumferential width bo : e..ir : 0.72 x 32.3: 23.3 mm.

Numerical example 9.3A 10-kW 2200-rpm electric motor operates at almost constant speed ac-

cording to the torque profile given in Fig.9.26. The overload capacity factorko"f : Trurr lTrh, : 1.8. Find the thermal utilisation coefficient of the motor.

Solution

The required rated shaft torque is

. r ,a . s n r -

Port 10,000

2rn 2r x (2200160)

The rms torque based on the given duty cycle is

: 43.4 Nm

T)|,,,"(tv+t2+. . .+f,) : T?tt+:rltz+.. .+Tlt. or T:^"Lto:\rlt i

310

Thus


Trrn" :

252 x 3 t 402 x8 + 652 x 5 + 382 x 30 + 152 x 103+B+5+30+10

38.1 Nm

The maximum torque in Fig. 9.26 cannot exceed the rated shaft torque timesthe overload capacity factor ko4Trhr : 1.8 x 43.4:78.72 Nm. Also, therequired 7"7." should be greater than or equal to fl--".

The coefficient of thermal utilisation of the motor is

l-r?tV I to

?ff " Trrovo :#' fioYo : B7'8%

Figure 9.26. Torque profile of the elechic motor accordingto Numerical example 9.3


A magnetic vector potential

A line current density; cross-section area

o number of parallel current paths of the stator (armature) winding

E vector magnetic flux density

B magnetic flux density; damping of the system

b instantaneous value of the magnetic flux density; width of slot

be pole shoe width

C y cost of frame

Ci* cost of insulat ion

Cs cost of all other components independent of the shape of the machine

Cpm cost of PMs

Cr. cost of the rotor core

C"h cost ofshaft

C- cost of winding

ccu cost ofcopper conductorper kg

cE armature constant (EMF constant)

cFe cost of ferromagnetic core per kg

cins cost of insulation per kg

cp specific heat at constant pressure

cptt cost of PMs per kg

csteet cost ofsteel per kg

cu heat capacity

312 AXIAL FLUX PERMANENT MAG}{ET BRUSHLESS MACHINES

D diameter; duty cycle of power semiconductor switches

Dn inner diameter of PMs equal to the inner diameter of stator bars

D,t,t. outer diameter of PMs equal to the outer diameter of stator bars

E EMF (rnzs value); electric field intensity

Ef EMF per phase induced by the rotor without armature reaction

Ei internal EMF per phase

e instantaneous EMF: eccentricitv

F force

Ftz shape factor of two surfaces involved in radiation

f space and/or time distribution of the MMF

fo armature reaction MMF

F"r" MMF of the rotor excitation system

f frequency; friction factor

G perrneance; gap ratio g f R

g air gap (mechanical clearance); gravitational acceleration

Gr Grashof number

g' equivalent air gap

fr vector magnetic field intensity

H magnetic field intensity

h height; heat transfer coefficient

hm height of the PM

1 electric current

Io stator (armature) current'

instantaneous value of current; enthalpy

vector electric current density

moment of inertia

cument density in the stator (armature) winding

current regulator gain

inverter gain

coefficient, general symbol; thermal conductivity

skin effect coefficient for the stator conductor resistance

reaction factor in d-axis

reaclion factor in o-axis


kg Carter's coefficient

l*,1 inner-to-outer diameter ratio ka: DinlDaut

kat distribution factor for fundamental

ks EMF constant kg : 6;6Q,

ky form factor of the fie1d excitation ky : B*,gf B*n

h stacking factor of laminations

koc.f overload capacity factor ko.y : Trro* /7"h,kpt pitch factor for fundamental

k"ot saturation factor of the magnetic circuit due to the main(linkage) magnetic flux

