EVS28 International Electric Vehicle Symposium and Exhibition 1

EVS28KINTEX, Korea, May 3-6, 2015

AAAA newnewnewnew torquetorquetorquetorque rippleripplerippleripple testtesttesttest methodmethodmethodmethod basedbasedbasedbased onononon PMSMPMSMPMSMPMSM torquetorquetorquetorquerippleripplerippleripple analysisanalysisanalysisanalysis forforforfor electricelectricelectricelectric vehiclevehiclevehiclevehiclessss

Wang Sibo1 , Zhao Huichao1 , Li Zhiyu1,Wang Xiaoxu11 .FAW R&D Center, E-motor system development Sec., Electric Vehicle Dept.

Changchun 13011 China

AbstractAbstractAbstractAbstractThis paper analyzes the reason of Low-speed vibration in an electric vehicle, builds the mathematical

equation of powertrain torsional vibration. Then, the model of torque ripple considering non-sinusoidal

magnetic field distribution is built, orders and frequencies of torque ripple in PMSM is predicted.

According to the relationship between the torsional vibration in low-speed of the electric vehicle and the

frequency of motor torque ripple, for the situation that there are few literatures on the torque ripple analyze

and test method of PMSM in electric vehicles, a dynamic torque ripple test bench is presented. The torque

ripple frequency analysis is verified by testing. Because there are amplitude and phase distortion caused by

the dynamic test, we presented a new locked-rotor static method.instead of the dynamic test. It provides an

accurate means of testing and evaluation for the torque ripple of PMSM in electric vehicles preliminarily.

Keywords: Electric vehicle, powertrain torsional vibration, PMSM, torque ripple, torque ripple test

1111 IntroductionIntroductionIntroductionIntroductionWith the explosive growth of the car’s number,fuel resource constrains and emissions problem isgetting worse. Now the mainstream automobilemanufacturers have invested a lot of money toresearch and develop the hybrid and pure electricvehicle. Permanent magnet synchronous motor(PMSM) with high torque density, wide speedrange and other advantages has been widely usedin the field of electric vehicles. However, PMSMalso has some disadvantages, such as coggingtorque and torque ripple[1-4]. The methods torestrain the torque ripple has also been extensiveanalyzed and researched in recent years[5-12].The new electric vehicle drive system increasesthe power motor system,which also increases anew dynamic characteristic to the powertrain.Generally, in high-speed field-weakening region,the motor torque ripple will be filtered out by the

rotor inertia. However the influence of motoroutput characteristic caused by torque ripple inlow-speed and high-torque region is quite obvious.Ripple will cause the vehicle shake in low speed,especially in the case that the ripple frequency issimilar to the resonant frequency of the drivesystem[13]. PMSM as the resonant excitation willinfluence the vehicle’s drivability and comfort.Study the frequency and the amplitudecharacteristics of the torque ripple is the basis toanalyze the system resonance. Permanent magnetsynchronous motor torque ripple suppression ofelectric vehicles is an important applicationtechnology. Although this part of the traditionalmotor technology is relatively mature and reliable,a new technical challenges we have to face is howto design a method to do the torque ripple test onthe test platform combining the PMSM and itscontrol characteristics, and further to give areasonable vehicle PMSM torque ripple evaluationmethod. Therefore, considering the torque ripple

