OptimizationDesignofaNewTypeofInteriorPermanent ...ϕ U ϕ mT +ϕ Tl +ϕ mQ +ϕ Ql πDα j α mB...

Research ArticleOptimization Design of a New Type of Interior PermanentMagnet Generator for Electric Vehicle Range Extender

Shilun Ma 1 Xueyi Zhang 1 Qinjun Du2 Liwei Shi1 and Xiangyu Meng1

1School of Transportation and Vehicle Engineering Shandong University of Technology Zibo 255049 China2School of Electrical and Electronic Engineering Shandong University of Technology Zibo 255049 China

Correspondence should be addressed to Xueyi Zhang zhangxueyisduteducn

Received 7 January 2019 Accepted 12 March 2019 Published 2 May 2019

Academic Editor Gorazd Stumberger

Copyright copy 2019 Shilun Ma et al is 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

Aiming at the disadvantages of large leakage flux and low magnetic flux density of radial magnetic circuit and tangential magneticcircuit a new type of permanent magnet (PM) rotor with parallel tangential and radial magnetic circuits is proposed Based onOhmrsquos law and Kirchhoffrsquos law of magnetic circuits equivalent magnetic circuits for rotor poles are developed e structureparameters of the generator are preliminarily determined At the same time by means of the Taguchi method and employing finiteelement analysis the rotor poles of generator are optimized to improve air gap magnetic density the cogging torque and thedistortion of back-EMF waveform Finally the validity of proposed design methods is validated by the analytical andexperimental results

1 Introduction

Electric vehicles have been widely used in peoplersquos daily lifedue to their advantages of low pollution low noise and zeroemission But the limited range has become a bottleneckrestricting its development Before electric vehicle batterystorage technology made a major breakthrough adding anextended-range generator for electric vehicles was one of theimportant ways to increase the endurance mileage [1 2] Sothe generator device is the key component of the powersupply system of electric vehicles With the perfection of theelectric automobile the power consumption is increasingand the silicon-rectifying generator has been unable to meetthe demand of electrical equipment for power consumptionHowever the permanent magnet generator is excited by PMwithout electric excitation winding and has the advantagesof simple structure high power density high reliability andso on so it has a broad market prospect in the power supplysystem of electric vehicles [3 4]

e literature [5] has proposed a novel surface-mountedand interior double radial PM synchronous generatorthrough the equivalent magnetic circuit (EMC) methodemagnetic permeance andmagnetic leakage permeance of the

generator are analyzed and the optimal structural param-eters of the generator are determined One study [6] showedthat using the level set method to optimize the PM syn-chronous generator the cogging torque of the generator isreduced and the performance of the motor is improved eliterature [7] has proposed an axial magnetic circuit gen-erator in which rotor pole is composed of core and PM andby optimizing the shape of the magnetic pole harmoniccontent is reducede literature [8] presented a new type ofrotor structure in which main magnetic flux and leakageflux of the PM are calculated by the EMC method the it-eration does not converge when iron core is severely sat-urated e literature [9] has established the open-circuitEMC model of the surface-mounted and interior synchro-nous PM motor and the EMC model under the armaturereaction e air gap magnetic field and the armature backEMF of the motor are solved the accuracy of the analyticalcalculation is verified by the finite element results e lit-erature [10] makes use of genetic algorithm and particleswarm optimization to improve the comprehensive per-formance of the motor but establishment and solutionanalysis of objective function in these algorithms are quitecomplex which not only makes it difficult to realize the fast

HindawiJournal of Electrical and Computer EngineeringVolume 2019 Article ID 3108053 10 pageshttpsdoiorg10115520193108053

calculation of the optimal parameters but also has certainlocalization in the multiobjective optimization designHowever the Taguchi method is a local optimization al-gorithm which can realize the multiobjective optimizationdesign of a generator It not only can realize the rapid designof the generator but also has high design precision It hasbeen widely used in the field of generator development anddesign in recent years [11 12]

In order to accurately design and analyze the relation-ship between the output characteristics of the tangential andradial parallel magnetic circuit permanent magnet generator(ITQPMG) the parameters of magnetic pole are de-termined By establishing the model of EMC the parametersof magnetic pole are preliminarily determined and thenthey are optimized by the Taguchi method In this study theparameters of magnetic pole have been selected as thehorizontal variables e multiobjective optimization ofoutput characteristics such as the peak value of air gapmagnetic density waveform distortion rate of no-load backEMF and the peak value of cogging torque is realized so theoptimal parameters combination can be obtained to improvethe performance of ITQPMG

2 Determination of Main Parameters

e magnetic circuit of the conventional PM generator isdivided into radial directions and tangential directionsAlthough the generator of radial magnetic circuit has lessleakage and back-EMF waveform has good sinusoidalproperty the peak value of air gap flux density is lower einterior radial permanent magnet generator (IRPMG) isshown in Figure 1(a) when the leakage of tangential

magnetic circuit generator is large tangential magnetic polescan produce a certain degree of magnet congregate effect Sothe peak value of air gap density is high and the distortionrate of back-EMF waveform is low [13] e interior tan-gential permanent magnet generator (ITPMG) is shown inFigure 1(b) In this study the advantages of two kinds of PMgenerator of magnetic circuit are discussed and a new type ofPM generator is proposed which reduces the magnetismleakage between magnetic poles and tends back-EMFwaveforms to be sinusoidal e radial and tangential fluxtogether provides the flux and synthesizes it in air gap whichhas remarkable magnetic concentration effect makes up thedepression of back-EMF waveforms and improves the ef-ficiency of the generatore structure of ITQPMG is shownin Figure 1(c) Initial design parameters are listed in Table 1

3 Establishment and Analysis of EMC Model

According to the PM layout form and the characteristics ofrotor topological structure the EMCmodel is established underthe no-load condition of the generator e model consists oftwo independent flux paths the first magnetic flux path is aclosed magnetic path independently formed by tangential PMand the second flux paths are closed magnetic circuits formedby two series radial rectangle PM connections e main fluxpath and leakage flux path of the new type structure of PMgenerator are shown in Figure 2 and the equivalent magneticcircuit of the ITQPMG is shown in Figure 3

When the generator is working in no-load state thedirect axis component of armature reaction is Fd 0According to Ohmrsquos law and Kirchhoffrsquos law of magneticcircuits we can establish the EMC model as follows

ϕmT minus ϕTl HcbmT

GmT middot GTl( 1113857 GmT + GTl( 1113857( 1113857 + 2 1Gr1( 1113857 + 1Gg1113872 1113873 + 1Gts( 1113857 + 1Gt( 11138571113872 1113873 + 1Gy1113872 1113873

ϕmQ minusϕQl 2HcbmQ

2 middot GmQ middot GQl1113872 1113873 GmQ + GQl1113872 11138731113872 1113873 + 4 1Gr1( 1113857 + 1Gg1113872 1113873 + 1Gts( 1113857 + 1Gt( 11138571113872 1113873 + 1Gy1113872 1113873 + 1Gr2( 1113857