ky torque constant ky : c7Q 1klrt winding factor k-1 : k4ykpt for fundamental

L inductance; length

lrc length ofthe one-sided end connection

Li armature stack effective length

174 axial length of PM

L|l mutual inductance

M' momentum

m number of phases; mass

m mass flow rate

rna, amplitude modulation ratio

mf frequency modulation ratio

N number of turns per phase; number of machines

Nu Nusselt number

n rotational speed in rpm; independent variables

no no-load speed

P active power

P"lrn electromagneticpower

Pr" input power

Pout output power

Pr Prandtl number

LP active power losses

LPtp" stator core losses

a l l

J I J

314 AXIAL FLUX PERMANENT MAGI,{ET BRUSHLESS MACHINES

LPt- stator winding losses

LPzp" rotor core losses

LP". eddy current losses in stator conductors

LPp friction losses

LPpm losses in PMs

LP,ot rotational (mechanical) losses

LP.,tnd windage losses

A,p specific core loss

p number of pole pairs; pressure

p, radial force per unit area

p wetted perimeter

a electric charge; reactive power; volumetric flow rate

Q".n, enclosed electric charge

R radius; resistance

Rt armature winding resistance of a.c. motors

Rt, inner radius of PMs equal to the inner radius of stator bars

Rout outer radius of PMs equal to the outer radius of stator bars

Re Reynolds number

ffirn air gap reluctance

$tpto external armature leakage reluctance

ffip,vl Permanent magnet reluctance

S apparent power; surface

Sw cross section area of PM; SM : uuLnr or,9,x1 -- boLnt

s cross section area ofstator conductor

sr number of stator slots equal to the number of stator teeth

T torque

Ta electromagnetic torque developed by the machine

Trt,"I reluctance torque

Td'u* synchronous or synchronizing torque

T*, mechanical time constant

Trt shaft torque (output or load torque)

t time; slot pitch

U internal energy

Symbo ls and Abbreviations 315

u tangential velocity

V electric voltage; volume

rr instantaneous value of electric voltage; linear velocity

W energy produced in outer space of PM; rate of change of the air gapenergy

W, stored magnetic energy

I-u energy per volume, J/m3;radial velocity'It)M width of PM

X reactance

Xy stator winding leakage reactance

Xod, d-axis armature reaction (mutual) reactance

f aa q-axis amature reaction (mutual) reactance

X",j, d-axis synchronous reactance; Xsd: Xt * Xo.a

Xss q-axis synchronous reactance; X"q: Xt I Xoq

Z impedance Z : R+ jX ; lZ1- - Z : \ /R +Ta complex attenuation constant of electromagnetic field

a.i effective pole arc coefficient a;: brf r

7 fotm factor of demagnetization curue of PM material

d power (load) angle

6; inner torque angle

€ eccentricity

s emissivity; surface spectral property

\ efficiency

1 equivalent sand grain roughness

d rotor angular position for brushless motors

?y temperature; angle between Io and Io4

l coefficient of leakage perrneance (specific leakage permeance)

),r turbulent parameter

p dynamic viscosity

lto magnetic permeability of free space po :0.4r < 10-6 H/m

Fr relative magnetic permeability

l-L,rec recoilmagneticpermeability

Itrrrec relative recoil penrreability ltr,ec : lrr""l Fo


number of the stator zth harmonic; kinematic viscosity

reduced height ofthe stator conductor

specific mass density

electric conductivity ; Ste fan-Bol tzmann constant

form factor to include the saturation effect

output coefficient

radiation factor

average pole pitch; thermal time constant

magnetic flux

excitation magnetic flux

leakage flux

power factor angle

flux linkage V : l/O; angle between Io and E1

flux linkage

angular speed O :2rn

angular frequency a :2trf

u

p

of

or

T

oQy

O1

6v4,au)

Subscripts

a armature (stator)

au[J average

c conduction

cu control volume

Cu copper

d direct axis; differential; developed

e end connection; eddy-current

eIm electromagnetic

eq equivalent

erc excitation

e.rt external

Fe ferromagnetic

f field; forced

.f r friction; free

Svmbols and Abbreviations

aff gap

hydraulic; hysteresis

inner

leakage

magnet

peak value (amplitude)

normal and tangential components

outpui, outer

quadrature axis

rated; remanent; radiation; rotor

cylindrical coordinate system

reluctance

rotational

slot; synchronous; system; stator

saturation

shaft

starting

synchronous or synchronizing

teeth; total

useful

convection

ventilation

windage

yoke

cartesian coordinate system

stator; fundamental harmonic; inlet

rotor; exit

317

h'l,n

I

M'tn

f r r t

out

o

T'

