research article design and experimental validation for...

Research ArticleDesign and Experimental Validation for Direct-DriveFault-Tolerant Permanent-Magnet Vernier Machines

Guohai Liu Junqin Yang Ming Chen and Qian Chen

School of Electrical and Information Engineering Jiangsu University Zhenjiang 212013 China

Correspondence should be addressed to Guohai Liu ghliuujseducn

Received 11 April 2014 Accepted 2 June 2014 Published 17 June 2014

Academic Editor Wenxiang Zhao

Copyright copy 2014 Guohai Liu et al This is an open access article distributed under the Creative Commons Attribution Licensewhich permits unrestricted use distribution and reproduction in any medium provided the original work is properly cited

A fault-tolerant permanent-magnet vernier (FT-PMV) machine is designed for direct-drive applications incorporating the meritsof high torque density and high reliability Based on the so-called magnetic gearing effect PMV machines have the ability of hightorque density by introducing the flux-modulation poles (FMPs) This paper investigates the fault-tolerant characteristic of PMVmachines and provides a design method which is able to not only meet the fault-tolerant requirements but also keep the abilityof high torque density The operation principle of the proposed machine has been analyzed The design process and optimizationare presented specifically such as the combination of slots and poles the winding distribution and the dimensions of PMs andteeth By using the time-stepping finite element method (TS-FEM) the machine performances are evaluated Finally the FT-PMVmachine is manufactured and the experimental results are presented to validate the theoretical analysis

1 Introduction

Currently the permanent-magnet vernier (PMV) machineis becoming a promising candidate for direct-drive appli-cation such as the electric vehicle propulsion and the windpower generation [1ndash4] For conventional direct-drive motortopologies magnetic circuits with a large number of polesslots and windings are usually required to generate hightorque at low speed Such machine design will inevitablyincrease the machine volume and weight However it hasbeen verified that a PMV machine with concentrated wind-ings can offer high torque capability at low speed whilereducing the number of slots and thus copper loss [1 3 4]Based on the ldquomagnetic gearing effectrdquo [5 6] PMVmachinescan effectively modulate the high-speed rotating field ofthe armature windings and the low-speed rotating field ofthe PM outer rotor by adopting the flux-modulation poles(FMPs) Hence the armature poles number can differ fromthe rotor poles one which breaks the traditional design ruleof PM machines Also the volume of the stator with vernierstructure will not increase with the large number of PMpoles

On the other hand besides the requirements of hightorque density high reliability operation of motor drives

is very important in such direct-drive applications [7 8]Thus the fault-tolerant capability ofmotor drives is becomingattractive A number of researchers have investigated variousmotor topologies for fault-tolerant applications Due to itssimple and rugged construction the switched reluctancemotor has the advantage of fault-tolerant capability [9 10]However it still suffers from the drawback of relatively lowpower density A PM machine is chosen in preference toswitched reluctance motor due to its high power densityhigh efficiency and equal fault-tolerance [11] The key tofault tolerance in PM machines is to have both a sufficientlyhigh phase inductance to limit short circuit currents anda sufficiently low mutual inductance between phases toavoid the performance degradation in the remaining healthyphases Design methods of special slot-pole combinationand concentrated windings can offer this characteristic asdemonstrated in [11] In addition the increase of the phasenumber is also an effective way to improve reliability inmotordrives Actually fault-tolerant feature is a significant advan-tage of multiphase machines over conventional three-phasemachines [12] For example in a five-phase PMmachine theloss of up to three phases will not prevent the machine fromcontinuous operation or even startup

Hindawi Publishing Corporatione Scientific World JournalVolume 2014 Article ID 241085 9 pageshttpdxdoiorg1011552014241085

2 The Scientific World Journal

In this paper a five-phase fault-tolerant PMV (FT-PMV)machine will be analyzed and designed aiming to incorpo-rate the merits of the PMV machine and the fault-tolerantmachine The operation principle of the proposed machinewill be presented The design process and optimization arepresented specifically such as the combination of slots andpoles the winding distribution and the dimensions of PMsand teeth By using the time-stepping finite element method(TS-FEM) the machine performances will be assessedFinally experimental results will be provided to validate thetheoretical analysis

2 Principle of Operation

The key of a PMV machine is the introduction of FMPsIts function is to modulate the high-speed rotating fieldgenerated by armature windings to the low-speed rotatingfield in the air-gap This low-speed rotating air-gap field inturn interacts with the PM poles surface-mounted on theouter rotor thus creating the desired low-speed high-torqueoperation Since this operating principle is based on theldquomagnetic gearing effectrdquo the relationship among the numberof PMs pole pairs armature winding fundamental pole pairsand FMPs should be satisfied

The number of pole pairs in the space harmonics of theflux density distribution and the corresponding rotationalspeed can be expressed as

119901119894119898119896=1003816100381610038161003816119898119901119894 + 119896119899119904

1003816100381610038161003816

120596119894119898119896=119898119901119894120596119894

1003816100381610038161003816119898119901119894 + 1198961198991199041003816100381610038161003816

(1)

where 119898 = 1 3 5 (according to all the PMs withdifferent pole pairs and most concentrated windings) and119896 = 0 plusmn1 plusmn2 119894 = 1 2 and 119894 = 1 implies that theharmonic component is excited by the armature windingswhile 119894 = 2 means that it is excited by the outer rotorPMs 119899

119904is the number of the FMPs and 120596

1and 120596

2are

the rotational speeds of the armature fundamental field andouter rotor respectively For a clear discussion it is assumedthat the harmonic component is excited by the armaturewindings namely 119894 = 1 Meanwhile themaximumharmoniccomponent only can be obtained based on 119896 = plusmn1 aftermodulation So by selecting 119896 = minus1 (1) can be rewritten as

1199011119898minus1= 119899119904minus 1198981199011 (2)

1205961119898minus1=11989811990111205961

119899119904minus 1198981199011

(3)

In order to transmit torque at different speeds the polepairs of the outer PMs (119901

2) must be equal to 119901

1119898minus1 namely

1199012= 119899119904minus 1198981199011 1205962= 11989811990111205961119899119904minus 1198981199011 Thus the high-to-low

speed ratio 119866119903is governed from (3) by

119866119903=1205961

1205962

=119899119904minus 1198981199011

1198981199011

(4)

Since 119898 is 1 3 5 (produced by Fourier decomposi-tion) it is very necessary to get the optimal value of 119898119901

1

Table 1 Machine design requirements

Rated output power 119875 18 KwRated current 119868

119904(RMS) 10A

Rated speed 119899 600 rpmCooling method Natural air convection

which means the order of the maximummagnetic field com-ponent induced by armature windings before modulationWhen this 119898119901