EVS28 International Electric Vehicle Symposium and Exhibition 2

effects on the vehicle and the permanent magnetmotor torque ripple characteristics, researchtorque ripple test platform of the PMSM used invehicle has important significance.Literature [14] demonstrates the principle ofengine vibration causing drive system resonance,and reduces the influence of resonance by enginetorque compensating actively. But there is not yeta literature detailedly analyzing the reason andthe characteristic of the motor drive systemresonance. Literature [15] analyzes the influenceof the motor air gap field harmonics on thetorque ripple, and optimizes the magnetic fieldby the chute or other methods to reduce theharmonic components. from the influence of theinverter control, test system errors, PWMmodulation and dead time effect, literature [16]studies the influence of time harmonic current ontorque ripple. Most of the above literaturesanalyze by FEA methods, and lack of rigoroustest evaluation to validate the optimizationmethod. Literature [17] designs a torque rippletest device, and illustrate the influence of thesensor stiffness, test system mechanical design,load dynamometer type on the torque rippletesting. Literature [18] uses the balance directmeasuring method, analyzes the dynamic testcharacteristic and the reason of test resultsdeviation, and gives the optimization method ofthe test system. The literature don’t give how tomeasure the torque ripple amplitude and phaseaccurately, nor the vector control angle andtorque ripple amplitude combined test.This paper combines the characteristic of thehybrid drive system structure, analyze the reasonof the drive system resonance caused by PMSMtorque ripple, derive the motor torque rippleproduction mechanism caused by the motor airgap magnetic field harmonics. For the low-speedcharacteristics of the drive system resonancecaused by PMSM used in vehicles, andconsidering the torque ripple amplitude-frequency characteristics in low-speed region, wedesign a dynamic and static test device, analyzethe influence of the dynamic test on the testresults’ amplitude and phase by modeling.Finally verify the correctness of the torque rippletheoretical analysis by testing, and by comparingand analyzing the results of the dynamic andstatic test, a torque ripple test and evaluationmethod has been determined. This provide anaccurate method for PMSM torque ripple testingand evaluation.

2222 EVEVEVEV DrivetrainDrivetrainDrivetrainDrivetrain ResonanceResonanceResonanceResonanceModelModelModelModel

Based on a hybrid drivetrain model, the impact onthe drivetrain caused by the motor torque ripplewill be analyzed in this chapter. The torque rippleprinciple of hybrid and pure electric vehicledrivetrain is similar to the engine. Motor outputtorque acts on the tires through transmission, driveshaft, differential , half shaft and othertransmission mechanism. By these elastic elements,a resonance point will be introduced in the systemso that the mechanical resonance will be caused.This paper analysis the resonance characteristics ofthe electric vehicle based on P2 structure, whichhas been widely applied in hybrid at present, suchas Mercedes E400L and red flag plug-in hybrid H7.The powertrain motor system with P2 structurearranges between engine and dual-clutchtransmission. The wet clutch connected to themotor and the engine can decouple the outputpower. When the clutch is separated, the vehicledriving by motor works as the pure electric vehicle.When the clutch is engaged, motor and engine arein serial, then the motor can help to driving orbraking for energy recovery. This structure causesnew features of the transmission resonance. Whenthe PMSM torque ripple frequency is close orequal to the natural resonant frequency ofdrivetrain, the vehicle’s longitudinal vibration willseriously affect the vehicle performance and thecomfort. At the same time, this resonance willcause a body vibration , which will increase theinterior noise, accelerate the fatigue of thetransmission parts[19].

Figure 1: An electric vehicle drive system topology

The simplified transmission system model isshown in figure 1. Compared with the traditionalpowertrain, the inertia of PMSM in P2 structurewhich composes a typical two-inertia system withthe drive shaft and wheel inertia is bigger.

EVS28 International Electric Vehicle Symposium and Exhibition 3

Transmission resonance can be expressed by thefollowing differential equation.

( )

( )

⎪⎪⎪⎪⎪⎪⎪

⎩

⎪⎪⎪⎪⎪⎪⎪

⎨

⎧

−⎟⎟⎠

⎞⎜⎜⎝

⎛⋅−+

⋅

−⋅−=⋅⋅

⎟⎟⎠

⎞⎜⎜⎝

⎛⋅−−⋅−

⋅−⋅−=⋅

•••

••

••

⋅•••

nTn

nD

nD

nnCn

nJ

nnDn

nC

nDTJ

vehradEM

swradveh

radEMsw

radveh

radEMsw

radEM

swEM

EMEMEMEM

θθθ

θθθ

θθθθ

θθ

2

22

2

22

(1)

EMJ — motor inertia,vehJ — vehicle inertia,swD — transmission shaft damping factor,swC — transmission shaft elasticity

coefficient,EMT — motor torque,vehT — load torque,EMD — equivalent damping coefficient of

motor,vehD — equivalent damping coefficient of

vehicle,n— transmission gear ratio.