r , 0 , z

reI'rot

5

sctt

sh

st

syn

t

u,I)

uent

uind

vT , U , Z

1

2

Superscripts

inc incremental

(sq) square wave

(tt ftapezoidal

318 AXTAL FL\.]X PERMANEAIT MAGNET BRUSHLESS MACHI],{ES

Abbreviations

A/D analog to digital

AFPM axial flux permanent magnet

AIFI American Iron and Steel Industry

a.c. alternating current

BPF band pass filtering

CAD computer-aided design

CPU central processor unit

DSP digital signal processor

d.c. direct current

EDM electro-discharge machining

EMALS electro-magneticaircraftlaunchsystem

EMF electromotive force

EMI electromagnetic interference

EV electric vehicle

FDB fluid dynamic bearing

FEM finite element method

FPGA field programmable gate anay

HDD hard disk drive

HEV hybrid electric vehicle

IC integrated circuit

IGBT insulated-gate bipolar transistor

ISG integrated starter-generator

LPF low pass filter

MMF magnetomotive force

MMT moving magnet technologies

MOSFET metal oxide semiconductor (MOS) field effect transistor

MVD magnetic voltage drop

NdFeB neodymium iron boron

PFM pulse frequency modulation

PLD programmable logic device

PM permanent magnet

Symbols and Abbrev iat ions

PWM

RFI

RFPM

SEMA

SMC

SmCo

SSC

pulse width modulation

radio frequency interference

radial flux permanent magnet

segmented electro-magnetic array

soft magnetic composite

samarium cobalt

solid state converter

3r9

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Index

Acoustic noise, 9, 237, 307Active rectifier, 66, 2 1 7Air conrpressor, 204, 297Air-cooled, 49, | 62, l1 4, 202, 254, 255, 282Applications of AFPM machines

Computer hard drsc drive (HDD), 152,306

Counterrotating marine propeller, 292Electric vehicle, 2, 285, 287, 289Electromagnetic aircraft launch system

(EMALS) ,295Electronic differential, 290Gear lesselevators,2T,299 302High speed generators, 281Hybrid electric vehicle, 285, 287Low speed generators, 281, 282Microturbine, 66, 97 , 281 , 282Mobile drill rigs, 297Mobile phone, I 54, I 89, 304, 305Power generatio n, 203, 240, 28 |Precision robotics, 203Propulsion system for submarine, 292Ship propulsion,29lMbration motors, I 8l , 303 , 305Wirrd generator, 1,282 - 285

Armature constant, (see EMF constant)Armature reaction. 27 , 57 , 58, 64,96, 128, 110,

1 1 1

Fotm factor, 58, 69lnductance, 1 30, 1 59Reactance, 61, 130, 147 , I 59, I 84, 209

Armature winding resistance, 42, 157Attenuation coefficient, 48Axial flux PM machines with

Coreless stator, 7, 32, l2l , 1 53, I 94Double-sided consruction, 6, 7, 10, 27

35 , 4 l , 54 , 111 , 125 , t 26 ,174 , 193 ,262,283

Intemal PM ro1or, 8, IIntemal stator, 7,24, 153

Iron core, 7, 125. 121 , 128,237Mult id isc construct ion, 8, 19, 32, 55,281Printed winding rotor, 4, 5, 1 14Sine-wave excitation, 51, 61, 136, 162Single-sided construct'ioll, 6, 27, 37, 89,

125, 143,299,303,306Square-wave excttation, 62, 1 4 1Wound rotor,4, 5

Battery electric vehicle, 285, 289Blowers, 5, 97Bottle-neck feature, I 7

Centrifugal force,174Coefficient of

Additional core losses, 44, 45Differential leakage, I 3 IDistortion, 44,49Drag,49,78Leakage perrneances, 131, 112Skin effec1, 42, 43Thermal expansion, 89, 253

Coi l shapes, 10, 153Rhomboidal, 10, 36, 3'7, 267Toroidal , 10,35Trapezoidal , 10, 35 - 37, l4 l ,162,197