1is determined the value of 119901

1119898minus1(119899119904minus

1198981199011) can be easily obtained which means the order of the

maximum magnetic field component induced by armaturewindings after modulation As a result only the PMs with 119901

2

pole-poles (1199012= 1199011119898minus1

) interact with this biggest 1199011119898minus1

thspace harmonic and themachine can produce themaximumtorque

Usually in conventional PM machines [13] the funda-mental stator space harmonic 119901

1th is the biggest namely

119898 = 1 Actually there is a traditional design rule that thenumber of pole pairs of fundamental stator space harmonic1199011and the number of rotor PMpole pairs119901

119903must be the same

(1199011= 119901119903) However in the PM machines with fractional-

slot concentrated windings (FSCWs) [14] this rule is notvery necessary The number of pole pairs of the fundamentalstator space harmonic 119901

1may be smaller than that of the

PM rotor 119901119903 The torque is developed by the interaction of

a higher order stator space harmonic with the PMs whichmeans 119898 = 1 Only if the 119898119901th space harmonic interactswith the 119901

119903pole pairs PM rotor the machine can produce

maximum continuous useful torque which means 1198981199011=

119901119903 As a result to determine the value of 119901

2(1199011119898minus1

th) aPMV machine should have found its ldquooriginal PM machinerdquowith 119901

119903pole pairs PMs in which their armature windings

are completely identical This is due to 1198981199011= 119901119903= 119899119904minus

1199012 To be concluded various armature winding connections

decide various vernier structures The winding design of theproposed PMVmachine will be presented in Section 32

3 Machine Design and Optimization

First of all the design objectives of the machine need to beclarifiedThe conventional design criteria are listed in Table 1The outside stator radius 119877

1 machine length 119871

119904 number of

phases119873ph current density 119869119886 and slot packing factor 119896119904are

kept invariant Since naturally cooled condition is chosenthe current density cannot be very high Also both hightorque density and high reliability are required Accordingto the operation principle of PMV machines discussed inSection 2 the aim of high torque density can be achievedby adopting the vernier structure In this section the fault-tolerant design aimed to have high reliability will be detailedwhile the vernier effect is still satisfied

31 Main Dimensions The initial design of any PMmachineincludes the determination of the outside stator radius119877

1 the

outside rotor radius 1198772 the stack length 119871

119904 and the air-gap

length 119877119892 For a machine with specific flux density electric

The Scientific World Journal 3

Table 2 Basic parameters of two prototypes

Items 119878 119901119903

119898 1199011

119899119904

1199012(119899119904minus 1198981199011)

Prototype 1 20 9 9 1 40 31Prototype 2 20 11 11 1 40 29

and magnetic loading and speed its rated output poweris proportional to the rotor volume Usually the air-gaplength in PM machines has little impact on power since thepermeance of PM is close to that of air Hence the thicknessof PM is the dominant part in the flux path However forPMVmachines the harmonics in air-gap are used to producetorque whichmeans that PMVmachines are very sensitive tothe air-gap length Meanwhile compared with PMmachinesPMV machines can have the thinner thickness of rotor andstator yoke due to their shorter flux path and larger polenumber Thus the volume can be minimized All these fourparameters have been determined as a list in Table 3 Theinfluences of the air-gap length thickness of PM and othercritical parameters will be analyzed and discussed

32 Design of Stator Phases and Winding ConfigurationSince fault tolerance and high reliability are the foundationsof this design theminimumelectricalmagnetic and thermalinteractions are required between phases As a result a fault inone phase does not undesirably affect the remaining healthyphases These requirements can be satisfied by designingthe appropriate armature windings with one-phase wind-ing per slot Meanwhile this topology has a coil woundaround a single tooth which is called single-layer FSCW (SL-FSCWs) This solution enhances thermal isolation and mini-mizes mutual coupling between phases In addition overlapsbetween end-windings of different phases are eliminated sothat the volume of copper can be significantly reduced inparticular when the axial length of the machine is smallConsidering that any PMV machine can be transformed byits ldquooriginal PMmachinerdquo discussed in Section 2 an ldquooriginalPM machinerdquo can be designed firstly before introducing thevernier structure

In any SL-FSCWPMmachine the basic winding module(with the smallest allowable number of slots and poles) hasjust two antiphase coils per phase For any such winding with119873ph phases and 119878 slots the required number of PM pole pairs119901119903is given by [8]

2119901119903= 119878(1 plusmn

119899

2119873ph) (5)

where 119899 = 1 or 119899 = any nonzero odd integer less than119873ph such that 119899 and 119873ph do not share any common factorsIt should be noted that a good design necessitates a highcoupling between the magnets and the coils which impliesthat 119899119873ph should be no greater than about 06 For a PMVmachine with FSCW a large number of slots will result ina small per slot cross-section area and a large number ofPMs which further reduce utilization of PMs and improvethe operating frequency Hence 119878 cannot be too large How-ever to improve the reliability further electrical machines


Items FT-PMVmachinePhases119873ph 5Number of stator slots 119878 20Number of rotor pole pairs 119901

231

Number of FMPs 119899119904

40Gear ratio 119866

119903minus31 9

Rated voltage 119880 (V) 70Current density 119869

119886(Amm2) 657

Outside stator radius 1198771(mm) 60

Outside rotor radius 1198772(mm) 70

Stack length 119871119904(mm) 60

Air-gap length 119877119892(mm) 05

PM thickness119867pm (mm) 32Fault-tolerant tooth 119871

1(mm) 19

Armature tooth 1198712(mm) 33

PM pole-arc coefficient 120572 1Per slot area 119860 slot (mm2) 1218Slot packing factor 119896

11990406

Stator turns per coil119873119888

48PM type NdFe35

are generally designed with a high phase number wherea corresponding increase in the number of slots happensaccording to (5) As a result a compromise between 119878 and119873ph is obtained with a selection of 119878 = 20 and 119873ph = 5Thus three basic parameters of an ldquooriginal PM machinerdquohave been determined in which 119878 119873ph and 119901119903 are 20 5 9or 11 respectively

The winding configurations with 119901119903= 9 and 11 are shown

in Figure 1 Clearly differing from the 119901119903= 11 winding

connection the 119901119903= 9 winding connection only has the

opposite direction of the rotating magnetic field It meansthat they will share the same space harmonic spectrums dueto armature windings So the space harmonic spectrum ofthem is shown in Figure 2 It can be seen that the order ofthe biggest space harmonic content 119898119901

1is 9 or 11 before

modulation but the fundamental stator space harmonic 1199011

is 1th Obviously 1198981199011= 119901119903and 119898 = 1 due to this kind of

SL-FSCWconfiguration validating the theoretical analysis inSection 2

For the stator structure only one adjustment is neededto transform the ldquooriginal PM topologyrdquo to its correspondingPMV topology It is to split the stator tooth into 119899