(1)

where FmT is the equivalent magnetomotive force of tan-gential PM steel Hc is the coercivity of PM bmT is thethickness of tangential PM steel in the magnetization di-rection FmQ is the equivalent magnetomotive force of radialPM steel Fd is d axis component of the armature reactionGmT is the permeance of tangential PM steel GmQ is thepermeance of radial PM steel GTl is the leakage permeanceof tangential PM steel GQl is the leakage permeance of radialPM steel Gr1 is the permeance between rotor core and airgap Gr2 is the permeance of rotor core between two radialPM steels Gg is the permeance of air gap between rotor andstator Gt is the permeance of stator tooth Gts is the per-meance of stator boot Gy is the permeance of stator yokeφmT is the flux provided by tangential PM steel φmQ is theflux provided by radial PM steel φQl is the leakage flux ofradial PM steel φTl is the leakage flux of radial PM steel andφU is the effective flux

e calculation formula of the phasersquos back EMF ofgenerator

E NdϕU

dt 444fNKwKφ ϕmT minusϕTl + ϕmQ minusϕQl1113872 1113873 (2)

where f is the frequency of the generator Kw is the windingcoefficient of the armature winding Kw Kd middot Kp middot Kswhere Kd is the distribution factor Kd (sin[180deg(2m)])(q sin[180deg(2mq)]) where q is the number of slots per poleof each phase q (Zs2pm) where Zs is the number ofstator slots and m is the number of phases m 3 Kp is theshort range factor Kq sin(180β2) β (ymq) where y isthe pitch of winding Kφ is the waveform coefficient of airgap flux Kφ 111 and N is the armature winding turns ofeach phase

e air gap circumferential flux produced by PM steel inrotor can be expressed in the following calculation formula

2 Journal of Electrical and Computer Engineering

ϕU ϕmT + ϕTl + ϕmQ + ϕQl πDαjαmBrL times 10minus4 (3)

where D is the rotor diameter αj is the mechanical pole arccoefficient of the generator αm is the magnetic pole arccoefficient Br is the remanent flux density and L is thegeneratorrsquos axial length

e wye connection method is used in this design so theno-load back EMF is equal to

3

radictimes the rated voltage

erefore the width of the tangential PM steel is 11mm thethickness of the magnetization direction is 4mm the widthof the radial PM steel is 6mm the thickness of the mag-netization direction is 2mm and the implanting depth of theradial PM is 14mm

4 Optimal Design of Rotor Pole

e size and position of the rotor pole have a significantinfluence on the performance of the PM generator Howeverthe parameters of magnetic pole calculated by the EMCmethod may not be the best performance parameter so it isnecessary to optimize the design of the rotor pole eTaguchi method is a local optimization algorithm which canoptimize multiple objectives at the same time By establishingthe orthogonal test table the optimal combination of mul-tiobjective optimization design parameters can be calculatedwith the least experiment times In this study the Taguchimethod is used to optimize the rotor poles of ITQPMG

41 Test Schemes For PM generator with parallel magneticcircuit the parameters of PM and implanting radial depth ofPM have great influence on the performance [14] ereforethere are three optimization objectives in this study such asthe peak value of the cogging torque (T) the peak value ofthe air gap flux density (G) and the distortion rate of the no-load back EMF (Kr) e width of tangential PM (hmT) thethickness of the magnetization direction of the tangentialPM (bmT) the width of the radial PM (hmQ) the thickness ofthe magnetization direction of the radial PM (bmQ) and theimplanting depth of the radial PM (b) are selected as var-iablese experimental matrix and finite element results areshown in Table 2

(a) (b) (c)

Figure 1 Structure of ITQPMG (a) IRPMG (b) ITPMG (c) ITQPMG

Table 1 Initial design parameters of the generator

Parameters ValuesStator inner diameter (mm) 106Stator outer diameter (mm) 135Axial length (mm) 30Air gap length (mm) 05Number of stator slots 36Rated power (W) 500Rated voltage (V) 28Rated speed (rmin) 4000Pole pairs 6Winding turns per slot 11

2

3

1

4

Figure 2 Diagram of magnetic flux of ITQPMG (1) e mainmagnetic flux of tangential PM steel (2) e main magnetic flux ofradial PM steel (3) e leakage flux of tangential PM steel (4) eleakage flux of tangential PM steel

Journal of Electrical and Computer Engineering 3

e calculation formula of back-EMF waveform dis-tortion rate for PM generator [15ndash17]

Kr

U22 + U2

3 + U24 + middot middot middot + U2

N

1113969

U1times 100 (4)

where UN is the amplitude of Nth harmonicsAccording to the factors and levels in Table 2 the

experimental matrix of L16(45) is established If thetraditional single-variable and single-objective optimi-zation method uses 45 1024 experiments the optimi-zation design of the multiparameter and multitarget ofpermanent magnet generator can be completed by theTaguchi method only with 16 experiments e orthog-onal experimental matrix of influencing factors isestablished and the experimental results are solved withfinite element analysis software e results of the ex-perimental orthogonal table and the simulation solutionare shown in Table 3

According to the formula the average value of the so-lution in Table 3 is calculated

M(S) 1n

1113944

n

i

Si 116

1113944

16

i1S(i) (5)

where n is the experiment times and Si is the average value ofthe target performance of the ith times

e calculation results are shown in Table 4en the average value of each factor level of the pa-

rameter to the specific target performance is calculated

Mxi 14

Mx(j) + Mx(k) + Mx(l) + Mx(n)1113858 1113859 (6)

where Mxi is the average value of the performance indexunder the ith factor of parameter x Mx is the performanceindex of parameter x under a certain experiment and J k land n are the serial numbers of the experiment

In order to facilitate the comprehensive analysis thechange of the indicators with the level of factors is repre-sented by broken lines as shown in Figures 4ndash6

From Figures 4ndash6 it is observed that these three sets ofhorizontal combinations are designed for optimization ofsingle performance indices For example considering theeffect of three performance indices on ITQPMG it is nec-essary to analyze the variance to further analyze the influ-ence of the changes of each parameter on the differentperformance indices and to determine the parametersChanging the proportion of the influence on its performanceindices and obtaining the optimization results we obtain

S(s) 1z

1113944

z

i1Mxi minusM(s)1113858 1113859

2 (7)

where s is the influence of factors such as b1 h1 b2 h2 and bS(s) is the variance of performance index under the pa-rameter s M(s) is the total average value of a performanceindex e calculation results of variance reflect the pro-portion of different level factors to each test indexe resultof S(s) is shown in Table 5

42 Determination of the Final Optimization Scheme As canbe seen from Table 5 the size of variance can directly reflectthe proportion of the impact of optimization parameters onperformance indicators [18 19] e parameter bmT has thegreatest influence on the air gap magnetic density peak andthe back-EMF waveform of the PM generator Comparedwith the proportion of SKr and SG the width of tangentialPM steel hmT has great influence on the cogging torque of thePM generator e magnetization direction thickness of theradial PM steel bmQ and the implanting depth of PM steel bhave the greatest influence on the peak value of air gapmagnetic density