Computer hard disc drive (HDD), 154, 306HDD spindle motol 307Pole fingers, 306

Control ,213Conduction period, 21 4, 223Current angle, 230,232 234,242Current control, 219, 221, 229, 230, 232

_ ) 1 1 ) 1 0

Digital signal processor, 237High frequency voltage injection, 239Sensorless position control, 237 -239

Single sensor current controller, 2 I 9Sinusoidal AFPM machine, 223,224

338

Speed control, 1 54, 222, 230, 234, 237Trapezoidal AFPM machine, 213, 214

Convefier-fed AFPM machine &ive, 213Cooling of AFPM machine, 255

Direct water cooling, 112,267Extemal fan,265Extemal ventilation, 25 5, 264Heat p ipes, 265,277Self-ventilation, 255

Cost model, 198Current

Armature (stator), 45, 50, 52, 54, 59,62,64, 102,103,1s7

d-axis, 143,226,232Densi ty, 38, 39, 41, 54,72, 112, 197Fictitious field, 157, 227,228Instant average, 218, 219q-axis, I 39, 140, 143, 226,229, 246Ripple, 1 28, 221,222,236,237Starting, 306versus speed characteristic, 200

Cycloconverters , 295, 296

Disc motors, 3,32, 56Distributed generation system, 194, 203, 281

Flywheel motor-generator systems, I 94Nonrenewable, 28 IRenewable,28l

Duties (operation)Continuous duty, 270Drty cycle,272Intermittent duty, 65, 270, 272Short{ime ilrty. 27 0. 27 1

Dynamic v t scosity, 49, 267

Eddy cunent brake, I 3, 2 IEddy current loss resistance, 1 56, I 63Efficiency, 32, 42, 50,66, 138, 156, 194, 199,

202,285,295,299Elevators, 2, 27 , 299, 302EMF

Armature reaction, 59Sine-wave motor,41, 61, 137Sinusoidal , 6, 141 ,223Square-wave fioro1 62, 1 4lTrapezoidal, 5, 141, 213Waveform, 5, 6, 1 41, 213, 214, 223

EMF constant, 41, 63

Fabrication ofCoreless windings, 114 116Laminated siator cores, 87Rotor magnetic circuits, 109 - I I ISlotted windings, 112 - 114Soft magnetic powder cores, 87 89Wind ings , 112 116

Factor


Accounting for increase in losses,45Carter factor, 8, 9, 46, 59, 106, 129Distributron factor, 34Form lactor ofdemagnetization curve, 93of impedance increase, 16, 23Pitch factor, 34Saturation factor, 20, 59, 106, 134, 180Stacking factol 80, 82

Failure of rotor-shaft mechanical joint, 2, I 9F an, l, 2, 5, 50, 9'7, 252, 254, 255, 262, 265, 282Faraday's disc, 3, 20Fi lm coi l winding, 114,116,154Fini te e lement method, 45, 141,160,175

Axial-symrnetric element, I 75Boundary conditions, 1 41, 17 5Dirichlet boundary conditions, 1 42Neumann boundary conditions, I 42Periodic boundary conditions, 14iShell element, 175So'lver, 142Triangular element, 1 60Virlual work method, 175

Fourier expansion, 143

Gap rat io, 254,255Gauss-Serdel iteration, 27 0, 2'7 7

Halbach array, 109 lll, 121, 123, 153, 192,193,196,201

Hall effects, 220,222Heat transfer, 179,249

Conduction, 250,268Convection, 250 - 253,267,268Emissivity, 250Radiation, 250,268Shape factor,25lThermal conductivity, 250, 268

High speed generators, 281Microturbine, 66, 97, 28 1, 282Miniature generator set, 282Turbocenset,28l

Hydraulic diameter, 261

Inductance, 9, 62, 137, 143, 159, 160, 162, 202,226 ,227 , 231 , 232 ,237 , 240

Armature reaction, 59, 130, 159,227End winding, 162Leakage, 159,228Mutual, 1 57, 159, 227, 228Sel f , 157Synchronous, 128, 137, 141, 157, 159,