119904FMPs By

considering manufacturing technology symmetry verniereffect and electromagnetic performance 119899

119904= 40 is a better

choice [15] Up to here basic structures of two prototypeshave been designed as listed in Table 2 From Figure 2 it can


12

345678

9101112

131415161718

1920

1 2 3 4 5 6 7 8 9 10 11121314151617181920

AminusC+ Eminus B+ Dminus A+ Cminus E+ Bminus D+

(a)

12

345678

9101112

131415161718

1920

1 2 3 4 5 6 7 8 9 10 11121314151617181920

AminusC+EminusB+DminusA+ CminusE+BminusD+

(b)

Figure 1 Winding configurations (a) 119901119903= 9 (b) 119901

119903= 11

0 5 10 15 20 25 30 3500

01

02

03

04

05

Am

plitu

de (T

)

Pole pair number

In stator yokeIn tooth under FMPs (before modulation)In air gap (after modulation)

Useful harmonic for PM machine

Useful harmonic for PMV machine

Fundamentalharmonic p1

mp1(m = 9 or 11)

p1mminus1

Figure 2 Space harmonic spectrum due to armature windings

be clearly seen that the amplitudes of most harmonics arereduced in the air gap since the different permeances existin the full flux path from stator yoke to air gap Howeverthe increased amplitudes of 31st and 29th are significantwhich can be known from the comparison of red and bluecolumns The reason is that the increased parts of 31st and29th result from the maximum magnetic field components(9th and 11th) by modulation effect which is in agreementwith the theoretical analysis in Section 2 Thus in order toproduce the maximum torque the number of PM pole pairs1199012should be equal to 31 or 29 as listed in Table 2Furthermore Figure 3 compares the space harmonic

spectrums of both prototypes in the air gap due to thePMs It also can be seen that corresponding to 119901

2pole

pairs of the rotor rotating field the highest asynchronousharmonic component is that with 119901

2119898minus1pole pairs (119901

2119898minus1=

1198981199011) Obviously the effect of flux modulation is verified by

Figures 2 and 3 A fault-tolerant machine with large numberof PM poles can be designed by introducing the vernierstructure rather than the increase of the volume and thenumber of slots

In order to find which prototype possesses the advanta-geous performance Figure 4 shows the back-EMFwaveformsat the speed of 600 rpm and Figure 5 shows the output torquewaveforms under the rated operation It can be known thatback-EMFs of both machines are almost the same but that ofthe prototype 1 is a little more sinusoidal and the root meansquare (RMS) value is 171 V As a result the average output

0 5 10 15 20 25 30 35 4000

02

04

06

08

10

12

Am

plitu

de (T

)Pole pair number

p2mminus1(p2mminus1 = mp1 = pr)

p2(p2 = p1mminus1)

Prototype 1

Prototype 2

Figure 3 Space harmonic spectrum due to PMs

0

20

40

60

0 90 180 270 360Rotor position (elec deg)

Back

-EM

F (V

)

minus60

minus40

minus20

Prototype 1

Prototype 2

Figure 4 Comparison of back-EMF

torque as shown in Figure 5 of prototype 1 is 1 Nm larger thanthat of prototype 2 Finally prototype 1 is selected

33 Optimization of Air-Gap Length As discussed abovePMV machines are very sensitive to the air-gap lengthFigure 6 shows the variation of torque characteristics withair-gap length 119877

119892 The torque transmission characteristics

are obtained based on the locked-rotor operation Obviouslythe maximum output torque increases linearly when 119877

119892

decreases In addition it can be seen that the current angle 120573is almost equal to zero when 119877

119892is large and 120573 increases with

the decrease of 119877119892 This phenomenon occurs due to the flux

concentration and the saturation at the FMPs topMeanwhile


20

22

24

26

28

30


Torq

ue (N

m)

Prototype 1

Prototype 2

Figure 5 Comparison of output torque

0

20

40

Torq

ue (N

m)

minus40

minus20

minus180 90 0 90 180

Current angle (elec deg)

Rg = 01mmRg = 08mmRg = 03mm

Rg = 1mmRg = 05mm

Trend of changes onthe current angle 120573of maximum output

torque

Figure 6 Variations of torque characteristic with air-gap length 119877119892

it indicates that 119871119889= 119871119902 and thus reluctance torque has

no contribution to the output torque when 119877119892is large By

considering machining accuracy of the air-gap 119877119892= 05mm

is chosen With 119877119892= 05mm 119871

119889can be thought to be equal

to 119871119902approximately which means that the maximum torque

per ampere control can be achieved by ldquo119894119889= 0rdquo control

method

34 Magnet Design The PM radial thickness 119867pm is asignificant parameter since it affects the flux density in theair gap the demagnetization withstand capability and thecost In general the increase of 119867pm can enhance air-gapflux density and thus torque in PM machines However forsurface-mounted PMV machines the main function of 119867pmis to increase the resistance to demagnetization The peakvalue variations of the back-EMF and the cogging torquewith119867pm are shown in Figure 7 Clearly the amplitude of coggingtorque increases with119867pm increasing all along but only when119867pm lt 2mm with 119867pm increasing the amplitude of back-EMF increases In fact there is an optimal value of 119867pmcorresponding to the largest amplitude of back-EMF It differsfrom PM machines where the larger the 119867pm is the largerthe peak value of back-EMF becomes This is due to the fact

0

20

40

60

Thick (mm)

Back

-EM

F (V

)

0

300

600

900

Torq

ue (m

Nm

)

0 1 2 3 4 5

Back-EMFCogging torque

Figure 7 Peak value variations of back-EMF and cogging torquewith PM radial thickness119867pm

that the reluctance is also increased with the increasing119867pmThe permeance of PM is close to air which is far greater thanthat of stator or rotor ironThe reluctance increase will reducespace harmonic field in air gap thus reducing the back-EMFamplitude Hence the value of 119867pm must be optimized byconsidering the back-EMF amplitude

Partial demagnetization of PMs can influence motorperformances of both voltage and torque seriouslyThemotortemperature the magnitude of current and the power anglecan determine the partial demagnetization [16] In this workthe partial demagnetization is investigated when 119894

119889= 119894119904and

119894119902= 0 strategy is adopted at the operation temperature of

120∘C It means that the rated current is completely usedfor demagnetization in order to simulate an abominableoperating condition for PMs By this way the variation ofthe minimum flux density in PMs with PM radial thicknessis shown in Figure 8 It can be seen that the increase of 119867pmcan effectively increase the resistance to demagnetization AsNdFe35 PM material is usually employed the flux density inPMs less than 02 T can be thought as irreversible demagne-tization As a result 119867pm = 32mm is selected With 119867pm =32mm the proposed machine can provide a good back-EMFMoreover it can avoid the irreversible demagnetizationof the PMs to a great extent