EMT is the motor’s output torque given by HCU(vehicle control unit). Different transmission gearratio corresponds to different resonancefrequency. The frequency of the motor torqueripple is proportional to its speed. Then ignorethe half shaft damping, after Laplace transformthe above differential equation can be expressedas:

⎪⎪⎪⎪⎪⎪⎪

⎩

⎪⎪⎪⎪⎪⎪⎪

⎨

⎧

=

=

−=

−

−−−=⋅⋅

−

⋅−⋅⋅−=⋅⋅

•

•

vehrad

EMEM

radEM

sww

veh

radvehradEM

swradveh

radEM

swEM

EMEMEMEM

nCT

T

Dn

CsJ

nnCs

nDTsJ

ωθ

ωθ

θθ

θθθ

θ

θθ

θθ

)(

)(

)(

2

222

(2)

A transmission system model diagram shown inFigure 2 can be deduced from the equation above,then the transfer function (3) of the relationship

between motor speed, vehicle acceleration andelectromagnetic torque can also be deduced.

⎪⎪⎩

⎪⎪⎨

⎧

⋅⋅⋅==

=

)()()(

)(

)()(

)(

sTRsnC

sTsasG

sTssG

EM

tsw

EM

vehacc

EM

EMωω

(3)

In the formula,

vehsw

EMswvehswvehEMEMsw

EMvehvehEMvehEMEM

DCDCnsJCDDnJCns

DJnDJnsJJnsT

⋅+⋅⋅+⋅⋅+⋅⋅+⋅+⋅

⋅⋅+⋅⋅+⋅⋅⋅=

)(

)()(22

232

swvehvehEM CnsDnsJns ⋅+⋅⋅+⋅⋅= 2222)(ω

Figure 2: Transmission model diagram

It’s easy to get the reason of the resonancephenomena by analyzing the transmission systemmodel in frequency domain. The amplitude-frequency and phase-frequency curve of equation(3) show in figure 3, namely the transitive relationbetween )(sGω and )(sGacc . From it we can seethe gain of speed and acceleration is increasesuddenly at resonant frequency, and the influenceto the transmission system at this frequency isstronger. The motor of inertia EMJ , the equivalentof inertia of the vehicle vehJ , the shaft stiffnesscoefficient swC are the main parameters affectingthe system poles. The transmission system modelused in this paper comes from vehicle simulationand test data. vehJ is about 240kg/m, EMJ is about0.122kg/m, transmission ratio of the first gear isabout 4.4, swC is about 6200Nm/rad. When thefrequency of motor torque ripple is around 8Hz,the transmission system resonance will occurs. Theresonance frequency of the first gear transmissionsystem is about 2Hz.Based on the transmission system technology andthe development of material, electric vehiclepowertrain inherits the traditional vehicle’scharacteristics. Except for in-wheel motor there aregearbox and transmission shaft between motor and

EVS28 International Electric Vehicle Symposium and Exhibition 4

electrical vehicle as P2 structure. The impact ofvehicle inertia, transmission ratio, transmissionsystem elasticity coefficient, damping coefficientand other parameters on the resonant frequencyhave little difference, and the resonant frequencycaused by torque ripple is generally below 10Hz.Because of its low-speed character, the above-mentioned analysis has a very important guidingsignificance to the following design of the torqueripple test platform. Because PMSM torqueripple tests more concern about the evaluation oflow speed testing, the low frequency torqueripple test platform shall be considered.