GmT

FcT

GTl

GmQ

Gr2

GmQ

FcQ

FcQ

GQl

GQl

Gr1 Gg Gts Gt

Gr1 Gg Gts Gt

Gy

FdΦmT

ΦmT ndash ΦTl

ΦTl

ΦmQ

ΦmQ

ΦQl

ΦQl

ΦU

Figure 3 EMC diagram of the ITQPMG

Table 2 Test table of optimization parameters and factor level

Parameters hmT(mm)

bmT(mm)

hmQ(mm)

bmQ(mm)

b(mm)

Factor level 1 10 2 4 2 10Factor level 2 11 3 5 3 12Factor level 3 12 4 6 4 14Factor level 4 13 5 7 5 16


Table 3 Experimental matrix and finite element analysis

NoExperimental matrix

Kr () T (Nmiddotm) G (T)hmT (mm) bmT (mm) hmQ (mm) bmQ (mm) b (mm)

1 1 1 1 1 1 471 058 0512 1 2 2 2 2 402 081 0633 1 3 3 3 3 362 104 0744 1 4 4 4 4 314 132 0835 2 1 2 3 4 453 075 0586 2 2 1 4 3 418 085 0627 2 3 4 1 2 358 112 0808 2 4 3 2 1 314 129 0829 3 1 3 4 2 431 104 06910 3 2 4 3 1 393 137 07911 3 3 1 2 4 362 117 07512 3 4 2 1 3 305 116 08113 4 1 4 2 3 426 122 07414 4 2 3 1 4 404 146 08015 4 3 2 4 1 358 117 07616 4 4 1 3 2 314 133 084

Table 4 Average value of performance index

Optimization index Kr () T (Nmiddotm) G (T)m 38 1105 073

1 2 3 420

25

30

35

40

45

50

1 2 3 4 1 2 3 4 1 2 3 4 1 2 3 4

K r (

)

hmT bmT hmQ bmQ b

Figure 4 Impact of various factors on Kr

1 2 3 408

09

10

11

12

13

14

1 2 3 4 1 2 3 4 1 2 3 4 1 2 3 4

T (N

m)

hmT bmT hmQ bmQ b

Figure 5 Impact of various factors on T


According to the above analysis the selection of all factorsshould be based on the optimization standard of the unloadedback EMF-waveform distortion rate peak value of air gapmagnetic densitymaximum and peak value of cogging torqueminimum Finally the parameter combination [hmT (1) bmT(4) hmQ (1) bmQ (3) b(2)] is determined to be the bestcombination e magnetization direction of tangential PMsteel is 5mm the width of radial rectangular PM steel is 4mmthe thickness of the magnetization direction of radial rect-angular PM steel is 4mm and the radial rectangular PM steelis implanted deep e implanting depth of PM steel is12mm

5 Result of Finite Element Analysis

In order to verify the superiority of the optimized PMgenerator the initial design structure calculated by the EMCmethod and the optimized structure parameters obtained bythe Taguchi method are compared and analyzed In the caseof the same stator structure winding mode rotor diametersilicon steel sheet and PMmaterial of the two PM generatorsmentioned above both are compared and analyzed by thefinite element method

Figure 7 is the no-load back-EMF waveform of the twocycles before and after optimization It can be seen that thepeak value of the no-load back-EMF wave before optimi-zation has obvious depression and the no-load back-EMFwaveform of the optimized ITQPMG is closer to the si-nusoidal wave It is shown that the sinusoidal EMF wave-form can be obtained by the optimized design

Figure 8 shows the amplitude of each harmonic contentin the no-load back EMF before and after the optimizationIt can be seen that the amplitude of the fundamental wavebefore optimization is 3677 V the waveform distortionrate is 45 the amplitude of the fundamental wave afteroptimization is 3863 V and the waveform distortion rate is33

Figure 9 shows the cogging torque before and after theoptimization of the generator It can be seen that the op-timized cogging torque decreases from 112Nmiddotm to 055Nmiddotmafter optimization which is reduced by about 51

1 2 3 4060

065

070

075

080

085

1 2 3 4 1 2 3 4 1 2 3 4 1 2 3 4

GT

hmT bmT hmQ bmQ b

Figure 6 Impact of various factors on G

Table 5 Variance and proportion of the performance indices of each parameter under 4 level factors

ParametersSKr ST SG

Variance Proportion () Variance Proportion () Variance Proportion ()hmT 0396 085 00210 2328 00016 1650bmT 24760 5365 00180 1996 00053 5464hmQ 20743 4500 00490 5432 00020 2062bmQ 0116 035 00003 033 000005 051b 0072 015 00019 211 000075 773Total 46087 100 00902 100 000970 100

0 1 2 3 4 5

ndash40

ndash20

0

20

40

No-

load

bac

k-EM

F (V

)

Time (ms)

Before optimizationOptimized results

Figure 7 Comparison results of back-EMF waveforms


0 1 2 3 4 5 6 7 8 9 10 11 120

5

10

15

20

25

30

35

40

No-

load

bac

k-EM

F (V

)

Order of harmonics

(a)

1 2 3 4 5 6 7 8 9 10 110

5

10

15

20

25

30

35

40

No-

load

bac

k-EM

F (V

)

Order of harmonics

(b)

Figure 8 Comparison results of each harmonic content of no-load back EMF (a)e amplitude of harmonics before optimization (b)eamplitude of harmonics after optimization

0 1 2 3 4 5ndash15

ndash10

ndash05

00

05

10

15

Cogg

ing

torq

ue (N

middotm)

Time (ms)


Figure 9 Comparison results of cogging torque

Peak

val

ue o

f air

gap

mag

netic

den

sity

(T)

1090807060504030201

00

50100

150200

250300

Circumferential distance (mm)

05

1015

2025 Axis distance (mm)

(a)

12

1

08

06

04

02

0

Peak

val

ue o

f air

gap

mag

netic

den

sity

(T)

050

100150

200250

300

50

1015

2025

Circumferential distance (mm) Axis distance (mm)

(b)

Figure 10 Comparison results of peak value of air gapmagnetic density (a)e peak value of air gap magnetic density before optimization(b) e peak value of air gap magnetic density after optimization


0 1000 2000 3000 4000 500040

50

60

70

80

90

100

Effic

ienc

y (

)

Speed (rmiddotminndash1)

ITQPMGIRPMGITPMG

Figure 11 Efficiency curves of three permanent magnet generators

(a) (b) (c)

Figure 12 e photographs of ITQPMG (a) e stator of ITQPMG (b) e rotor before optimization (c) Optimized rotor

