7. magnetic circuitslund university / lth / iea / avo reinap / eien20 / 2020-02-11 2 l7: magnetic...

11-FEB-2020EIEN20 Design of Electrical Machines

7. Magnetic circuits Soft and hard magnetic materials Magnetic design

Lund University / LTH / IEA / Avo Reinap / EIEN20 / 2020-02-11 2

L7: Magnetic circuits• Soft and hard magnetic materials• Design of magnetic core

– Torque expression– Main magnetizing flux path

• Permanent magnet machines – Assignment A4 (continuation of A3)– PMSM, BLDC and Dimensioning– Powder core machines

• Exploring single-fed machines: inductance and reluctance machines through FEMM and Ansys- RMxprt


Electromagnetically active parts• Coil or winding – to produce

variable magnetic flux• Permanent magnet – to

produce invariable magnetic flux

• Soft magnetic core – to provide an easy path for the flux

• Torque = excitation alignment torque + reluctance torque

– T=ψm isq +isd isq (Ld -Lq )


Analysis->synthesis->design• Specify magnetisation

arrangement B() and winding layout N()I(t)

– Magnetisation paths– Find induced voltage, forces

and torque and power loss mechanisms

• Interaction– Estimation of linking flux – Determination of current I– Deriving torque from I…

• Attraction– Estimation of gap

permeances G– Estimation of linking flux – Deriving torque from energy

B()F()

dMMFBrlT 2

0


Design Target

mech

T

el PTdttituT

P 0

1• Energy conversion

• Torque per rotor volume

• Air-gap shear stress

• Product of magnetic and electric loadings

B

l

r

wz K

T

F

222

gapRT AF

lrFr

VT

BKA

BKwzABIz

AF

gapgapgap

η - efficiency

σ=kBK


Forces on wire, slotting, leakage

• Force on current-carrying conductor in an uniform magnetic field Fx =By Iz z

• Slotted coils = mechanical support + reduced reluctance of the mutual flux path Fx =tx Axz =1/μ0 *Bx By xz

• Leakage flux, does not contribute gap (mutual) flux and torque generation


Electrical machine examples• Electrical machines with stator magnetization

– Induction machine– Reluctance machine

• Presence of magnetic core and very small air- gap are essential

• Same size, voltage and power

– Ø155/94-H120 mm– 2.2kW, 400V, 50Hz

-B-B

-B+A

+A+A

-C-C-C+B+B+B-A

-A-A

+C+C+C-B-B

-B+A

+A+A

-C -C -C +B +B +B-A

-A-A

+C+C+C47.3 7715.0

+A

-C

+C-B

+B

-A

+A

-C

+C -B

+B

-A

47.3 7715.0


Induction machine

• Induction machine is an electrical transformer– the magnetizing circuit is seen from no load test (NLT)– leakage inductances are found from locked rotor test (LRT)

• Load resistance Rr ’/s consists of equivalent electromechanical load resistance Rr ’(1-s)/s and actual winding resistance Rr ’

sRIsT rr

em

'2'3,

Lund University / LTH / IEA / Avo Reinap / EIEN20 / 2020-02-11 9© Avo R 9

Induction machine – 2SIE 100L4A

• FEMM quasi-static @ slip-frequency

• Ansys RMxprt – machine geometry library + ”non FE” models

Stator size Do /Di -H mm 155/95-100Power Pn , @50Hz W 2200Speed nn , @50Hz rpm 1440Current In , @400V A 4.5 (7 max)Efficiency η, % 84.7,85.5,84.6Power factor cosφ - 0.83Start current Ia /In - 7.3Start torque Ta /Tn - 2.4Knee torque Tkn /Tn - 2.8Inertia J kgm2 0.0070Weight w kg 25.5Cost* SEK 6840


• Geometry– Rotor and stator– Do/Di-H

• Windings– #Slots, #Poles,

#Phases• Materials

– BH-curve– Loss characterisation

• Operation point– Current distribution

Model specification


Semi-closed slots• Semi-closed slots are

most common for Ems• Slot geometry defined by

– Bredth b– Height h

• Slot can slightly vary in respect to slot opening and slot bed

b2

b1

b0

h2

h1

h0


Series of quasi-static analyses• Nominal current & slip

frequency


FEMM Tω - characteristics• Expected ~15Nm @ 1440 rpm• Unstable operation point under

“knee”

1410 1420 1430 1440 1450 1460 1470 1480 1490 1500-18

-16

-14

-12

-10

-8

-6

-4

-2to

rque

, T [N

m]

1410 1420 1430 1440 1450 1460 1470 1480 1490 15000.02

0.04

0.06

0.08

0.1

0.12

0.14

0.16

0.18

0.2

indu

ctan

ce, L

[H]

speed, n [rpm]

Re(B)+Im(J) Im(B)+Re(J)


IM @ Ansys RMxprt


Winding Layout


• Torque, current and efficiency @ 400V from 50 to 100Hz

Characteristics


Reluctance machine

0 20 40 60 80 100 120 140 160 180-25

-20

-15

-10

-5

0

5

10

15

20

25

torq

ue, T

[Nm

]