The pole-arc coefficient 120572 of PMs also has great effects onback-EMF and cogging torque An appropriate120572 can increasethe back-EMF and reduce the cogging torque Inmost cases acompromise between the low cogging torque and high back-EMF should be considered For a PMV machine its 120572 onlyinfluences the peak values of the back-EMF and the coggingtorque rather than their shapes Figure 9 shows the peakvalue variations of the back-EMF and the cogging torquewithdifferent pole-arc coefficient 120572 It can be seen that the peakcogging torque is relatively small although it increases when120572 increases However the peak back-EMF increases greatlywhen120572 increases Finally by considering the easy assembling120572 = 1 is selected

35 Optimization of Tooth Width Tooth width can affectslot area and saturation level on tooth thus it has a great


0

02

04

06

08

Thick (mm)

B (T

)

0 1 2 3 4

Figure 8 Variation ofminimumflux density in PMswith PM radialthickness119867pm

0

20

40

60

Pole-arc coefficient

Back

-EM

F (V

)

0

300

600

900To

rque

(mN

m)


04 05 06 07 08 09 1

Figure 9 Peak value variations of back-EMF and cogging torquewith PM pole-arc coefficient 120572

influence on output torque With SL-FSCWs the proposedFT-PMV machine has a coil wound on alternate teeth calledarmature tooth The unwound teeth are usually called fault-tolerant tooth which provide a special flux path to decreasethe electromagnetic coupling between phases Tooth width offault-tolerant tooth 119871

1can be unequal to that of armature

tooth 1198712to optimize the flux linkage and enlarge the slot

area as possible without performance degradation [13] Thevariation of average output torque with tooth width is shownin Figure 10 Firstly119871

2can be optimized by assuming119871

2= 1198711

as shown in Figure 10 (blue curve) It can be seen that theaverage output torque tended to be a constant when 119871

2and

1198711are over 33mmThen after determining119871

2= 33mm the

optimal value of 1198711can be found as shown in Figure 10 (red

curve) Clearly the average output torque remains unchangedwhen 119871

1gt 19mm which means that all the flux lines can

run through the fault-tolerant tooth just with 1198711= 19mm

Finally 1198712= 33mm and 119871

1= 19mm are selected which

have the same effect as 1198712= 1198711= 33mm Based on this

optimal value of tooth width the slot area can be significantlyenlarged

10

15

20

25

30

Tooth width (mm)

Torq

ue (N

m)

0 1 2 3 4

L1

L2

Condition L2 = L1

Condition L2 = 33mm

Figure 10 Variation of average output torque with fault-toleranttooth width 119871

1and armature tooth width 119871

2

36 Final Solution The detailed dimensions materials andstructure parameters are listed in Table 3 The cross sectionof the proposed FT-PMV machine is shown in Figure 11(a)Meanwhile a partial amplification of the cross section isgiven in Figure 11(b) in which the corresponding importantstructure parameters are marked It should be noted that inthis design the FMP-slot width 120579

1 FMP width 120579

2 and stator

slot opening width 1205793are made equal (120579

1= 1205792= 1205793) In

addition FMP-slot depth 1198713is set to be 4mm In fact as 119871

3

changes between 2mm and 5mm the performances of theproposed machine almost remain unchanged

4 Simulated Performance

In order to verify the advantages of the proposed FT-PMVmachine its performance is analyzed by using TS-FEM

41 Torque Performance While the FMPs provide uniquemagnetic path to modulate between the rotor field and thestator field there are different air-gap lengths at differentpositions for example different magnetic resistance Thusthe interaction between the FMPs and the PMs causesthe cogging torque Figure 12 shows the predicted coggingtorque The peak value of the cogging torque is 088NmIn addition the static torque waveform of the proposed FT-PMV machine in BLAC operation mode is also shown inFigure 12 It can be clearly observed that the output torqueripple induces mainly due to the cogging torque It has beenknown that for the PM machines operated in BLAC modethe harmonic distortion in the back-EMF and the coggingtorque are the twomain sources of ripple in the output torque[16] For a five-phasemachine only the 5119896plusmn1th (5119896plusmn1 = 3119895 119896119895 is an integer) harmonic components will contribute to thegeneration of torque ripple In fact the harmonic componentsof the back-EMF of the proposed machine will hardly everresult in the torque ripple which will be verified in Section 5

42 Fault-Tolerant Capability The self-inductance and themutual inductance between phases have been calculated as


Armature tooth

FMP

Fault-tolerant tooth

Armature winding

PM

Rotor

Stator

Slot opening

FMP-slot

(a)

L1L2

L3

12057911205792

1205793 R1

(b)

Figure 11 Proposed FT-PMVmachine (a) Cross section (b) Parameters

0

10

20

30

40

Rotor position (elec deg)

Torq

ue (N

m)

CoggingOutput

minus100 180 360 540

Figure 12 Cogging torque and output torque waveforms

listed in Table 4 It can be seen that the proposed machinehas the very low ratios of the mutual inductance to theself-inductances showing that there is nearly zero magneticcoupling between phases Namely a fault in one phase doesnot undesirably affect the remaining healthy phases Besidesinductance affects the power factor greatly which can be seenfrom the following formula

PF = 1

radic1 + (119871119904119868120595119898)

(6)

where 120595119898

is the magnet flux linkage 119868 is the rms phasecurrent and 119871

119904is the synchronous inductance However the

influence of inductance to the power factor is not absolute Infact when the electric load of the motor is determined thechange on power factor would be unconspicuous regardlessof the changes of other parameters

Figure 13 shows the current responses under the short-circuit fault condition at the speed of 600 rpm Only onephase is short-circuit and other phases operate normallyIt can be seen that the short-circuit current is limited wellHence it can be concluded that the proposed machine canoffer high fault-tolerant capability

Table 4 Comparison of inductances

Items A-A A-B A-C A-D A-EInductance (mH) 322 00033 00113 00113 00033Ratio () 100 0102 035 035 0102

0

5

10

15

Times (ms)

Curr

ent (

A)

minus15

minus10

minus5

0 10 20 30 40

Figure 13 Short-circuit current

5 Experimental Validation

The proposed FT-PMV machine is fabricated and tested toverify the theoretical analysis which is shown in Figure 14Clearly the above discussed fault-tolerant tooth unequaltooth width SL-FSCW and FMP design are adopted in thestators of the prototype