160,2t4,215,227Induction machine,4, 6, 156, 159

Differential leakage factol 134Differential leakage flux, 134,159Disc-type, 4, 6

INDEX

Kinematic viscosity of fluid, 253Krnetic energy, 289, 296

Laplace transform, 221Large AFPM motors,29l

Basic pafis. 29 ICold plate, 291,292For ship propulsion, 291 294Water cooling, 32, 3"1 , 112,267

LawsFourier's law, 250Kirchhoff's magnetic voltage law, 20Newton's law of cooling, 251

Line current density, 38, 39, 41, 54Litz wires, 167, 169Load angle, 53, 140, 156Lorentz force theorem, 153Losses

Armature (stator) winding, 42, 43, 50,131 ,140 , t 56 ,16 ' . 7 , 249

Core , 10 , 32 , 44 ,45 ,47 , 50 , 52 , ' 19 ,8 l83 , 85 , 127 , 128 ,137 ,153 , 156 ,

163, t90,229Eddy-current , 9, 32, 44, 45, 48,74, '75,

80 ,84 ,97 ,138 , 153 , 156 , 163 , 164 ,l 67, I 68, 170, 17 1, 190, 200, 268

Excess, 44For nonsinuso'idal cunent, 50Frequency dependent, 50Friction, 49, 258Hysteresis, 44,45,17In PMs, 32, 45, 46, 156,268Minimization of, 281Rotational, 49, 138, 249, 268, 272Ventilation,49Windage, 49,7&,170,183, 208, 281

Low speed generators, 28 l, 282Performance characteristics, 285Wind turbrne generator, 282, 283, 285

Magnetic circuit, I 7, 2'.7 -32, 90,94, 101, 109 -

l l lCalculation, 94,107 109Fab r i ca t i on ,109 l l l

Magnetic flux densityAir gap, 32, 38, 39. 64, 68, 94,95, I I 6,

117, 142, 143, 192, 197At the surface ofHalbach anay, I I 1Average, 38,39,76Average-tG-peak ratio, 38Coefficient of distoftion, 44, 49,73, 180d-axis, 57Distribution in the air gap, 128, 130Peak value, 38, 39, 68, 75, 11l ,121q-axis, 58Remanent, 19, 91, 92, 95 - 97, 100, 1 1 1,

117 . l 2 t . 192

339

Saturation, 73,85,92Magnetic permeability, 20, 47Magnetic saturation, 9, 57, 106, 154, 161.205,

zzoMagnetic vector potential, 13, 14, 160Miniature

AFPM brushless motor, 302, 303Generator set, 282

Moment of inertia, | , 222, 288,306Moody diagram, 261Mutual inductance, (see Armature reaction in-

ductance)

Noise, 9, 130, 174, 194,23'7,306, 307Nusselt number, 252 254,267

Park's transform ation, | 6 l, 225Penny-motor, 302, 303Permanent magnet, l, 90, 95

Alnico, 3, 5, 95, 96Classes, 95Coefficient ofleakage flux, 93Coerciv i ty , 91, l0 l , 192Demagnetization curve, 90, 92, 93 98,

100 ,103Feni te,3,95 97Intrinsic coercivity, 92Leakage f lux, 93,94, 103, 107, 108, 109,

130Magnet ic c i rcui t , 86, 90,94,99,100, 102,

103 , 106 , 107 , 109 - r r lMaximum magnetic energy, 93, 101NdFeB , 3 ,45 , 95 , 98 , 99 ,192 ,197 , 198 ,

294,302Operating diagram, 99Operating point, 95, 103Rare-earth, 3, 93, 95, 97 99Reco i l l i ne ,9 l , 95 , 101 - 103Recoil permeability, 58, 91, 93, 95Remanence, 5, 90, 9lSmCo, 45, 95, 97, 98Stabilization, I 03Volume of, 94, 128

Pemreance, l0 l - 103, 106Air gap, 40, 95, I 03, I 07Differential leakage, 134, 159Dividing the magnetic field into simple

solids, 103 - 106End connection leakage, 132, 133, 14'1.