0 20 40 60 80 100 120 140 160 1800.02

0.03

0.04

0.05

0.06

0.07

0.08

0.09

0.1

0.11

0.12

indu

ctan

ce, L

[H]

position, e [deg]

Torque and flux linkage at nominal current 6.5Apk and at the doubled current level

0 20 40 60 80 100 120 140 160 180-40

-30

-20

-10

0

10

20

30

40

torq

ue, T

[Nm

]

0 20 40 60 80 100 120 140 160 1800

0.05

0.1

0.15

0.2

0.25

indu

ctan

ce, L

[H]

position, e [deg]

+A

-C

+C -B

+B

-A

47.3 7715.0


RM @ Ansys RMxprt

• Aligned and unaligned flux linkage


RM Tω - characteristics

IT

P

η

Home assignment A3Performance estimation for a three-

phase PM synchronous machine

B

Hc

Do

B A

[mch]=EMK_task_3(con)

[geom,mch]=EMK_geom_1(md,con)

EMK_gofem_1(geom,md,task)


Multi-phase winding distribution

• Multi-phase constant balanced instantaneous power• A sinusoidal generated voltage is desirable • A sinusoidal variation of flux density round the rotor• Magnetic cores, distributed and concentrated windings


Sinusoidally-fed PM motor• N-phase system: Nph =3• P-pole excitation: Np =2 (4,6..)• S-slot stator: Ns={3,6,9,12, …}• Sinusoidal distribution

tPiDNk

tPrPK

dd

rKdrK

iPNktP

eis

s

espis

s

sp

ississsp

sspespsp

2cosˆ6

2cos

2)(

)(1)()()(

ˆ423

2sin)(

1

1

2

0

111

s

s

F

FF

FFF


Total force in the gap• The force on a current carrying conductor in the

presence of a magnetic field

σshear

B

I

ssgmesgmeis

eisesegm

eissgm

iNkBlKBlD

dlrtPKtPB

dlrKBF

ˆ32

2cos

2cos

)()(

1111

2

011

2

0


Magnetic shear stress• Maximum force is when flux density B() and surface

current K() waves are coincident i.e. peak of Bgm1 and MMF Fs1 per pole are orthogonal

σshear

B

I

eisssgm

sgmeissgm

eisis

sgm

eis

sgmeis

avg

lDiNkB

KBlDKB

lDrT

mNKB

lD

KBlD

AF

ˆ23

42

/2

2

11

11211

21111


Magnetisation

• % magnetic dimensioning• mu0 = 4*pi*1e-7; % magnetic permeability in vacuum• K_C = 1.2; % Carter's coefficient• Bgm = 0.8; % maximum flux density in the air-gap• mu_pm = 1.219; % permeability of permanent magnet• Br = 1.1; % remanence flux ensity of permanent magnet• K_m=2/3; % relative width of magnet• % fundamental space component of gap magnet flux density• Bgm1=4/pi*Bgm*sin(K_m*pi/2);

000

C

gpm

pm

rpm kgB

hBB


Magnetic coupling & loadingE=Ψm ω

Ψm I=T

BmstBmsy

Ψm /A==PN/A<Bsat


Main flux path• A linear characteristics

can be assumed in materials

• μpm =1, μfe =∞,• The hysteresis and eddy

currents are neglected, if the study does not require them explicitly.

• The geometry is simplified by excluding small radii, holes etc

Φ½Φ

½Φ

½Φ½Φ


Choice of magnetic materials• Hard magnetic material

– Remanence flux density Br

– Stability: temperature dependence & risk of demagnetization

• Soft magnetic material– Relative permeability μr

– Specfic core loss pc

ΦR=BRApm

FCJ=HCJlpm F

permanent magnet

iron core air-gap 2 air-gap 1

load 2load 1

P2

P1

Φ

Φ

F

Φpm

FfeFpmFg

Φd

FCB

air-gap 2 iron core

common 2


Permanent magnet excitation I

• Surface mounted magnets (Lx≥Ly), inset magnets (Lx<Ly) or interior (buried) magnets (Lx<Ly)

• Rotor design: Mechanic strength, magnetic protection smaller mechanical air-gap


Permanent magnet excitation II• Single-piece magnet &

multi-pole magnetisation• Self-shielding, some

cases the back core is not needed

• Anisotropic magnet is magnetised during Injection moulding

• Isotropic magnet can be magnetised after compression moulding

M1() M2() M3() M4()

21 pN

p

p NN

sin62

1


Hard magnetic materials

• Typical materials: Ferrite, Alnico, SmCo, NdFeB• Techniques: Sintered, compression or injection molded