The measured phase back-EMFs at the speed of 600 rpmare shown in Figure 15 which agrees with the simulatedresults in Figure 4 The measured value is about 8 lowerthan the predicted both lamination factor and end effectare the key affective factors that contributed to this resultFurthermore the harmonic spectrum of the measured phaseback-EMFs is normalized by the respective fundamentalcomponents as shown in Figure 16 The total harmonicdistortion (THD) is 32 Hence the proposed machine isvery suitable for BLAC operation Moreover it can be seenthat the contents of harmonics of the proposed machinewhich is useful for the torque ripple are almost none Hence


(a) (b)

Figure 14 Prototype machine (a) Stator and rotor assembly (b) FMPs in stator

Figure 15 Measured phase back-EMFs (1msdiv 20Vdiv)

0

05

1

15

2

25

3

35

Harmonic order1 2 3 4 5 6 7 8 9 10 11 12 13

Fund

amen

tal a

mpl

itude

()

Figure 16 Harmonic distributions of back-EMF

Figure 17 Measured short-circuit current and adjacent phase back-EMFs (4msdiv 50Vdiv 20Adiv 50Vdiv)

the output torque ripple mainly results from the coggingtorque

Figure 17 shows the measured current responses underthe short-circuit fault condition at the speed of 600 rpmAlso the measured adjacent phase back-EMFs are showntogether It can be seen that the short-circuit current is limitedwell which agrees with the simulated results in Figure 13Meanwhile it can be observed that the back-EMFs are not

affected entirely by the adjacent short-circuit current So itcan be concluded that the independence between adjacentphases in the proposed FT-PMV machine is high and it canoffer high fault-tolerance [16]

6 Conclusion

In this paper a FT-PMV machine has been designedanalyzed and tested The operation principle of the pro-posed machine has been presented The design process andoptimization have been discussed specifically such as thecombination of slots and poles the winding distributionand the dimensions of PMs and tooth width By usingthe TS-FEM the machine performance has been assessedCompared with its PMV counterpart the proposed machinecan offer high fault-tolerant performance thus improving themachine reliability Compared with its fault-tolerant counter-part the PMV structure of the proposed machine can offera high torque density nearly up to 30NmL thus reducingthe machine volume and weight Finally a prototype hasbeen manufactured and experimental results are provided tovalidate the theoretical analysis

Nomenclature

120572 Pole-arc coefficient119867pm Permanent magnet thickness120591 Pole pitch119873ph Number of phases119860 slot Per slot area119869119886 Current density119873119888 Stator turns per coil119877119892 Air-gap length1198711 Fault-tolerant tooth width1198712 Armature tooth width1198713 FMP-slot depth119871119904 Stack length1198771 Outside stator radius1198772 Outside rotor radius1205791 FMP-slot width1205792 FMP width1205793 Stator slot opening width1199011 Pole pairs of the fundamental stator space harmonic1199012 Pole pairs of the PMs of PMVmachines119901119903 Pole pairs of the PMs of conventional PM machines


Conflict of Interests

The authors declare that they have no conflict of interestsregarding the publication of this paper

Acknowledgments

This work was supported in part by the National Natural Sci-ence Foundation of China (Projects 61273154 and 51277194)by the Specialized Research Fund for the Doctoral Programof Higher Education of China (Project 20123227110012)by the Natural Science Foundation of Jiangsu Province(BK20130011) and by the Priority Academic Program Devel-opment of Jiangsu Higher Education Institutions

References

[1] J Li K T Chau J Z Jiang C Liu and W Li ldquoA newefficient permanent-magnet vernier machine for wind powergenerationrdquo IEEE Transactions on Magnetics vol 46 no 6 pp1475ndash1478 2010

[2] W Li K T Chau C Liu S Gao and DWu ldquoAnalysis of tooth-tip flux leakage in surface-mounted permanent magnet linearvernier machinesrdquo IEEE Transactions on Magnetics vol 49 no7 pp 3949ndash3952 2013

[3] L Xu J Ji G Liu Y Du and H Liu ldquoDesign and analysis oflinear fault-tolerant permanent-magnet vernier machinesrdquoTheScientific World Journal vol 2014 Article ID 483080 8 pages2014

[4] S-U Chung J-W Kim B-C Woo D-K Hong J-Y Lee andD-H Koo ldquoA novel design of modular three-phase permanentmagnet vernier machine with consequent pole rotorrdquo IEEETransactions on Magnetics vol 47 no 10 pp 4215ndash4218 2011

[5] K Atallah S D Calverley and D Howe ldquoDesign analysisand realisation of a high-performance magnetic gearrdquo IEEProceedings Electric Power Applications vol 151 no 2 pp 135ndash143 2004

[6] L Jian G Xu C C Mi K T Chau and C C ChanldquoAnalyticalmethod formagnetic field calculation in a low-speedpermanent-magnet harmonic machinerdquo IEEE Transactions onEnergy Conversion vol 26 no 3 pp 862ndash870 2011

[7] W Zhao M Cheng K T Chau R Cao and J Ji ldquoReme-dial injected-harmonic-current operation of redundant flux-switching permanent-magnet motor drivesrdquo IEEE Transactionson Industrial Electronics vol 60 no 1 pp 151ndash159 2013

[8] W Zhao M Cheng W Hua H Jia and R Cao ldquoBack-EMF harmonic analysis and fault-tolerant control of flux-switching permanent-magnet machine with redundancyrdquo IEEETransactions on Industrial Electronics vol 58 no 5 pp 1926ndash1935 2011

[9] H Torkaman and E Afjei ldquoSensorless method for eccentricityfaultmonitoring and diagnosis in switched reluctancemachinesbased on stator voltage signaturerdquo IEEE Transactions on Mag-netics vol 49 no 2 pp 912ndash920 2013

[10] M Ruba I A Viorel and L Szabo ldquoModular stator switchedreluctance motor for fault tolerant drive systemsrdquo IET ElectricPower Applications vol 7 no 3 pp 159ndash169 2013

[11] Q Chen G Liu W Gong and W Zhao ldquoA new fault-tolerantpermanent-magnet machine for electric vehicle applicationsrdquoIEEE Transactions on Magnetics vol 47 no 10 pp 4183ndash41862011

[12] E Levi ldquoMultiphase electric machines for variable-speed appli-cationsrdquo IEEE Transactions on Industrial Electronics vol 55 no5 pp 1893ndash1909 2008

[13] G LiuWGongQ Chen L Jian Y Shen andWZhao ldquoDesignand analysis of new fault-tolerant permanentmagnetmotors forfour-wheel-driving electric vehiclesrdquo Journal of Applied Physicsvol 111 no 7 Article ID 07E713 2012

[14] P B Reddy A M El-Refaie and K K Huh ldquoGeneralizedapproach of stator shifting in interior permanent-magnetmachines equipped with fractional-slot concentrated wind-ingsrdquo IEEE Transactions on Industrial Electronics vol 61 no 9pp 5035ndash5046 2014