1 5 9Fringing flur, 107,Slot leakage, 130 - 132, 159

Pole pitch, 10, 12, 16, 34, 3'1, 40, 47, 106, 129,t4 l

PowerApparent, 148,232

340 AXIAL FLUX PERMANENT MAGNET BRUSHLESS MACHII{ES

Electromagnetic , 54 - 56, 1 36 - 1 38, 1 40,l 4 l , 150 , 156 , 158 , 216 ,226

Input, 66, 137, 138, 156, 158Ou tpu t . l , 19 , 50 , 56 , 66 ,79 ,137 ,138 ,

141, 156, 158, 162, 249, 281, 292Pulse width modulation (PWM), 44, 141,194,

218 - 220, 224, 234, 236, 237, 246Pumps, l, 2, 97, 255, 266, 29'7, 298

Reactance, 130Armature react'ion, 5l , 61, 130, 159Differential leakage, l3 IEnd connection leakage, 1 3 1Leakage , 51 , 130 , 131 , 155Synchronous, 51, 65, 121, 130, 197Synchronous d-axis, 158, 185Synchronous q-axis, 158, 185

Relative recoil permeability, 58, 93, 95Reynolds number, 49, 253, 254, 261Rotary actuator, 303

Sa l i en t po le , 6 ,8 ,9 ,31 ,88 , 89 , 138 , 157 ,230Salurat ion factor ,59, 106, lJ4Shapes of PMs, 109Shock, leakage and friction, 259Si l icon steel , 7 j , '79, 128Sinusoidal excitation, 6 ISizing equations,54 56Skewed slot, 87Skin effect coeficient, 42, 43, 50, 131Slip factor, 258, 259, 261Soft magnetic composite, 84, 85, 87, 88Solid-state convefter, 128, 213, 214, 216, 221,

224,234,238Stacking factor, 80, 82Stefan-Boltzmann constant, 25 IStokes'theorem, 160Synchronization with utility grid, 66

Infinite bus, 66Power circuit, 6'7, 214, 216Synchroscope, 66

System losses, 260,261

Thermal equivalent circuit, 268, 27 0, 2'/ 5Conservation of energy, 25'7 ,269Control volume, 256,269 -271

Thermal capacitance, 267 - 210Thermal resistance, 26'7 , 268,27{)

Time constantElectrical, 205,234Electromagnetic, 1 85, 1 87, 1 88

Mechanical, 18"1, 218, 234Thermal,270,272

Transverse flux machines, iTopologies, l, 3, 6, 125, 249, 262Torque,37 39

Cogging, 9, 31, 32, 87, 194, 200, 306Control. 219,299Developed, 41, 137, 1 50, 216, 227Electromagnetic, 3\, 37, 39, 40, 41, 56,

61 , 63 , 153 , 156 , 158 , 189 , 192 ,193,224,232

sha f r , 138 ,150 ,156Torque-curent characteristics, | 54. 304Torque-speed characteristics, 64, 134,

197,285Torque constant, 4I, 61, 63, 162, 197, 203, 233,

302,307Toys,97Turbulence parametet, 254Types ofAFPM machines, 4,125,213

Induction machines, 4, 6, 156PM brushless d.c. machines, 4PM d.c. commutator machines,4Synchronous machines, 4, 5, 5l ,224

Unbalanced force, 178, 304, 306

Vibrat ion, 174, 178, 189, 194, 286,292, 303,304, 306

Vibration motor, 189, 303 - 305Coil-type motor, 304Cylindrical, 304

Voltage gain, 221

Wind turbine, 282 , 283 , 285Winding

Coil pitch to pole pitch ratio, 34Coreless stator winding, 35, 153, 169,

192,194Distribution factor, 34DoubleJayer winding, 42,72, 132Drum-type stator winding, 35Pitch factor, 34Printed, (see also Film coil winding). 4, 5,

1 1 4 - 1 r 6 , 1 5 4 , 3 0 3Salient pole winding, 37Single- layer winding, 33, 35, 132, 133Slot less windings, 1,9Winding factor, 34, 41, 57, 68,'71, 133,

145 ,181 ,206Windscreen wipers, 97

axial flux permanent magnet brushless machines

Documents

doublesided machines

stator core losses2

stator conductors2

stator winding losses2

coreless stator winding2

magnetic flux2

internal coreless stator2

magnetic circuits2