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806IEEETRANSACTIONSONINDUSTRYAPPLICATIONS,VOL.40,NO.3,MAY/JUNE2004MechanicalDesignConsiderationsforConventionallyLaminated,HighSpeed,InteriorPMSynchronousMachineRotorsEdwardC.Lovelace,Member,IEEE,ThomasM.Jahns,Fellow,IEEE,ThomasA.Keim,Member,IEEE,andJeffreyH.Lang,Fellow,IEEEAbstractThispaperdiscussesmechanicaldesignconsiderationsthatareparticulartoconventionallyi.e.,radiallylaminatedrotorsofinteriorpermanentmagnetsynchronousmachines.Focusisplacedonapplicationswheretheradialforcesduetohighspeedoperationarethemajormechanicallylimitingdesignfactor.Properdesignofthelaminationbridges,orribs,attherotorouterdiameterisexplainedintermsofthebothmaterialconsiderationsandelectromagneticperformanceimpact.Thetradeoffofcomplexityversusperformanceassociatedwithusingstrengtheningribsinthemagnetcavitiesisdiscussed.Thesensitivityofthemechanicaldesignlimitationstotherotorshaftmountingmechanismisalsohighlighted.Theseeffectsarethenanalyzedusingfiniteelementanalysisfora150Nm/6kWintegratedstarter/alternatordesignedforoperationupto6000r/minwithanannularrotortoaccommodateatorqueconverterorclutchassembly.Thisexampledemonstratesthatitispossibletosignificantlyimprovetherotorsstructuralintegrityusingthetechniquesdescribedinthispaperwithonlyaverymodestimpactontheprojectedmachinedrivecost.IndexTermsElectricalsteel,finiteelementanalysisFEA,highspeed,interiorpermanentmagnetIPMsynchronousmachine,laminations,magneticsaturation.I.INTRODUCTIONROTORDESIGNandconstructionofinteriorpermanentmagnetIPMmachinesisachallengingtaskduetotheconflictingcharacteristicsofimprovedperformanceandrotorcomplexity.IPMmachinesareofinterestbecausetheyareparticularlyattractivefromaperformancestandpointintractionandspindleapplications1,2.IPMmachinescanbedesignedwithwide,andtheoreticallyinfinite,speedrangesforconstantpoweroperationwithexcellentinverterutilization.ThisisachievedthroughuseofasalientrotorgeometrywithlimitedPaperIPCSD03–084,presentedatthe2001IEEEInternationalElectricMachinesandDrivesConference,Cambridge,MA,June17–20,andapprovedforpublicationintheIEEETRANSACTIONSONINDUSTRYAPPLICATIONSbytheElectricMachinesCommitteeoftheIEEEIndustryApplicationsSociety.ManuscriptsubmittedforreviewNovember5,2002andreleasedforpublicationJanuary20,2004.ThisworkwassupportedbytheMITConsortiumonAdvancedAutomotiveElectrical/ElectronicComponentsandSystems.E.C.LovelaceiswithSatConTechnologyCorporation,Cambridge,MA02142lUSAemaillovelacealum.mit.edu.T.M.JahnsiswiththeWisconsinElectricMachinesandPowerElectronicsConsortium,DepartmentofElectricalandComputerEngineering,UniversityofWisconsin,Madison,WI537061691USAemailjahnsengr.wisc.edu.T.A.KeimandJ.H.LangarewiththeLaboratoryforElectromagneticandElectronicSystems,DepartmentofElectricalEngineeringandComputerScience,MassachusettsInstituteofTechnology,Cambridge,MA02139USAemailtkeimmit.edu,langmit.edu.DigitalObjectIdentifier10.1109/TIA.2004.827440fluxcontributionfromPMsburiedwithintherotorstructure.Toachievethedesireddegreeofsaliency,speciallaminationdesignandassemblystrategiesaretypicallyrequiredcomparedtothoserequiredforcompetingmachinetypessuchassurfacePMandinductionmachines.TherotordesignstrategiesforIPMmachinescangenerallybedividedintoaxiallyandradiallylaminatedconfigurations