Hard magnetic materialsFerrite

sint/moldSmCo

sint/moldNdFeB

sint/moldRemanence Br T 0.4/0.2 1.1/0.6 1.3/0.7

Temp dep KTB Br%/K -0.2 -0.03 -0.1/-0.1

Op temp max

0C /150 250/110 <180/110

Price Low High Moderate


PM loading

• Magnetic loading, demagnetisation• Temperature dependence


Soft magnetic core

• Magnetic core facilitate magnetic coupling and manufacturing of the machine

• Core (rot+sta) manufacturing: stamping + stacking• Insertion of electric insulation system: slot liner• Winding assembling: premade coils dragged into the stator slots • PM assembling: mounted or inserted on/into the rotor slots


Soft magnetic materials• Magnetic materials

– Bulky magnetic material,– Laminated electromagnetic

steel, – compressed molded

powder core– injection molded powder

core• Different material types

have their advantageous features at– Higher operational

frequency– Higher magnetic loading


Soft magnetic materials

laminated steel3% Si

Compressed iron powder

Injection moulded iron powder

Permeability μr.max

9250 200-700 10-20

Coercivity HC A/m 35 400 100-400

Thermal con λ W/mK 28 / 0.71 17 1-3

Specific loss pfe W/kg 1T 0.92 7 -


Soft magnetic materials development

• Material engineering = production engineering

• Saving energy vs reducing size

• Bs decreases / increases with decreasing / increasing core loss

A.Inoue 1997


Pre-study

• Material selection and suitability for different applications

• Magnetic EC based study– PMSM vs IM– Laminated core vs Powder core


PM machine with laminated core• 1-pole magnetic circuit

using laminated core (μ=2000)

• Surface mounted PMSM

Fpm=2240.9 A

fpm=605.2 A

Rpm

=366190 1/H

Fg=474.4 A

Rg=106204 1/H

Fst=10.0 A

Rst

=2230 1/H

Fwin=0.0 A

Fsy=51.9 A

Rsy

=11608 1/H

Fry=17.1 A

Rry

=3837 1/H

Bpm

=0.80 T

Bg=0.75 T

Bst

=1.75 T

Bsy

=1.71 T

Bry

=1.63 T


PM machine with powder core• 1-pole magnetic circuit

using powder core (μ=200)

• Powder core allows new design and production freedoms – advantageous if design is right

• Copper savings but slightly more iron

Fpm=2240.9 A

fpm=1168.6 A

Rpm

=366190 1/H

Fg=311.0 A

Rg=106204 1/H

Fst=65.3 A

Rst

=22304 1/H

Fwin=0.0 A

Fsy=339.9 A

Rsy

=116080 1/H

Fry=112.4 A

Rry

=38374 1/H

Bpm

=0.53 T

Bg=0.49 T

Bst

=1.15 T

Bsy

=1.12 T

Bry

=1.07 T


Induction machine with laminated core• 1-pole magnetic circuit

using laminated core (μ=2000)

• PM machine is usually smaller but more expensive than induction machine for the same performanceFpm=0.0 A

fpm=0.0 A

Rpm

=0 1/H

Fg=470.3 A

Rg=106204 1/H

Fst=9.9 A

Rst

=2230 1/H

Fwin=600.0 A

Fsy=51.4 A

Rsy

=11608 1/H

Fry=17.0 A

Rry

=3837 1/H

Bpm

=0.80 T

Bg=0.74 T

Bst

=1.74 T

Bsy

=1.70 T

Bry

=1.61 T


Induction machine with powder core• 1-pole magnetic circuit

using powder core (μ=200)

• Low permeability gives a high magnetising current

• Simply replacing a lamination stack is bound to be worse in performance and cost

Fpm=0.0 A

fpm=0.0 A

Rpm

=0 1/H

Fg=159.7 A

Rg=106204 1/H

Fst=33.5 A

Rst

=22304 1/H

Fwin=600.0 A

Fsy=174.5 A

Rsy

=116080 1/H

Fry=57.7 A

Rry

=38374 1/H

Bpm

=0.27 T

Bg=0.25 T

Bst

=0.59 T

Bsy

=0.58 T

Bry

=0.55 T


Assignment A4: step 1• Electromagnetic FE analysis of 3φ PMSM

– con.fem=1 - calculate loaded and unloaded machine

0 20 40 60 80 100 120 140 160 180-1.5

-1

-0.5

0

0.5

1

1.5

Mag

netic

flux

den

sity

inth

e ai

rgap

Bg, [

T]

BgnL(), [T]BgtL(), [T]Bgn0(), [T]Bgt0(), [T]

0 2 4 6 8 10 12 140

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

harmonic order, [-]

Mag

netic

flux

den

sity

in th

e ai

rgap

Bg, [

T]

BgnL(), [T]BgtL(), [T]Bgn0(), [T]Bgt0(), [T]


Assignment A4: step 2• Electromagnetic FE analysis of 3φ PMSM

– con.fem=2 – static characteristics

• Change rotor position and current vector accordingly• Record flux linkage of windings and flux density in

magnetic core parts

7. magnetic circuitslund university / lth / iea / avo reinap / eien20 / 2020-02-11 2 l7: magnetic...

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