Communicationport

IPC

Signalprocessing

unit

Dataacquisition

chip

Electronic load

Electronicalcontrol unit

Control signal

Voltage andcurrent sensors

Speed signal

Drive motor

Frequencyconverter

ITQPMG

Oscilloscope

IPC

ITQPMG

Frequency converter

Drive motor

Figure 13 Generator performance test system and its principle block diagram


Figure 10 shows the variation pattern of the peak value ofair gap magnetic density along the axial and radial directionsof the rotor before and after optimization It can be seen thatthe peak value of air gap magnetic density before optimi-zation is 083 T and it appeared at the position of 12mm inthe axial direction and 94mm in the radial direction whilethe optimized peak value of air gap magnetic density is112 T it appears at the position of 5mm axial distance and27mm circumferential distance Compared to the optimi-zation the peak value of air gap magnetic density has beenimproved by about 35

In order to verify the advantages of the ITQPMG it iscompared with the efficiency of two other traditional PMgenerators as shown in Figure 11 With the increase of speedthe efficiency of ITQPMG is higher than that of the other twotraditional PM generators e maximum efficiency ofITPMG is 865 and the maximum efficiency of IRPMG is886 while the maximum efficiency of ITQPMG can reach912 is is because ITQPMG not only has less magneticleakage but also has significant magnet congregate effect

6 Performance Test

e photographs are shown in Figure 12 and the generatortest system and its principle block are shown in Figure 13eworking process of the generator test system is mainlycontrolled by IPC to control the speed of frequency motor soas to change the speed of ITQPMG and electronic load fortesting Data acquisition chip and signal processing unit areused to collect and analyze the signals of voltage current andspeed en the test data are fed back to the electrical controlunit to complete the automatic adjustment of the electronicload thus completing the performance test of the generator

e experimental platform is driven by a 11 kW variablefrequency motor as the drive motor to operate the generatorand the no-load and load experiments are carried outrespectively

When the ITQPMG prototype is running at the ratedspeed of 4000 rmin the no-load back-EMF waveform be-fore and after optimization is shown in Figure 14 It can beseen that the optimized no-load back-EMF waveform is

closer to the sine wave the peak value of the no-load back-EMF is increased and the distortion rate of the waveform isreduced e experimental test is basically consistent withthe result of the finite element analysis method

Finally in the case of load power of 480W 500W and520W the load performance test of the optimized ITQPMG iscarried out and the experimental results are shown in Table 6

It is found from Table 6 that the output voltage maintainsaround 262 Vsim286V for the generator speed of 2000 rminsim4800 rmin and load power of 480Wsim520W whichmeets the design requirements

7 Conclusion

A new type of rotor topology of PM generator with tan-gential magnetic circuit and radial magnetic circuit whichprovide a common air gap magnetic field is developed isstructure has less magnetic flux lower cogging torque andsignificant magnetic congregate effect

e structural parameters of the PM generator arepreliminarily determined by the analytical calculation ofthe EMC method and the Taguchi method is introducedto optimize the multiobjective design of the tangential andradial parallel magnetic circuits of the PM generator eoptimum combination of ITQPMG is obtained Com-bined with the finite element method the optimizationresults are compared and analyzed e cogging torque isreduced by 51 the air gap magnetic density is increased

(a) (b)

Figure 14 Comparison experimental results of no-load back-EMF waveforms (a) No-load back-EMF waveforms before optimization (b)No-load back-EMF waveforms after optimization

Table 6 Test results of the generator output voltage

Speed (rmin) Load power (W) Output voltage (V)

2000480 268500 266520 262

4000480 283500 284520 283

4800480 286500 286520 285


by 35 the peak value of no-load back-EMF waveform isreduced by 12 and the waveform is closer to the sine

e performance test is performed with various rotaryspeeds and load powers When the generator speedchanges from 2000 rminsim4800 rmin and the load powervaries from 480Wsim520W the output voltage maintainsaround 262 Vsim286 V which has an excellent regulatorperformance

Data Availability

e data used to support the findings of this study are in-cluded within the article

Conflicts of Interest

e authors declare that they have no conflicts of interest

Authorsrsquo Contributions

M S built the equivalent magnetic circuit model and wrotemost of the paper X Z proposed the new type of motorstructure Q D analyzed the finite element simulationanalysis of the generator L S optimized the parameters ofmagnetic pole of the generator X M was in charge ofanalysis of equations and drawing some charts

Acknowledgments

is work was supported by grants from the NationalNatural Science Foundation of China (Project no 51875327)and the Natural Science Foundation of Shandong Province(Project nos ZR2018LE010 and ZR2017MF045)

References

[1] X Zhang L Shi and YWang ldquoDesign and stabilivolt analysisof Nd-Fe-B permanent magnet generator for electric vehiclerange extenderrdquo International Journal of Electric and HybridVehicles vol 3 no 3 pp 259ndash271 2011

[2] Q Du S Ma W Hu H Geng and X Zhang ldquoMagnetic fluxanalysis and performance test of permanent magnet and claw-pole electromagnetic hybrid excitation generator for electricvehicle range extenderrdquo International Journal of Electric andHybrid Vehicles vol 9 no 3 p 187 2017

[3] L Shi B Yan X Zhou and X Zhang ldquoOpen-circuit fault-tolerant characteristics of a new four-phase doubly salientelectro-magnetic generatorrdquo Sustainability vol 10 no 11p 4136 2018

[4] X Zhang Q Du C Ma et al ldquoNd-Fe-B permanent magnetgenerator and voltage stabilizing control technology for ve-hiclesrdquo Advances in Mechanical Engineering vol 8 no 9article 168781401666963 2016

[5] X Zhang Q Du S Ma et al ldquoPermeance analysis and cal-culation of the double-radial rare-earth permanent magnetvoltage-stabilizing generation devicerdquo IEEE Access vol 6pp 23939ndash23947 2018

[6] S Lim S Min and J-P Hong ldquoLevel-set-based optimal statordesign of interior permanent-magnet motor for torque ripplereduction using phase-field modelrdquo IEEE Transactions onMagnetics vol 47 no 10 pp 3020ndash3023 2011

[7] H Wang Z Qu S Tang M Pang and M Zhang ldquoAnalysisand optimization of hybrid excitation permanent magnetsynchronous generator for stand-alone power systemrdquoJournal of Magnetism and Magnetic Materials vol 436pp 117ndash125 2017

[8] G Xu G Liu S Jiang and Q Chen ldquoAnalysis of a hybridrotor permanent magnet motor based on equivalent magneticnetworkrdquo IEEE Transactions on Magnetics vol 54 no 4pp 1ndash9 2018

[9] S I Ji-Kai H E Song H C Feng et al ldquoCharacteristicanalysis of surface-mounted and interior hybrid permanentmagnet synchronous motor based on equivalent magneticcircuit methodrdquo Journal of China Coal Society vol 40 no 5pp 1199ndash1205 2015

[10] A Mahmoudi S Kahourzade N A Rahim and W P HewldquoDesign analysis and prototyping of an axial-flux permanentmagnet motor based on genetic algorithm and finite-elementanalysisrdquo IEEE Transactions on Magnetics vol 49 no 4pp 1479ndash1492 2013