,eachwithitsownadvantages3,4.Theaxiallylaminatedrotorisconstructedusingmanyalternatinglayersofsoftandhardmagneticsheetsthatarelaidalongtheaxisofthemachine,eachbentandindividuallysizedtoformthepolesoftherotor1.Thisdesignapproachcanachievehighinductancesaliencyratiosinexcessof101.However,theaxiallylaminatedrotorisrelativelyexpensivetomanufactureduetothesortedcutting,shaping,andassemblyofthemanydifferentlaminationsthatmustbeemployed.Furthermore,aconstrainingrotorsleevemaybenecessaryforhighspeedoperationtopreventlaminationintrusionsintotheairgap.Suchsleevestypicallyreducethesaliencyduetotheirfinitethicknessesandoftenincreaselossesduetoeddycurrentswhenhighstrengthstainlesssteele.g.,Inconelischosenforthesleevematerial.Bycontrast,radiallylaminatedrotorsaretypicallydesignedwith1–4layersofhardmagneticmaterialineachpole.Eachlamination,aswithotherconventionalmachinetypes,ispunchedorcutasasingleunitarypieceforthecrosssectionoftherotor.Cavitiesarepunchedorcutintotherotorlaminations,andthemagnetmaterialisinsertedintothesecavities.ThelaminationscanbestackedusingconventionalmeanssothattherotorisgenerallyeasiertomanufacturethanitsaxiallylaminatedIPMcounterpart.However,adoptionoftheradiallylaminatedrotorcomesattheexpenseofsaliencywithtypicalinductanceratiosrangingfrom1.5upto101,dependingonthenumberofmagnetcavitylayersandtheirconfiguration.Forgoodelectromagneticperformance,itisnecessarytominimizethesteelbridgessurroundingthemagneticcavitiesthatarenecessarytolinktherotorironsegmentsintoaunitarylamination.EachbridgeeffectivelycreatesamagneticshortciruitacrossthePMs,therebyreducingthemagnetscontributiontotheoverallairgapflux.ThispaperexaminesthemechanicaldesignissuesofconventionallyalsoreferredtoastransverseorradiallylaminatedIPMrotors.Onlythecentrifugalforceisconsideredasthisislikelytobethedominantsourceofmechanicalstressinhighspeeddesigns.Eachofseveralkeyrotordesignfeaturesareexaminedinturnwithrespecttotheirinfluenceontherotorstress00939994/0420.00©2004IEEELOVELACEetal.CONVENTIONALLYLAMINATED,HIGHSPEED,IPMSYNCHRONOUSMACHINEROTORS807Fig.1.Crosssectionofa12poleIPMmachine.stateandelectromagneticperformance.Designstrategieswithrespecttofeaturesthatcanmitigatetheresultantmechanicalstressstatearealsopresented.ThediscussionissubstantiatedthroughfiniteelementanalysisFEAtoverifythearguments.AnIPMrotordesignforanintegratedstarter/generatorISGapplicationisusedthroughoutthepapertoillustratethesignificanceofthesemechanicalissues5–7.Acrosssectionfora12poletwolayerdesignisshowninFig.1.Inparticular,themechanicalstressstateofthisrotorisalimitingdesignconstraintduetothehighrotortipspeedoperationthatisrequiredofannulardirectdriveautomotivemachinery.ThepertinentdesignspecificationsforthisISGdesignare6000r/minmaximumoperatingspeed10000r/mindesignburstspeedminimumrotorinnerdiameterIDmmmaximumstatorouterdiameterODmmbondedPMmaterialincavities.II.MECHANICALDESIGNOFIPMROTORSForthepurposeofthisdiscussion,themechanicaldesignpointcorrespondstotheapplicationspecificationthatproducestheworstcasemechanicalstressintheIPMrotor.TheassumptionsemployedinthisdevelopmentareasfollowssteadystatespeedconditionsonlytemperatureeffectsneglectedbaselinecorematerialM1929gageelectricalsteelyieldindicatedbyplanarVonMisesstressforcesofelectromagneticoriginconsiderednegligiblevibrationandrotorshaftdynamicalforcesneglected.Withtheseassumptions,theforcesontherotoraredominatedbythesteadystatecentrifugalforcesatconstantspeed.Therefore,themechanicaldesignpointcorrespondstosteadystateoperationatthedesignburstspeedvalue,10kr/min.AnalyticalcalculationsofthepeakstressesduetocentrifugalforcesactingonaradiallylaminatedIPMmachinerotorisachallengingtaskthatisnotattemptedinthispaperduetothecomplexityoftherotorlaminationdesignfeatures.However,thesepeakstressesaffecttheboundariesoftheoptimizationvariablesthatdeterminetheoptimalsystemdesign,soaqualitativediscussionoftheresultantforcesduetoinertialloadingisappropriate.ThediscussionisconductedemployingwellFig.2.Sketchofresultantforcesonasolidrotor.Fig.3.SketchofresultantforcesonanIPMrotorwithonemagnetfilledcavity.knownprinciplesthatdescribethebehaviorofmaterialsunderstaticloading8,9.Fig.2showsasolidrotorcrosssectionwithannotationstoindicatethemajorforcesonthecoreduetocentrifugalloading.Atthesimplestlevel,neglectingthemagnetcavities,therotorresemblesahoopwithconstantcentrifugalloading.Undertheseconditions,anelementalmemberoftherotorisundertangentialtensionandradialcompression.ThinwalledhoopapproximationscanbejustifiedformodelingtherotorbecauseofthenarrowdepthoftheISGrotorincomparisontotherotorID.Asaresult,therotorsegmentsmainlyexperiencetangentialtensionforces.Usingthisassumption,themajorfactorsaffectingthepeakstressaretheaverageradiusofthehoopandtherotationalspeed.TheVonMisesstressincreasesaccordingtothesquareofeachofthesefactors.IftherotorcavitiesarenowconsideredasinFig.3,whichonlycontainsonecavitylayer,thesteelpolepiececenteredontheaxisisnowonlyattachedtotherestofthelaminationbythethinsteelbridgesateachend.Therefore,thecentrifugalloadingonthepolepieceisnotevenlydistributedaroundthe808IEEETRANSACTIONSONINDUSTRYAPPLICATIONS,VOL.40,NO.3,MAY/JUNE2004Fig.4.SketchofresultantforcesonanIPMrotorwithmultiplelayers.rotorhoop,causingasubstantiallyradiallydirectedinertialloadonthetworetainingbridges.ItshouldbenotedthatthebondedPMmaterialinthecavitywillalsocontributetothisloadingbecauseitisgenerallylessstiffthanthesteelandwill,therefore,contributeadditionalloadingagainsttheinsideedgeofthepolepiece.Therefore,theequivalentmagnetmass,inFig.3,mustbethesumofboththesteelpolepieceandthemagnettheshadedportionofFig.3.Thebondedmagnetmaterialdoesnotprovideanysignificantbondingbetweenmagnetandsteeland,therefore,doesnottransmitforcefromtheyoketothepolepieces.Thechallengethenreducestomodelingthebridges,andthisislargelydependentonthespecificbridgeshape.Ifthebridgesareprincipallystraight,thenbeambendingapproximationsareappropriate.WhenmultiplelayersareconsideredasinFig.4,eachlayercanbeconsideredasbeingindependentlyloadediftheintercavitysteelsectionsarewideenoughtodistributeanystressconcentrationsbetweenadjacentbridges.Theloadoneachbridgeisthentheendloadintheradialdirectionduetotheinertialloadingontheremainingsectionofthepolepiecebetweenthebridgeunderconsiderationandtheaxis.Ifthebridgesoneachlayerhavethesamedimensions,thebridgeattheendofthelongestcavitywillbeunderthehigheststress.IfthecavityendsareroundedasshowninFig.5,thentheeffectivelengthofeachbeamisreduced,andthesimplebeamapproximationsdescribedabovearenolongerreasonable.EachtaperedbridgenowresemblesaroundnotchstressconcentrationelementundersideloadingasshowninFig.5.Thepreciselocationofthepeakstresswithineachbridgeconfigurationwouldrequiresignificantanalysistodeterminewithoutresortingtonumericalsolutions.Inparticular,theequivalentmountingfixedorsimpleattheendsofeachbeamforthestraightbridgemodelisnotclearlydefined.Iftheendsofeachbridgeexperienceminimalbendingcomparedtotherestofthebridge,itisreasonabletoassumethatthepeakstresswillbefoundattheends.Incontrast,thepeakstressintheroundedcavitystructuralmodelwouldbeexpectedattherootofthestressconcentration,correspondingtothemidpointofeachbridge.Fig.5.SketchofresultantforcesonanIPMrotorwithmultiplecavitylayerswithroundedtips.Atthisstage,somegeneralobservationscanbemadeaboutIPMrotordesigndecisionsthatwouldworsenorimprovethemechanicalstressconditions.MaximumrotorspeedA10reductioninthemechanicaldesignpointspeedwouldreducethepeakVonMisesstressbyalmost20.RotorODSimilarly,a10reductionintheradiusattherotorsurface,wherethebridgesarelocated,wouldalsoreducethestressbya20factor.RoundedbridgesThebeamstressesarereducedasthebeamgetsshorterwithallotherdimensionsequal.Basedonthecharacteristicsofthenotchstressconcentrationmodel,acircularlyroundedbridgeshapeshouldnearlyminimizethepeakstress.SmallerpolepiecesA10reductionofthedeflectingpolepiecemassperunitaxiallengthwillreducethestressalmostlinearly.Thiscanbeachievedbyreducingthefractionofthepolepitchthatthecavitiesspan.Increasingthenumberofmachinepolescanproducethesameeffect.StrengtheningribAddingaribredistributesthecentrifugalloadfromthepolepieceresultinginasignificantimprovementinthestressstate.Aribthatisaddedtothelaminationgeometryacrosstheaxisofeachcavityresiststhecentrifugalmotionofthepolemassesthroughtensionratherthanbending.Anotherfactorintheresultantforcescausedbytheinertialloadingistheeffectthattheradialdeflectionoftheentirerotorhasonthemagnitudeofthetensilecomponentofhoopstress.Thehooptensioninthebridgeisduetostretchingastherotorexpandsintotheairgapathigherspeeds.TheimplicitboundaryconditionsinhoopstresscalculationsarethattherotorIDandODboundariesareunconstrained.Asaresult,reductionofthedeflectionateitherboundarywillreducetheexpansionoftherotoratthebridgeradiusandthereforealsoreducethehoopstresscomponentofloading.ConstrainingtherotorODisproblematicsinceitwouldrequireamaterialsubstantiallystifferthansteeltodecreasetheradialdeflectionunderinertialload.Furthermore,addinganyLOVELACEetal.CONVENTIONALLYLAMINATED,HIGHSPEED,IPMSYNCHRONOUSMACHINEROTORS809Fig.6.RotorhubdesignusingdovetailedjointsbetweenthehubandrotorID.Fig.7.Rotorhubdesignusingaxialboltsthroughthestacktoanendplate.materialintheairgapthatadverselyaffectstheelectromagneticsaliencyoftheoriginalrotorwoulddegradetheperformanceofthemachine.ConstrainingtherotorIDisamorefeasiblesolutionforimprovingthestructuralintegrityoftherotor.Sincethereisalreadyahubthatmustattachtherotortothecrankshaft,thereisanopportunitytospeciallydesignthehubtoretaintherotorradially.Typically,ahubisonlydesignedtotransmitthetorqueinthecircumferentialdirectionaswouldoccurwithahubthatispressfitinsidetherotor.Apressfit,though,doesnothingtoconstraintherotorIDandsowouldnotmitigatethemaximumstressatthemechanicaldesignpoint.IftherearenospaceconstraintsinsidetherotorID,avarietyofdifferenthubfixturesmightbeconsidered.Aweldedhubmayworkbutcouldalterthemagneticpropertiesofthecore.OnealternativeisanaxialcylinderthatmateswiththerotorIDusingdovetailedsurfacesasshowninFig.6.AnotheralternativeistoconstructanendplatewithstudsdistributedaroundthecircumferenceoftheendplateoneperpoleasshowninFig.7.Thelaminationswouldbecutwithaholealongeachaxiswherethecoreiswidesti.e.,therenocavitiesalongtheaxis,andthenassembledontothestuds.Thisboltedsystemisonlypracticalifsufficientbolttensioncanbedevelopedandmaintainedsothattheradialloadistakenupbytheendplate.Ifadequatebolttensionisnotdeveloped,therewillbesignificantsideloadingonthestudsthatwouldlikelyresultinshearingoffthestudsatthesurfaceoftheendplate.TheadvantageofthedovetailfixtureFig.6oranyfixturealongtherotorIDsurfaceisthatitisstructurallyrobustandnearlysymmetriciftheradialplateportionofthehubislocatedaxiallynearthemidpointoftherotorstack.Itschiefdisadvantageisthatthehubcylinderhasafinitethicknessthatmaymakeitnecessarytoreducetheavailablespacefortherotorlaminations.Incontrast,theadvantageofanendplatestructureFig.7isthattheradialplateisattheendofthestackanddoesnotuseanyinternalrealestateinsidetheIDthatmightotherwisebereservedforaclutchortorqueconverter.Asaresult,thisapproachmayyieldthemostcompactISGconfiguration.Furthermore,theabsenceoftheinternalhuballowstherotortobedesignedwiththesmallestpossibleIDandOD,whichwillreducethepeakstresssquaredimpactonstress.However,anyendplateapproachmustsolvethepracticalinstallationproblemsassociatedwithheavilyloadedstudsandcompressedlaminations.InSectionIII,theendplatehubstructureisanalyzedincombinationwithproposedrotorcrosssectionmodificationstodemonstrateaplausiblesolutionforthemechanicaldesignofanIPMmachinefortheISGapplication.TheendplatedesignischosenforanalysisbecauseitallowsthesmallestmachinerotordiameterconsistentwiththegivenISGconstrainttoprovidespaceinsidetherotorIDforatorqueconverter.ThemechanicaldesignconsiderationsdiscussedaboveaffectthedesignperformanceoptimizationofIPMmachinesinseveralways6,7,10.RotordiameterConstrainingtherotordiameterandpolepiecesizesclearlyreducestheavailabledesignspaceforoptimization.RotormaterialThechoiceofrotorlaminationmaterialaffectsallowablestressstatebasedonthematerialyieldstrength,butitalsoaffectsthecorelosses11–14.Sincethefundamentalrotorfieldisdc,though,thecorelossesaresubstantiallyconfinedtoharmonicsintroducedbythelaminationgeometry.TherotormaterialalsoinfluencestherequiredmagnetstrengthforagivenPMfluxlinkagedesignbecausethechoiceofalloyingmaterialcontentaltersthesaturationfluxdensity.Thesaturationfluxdensity,inturn,affectstheproportionofthemagnetfluxthatisshortedthroughthebridgesandstrengtheningribs.BridgeandribgeometryThegeometryofthebridgesandstrengtheningribsdirectlyaffectsmagneticperformance.ForagivenIPMmachinedesign,changingfromstraighttocurvedcavitytipswiththesameminimumbridge/ribwidthincreasesthefluxthatisshuntedthroughthebridgesandribs.Addingadditionalstrengtheningribsalsoincreasestheproportionofshuntedmagnetflux.Allthesebridgeandribfactorsservetoreducetheavailableairgapfluxfromthepermanentmagnets,therebyreducingthemagnettorquecomponentforagivendesignorrequiringtheintroductionoflarger,strongermagnets.
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