Figure 3: Motor speed transfer function)(sGω and vehicle acceleration transfer function

)(sGacc

3333 PMSMPMSMPMSMPMSM TorqueTorqueTorqueTorque RippleRippleRippleRippleAnalysisAnalysisAnalysisAnalysis

At present, in order to increase PMSM torqueoutput capability and reduce losses, MTPAcontrol strategy commonly uses in the vehicle inlow speed region, and MTPV at high-speedfiled-weakening region. The reluctance torquewhich is an important component of the outputtorque can be increased by increasing thedI current. At the peak point of torque, dI and qI

are approximately equal. The motor outputtorque can be expressed as:

[ ]qdqdqf IILLIpT )(23

−+⋅⋅= ψ (4)

fψ— PM flux linkage

dL — d-axis inductanceqL — q-axis inductance

Ideally, the three-phase sinusoidal current flowingthrough the PMSM with space sinusoidaldistribution windings, the generatedelectromagnetic torque will keep constant withouttorque ripple. But actually, back-EMF harmonicand current time harmonic will cause torque ripple.In addition, the permanent magnet interacting withthe stator cogging will cause cogging torque,which changes periodically with the rotor’sposition, that is also a component of the torqueripple. Generally, the factors causing PMSMtorque ripple can be divided as follow:1.Air-gap field harmonic,2.Cogging torque,3.Stator ‘s current time harmonic,4.The influence of flux saturation,

The influence of manufacturing technique, such asstator and rotor eccentricity.Due to the good manufacturing quality of thedriving motor, the torque ripple caused by statorand rotor eccentricity can be excluded. The motorflux saturation effect and the smaller coggingtorque in vehicle motor can also be ignored . Thispaper mainly analyzes the impact of the air-gapmagnetic field harmonic to the torque ripple.Based on the above analysis, the motor outputtorque ripple can be defined as:

[ ] )(23

θψ cogqddqqfr TIILIpT +∆+∆⋅⋅= (5)

cogT— Cogging torque,fψ∆— Flux linkage amplitude variate with

the rotor’s electrical angle,dqL∆ — Inductance amplitude variate with the

rotor’s electrical angle,

The amplitude of the cogT changes with the rotor’selectrical angle, the periodicity is relevant to themotor poles and slot’s number.The rotor’s d-axis and q-axis harmonic voltageequation and electromagnetic torque equation are asfollow:

⎪⎪⎪⎪

⎩

⎪⎪⎪⎪

⎨

⎧

⎥⎦

⎤⎢⎣

⎡−⋅⋅=

−+−−−=

−++−=

∧∧)()(

23

)(

)(

θψθψ

ωθψωω

ωθω

qqddm

hdqfdqqsq

d

hqdqqdsd

d

iipT

fuiLiRdtdi

L

fuiLiRdtdiL

(6)

∧

dψ — d-axis flux harmonics induced on thestator,

EVS28 International Electric Vehicle Symposium and Exhibition 5

∧

qψ— q-axis flux harmonics induced on the

stator,

)(θψ∧

d , )(θψ∧

q Flux harmonic is a function ofthe electrical angle.Flux harmonic equation is:

⎪⎪⎪⎪⎪

⎩

⎪⎪⎪⎪⎪

⎨

⎧

=

−=

+=+=

+=+=∧

∧

q

qq

d

dd

hqqharmqqq

hddharmddd

Li

Li

f

f

ψ

ψψ

θψψψθψ

θψψψθψ

1

,

,

)()(

)()(

(7)

⎪⎪

⎩

⎪⎪

⎨

⎧

⋅+−=

⋅+=

∑

∑∞

=+−

∞

=+−

)6sin()()(

)6cos()()(

116,16,

116,16,

θψψθ

θψψθ

kf

kf

kkhkhhq

kkhkhhd

(8)

)(θhdf , )(θhqf — d-axis and q-axis fluxharmonic component,

nh,ψ— n-order flux harmonic amplitude.