[11] X Jannot J-C Vannier C Marchand M Gabsi J Saint-Michel and D Sadarnac ldquoMultiphysic modeling of a high-speed interior permanent-magnet synchronous machine for amultiobjective optimal designrdquo IEEE Transactions on EnergyConversion vol 26 no 2 pp 457ndash467 2011

[12] S Lee S Cho K Kim J Jang T Lee and J Hong ldquoOptimaldesign of interior permanent magnet synchronous motorconsidering the manufacturing tolerances using Taguchi ro-bust designrdquo IET Electric Power Applications vol 8 no 1pp 23ndash28 2014

[13] G Hong and Q Hao ldquoRobust design for reducing torqueripple in permanent magnet synchronous motorrdquo ChineseSociety of Electrical Engineering vol 32 no 24 pp 88ndash952012

[14] J Du X Wang and H Lv ldquoOptimization of magnet shapebased on efficiency map of IPMSM for EVsrdquo IEEE Trans-actions on Applied Superconductivity vol 26 no 7 pp 1ndash72016

[15] M Si X Yu Yang S Wei Zhao and S Gong ldquoDesign andanalysis of a novel spoke-type permanent magnet synchro-nous motorrdquo IET Electric Power Applications vol 10 no 6pp 571ndash580 2016

[16] Z Lan X Yang F Wang et al ldquoApplication for optimaldesigning of sinusoidal interior permanent magnet syn-chronous motors by using the Taguchi methodrdquo Journal ofElectrical Engineer vol 26 no 12 pp 37ndash42 2011

[17] S I Kim J Y Lee Y K Kim et al ldquoOptimization for re-duction of torque ripple in interior permanent magnet motorby using the Taguchi methodrdquo IEEE Transactions on Mag-netics vol 41 no 5 pp 1796ndash1799 2005

[18] S Jikai L Zhang F Haichao et al ldquoMulti-objective optimaldesign of a surface-mounted and interior permanent magnetsynchronous motorrdquo Journal of China Coal Society vol 41no 12 pp 3167ndash3173 2016

[19] C Hwang S Hung C Liu et al ldquoOptimal design of a highspeed SPM motor for machine tool applicationsrdquo IEEETransactions on Magnetics vol 50 no 1 2014


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calculation of the optimal parameters but also has certainlocalization in the multiobjective optimization designHowever the Taguchi method is a local optimization al-gorithm which can realize the multiobjective optimizationdesign of a generator It not only can realize the rapid designof the generator but also has high design precision It hasbeen widely used in the field of generator development anddesign in recent years [11 12]

In order to accurately design and analyze the relation-ship between the output characteristics of the tangential andradial parallel magnetic circuit permanent magnet generator(ITQPMG) the parameters of magnetic pole are de-termined By establishing the model of EMC the parametersof magnetic pole are preliminarily determined and thenthey are optimized by the Taguchi method In this study theparameters of magnetic pole have been selected as thehorizontal variables e multiobjective optimization ofoutput characteristics such as the peak value of air gapmagnetic density waveform distortion rate of no-load backEMF and the peak value of cogging torque is realized so theoptimal parameters combination can be obtained to improvethe performance of ITQPMG

2 Determination of Main Parameters

e magnetic circuit of the conventional PM generator isdivided into radial directions and tangential directionsAlthough the generator of radial magnetic circuit has lessleakage and back-EMF waveform has good sinusoidalproperty the peak value of air gap flux density is lower einterior radial permanent magnet generator (IRPMG) isshown in Figure 1(a) when the leakage of tangential

magnetic circuit generator is large tangential magnetic polescan produce a certain degree of magnet congregate effect Sothe peak value of air gap density is high and the distortionrate of back-EMF waveform is low [13] e interior tan-gential permanent magnet generator (ITPMG) is shown inFigure 1(b) In this study the advantages of two kinds of PMgenerator of magnetic circuit are discussed and a new type ofPM generator is proposed which reduces the magnetismleakage between magnetic poles and tends back-EMFwaveforms to be sinusoidal e radial and tangential fluxtogether provides the flux and synthesizes it in air gap whichhas remarkable magnetic concentration effect makes up thedepression of back-EMF waveforms and improves the ef-ficiency of the generatore structure of ITQPMG is shownin Figure 1(c) Initial design parameters are listed in Table 1

3 Establishment and Analysis of EMC Model

According to the PM layout form and the characteristics ofrotor topological structure the EMCmodel is established underthe no-load condition of the generator e model consists oftwo independent flux paths the first magnetic flux path is aclosed magnetic path independently formed by tangential PMand the second flux paths are closed magnetic circuits formedby two series radial rectangle PM connections e main fluxpath and leakage flux path of the new type structure of PMgenerator are shown in Figure 2 and the equivalent magneticcircuit of the ITQPMG is shown in Figure 3

When the generator is working in no-load state thedirect axis component of armature reaction is Fd 0According to Ohmrsquos law and Kirchhoffrsquos law of magneticcircuits we can establish the EMC model as follows

ϕmT minus ϕTl HcbmT

GmT middot GTl( 1113857 GmT + GTl( 1113857( 1113857 + 2 1Gr1( 1113857 + 1Gg1113872 1113873 + 1Gts( 1113857 + 1Gt( 11138571113872 1113873 + 1Gy1113872 1113873

ϕmQ minusϕQl 2HcbmQ

2 middot GmQ middot GQl1113872 1113873 GmQ + GQl1113872 11138731113872 1113873 + 4 1Gr1( 1113857 + 1Gg1113872 1113873 + 1Gts( 1113857 + 1Gt( 11138571113872 1113873 + 1Gy1113872 1113873 + 1Gr2( 1113857

(1)

where FmT is the equivalent magnetomotive force of tan-gential PM steel Hc is the coercivity of PM bmT is thethickness of tangential PM steel in the magnetization di-rection FmQ is the equivalent magnetomotive force of radialPM steel Fd is d axis component of the armature reactionGmT is the permeance of tangential PM steel GmQ is thepermeance of radial PM steel GTl is the leakage permeanceof tangential PM steel GQl is the leakage permeance of radialPM steel Gr1 is the permeance between rotor core and airgap Gr2 is the permeance of rotor core between two radialPM steels Gg is the permeance of air gap between rotor andstator Gt is the permeance of stator tooth Gts is the per-meance of stator boot Gy is the permeance of stator yokeφmT is the flux provided by tangential PM steel φmQ is theflux provided by radial PM steel φQl is the leakage flux ofradial PM steel φTl is the leakage flux of radial PM steel andφU is the effective flux

e calculation formula of the phasersquos back EMF ofgenerator

E NdϕU

dt 444fNKwKφ ϕmT minusϕTl + ϕmQ minusϕQl1113872 1113873 (2)

where f is the frequency of the generator Kw is the windingcoefficient of the armature winding Kw Kd middot Kp middot Kswhere Kd is the distribution factor Kd (sin[180deg(2m)])(q sin[180deg(2mq)]) where q is the number of slots per poleof each phase q (Zs2pm) where Zs is the number ofstator slots and m is the number of phases m 3 Kp is theshort range factor Kq sin(180β2) β (ymq) where y isthe pitch of winding Kφ is the waveform coefficient of airgap flux Kφ 111 and N is the armature winding turns ofeach phase

e air gap circumferential flux produced by PM steel inrotor can be expressed in the following calculation formula