[15] G Liu J Yang W Zhao J Ji Q Chen and W Gong ldquoDesignand analysis of a new fault-tolerant permanent-magnet verniermachine for electric vehiclesrdquo IEEE Transactions on Magneticsvol 48 no 11 pp 4176ndash4179 2012

[16] Q Chen G Liu W Zhao M Shao L Sun and Z Liu ldquoDesignand comparison of two fault-tolerant interior permanent-magnet motorsrdquo IEEE Transactions on Industrial Electronics2014

TribologyAdvances in

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

International Journal of

AerospaceEngineeringHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

FuelsJournal of


Journal ofPetroleum Engineering


Industrial EngineeringJournal of


Power ElectronicsHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Advances in

CombustionJournal of


Journal of


Renewable Energy

Submit your manuscripts athttpwwwhindawicom


StructuresJournal of


RotatingMachinery


EnergyJournal of


Hindawi Publishing Corporation httpwwwhindawicom

Journal ofEngineeringVolume 2014

Hindawi Publishing Corporation httpwwwhindawicom Volume 2014

International Journal ofPhotoenergy


Nuclear InstallationsScience and Technology of


Solar EnergyJournal of


Wind EnergyJournal of


Nuclear EnergyInternational Journal of


High Energy PhysicsAdvances in

The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014


In this paper a five-phase fault-tolerant PMV (FT-PMV)machine will be analyzed and designed aiming to incorpo-rate the merits of the PMV machine and the fault-tolerantmachine The operation principle of the proposed machinewill be presented The design process and optimization arepresented specifically such as the combination of slots andpoles the winding distribution and the dimensions of PMsand teeth By using the time-stepping finite element method(TS-FEM) the machine performances will be assessedFinally experimental results will be provided to validate thetheoretical analysis

2 Principle of Operation

The key of a PMV machine is the introduction of FMPsIts function is to modulate the high-speed rotating fieldgenerated by armature windings to the low-speed rotatingfield in the air-gap This low-speed rotating air-gap field inturn interacts with the PM poles surface-mounted on theouter rotor thus creating the desired low-speed high-torqueoperation Since this operating principle is based on theldquomagnetic gearing effectrdquo the relationship among the numberof PMs pole pairs armature winding fundamental pole pairsand FMPs should be satisfied

The number of pole pairs in the space harmonics of theflux density distribution and the corresponding rotationalspeed can be expressed as

119901119894119898119896=1003816100381610038161003816119898119901119894 + 119896119899119904

1003816100381610038161003816

120596119894119898119896=119898119901119894120596119894

1003816100381610038161003816119898119901119894 + 1198961198991199041003816100381610038161003816

(1)

where 119898 = 1 3 5 (according to all the PMs withdifferent pole pairs and most concentrated windings) and119896 = 0 plusmn1 plusmn2 119894 = 1 2 and 119894 = 1 implies that theharmonic component is excited by the armature windingswhile 119894 = 2 means that it is excited by the outer rotorPMs 119899

119904is the number of the FMPs and 120596

1and 120596

2are

the rotational speeds of the armature fundamental field andouter rotor respectively For a clear discussion it is assumedthat the harmonic component is excited by the armaturewindings namely 119894 = 1 Meanwhile themaximumharmoniccomponent only can be obtained based on 119896 = plusmn1 aftermodulation So by selecting 119896 = minus1 (1) can be rewritten as

1199011119898minus1= 119899119904minus 1198981199011 (2)

1205961119898minus1=11989811990111205961

119899119904minus 1198981199011

(3)

In order to transmit torque at different speeds the polepairs of the outer PMs (119901

2) must be equal to 119901

1119898minus1 namely

1199012= 119899119904minus 1198981199011 1205962= 11989811990111205961119899119904minus 1198981199011 Thus the high-to-low

speed ratio 119866119903is governed from (3) by

119866119903=1205961

1205962

=119899119904minus 1198981199011

1198981199011

(4)

Since 119898 is 1 3 5 (produced by Fourier decomposi-tion) it is very necessary to get the optimal value of 119898119901

1


Rated output power 119875 18 KwRated current 119868

119904(RMS) 10A

Rated speed 119899 600 rpmCooling method Natural air convection

which means the order of the maximummagnetic field com-ponent induced by armature windings before modulationWhen this 119898119901

1is determined the value of 119901

1119898minus1(119899119904minus

1198981199011) can be easily obtained which means the order of the

maximum magnetic field component induced by armaturewindings after modulation As a result only the PMs with 119901

2

pole-poles (1199012= 1199011119898minus1

) interact with this biggest 1199011119898minus1

thspace harmonic and themachine can produce themaximumtorque

Usually in conventional PM machines [13] the funda-mental stator space harmonic 119901

1th is the biggest namely

119898 = 1 Actually there is a traditional design rule that thenumber of pole pairs of fundamental stator space harmonic1199011and the number of rotor PMpole pairs119901

119903must be the same

(1199011= 119901119903) However in the PM machines with fractional-

slot concentrated windings (FSCWs) [14] this rule is notvery necessary The number of pole pairs of the fundamentalstator space harmonic 119901

1may be smaller than that of the

PM rotor 119901119903 The torque is developed by the interaction of

a higher order stator space harmonic with the PMs whichmeans 119898 = 1 Only if the 119898119901th space harmonic interactswith the 119901

119903pole pairs PM rotor the machine can produce

maximum continuous useful torque which means 1198981199011=

119901119903 As a result to determine the value of 119901

2(1199011119898minus1

th) aPMV machine should have found its ldquooriginal PM machinerdquowith 119901

119903pole pairs PMs in which their armature windings

are completely identical This is due to 1198981199011= 119901119903= 119899119904minus

1199012 To be concluded various armature winding connections

decide various vernier structures The winding design of theproposed PMVmachine will be presented in Section 32

3 Machine Design and Optimization

First of all the design objectives of the machine need to beclarifiedThe conventional design criteria are listed in Table 1The outside stator radius 119877

1 machine length 119871

119904 number of

phases119873ph current density 119869119886 and slot packing factor 119896119904are

kept invariant Since naturally cooled condition is chosenthe current density cannot be very high Also both hightorque density and high reliability are required Accordingto the operation principle of PMV machines discussed inSection 2 the aim of high torque density can be achievedby adopting the vernier structure In this section the fault-tolerant design aimed to have high reliability will be detailedwhile the vernier effect is still satisfied

31 Main Dimensions The initial design of any PMmachineincludes the determination of the outside stator radius119877

1 the

outside rotor radius 1198772 the stack length 119871

119904 and the air-gap

length 119877119892 For a machine with specific flux density electric



Items 119878 119901119903

119898 1199011

119899119904

1199012(119899119904minus 1198981199011)