The equation of the three-phase sine wave can beas follow:

⎩⎨⎧

−==

elq

eld

iiii

ϕϕ

cossin

1

1 (9)

elϕ is power factor angle. Because the three-phase current doesn’t have harmonic, the stator

core saturation can be ignored , and dL , qL arenot affected by the stator slot and potential angle.Then, the electromagnetic torque containingharmonic can be expressed as:

[ ] )()()(23

1 θθψ hdqhqdqdqdq fifiiiLLipT −+−+= (10)

[ ]

)]tanarctan(6sin[

sin4)(

sin)(cos23

16,16,

16,16,

1

216,16,

216,16,

1111

elkhkh

khkh

kelkhkhkhkh

elqdel

ck

iiLLpiT

ϕψψ

ψψθ

ϕψψψψ

ϕψϕ

−+

−+

∞

=−+−+

−

++

⋅−+

+−+−=

∑ (11)

1ψ — fundamental component of air-gapmain flux,

qip 123

ψ— permanent-magnet torque,

qdqd iiLLp )(23

−— reluctance torque,

)]tanarctan(6sin[

sin4)(

16,16,

16,16,

1

216,16,

216,16,1

elkhkh

khkh

kelkhkhkhkh

ck

i

ϕψψψψ

θ

ϕψψψψ

−+

−+

∞

=−+−+

−

++⋅

−+∑

— torque ripple caused by magnetic fieldharmonic.We can see that the frequency of the torque rippleis n6 times of the motor electrical frequency, thatmeans the frequency of the n6 order torque rippleis nfe6 , fe is motor electrical frequency,

∞……= 3,2,1n 。Because elϕ doesn’ t change withfe in the MTPA region, the amplitude of thetorque ripple has nothing to do with the electricalfrequency, but it can be determined by the rotorposition.

4444 TorqueTorqueTorqueTorque RippleRippleRippleRipple TestTestTestTest PlatformPlatformPlatformPlatformDesignDesignDesignDesign andandandand AnalysisAnalysisAnalysisAnalysis

From the above two chapters we know that thefrequency of motor torque ripple caused by theresonant frequency is low, and the amplitude of theripple has nothing to do with the electricalfrequency, but relates to the rotor position.According to the above features, the following partwill describe the design of dynamic and statictorque ripple test platform.

4.14.14.14.1 TorqueTorqueTorqueTorque RippleRippleRippleRipple DynamicDynamicDynamicDynamic TestTestTestTestPlatformPlatformPlatformPlatform DesignDesignDesignDesign

Torque ripple dynamic test platform mainlyconsiders two points: 1.The limit of torque sensordynamic testing sample rate. 2. The limit ofdynamic testing system resonance. The structurechart of the torque ripple test platform used in thispaper shows as follow, which consists ofdynamometer, torque sensors, iron floor, thesupport system of the tested units, inverter, dataacquisition system and so on.

EVS28 International Electric Vehicle Symposium and Exhibition 6

Figure 4: The structure fo the torque fluctuationdetection system

In order to improve the sampling accuracy of thesensors, and measure the motor torque ripple atlow frequency accurately, in this paper, wechoose the sensors with higher sampling rate andaccuracy, which is the Germany HBMcompany’s non-contact sensors. The centringaccuracy between motor and dynamometer shallbe within 0.05mm to exclude the torque rippleinfluence caused by centring. The position sensorused in load dynamometer is a high resolutionresolver sensor, which can ensure the highcontrol accuracy and stability at low speed, andcan exclude the test system’s influence caused bythe dynamometer torque ripple.

4.24.24.24.2 TorqueTorqueTorqueTorque RippleRippleRippleRipple DynamicDynamicDynamicDynamic TestTestTestTest andandandandAnalysisAnalysisAnalysisAnalysis

Double inertia torque ripple dynamic test modelis shown as figure 4. Dynamometer and thetested unit compose a typical double inertiasystem, and the dynamic equations is:

[ ] [ ]

⎪⎩

⎪⎨

⎧

−=

−=

−+−=

)()(

)()(

)()()()()(

2

2

sTsTsJ

sTsTsJ

sssDssKsT

lWll

Wemm

lmslmsW

θ

θ

θθθθ

(12)

Due to the low speed, the damping parts can beignored. The simplified system transfer functionis as follow.

l

ml

s

me

Wtest

JJJ

KJssT

sTsG+

+==

2

1)()(

)( (13)

Take the load inertia, motor inertia and sensor’selastic coefficient into (13) . Bode plot of thetransfer function is shown in figure 5. When thetorque ripple frequency is close to the resonantfrequency, the amplitude will change suddenlyand distort, the phase will change 180°。