3






(a) (b) (c)




2

3

1

4




Kr

U22 + U2


N

1113969

U1times 100 (4)




M(S) 1n

1113944

n

i

Si 116

1113944

16

i1S(i) (5)




Mxi 14

Mx(j) + Mx(k) + Mx(l) + Mx(n)1113858 1113859 (6)




S(s) 1z

1113944

z

i1Mxi minusM(s)1113858 1113859

2 (7)



GmT

FcT

GTl

GmQ

Gr2

GmQ

FcQ

FcQ

GQl

GQl

Gr1 Gg Gts Gt

Gr1 Gg Gts Gt

Gy

FdΦmT

ΦmT ndash ΦTl

ΦTl

ΦmQ

ΦmQ

ΦQl

ΦQl

ΦU



Parameters hmT(mm)

bmT(mm)

hmQ(mm)

bmQ(mm)

b(mm)






1 1 1 1 1 1 471 058 0512 1 2 2 2 2 402 081 0633 1 3 3 3 3 362 104 0744 1 4 4 4 4 314 132 0835 2 1 2 3 4 453 075 0586 2 2 1 4 3 418 085 0627 2 3 4 1 2 358 112 0808 2 4 3 2 1 314 129 0829 3 1 3 4 2 431 104 06910 3 2 4 3 1 393 137 07911 3 3 1 2 4 362 117 07512 3 4 2 1 3 305 116 08113 4 1 4 2 3 426 122 07414 4 2 3 1 4 404 146 08015 4 3 2 4 1 358 117 07616 4 4 1 3 2 314 133 084



1 2 3 420

25

30

35

40

45

50

1 2 3 4 1 2 3 4 1 2 3 4 1 2 3 4

K r (

)

hmT bmT hmQ bmQ b


1 2 3 408

09

10

11

12

13

14

1 2 3 4 1 2 3 4 1 2 3 4 1 2 3 4

T (N

m)

hmT bmT hmQ bmQ b









1 2 3 4060

065

070

075

080

085

1 2 3 4 1 2 3 4 1 2 3 4 1 2 3 4

GT

hmT bmT hmQ bmQ b



ParametersSKr ST SG


0 1 2 3 4 5

ndash40

ndash20

0

20

40

No-

load

bac

k-EM

F (V

)

Time (ms)




0 1 2 3 4 5 6 7 8 9 10 11 120

5

10

15

20

25

30

35

40

No-

load

bac

k-EM

F (V

)

Order of harmonics

(a)

1 2 3 4 5 6 7 8 9 10 110

5

10

15

20

25

30

35

40

No-

load

bac

k-EM

F (V

)

Order of harmonics

(b)


0 1 2 3 4 5ndash15

ndash10

ndash05

00

05

10

15

Cogg

ing

torq

ue (N

middotm)

Time (ms)



Peak

val

ue o

f air

gap

mag

netic

den

sity

(T)

1090807060504030201

00

50100

150200

250300


05

1015


(a)

12

1

08

06

04

02

0

Peak

val

ue o

f air

gap

mag

netic

den

sity

(T)

050

100150

200250

300

50

1015

2025


(b)



0 1000 2000 3000 4000 500040

50

60

70

80

90

100

Effic

ienc

y (

)


ITQPMGIRPMGITPMG


(a) (b) (c)


Communicationport

IPC

Signalprocessing

unit

Dataacquisition

chip

Electronic load


Control signal


Speed signal

Drive motor

Frequencyconverter

ITQPMG

Oscilloscope

IPC

ITQPMG

Frequency converter

Drive motor





6 Performance Test







7 Conclusion



(a) (b)




2000480 268500 266520 262

4000480 283500 284520 283

4800480 286500 286520 285




Data Availability






Acknowledgments


References























RoboticsJournal of




VLSI Design



Shock and Vibration







Journal of



Volume 2018



Volume 2018


Journal of




SensorsJournal of



RotatingMachinery





Propagation






Hindawi


Advances in

Multimedia





3






(a) (b) (c)




2

3

1

4




Kr

U22 + U2


N

1113969

U1times 100 (4)




M(S) 1n

1113944

n

i

Si 116

1113944

16

i1S(i) (5)




Mxi 14

Mx(j) + Mx(k) + Mx(l) + Mx(n)1113858 1113859 (6)




S(s) 1z

1113944

z

i1Mxi minusM(s)1113858 1113859

2 (7)



GmT

FcT

GTl

GmQ

Gr2

GmQ

FcQ

FcQ

GQl

GQl

Gr1 Gg Gts Gt

Gr1 Gg Gts Gt

Gy

FdΦmT

ΦmT ndash ΦTl

ΦTl

ΦmQ

ΦmQ

ΦQl

ΦQl

ΦU



Parameters hmT(mm)

bmT(mm)

hmQ(mm)

bmQ(mm)

b(mm)






1 1 1 1 1 1 471 058 0512 1 2 2 2 2 402 081 0633 1 3 3 3 3 362 104 0744 1 4 4 4 4 314 132 0835 2 1 2 3 4 453 075 0586 2 2 1 4 3 418 085 0627 2 3 4 1 2 358 112 0808 2 4 3 2 1 314 129 0829 3 1 3 4 2 431 104 06910 3 2 4 3 1 393 137 07911 3 3 1 2 4 362 117 07512 3 4 2 1 3 305 116 08113 4 1 4 2 3 426 122 07414 4 2 3 1 4 404 146 08015 4 3 2 4 1 358 117 07616 4 4 1 3 2 314 133 084



1 2 3 420

25

30

35

40

45

50

1 2 3 4 1 2 3 4 1 2 3 4 1 2 3 4

K r (

)

hmT bmT hmQ bmQ b


1 2 3 408

09

10

11

12

13

14

1 2 3 4 1 2 3 4 1 2 3 4 1 2 3 4

T (N

m)

hmT bmT hmQ bmQ b









1 2 3 4060

065

070

075

080

085

1 2 3 4 1 2 3 4 1 2 3 4 1 2 3 4

GT

hmT bmT hmQ bmQ b



ParametersSKr ST SG


0 1 2 3 4 5

ndash40

ndash20

0

20

40

No-

load

bac

k-EM

F (V

)

Time (ms)




0 1 2 3 4 5 6 7 8 9 10 11 120

5

10

15

20

25

30

35

40

No-

load

bac

k-EM

F (V

)

Order of harmonics

(a)

1 2 3 4 5 6 7 8 9 10 110

5

10

15

20

25

30

35

40

No-

load

bac

k-EM

F (V

)