2119901119903= 119878(1 plusmn

119899

2119873ph) (5)




231


40Gear ratio 119866

119903minus31 9


119886(Amm2) 657






1(mm) 19



11990406


48PM type NdFe35






1is 9 or 11 before





119904FMPs By





12

345678

9101112

131415161718

1920

1 2 3 4 5 6 7 8 9 10 11121314151617181920


(a)

12

345678

9101112

131415161718

1920

1 2 3 4 5 6 7 8 9 10 11121314151617181920


(b)


119903= 11

0 5 10 15 20 25 30 3500

01

02

03

04

05

Am

plitu

de (T

)

Pole pair number





mp1(m = 9 or 11)

p1mminus1




2pole



2119898minus1=




0 5 10 15 20 25 30 35 4000

02

04

06

08

10

12

Am

plitu

de (T

)Pole pair number


p2(p2 = p1mminus1)

Prototype 1

Prototype 2


0

20

40

60


Back

-EM

F (V

)

minus60

minus40

minus20

Prototype 1

Prototype 2






119892






20

22

24

26

28

30


Torq

ue (N

m)

Prototype 1

Prototype 2


0

20

40

Torq

ue (N

m)

minus40

minus20

minus180 90 0 90 180



Rg = 1mmRg = 05mm


torque





is chosen With 119877119892= 05mm 119871




method


0

20

40

60

Thick (mm)

Back

-EM

F (V

)

0

300

600

900

Torq

ue (m

Nm

)

0 1 2 3 4 5





119889= 119894119904and






0

02

04

06

08

Thick (mm)

B (T

)

0 1 2 3 4


0

20

40

60


Back

-EM

F (V

)

0

300

600

900To

rque

(mN

m)


04 05 06 07 08 09 1







2= 1198711


2and


2= 33mm the





Finally 1198712= 33mm and 119871




10

15

20

25

30

Tooth width (mm)

Torq

ue (N

m)

0 1 2 3 4

L1

L2

Condition L2 = L1

Condition L2 = 33mm



2


1 FMP width 120579

2 and stator


1= 1205792= 1205793) In


3







Armature tooth

FMP


Armature winding

PM

Rotor

Stator

Slot opening

FMP-slot

(a)

L1L2

L3

12057911205792

1205793 R1

(b)


0

10

20

30

40


Torq

ue (N

m)

CoggingOutput

minus100 180 360 540



PF = 1

radic1 + (119871119904119868120595119898)

(6)

where 120595119898







0

5

10

15

Times (ms)

Curr

ent (

A)

minus15

minus10

minus5

0 10 20 30 40






(a) (b)



0

05

1

15

2

25

3

35

Harmonic order1 2 3 4 5 6 7 8 9 10 11 12 13

Fund

amen

tal a

mpl

itude

()






6 Conclusion


Nomenclature





Acknowledgments


References





















FuelsJournal of







Advances in



Journal of


Renewable Energy





RotatingMachinery


EnergyJournal of



















Items 119878 119901119903

119898 1199011

119899119904

1199012(119899119904minus 1198981199011)





2119901119903= 119878(1 plusmn

119899

2119873ph) (5)




231


40Gear ratio 119866

119903minus31 9


119886(Amm2) 657






1(mm) 19



11990406


48PM type NdFe35






1is 9 or 11 before





119904FMPs By





12

345678

9101112

131415161718

1920

1 2 3 4 5 6 7 8 9 10 11121314151617181920


(a)

12

345678

9101112

131415161718

1920

1 2 3 4 5 6 7 8 9 10 11121314151617181920


(b)


119903= 11

0 5 10 15 20 25 30 3500

01

02

03

04

05

Am

plitu

de (T

)

Pole pair number





mp1(m = 9 or 11)

p1mminus1




2pole



2119898minus1=




0 5 10 15 20 25 30 35 4000

02

04

06

08

10

12

Am

plitu

de (T

)Pole pair number


p2(p2 = p1mminus1)

Prototype 1

Prototype 2


0

20

40

60


Back

-EM

F (V

)

minus60

minus40

minus20

Prototype 1

Prototype 2






119892






20

22

24

26

28

30


Torq

ue (N

m)

Prototype 1

Prototype 2


0

20

40

Torq

ue (N

m)

minus40

minus20

minus180 90 0 90 180



Rg = 1mmRg = 05mm


torque





is chosen With 119877119892= 05mm 119871




method


0

20

40

60

Thick (mm)

Back

-EM

F (V

)

0

300

600

900

Torq

ue (m

Nm

)

0 1 2 3 4 5





119889= 119894119904and






0

02

04

06

08

Thick (mm)

B (T

)

0 1 2 3 4


0

20

40

60


Back

-EM

F (V

)

0

300

600

900To

rque

(mN

m)


04 05 06 07 08 09 1







2= 1198711


2and


2= 33mm the





Finally 1198712= 33mm and 119871




10

15

20

25

30

Tooth width (mm)

Torq

ue (N

m)

0 1 2 3 4

L1

L2

Condition L2 = L1

Condition L2 = 33mm



2


1 FMP width 120579

2 and stator


1= 1205792= 1205793) In


3







Armature tooth

FMP


Armature winding

PM

Rotor

Stator

Slot opening

FMP-slot

(a)

L1L2

L3

12057911205792

1205793 R1

(b)


0

10

20

30

40


Torq

ue (N

m)

CoggingOutput

minus100 180 360 540



PF = 1

radic1 + (119871119904119868120595119898)

(6)

where 120595119898







0

5

10

15

Times (ms)

Curr

ent (

A)

minus15

minus10

minus5

0 10 20 30 40






(a) (b)



0

05

1

15

2

25

3

35

Harmonic order1 2 3 4 5 6 7 8 9 10 11 12 13

Fund

amen

tal a

mpl

itude

()






6 Conclusion


Nomenclature





Acknowledgments


References





















FuelsJournal of







Advances in



Journal of


Renewable Energy





RotatingMachinery


EnergyJournal of


















12

345678

9101112

131415161718

1920

1 2 3 4 5 6 7 8 9 10 11121314151617181920


(a)

12

345678

9101112

131415161718

1920

1 2 3 4 5 6 7 8 9 10 11121314151617181920


(b)


119903= 11

0 5 10 15 20 25 30 3500

01

02

03

04

05

Am

plitu

de (T

)

Pole pair number





mp1(m = 9 or 11)

p1mminus1




2pole



2119898minus1=




0 5 10 15 20 25 30 35 4000

02

04

06

08

10

12

Am

plitu

de (T

)Pole pair number


p2(p2 = p1mminus1)

Prototype 1

Prototype 2


0

20

40

60


Back

-EM

F (V

)

minus60

minus40

minus20

Prototype 1

Prototype 2






119892






20

22

24

26

28

30


Torq

ue (N

m)