Figure 5 : Bode plots of the torque ripple dynamictesting transfer function

Assume the torque ripple signal put into the testsystem is sinusoidal, figure 6 show the excitationsignal frequency is 1/2 ω , ω ,2 ω ,4 ω and theresponse signal corresponding to the excitationsignal. The solid line is the input sinusoidal signalby given 1, the other dotted line is the system’sresponse signal. From figure 6(a), we can see thatthe torque ripple test results have appeareddistortion at the point 1/2 ω , and the harmoniccontent increases. When the frequency reaches twoor four times, the amplitude of the torque ripplebegins to decrease, the distortion of thefundamental frequency and the the phase is serious.Thus, the torque ripple frequency dynamic test hassome limitations.

(a)1/2ω excitation signal and its response signal

(b)ω excitation signal and its response signal

EVS28 International Electric Vehicle Symposium and Exhibition 7

(c)2ω excitation signal and its response signal

(d)4ω excitation signal and its response signal

Figure 6 : different excitation signal and itsresponse signal

4.34.34.34.3 TorqueTorqueTorqueTorque RippleRippleRippleRipple StaticStaticStaticStatic TestTestTestTestPlatformPlatformPlatformPlatform DesignDesignDesignDesign

To eliminate the amplitude and phase distortionof the dynamic test, in figure 4, a static stalldevice has been designed between thedynamometer and the torque and speed sensor.The tested motor can be fixed in a stationaryrotor position under the dynamometer anglecontrol mode. The device is similar to a brakecan pressed the connecting shaft tightly. Thisdevice can assure the static system can withstanda sufficient reverse torque by the clamping forceprovided by the hydraulic system. Dynamometerhas an angle control function which can keep thetested unit at any angle position. Under the samegiven conditions, the PMSM output torque canbe tested at different rotor position through amulti-angle locked-rotor, while recording theposition angle from resolver and A, B, C phasecurrent. Thus, motor torque ripple test can bedone by such a static locked-rotor test.

5555 TestTestTestTest ResultsResultsResultsResults andandandand AnalysisAnalysisAnalysisAnalysisIn order to validate the theory analysis mentionedabove, we chose a three-phase PMSM with P2structure using in a electric vehicle as the testedunit.Test the motor torque ripple under differentspeed and different torque. The motor speed is120rpm, 240rpm, 300rpm, 360rpm. Figure 7shows the torque ripple waveform at 120rpm,240rpm, 300rpm, 360rpm. The torque ripple’sfrequency domain characteristics can be obtained

by FFT. Figure 8 shows the torque ripple testspectrum at 120rpm, 240rpm, 300rpm, 360rpm.

（a）120rpm@100Nm

（b）240rpm@100Nm

（c）300rpm@100Nm

（d）360rpm@100Nm

Figure 7: Under different speed 100Nm torqueripple test curve

EVS28 International Electric Vehicle Symposium and Exhibition 8

Torque(Nm)

Torque(Nm)

Torque(Nm)

Torque(Nm)

（a）120rpm@fe=20Hz

（b）240rpm@fe=40Hz

（c）300rpm@fe=50Hz

（b）360rpm@fe=60Hz

Figure8: Under different speed 100Nm torqueripple test spectrum

5.15.15.15.1 RippleRippleRippleRipple HarmonicHarmonicHarmonicHarmonic TestTestTestTest ResultResultResultResultFrom figure 7, it is obviously that there are sixpulsations in a electric cycle at 120rpm and240rpm. But the torque ripple has no regularity at300rpm and 360rpm. By analyzing the torqueripple FFT graphic at four different speeds, wecan see clearly that there are obvious torqueripple components at fe6 . It has the sameconclusion as the chapter 3 that air gap fluxharmonic generates electromagnetic torque ripple

with frequency nfe6 , 1=n . From chapter 4dynamic test analysis, we can see test system hasamplitude suppression effect on the dynamic signalof which frequency is greater than the resonantfrequency. So the ripple amplitude of the testedfrequency fe12 , fe18 is very small. The amplitudeof the tested point at 300rmp corresponding tofe12 (600Hz) is 0.1Nm by FFT.