Order of harmonics

(b)


0 1 2 3 4 5ndash15

ndash10

ndash05

00

05

10

15

Cogg

ing

torq

ue (N

middotm)

Time (ms)



Peak

val

ue o

f air

gap

mag

netic

den

sity

(T)

1090807060504030201

00

50100

150200

250300


05

1015


(a)

12

1

08

06

04

02

0

Peak

val

ue o

f air

gap

mag

netic

den

sity

(T)

050

100150

200250

300

50

1015

2025


(b)



0 1000 2000 3000 4000 500040

50

60

70

80

90

100

Effic

ienc

y (

)


ITQPMGIRPMGITPMG


(a) (b) (c)


Communicationport

IPC

Signalprocessing

unit

Dataacquisition

chip

Electronic load


Control signal


Speed signal

Drive motor

Frequencyconverter

ITQPMG

Oscilloscope

IPC

ITQPMG

Frequency converter

Drive motor





6 Performance Test







7 Conclusion



(a) (b)




2000480 268500 266520 262

4000480 283500 284520 283

4800480 286500 286520 285




Data Availability






Acknowledgments


References























RoboticsJournal of




VLSI Design



Shock and Vibration







Journal of



Volume 2018



Volume 2018


Journal of




SensorsJournal of



RotatingMachinery





Propagation






Hindawi


Advances in

Multimedia



Kr

U22 + U2


N

1113969

U1times 100 (4)




M(S) 1n

1113944

n

i

Si 116

1113944

16

i1S(i) (5)




Mxi 14

Mx(j) + Mx(k) + Mx(l) + Mx(n)1113858 1113859 (6)




S(s) 1z

1113944

z

i1Mxi minusM(s)1113858 1113859

2 (7)



GmT

FcT

GTl

GmQ

Gr2

GmQ

FcQ

FcQ

GQl

GQl

Gr1 Gg Gts Gt

Gr1 Gg Gts Gt

Gy

FdΦmT

ΦmT ndash ΦTl

ΦTl

ΦmQ

ΦmQ

ΦQl

ΦQl

ΦU



Parameters hmT(mm)

bmT(mm)

hmQ(mm)

bmQ(mm)

b(mm)






1 1 1 1 1 1 471 058 0512 1 2 2 2 2 402 081 0633 1 3 3 3 3 362 104 0744 1 4 4 4 4 314 132 0835 2 1 2 3 4 453 075 0586 2 2 1 4 3 418 085 0627 2 3 4 1 2 358 112 0808 2 4 3 2 1 314 129 0829 3 1 3 4 2 431 104 06910 3 2 4 3 1 393 137 07911 3 3 1 2 4 362 117 07512 3 4 2 1 3 305 116 08113 4 1 4 2 3 426 122 07414 4 2 3 1 4 404 146 08015 4 3 2 4 1 358 117 07616 4 4 1 3 2 314 133 084



1 2 3 420

25

30

35

40

45

50

1 2 3 4 1 2 3 4 1 2 3 4 1 2 3 4

K r (

)

hmT bmT hmQ bmQ b


1 2 3 408

09

10

11

12

13

14

1 2 3 4 1 2 3 4 1 2 3 4 1 2 3 4

T (N

m)

hmT bmT hmQ bmQ b









1 2 3 4060

065

070

075

080

085

1 2 3 4 1 2 3 4 1 2 3 4 1 2 3 4

GT

hmT bmT hmQ bmQ b



ParametersSKr ST SG


0 1 2 3 4 5

ndash40

ndash20

0

20

40

No-

load

bac

k-EM

F (V

)

Time (ms)




0 1 2 3 4 5 6 7 8 9 10 11 120

5

10

15

20

25

30

35

40

No-

load

bac

k-EM

F (V

)

Order of harmonics

(a)

1 2 3 4 5 6 7 8 9 10 110

5

10

15

20

25

30

35

40

No-

load

bac

k-EM

F (V

)

Order of harmonics

(b)


0 1 2 3 4 5ndash15

ndash10

ndash05

00

05

10

15

Cogg

ing

torq

ue (N

middotm)

Time (ms)



Peak

val

ue o

f air

gap

mag

netic

den

sity

(T)

1090807060504030201

00

50100

150200

250300


05

1015


(a)

12

1

08

06

04

02

0

Peak

val

ue o

f air

gap

mag

netic

den

sity

(T)

050

100150

200250

300

50

1015

2025


(b)



0 1000 2000 3000 4000 500040

50

60

70

80

90

100

Effic

ienc

y (

)


ITQPMGIRPMGITPMG


(a) (b) (c)


Communicationport

IPC

Signalprocessing

unit

Dataacquisition

chip

Electronic load


Control signal


Speed signal

Drive motor

Frequencyconverter

ITQPMG

Oscilloscope

IPC

ITQPMG

Frequency converter

Drive motor





6 Performance Test







7 Conclusion



(a) (b)




2000480 268500 266520 262

4000480 283500 284520 283

4800480 286500 286520 285




Data Availability






Acknowledgments


References























RoboticsJournal of




VLSI Design



Shock and Vibration







Journal of



Volume 2018



Volume 2018


Journal of




SensorsJournal of



RotatingMachinery





Propagation






Hindawi


Advances in

Multimedia





1 1 1 1 1 1 471 058 0512 1 2 2 2 2 402 081 0633 1 3 3 3 3 362 104 0744 1 4 4 4 4 314 132 0835 2 1 2 3 4 453 075 0586 2 2 1 4 3 418 085 0627 2 3 4 1 2 358 112 0808 2 4 3 2 1 314 129 0829 3 1 3 4 2 431 104 06910 3 2 4 3 1 393 137 07911 3 3 1 2 4 362 117 07512 3 4 2 1 3 305 116 08113 4 1 4 2 3 426 122 07414 4 2 3 1 4 404 146 08015 4 3 2 4 1 358 117 07616 4 4 1 3 2 314 133 084



1 2 3 420

25

30

35

40

45

50

1 2 3 4 1 2 3 4 1 2 3 4 1 2 3 4

K r (

)

hmT bmT hmQ bmQ b


1 2 3 408

09

10

11

12

13

14

1 2 3 4 1 2 3 4 1 2 3 4 1 2 3 4

T (N

m)

hmT bmT hmQ bmQ b









1 2 3 4060

065

070

075

080

085

1 2 3 4 1 2 3 4 1 2 3 4 1 2 3 4

GT

hmT bmT hmQ bmQ b



ParametersSKr ST SG


0 1 2 3 4 5

ndash40

ndash20

0

20

40

No-

load

bac

k-EM

F (V

)

Time (ms)




0 1 2 3 4 5 6 7 8 9 10 11 120

5

10

15

20

25

30

35

40

No-

load

bac

k-EM

F (V

)

Order of harmonics

(a)

1 2 3 4 5 6 7 8 9 10 110

5

10

15

20

25

30

35

40

No-

load

bac

k-EM

F (V

)

