直流电动机反电动势对其电流脉动频率的影响

2730Vol.27No.30Oct.2007200710ProceedingsoftheCSEE©2007Chin.Soc.forElec.Eng.0258-8013(2007)30-0092-05TM33A470⋅40112(12012092NC28223-0001)EffectofCounterEMFonRippleFrequencyofCurrentinDCMotorYUANBao-guo1,CAOZhen-rong1,WANGSheng-Guo2(1.ShanghaiSecondPolytechnicUniversity,PudongxinDistrict,Shanghai201209,China;2.UniversityofNorthCarolinaatCharlotte,Charlotte,28223,USA)ABSTRACT:ThefrequencyofthecurrentrippleintheDCmotorcausedbyitscounter-EMFisanalyzed.Itisprovedthatthisfrequencyisdeterminednotonlybyitsrotationspeed,butalsobythenumberofwindingsinseries,thenumberofpole-pairs,andthenumberofparallelpathsinwhichcurrentripplewavesdoeachother.Itdoesnothavedirectlinkagewiththenumberofbrush-pairs,thenumberofcommutatorbars,andthenumberofarmatureslots.Thisresultprovidesananalyticbasisforthesensorlessspeedestimationof.DCmotor.KEYWORDS:sensorlessspeedestimation;DCmotor;counter-EMF;superpositionofsignal0(sensorless)[1-7](XSX104002)()1978[8][9-10]FFTSFFT[11-15]()[8-10,16]f=2kn/60f=kn/60kn/[8]25[9-10]212[16]23[17]f=2kn/60f=kn/60kn/3093[17]2512169[11-15]f=cknp/60knpckc=1kc=2[18-20]200320043[21]2006/shrrmfnNpf=nrfmNrp[21]p[21]p=1[8,10][17][11-14][14][21](rotorslotharmonics)211(a)21AXB1B2AXeBlvθ=BθθlveXABθ1(b)eXABθ1(c)B1B2eB1B21(d)(b)(c)(d)(a)NSB1B2−+02π3ππωt02π3ππωt02π3ππωteB1B2eAXB1Fig.1TheoperationprincipleschemeofthesimplesttwopolesDCmotor22m2B(x)109427SB(x)12345678910192012ωtN210Fig.2DCmotorwhichhas10windingelementsinseriesundereachpole101iiee==∑eie2m2m()()gtgtT=+(1)Tf=1/T(1)(),{0,1,,1}kTgtkmm+∈−(2)mg(t)(/)gtkTm+()()kTkTgtgtTmm+=++(3)G(t)10()()mkkTGtgtm−==+∑(4)G(t)G(t)1g(t)T()()gtgtT=+(4)G(t)Tc=T/m(5)()()gtgtT=[phone]()()(1)()()()()()()()()mcckmmkkmkmmkkkTGtTgtTmkTkTgtgtmmkTgtTgtgtmkTkTgtgtGtmm−=−==−=−−==+=++=++=+=+++=++=+=∑∑∑∑∑∑(6)G(t)Tc=T/mfc1//ccfTmTmf===(7)2m2m33(m=3)3326112T1EMFT1f1=1/T11Tc=T1/m=T1/3f1=1/Tc=m/T1=mf1=3f132T1643432T16T1f1=1/T1m(tu33Fig.3TheresultofsuperpositionoftheEMFripplewavesfor3windingsinseries3095ut43Fig.4TheresultofsuperpositionoftheEMFripplewavesfor3unevenlydistributedwindingsinseries3)(),{0,1,,1}kgtkm∈−()(),{0,1,,1}kkkgtAgtkmφ=+∈−(8)AkkφkkG(t)G(t)=∑+∑===1-01-0)()(mkkKmkktgAtgφ(9)-1-100()()[()(/)]mmkkkkkTGtAgtAgtmAgtkTmφ===+++−+∑∑(10)1k=0A=A0φ0=0-1-101()()[()(/)]mmKkkkkTGtAgtAgtmAgtkTmφ===+++−+∑∑(11)12221121(11)211mm33.11pm1m12m1p2mpn/12/60fmpn=(Hz)3.22/60fmpnj′=j′fnpmj′12()k=2m4fnpmj’1[1]SchmidtPBWijenayakeAHSensorlesscontrolofapermanentmagnetsynchronousmachinedowntonearzerospeedappliedtopositionmotioncontrol[C]ProcofIEEEIASSanDiegoCAOct199621-28[2]HarneforsLNeeHAgeneralalgorithmforspeedandpositionestimateofacmotors[J]IEEETrans.onIndustrialElectronics200047(1)77-83[3][J]200222(12)47-49ZouJibinXuYongxiangYuChenglongAnoveldetectingmethodoftherotorpositionofPMSM[J]ProceedingsoftheCSEE2002962722(12)47-49(inChinese)[4][J]200323(2)88-93ChenShuoTsujiMineoYamadaEijiOn-lineidentificationofstatorresistanceforsensorlessvectorcontrolsystemofinductionmotors[J]ProceedingsoftheCSEE200323(2)88-93(inChinese)[5][J]200525(17)121-126LiuYiHeYikangQinFengetalInvestigationofrotorsaliency-trackingbasedsensorlessvectorcontroldriveforpmsm[J]ProceedingsoftheCSEE200525(17)121-126(inChinese)[6][J]200525(22)136-141ZhangQianfanPeiYulongChengShukangPositionsensorprincipleandaxialexcitingcoilemfofaxialandracialairgaphybridmagnetcircuitmulti-couplingmotor[J]ProceedingsoftheCSEE200525(22)136-141(inChinese)[7][J]200525(23)163-166WanJunWangJianhaiMaYanbingetalSpeedsensorlessvectorcontrolsystembasedonmutualmrasscheme[J]ProceedingsoftheCSEE200525(23)163-166(inChinese)[8][J]1978(3)7ZhangWenhaiAmethodfortestingrotaryspeedofdcmicromotor[J]Radio1978(3)7(inChinese)[9][J]199932(1)36-37ChenZhiwenAnovelmethodforspeedmeasurementofdcmicromotor[J]Micromotor199932(1)36-37(inChinese)[10][J]199932(3)33-3436ChenZhiwenImprovingspeedmeasurementprecisionofdcmotorbyusingfrequencyspectra[J]Micromotor199932(3)33-36(inChinese)[11]-[J]200128(2)49-53HuangJinHuangJianhuaChenDunetalMeasurementofDCmotortorque-speedcharac-teristicbasedonwaveletanalysis[J]S&MElectricMachines200128(2)49-53(inChinese)[12][J]200116(5)64-67WeiYunbingHuangJinHuangJianhuaRemovingnoisesfromsignalsofmotormeasurementbywaveletpacket[J]TransactionsofChinaElectrotechnicalSociety200116(5)64-67(inChinese)[13][J]()200337(2)235-238ChenTunHuangJinMaJianetalApplicationofwaveletpackettransforminmotorperformancetest[J]JournalofZhejiangUniversity(EngineeringScience)200337(2)235-238(inChinese)[14][D]2003ChenTunTheapplicationsofwaveletanalysistheoryinthedomainofmotortest[D]HangzhouZhejiangUniversity2003(inChinese)[15][J]200621(4)122-126NiuFaliangHuangJinInstantaneousfrequencyextractionofasymptoticsignalanditsapplica-tionsinmotorperformancetest[J]TransactionsofChinaElectrotechnicalSociety200621(4)122-126(inChinese)[16][J]198513(3)31-33LuDaomingWangXiaomingAmethodofmea-suringrotaryspeedofdcmicromotor[J]Small&SpecialElectricalMachines198513(3)31-33(inChinese)[17][J]1997(3)40-42ZhangWenhaiSpecialapproachtotestrotaryspeedofdcmotor[J]ElectrotechnicalJournal1997(3)40-42(inChinese)[18]TobiasGMethodfordeter