5.25.25.25.2 TestTestTestTest ResultsResultsResultsResults AnalysisAnalysisAnalysisAnalysisBy comparing the four FFT figures, it is obviouslythat torque ripple all includes 60Hz~170Hzfrequency components, which has nothing to dowith speed. At 40rpm, 300rpm, 360rpmcorresponding to 240Hz, 300Hz, 360Hz, theamplitude of the torque ripple damps obviouslywith the increasing frequency. And the differenceof torque ripple phase at 120Hz and 240Hz is 180° ， which verifies the conclusion in chapter 4.160Hz~170Hz is the resonant frequency of the testsystem. The torque at resonance point is caused bythe torque ripple of current-time harmonic, systemerror, and etc.

5.35.35.35.3 StaticStaticStaticStatic Locked-rotorLocked-rotorLocked-rotorLocked-rotor TestTestTestTest ResultResultResultResultStatic locked-rotor test also choose the testedtorque 100Nm. Figure 9 is the static locked-rotortest result. In one electric cycle, there are sixpulsations at the rotor position from 0 to 360electrical angle, and the frequency of the torqueripple is 6 times of the electrical angle. The 12times and 18 times harmonic ripple can beobtained by FFT. Torque ripple amplitude is about5Nm under locked-rotor state, compared to thedynamic test result 10Nm at 120rpm, locked-rotortest result is more true and accurate whichexcludes the influence caused by the resonanceamplitude. At each locked-rotor point, it’s equal toDC passing through the three-phase winding. Thethree phase currents are sinusoidal after fitting thecurrents at each tested point in figure 9。Through the above static locked-rotor test, we canget a more accurate relationship between torqueripple at different rotor position and three-phasecurrent. Compared to dynamic test, static testexcludes the effects of the system error to ensurethe reality of the torque ripple phase and amplitude.Dynamic test can reflect the torque rippleamplitude and frequency to some extent, but theaccuracy of the dynamic test results will beaffected by the resonance of the test platform.Static locked-rotor test can verify the effect oftorque ripple elimination method at low speed in

Torque Ripple

Resonance

Resonance

Torque Ripple

Torque RippleResonance

Resonance

Torque Ripple

EVS28 International Electric Vehicle Symposium and Exhibition 9

vehicle, namely the motor MTPA control area,and can also provide a basis for toque ripplecompensation algorithm depending on thedifferent rotor position.

Figure 9: Static locked rotor test three-phasecurrent and rotor position angle corresponding to

100Nm torque ripple test curve

6666 ConclusionConclusionConclusionConclusionIn this paper, there are the following conclusionsby analyzing the calculation and testing.1. If PMSM torque ripple frequency is similar

to drivetrain resonance frequency, a vehicledrivetrain resonance with a low-speed characterwill be caused.2. PMSM non-sinusoidal air gap magnet

harmonic will cause n6 order torque ripple. Theripple amplitude at low-speed using MTPAcontrol method is only associated with the rotorposition.3. Torque ripple dynamic test will be affected

by the test platform’s parameters. test platformresonance will cause the distortion of the torqueripple amplitude and phase.4. Static locked-rotor test can reflect the low-

speed torque ripple phase and amplitude of theelectric vehicle truly and steadily. It can providea accurate test and evaluation method of thePMSM torque ripple in electric vehicles.

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AuthorsAuthorsAuthorsAuthorsWang sibo, male, born in 1986,master, designer, in charge of vehiclemotor system testing and evaluationtechnology.

Zhao Huichao, male, born in 1977,master, department director, in chargeof vehicle motor system development.

Li Zhiyu, male, born in 1986,bachelor, designer, in charge ofvehicle motor system testing andevaluation technology.

Wang Xiaoxu, female, born in 1986,master, designer, in charge of vehiclemotor system testing and evaluationtechnology.