Prototype 1

Prototype 2


0

20

40

Torq

ue (N

m)

minus40

minus20

minus180 90 0 90 180



Rg = 1mmRg = 05mm


torque





is chosen With 119877119892= 05mm 119871




method


0

20

40

60

Thick (mm)

Back

-EM

F (V

)

0

300

600

900

Torq

ue (m

Nm

)

0 1 2 3 4 5





119889= 119894119904and






0

02

04

06

08

Thick (mm)

B (T

)

0 1 2 3 4


0

20

40

60


Back

-EM

F (V

)

0

300

600

900To

rque

(mN

m)


04 05 06 07 08 09 1







2= 1198711


2and


2= 33mm the





Finally 1198712= 33mm and 119871




10

15

20

25

30

Tooth width (mm)

Torq

ue (N

m)

0 1 2 3 4

L1

L2

Condition L2 = L1

Condition L2 = 33mm



2


1 FMP width 120579

2 and stator


1= 1205792= 1205793) In


3







Armature tooth

FMP


Armature winding

PM

Rotor

Stator

Slot opening

FMP-slot

(a)

L1L2

L3

12057911205792

1205793 R1

(b)


0

10

20

30

40


Torq

ue (N

m)

CoggingOutput

minus100 180 360 540



PF = 1

radic1 + (119871119904119868120595119898)

(6)

where 120595119898







0

5

10

15

Times (ms)

Curr

ent (

A)

minus15

minus10

minus5

0 10 20 30 40






(a) (b)



0

05

1

15

2

25

3

35

Harmonic order1 2 3 4 5 6 7 8 9 10 11 12 13

Fund

amen

tal a

mpl

itude

()






6 Conclusion


Nomenclature





Acknowledgments


References





















FuelsJournal of







Advances in



Journal of


Renewable Energy





RotatingMachinery


EnergyJournal of


















20

22

24

26

28

30


Torq

ue (N

m)

Prototype 1

Prototype 2


0

20

40

Torq

ue (N

m)

minus40

minus20

minus180 90 0 90 180



Rg = 1mmRg = 05mm


torque





is chosen With 119877119892= 05mm 119871




method


0

20

40

60

Thick (mm)

Back

-EM

F (V

)

0

300

600

900

Torq

ue (m

Nm

)

0 1 2 3 4 5





119889= 119894119904and






0

02

04

06

08

Thick (mm)

B (T

)

0 1 2 3 4


0

20

40

60


Back

-EM

F (V

)

0

300

600

900To

rque

(mN

m)


04 05 06 07 08 09 1







2= 1198711


2and


2= 33mm the





Finally 1198712= 33mm and 119871




10

15

20

25

30

Tooth width (mm)

Torq

ue (N

m)

0 1 2 3 4

L1

L2

Condition L2 = L1

Condition L2 = 33mm



2


1 FMP width 120579

2 and stator


1= 1205792= 1205793) In


3







Armature tooth

FMP


Armature winding

PM

Rotor

Stator

Slot opening

FMP-slot

(a)

L1L2

L3

12057911205792

1205793 R1

(b)


0

10

20

30

40


Torq

ue (N

m)

CoggingOutput

minus100 180 360 540



PF = 1

radic1 + (119871119904119868120595119898)

(6)

where 120595119898







0

5

10

15

Times (ms)

Curr

ent (

A)

minus15

minus10

minus5

0 10 20 30 40






(a) (b)



0

05

1

15

2

25

3

35

Harmonic order1 2 3 4 5 6 7 8 9 10 11 12 13

Fund

amen

tal a

mpl

itude

()






6 Conclusion


Nomenclature





Acknowledgments


References





















FuelsJournal of







Advances in



Journal of


Renewable Energy





RotatingMachinery


EnergyJournal of


















0

02

04

06

08

Thick (mm)

B (T

)

0 1 2 3 4


0

20

40

60


Back

-EM

F (V

)

0

300

600

900To

rque

(mN

m)


04 05 06 07 08 09 1







2= 1198711


2and


2= 33mm the





Finally 1198712= 33mm and 119871




10

15

20

25

30

Tooth width (mm)

Torq

ue (N

m)

0 1 2 3 4

L1

L2

Condition L2 = L1

Condition L2 = 33mm



2


1 FMP width 120579

2 and stator


1= 1205792= 1205793) In


3







Armature tooth

FMP


Armature winding

PM

Rotor

Stator

Slot opening

FMP-slot

(a)

L1L2

L3

12057911205792

1205793 R1

(b)


0

10

20

30

40


Torq

ue (N

m)

CoggingOutput

minus100 180 360 540



PF = 1

radic1 + (119871119904119868120595119898)

(6)

where 120595119898







0

5

10

15

Times (ms)

Curr

ent (

A)

minus15

minus10

minus5

0 10 20 30 40






(a) (b)



0

05

1

15

2

25

3

35

Harmonic order1 2 3 4 5 6 7 8 9 10 11 12 13

Fund

amen

tal a

mpl

itude

()






6 Conclusion


Nomenclature





Acknowledgments


References





















FuelsJournal of







Advances in



Journal of


Renewable Energy





RotatingMachinery


EnergyJournal of


















Armature tooth

FMP


Armature winding

PM

Rotor

Stator

Slot opening

FMP-slot

(a)

L1L2

L3

12057911205792

1205793 R1

(b)


0

10

20

30

40


Torq

ue (N

m)

CoggingOutput

minus100 180 360 540



PF = 1

radic1 + (119871119904119868120595119898)

(6)

where 120595119898







0

5

10

15

Times (ms)

Curr

ent (

A)

minus15

minus10

minus5

0 10 20 30 40






(a) (b)



0

05

1

15

2

25

3

35

Harmonic order1 2 3 4 5 6 7 8 9 10 11 12 13

Fund

amen

tal a

mpl

itude

()






6 Conclusion


Nomenclature





Acknowledgments


References





















FuelsJournal of







Advances in



Journal of


Renewable Energy





RotatingMachinery


EnergyJournal of


















(a) (b)



0

05

1

15

2

25

3

35

Harmonic order1 2 3 4 5 6 7 8 9 10 11 12 13

Fund

amen

tal a

mpl

itude

()






6 Conclusion


Nomenclature





Acknowledgments


References





















FuelsJournal of







Advances in



Journal of


Renewable Energy





RotatingMachinery


EnergyJournal of




















Acknowledgments


References





















FuelsJournal of







Advances in



Journal of


Renewable Energy





RotatingMachinery


EnergyJournal of





















FuelsJournal of







Advances in



Journal of


Renewable Energy





RotatingMachinery


EnergyJournal of

















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