Order of harmonics

(b)


0 1 2 3 4 5ndash15

ndash10

ndash05

00

05

10

15

Cogg

ing

torq

ue (N

middotm)

Time (ms)



Peak

val

ue o

f air

gap

mag

netic

den

sity

(T)

1090807060504030201

00

50100

150200

250300


05

1015


(a)

12

1

08

06

04

02

0

Peak

val

ue o

f air

gap

mag

netic

den

sity

(T)

050

100150

200250

300

50

1015

2025


(b)



0 1000 2000 3000 4000 500040

50

60

70

80

90

100

Effic

ienc

y (

)


ITQPMGIRPMGITPMG


(a) (b) (c)


Communicationport

IPC

Signalprocessing

unit

Dataacquisition

chip

Electronic load


Control signal


Speed signal

Drive motor

Frequencyconverter

ITQPMG

Oscilloscope

IPC

ITQPMG

Frequency converter

Drive motor





6 Performance Test







7 Conclusion



(a) (b)




2000480 268500 266520 262

4000480 283500 284520 283

4800480 286500 286520 285




Data Availability






Acknowledgments


References























RoboticsJournal of




VLSI Design



Shock and Vibration







Journal of



Volume 2018



Volume 2018


Journal of




SensorsJournal of



RotatingMachinery





Propagation






Hindawi


Advances in

Multimedia








1 2 3 4060

065

070

075

080

085

1 2 3 4 1 2 3 4 1 2 3 4 1 2 3 4

GT

hmT bmT hmQ bmQ b



ParametersSKr ST SG


0 1 2 3 4 5

ndash40

ndash20

0

20

40

No-

load

bac

k-EM

F (V

)

Time (ms)




0 1 2 3 4 5 6 7 8 9 10 11 120

5

10

15

20

25

30

35

40

No-

load

bac

k-EM

F (V

)

Order of harmonics

(a)

1 2 3 4 5 6 7 8 9 10 110

5

10

15

20

25

30

35

40

No-

load

bac

k-EM

F (V

)

Order of harmonics

(b)


0 1 2 3 4 5ndash15

ndash10

ndash05

00

05

10

15

Cogg

ing

torq

ue (N

middotm)

Time (ms)



Peak

val

ue o

f air

gap

mag

netic

den

sity

(T)

1090807060504030201

00

50100

150200

250300


05

1015


(a)

12

1

08

06

04

02

0

Peak

val

ue o

f air

gap

mag

netic

den

sity

(T)

050

100150

200250

300

50

1015

2025


(b)



0 1000 2000 3000 4000 500040

50

60

70

80

90

100

Effic

ienc

y (

)


ITQPMGIRPMGITPMG


(a) (b) (c)


Communicationport

IPC

Signalprocessing

unit

Dataacquisition

chip

Electronic load


Control signal


Speed signal

Drive motor

Frequencyconverter

ITQPMG

Oscilloscope

IPC

ITQPMG

Frequency converter

Drive motor





6 Performance Test







7 Conclusion



(a) (b)




2000480 268500 266520 262

4000480 283500 284520 283

4800480 286500 286520 285




Data Availability






Acknowledgments


References























RoboticsJournal of




VLSI Design



Shock and Vibration







Journal of



Volume 2018



Volume 2018


Journal of




SensorsJournal of



RotatingMachinery





Propagation






Hindawi


Advances in

Multimedia


0 1 2 3 4 5 6 7 8 9 10 11 120

5

10

15

20

25

30

35

40

No-

load

bac

k-EM

F (V

)

Order of harmonics

(a)

1 2 3 4 5 6 7 8 9 10 110

5

10

15

20

25

30

35

40

No-

load

bac

k-EM

F (V

)

Order of harmonics

(b)


0 1 2 3 4 5ndash15

ndash10

ndash05

00

05

10

15

Cogg

ing

torq

ue (N

middotm)

Time (ms)



Peak

val

ue o

f air

gap

mag

netic

den

sity

(T)

1090807060504030201

00

50100

150200

250300


05

1015


(a)

12

1

08

06

04

02

0

Peak

val

ue o

f air

gap

mag

netic

den

sity

(T)

050

100150

200250

300

50

1015

2025


(b)



0 1000 2000 3000 4000 500040

50

60

70

80

90

100

Effic

ienc

y (

)


ITQPMGIRPMGITPMG


(a) (b) (c)


Communicationport

IPC

Signalprocessing

unit

Dataacquisition

chip

Electronic load


Control signal


Speed signal

Drive motor

Frequencyconverter

ITQPMG

Oscilloscope

IPC

ITQPMG

Frequency converter

Drive motor





6 Performance Test







7 Conclusion



(a) (b)




2000480 268500 266520 262

4000480 283500 284520 283

4800480 286500 286520 285




Data Availability






Acknowledgments


References























RoboticsJournal of




VLSI Design



Shock and Vibration







Journal of



Volume 2018



Volume 2018


Journal of




SensorsJournal of



RotatingMachinery





Propagation






Hindawi


Advances in

Multimedia


0 1000 2000 3000 4000 500040

50

60

70

80

90

100

Effic

ienc

y (

)


ITQPMGIRPMGITPMG


(a) (b) (c)


Communicationport

IPC

Signalprocessing

unit

Dataacquisition

chip

Electronic load


Control signal


Speed signal

Drive motor

Frequencyconverter

ITQPMG

Oscilloscope

IPC

ITQPMG

Frequency converter

Drive motor





6 Performance Test







7 Conclusion



(a) (b)




2000480 268500 266520 262

4000480 283500 284520 283

4800480 286500 286520 285




Data Availability






Acknowledgments


References























RoboticsJournal of




VLSI Design



Shock and Vibration







Journal of



Volume 2018



Volume 2018


Journal of




SensorsJournal of



RotatingMachinery





Propagation






Hindawi


Advances in

Multimedia




6 Performance Test







7 Conclusion



(a) (b)




2000480 268500 266520 262

4000480 283500 284520 283

4800480 286500 286520 285




Data Availability






Acknowledgments


References























RoboticsJournal of




VLSI Design



Shock and Vibration







Journal of



Volume 2018



Volume 2018


Journal of




SensorsJournal of



RotatingMachinery





Propagation






Hindawi


Advances in

Multimedia




Data Availability






Acknowledgments


References























RoboticsJournal of




VLSI Design



Shock and Vibration







Journal of



Volume 2018



Volume 2018


Journal of




SensorsJournal of



RotatingMachinery





Propagation






Hindawi


Advances in

Multimedia




RoboticsJournal of




VLSI Design



Shock and Vibration







Journal of



Volume 2018



Volume 2018


Journal of




SensorsJournal of



RotatingMachinery





Propagation






Hindawi


Advances in

Multimedia


OptimizationDesignofaNewTypeofInteriorPermanent ...ϕ U ϕ mT +ϕ Tl +ϕ mQ +ϕ Ql πDα j α mB...

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