806IEEETRANSACTIONSONINDUSTRYAPPLICATIONS,VOL.40,NO.3,MAY/JUNE2004MechanicalDesignConsiderationsforConventionallyLaminated,High-Speed,InteriorPMSynchronousMachineRotorsEdwardC.Lovelace,Member,IEEE,ThomasM.Jahns,Fellow,IEEE,ThomasA.Keim,Member,IEEE,andJeffreyH.Lang,Fellow,IEEEAbstractThispaperdiscussesmechanicaldesignconsid-erationsthatareparticulartoconventionally(i.e.,radially)laminatedrotorsofinteriorpermanent-magnetsynchronousmachines.Focusisplacedonapplicationswheretheradialforcesduetohigh-speedoperationarethemajormechanicallylimitingdesignfactor.Properdesignofthelaminationbridges,orribs,attherotorouterdiameterisexplainedintermsofthebothmaterialconsiderationsandelectromagneticperformanceimpact.Thetradeoffofcomplexityversusperformanceassociatedwithusingstrengtheningribsinthemagnetcavitiesisdiscussed.Thesensitivityofthemechanicaldesignlimitationstotherotor-shaftmountingmechanismisalsohighlighted.Theseeffectsarethenanalyzedusingfinite-elementanalysisfora150-Nm/6-kWintegratedstarter/alternatordesignedforoperationupto6000r/minwithanannularrotortoaccommodateatorqueconverterorclutchassembly.Thisexampledemonstratesthatitispossibletosignificantlyimprovetherotorsstructuralintegrityusingthetechniquesdescribedinthispaperwithonlyaverymodestimpactontheprojectedmachinedrivecost.IndexTermsElectricalsteel,finite-elementanalysis(FEA),highspeed,interiorpermanent-magnet(IPM)synchronousmachine,laminations,magneticsaturation.I.INTRODUCTIONROTORDESIGNandconstructionofinteriorperma-nent-magnet(IPM)machinesisachallengingtaskduetotheconflictingcharacteristicsofimprovedperformanceandrotorcomplexity.IPMmachinesareofinterestbecausetheyareparticularlyattractivefromaperformancestandpointintractionandspindleapplications1,2.IPMmachinescanbedesignedwithwide,andtheoreticallyinfinite,speedrangesforconstantpoweroperationwithexcellentinverterutilization.ThisisachievedthroughuseofasalientrotorgeometrywithlimitedPaperIPCSD03084,presentedatthe2001IEEEInternationalElectricMa-chinesandDrivesConference,Cambridge,MA,June1720,andapprovedforpublicationintheIEEETRANSACTIONSONINDUSTRYAPPLICATIONSbytheElectricMachinesCommitteeoftheIEEEIndustryApplicationsSociety.Man-uscriptsubmittedforreviewNovember5,2002andreleasedforpublicationJan-uary20,2004.ThisworkwassupportedbytheMITConsortiumonAdvancedAutomotiveElectrical/ElectronicComponentsandSystems.E.C.LovelaceiswithSatConTechnologyCorporation,Cambridge,MA02142lUSA(e-mail:).T.M.JahnsiswiththeWisconsinElectricMachinesandPowerElectronicsConsortium,DepartmentofElectricalandComputerEngineering,UniversityofWisconsin,Madison,WI53706-1691USA(e-mail:).T.A.KeimandJ.H.LangarewiththeLaboratoryforElectromagneticandElectronicSystems,DepartmentofElectricalEngineeringandComputerScience,MassachusettsInstituteofTechnology,Cambridge,MA02139USA(e-mail:,).DigitalObjectIdentifier10.1109/TIA.2004.827440fluxcontributionfromPMsburiedwithintherotorstructure.Toachievethedesireddegreeofsaliency,speciallaminationdesignandassemblystrategiesaretypicallyrequiredcomparedtothoserequiredforcompetingmachinetypessuchassurfacePMandinductionmachines.TherotordesignstrategiesforIPMmachinescangenerallybedividedintoaxiallyandradiallylaminatedconfigurations,eachwithitsownadvantages3,4.Theaxiallylaminatedrotorisconstructedusingmanyalternatinglayersofsoftandhardmag-neticsheetsthatarelaidalongtheaxisofthemachine,eachbentandindividuallysizedtoformthepolesoftherotor1.Thisdesignapproachcanachievehigh-inductancesaliencyra-tiosinexcessof10:1.However,theaxiallylaminatedrotorisrelativelyexpensivetomanufactureduetothesortedcut-ting,shaping,andassemblyofthemanydifferentlaminationsthatmustbeemployed.Furthermore,aconstrainingrotorsleevemaybenecessaryforhigh-speedoperationtopreventlamina-tionintrusionsintotheairgap.Suchsleevestypicallyreducethesaliencyduetotheirfinitethicknessesandoftenincreaselossesduetoeddycurrentswhenhigh-strengthstainlesssteel(e.g.,Inconel)ischosenforthesleevematerial.Bycontrast,radiallylaminatedrotorsaretypicallydesignedwith14layersofhardmagneticmaterialineachpole.Eachlamination,aswithotherconventionalmachinetypes,ispunchedorcutasasingleunitarypieceforthecrosssectionoftherotor.Cavitiesarepunchedorcutintotherotorlaminations,andthemagnetmaterialisinsertedintothesecavities.ThelaminationscanbestackedusingconventionalmeanssothattherotorisgenerallyeasiertomanufacturethanitsaxiallylaminatedIPMcounterpart.However,adoptionoftheradiallylaminatedrotorcomesattheexpenseofsaliencywithtypicalinductanceratiosrangingfrom1.5upto10:1,dependingonthenumberofmagnetcavitylayersandtheirconfiguration.Forgoodelectromagneticperfor-mance,itisnecessarytominimizethesteelbridgessurroundingthemagneticcavitiesthatarenecessarytolinktherotorironsegmentsintoaunitarylamination.Eachbridgeeffectivelycre-atesamagneticshortciruitacrossthePMs,therebyreducingthemagnetscontributiontotheoverallair-gapflux.Thispaperexaminesthemechanicaldesignissuesofcon-ventionally(alsoreferredtoastransverseorradially)laminatedIPMrotors.Onlythecentrifugalforceisconsideredasthisislikelytobethedominantsourceofmechanicalstressinhigh-speeddesigns.Eachofseveralkeyrotordesignfeaturesareex-aminedinturnwithrespecttotheirinfluenceontherotorstress0093-9994/04$20.002004IEEELOVELACEetal.:CONVENTIONALLYLAMINATED,HIGH-SPEED,IPMSYNCHRONOUSMACHINEROTORS807Fig.1.Crosssectionofa12-poleIPMmachine.stateandelectromagneticperformance.Designstrategieswithrespecttofeaturesthatcanmitigatetheresultantmechanicalstressstatearealsopresented.Thediscussionissubstantiatedthroughfinite-elementanalysis(FEA)toverifythearguments.AnIPMrotordesignforanintegratedstarter/generator(ISG)applicationisusedthroughoutthepapertoillustratethesignif-icanceofthesemechanicalissues57.Acrosssectionfora12-poletwo-layerdesignisshowninFig.1.Inparticular,themechanicalstressstateofthisrotorisalimitingdesigncon-straintduetothehighrotortipspeedoperationthatisrequiredofannulardirect-driveautomotivemachinery.ThepertinentdesignspecificationsforthisISGdesignare:6000-r/minmaximumoperatingspeed；10000-r/mindesignburstspeed；minimumrotorinnerdiameter(ID)mm；maximumstatorouterdiameter(OD)mm；bondedPMmaterialincavities.II.MECHANICALDESIGNOFIPMROTORSForthepurposeofthisdiscussion,themechanicaldesignpointcorrespondstotheapplicationspecificationthatproducestheworstcasemechanicalstressintheIPMrotor.Theassump-tionsemployedinthisdevelopmentareasfollows:steady-statespeedconditionsonly；temperatureeffectsneglected；baselinecorematerial:M1929-gageelectricalsteel；yieldindicatedbyplanarVonMisesstress；forcesofelectromagneticoriginconsiderednegligible；vibrationandrotorshaftdynamicalforcesneglected.Withtheseassumptions,theforcesontherotoraredominatedbythesteady-statecentrifugalforcesatconstantspeed.There-fore,themechanicaldesignpointcorrespondstosteady-stateoperationatthedesignburstspeedvalue,10kr/min.AnalyticalcalculationsofthepeakstressesduetocentrifugalforcesactingonaradiallylaminatedIPMmachinerotorisachallengingtaskthatisnotattemptedinthispaperduetothecomplexityoftherotorlaminationdesignfeatures.However,thesepeakstressesaffecttheboundariesoftheoptimizationvariablesthatdeterminetheoptimalsystemdesign,soaquali-tativediscussionoftheresultantforcesduetoinertialloadingisappropriate.Thediscussionisconductedemployingwell-Fig.2.Sketchofresultantforcesonasolidrotor.Fig.3.SketchofresultantforcesonanIPMrotorwithonemagnet-filledcavity.knownprinciplesthatdescribethebehaviorofmaterialsunderstaticloading8,9.Fig.2showsasolidrotorcrosssectionwithannotationstoindicatethemajorforcesonthecoreduetocentrifugalloading.Atthesimplestlevel,neglectingthemagnetcavities,therotorresemblesahoopwithconstantcentrifugalloading.Undertheseconditions,anelementalmemberoftherotorisundertangentialtensionandradialcompression.Thin-walledhoopapproximationscanbejustifiedformod-elingtherotorbecauseofthenarrowdepthoftheISGrotorincomparisontotherotorID.Asaresult,therotorsegmentsmainlyexperiencetangentialtensionforces.Usingthisassump-tion,themajorfactorsaffectingthepeakstressaretheaverageradiusofthe“hoop”andtherotationalspeed.TheVonMisesstressincreasesaccordingtothesquareofeachofthesefactors.IftherotorcavitiesarenowconsideredasinFig.3,whichonlycontainsonecavitylayer,thesteelpolepiececenteredontheaxisisnowonlyattachedtotherestofthelaminationbythethinsteelbridgesateachend.Therefore,thecentrifugalloadingonthepolepieceisnotevenlydistributedaroundthe808IEEETRANSACTIONSONINDUSTRYAPPLICATIONS,VOL.40,NO.3,MAY/JUNE2004Fig.4.SketchofresultantforcesonanIPMrotorwithmultiplelayers.rotor“hoop,”causingasubstantiallyradiallydirectedinertialloadonthetworetainingbridges.ItshouldbenotedthatthebondedPMmaterialinthecavitywillalsocontributetothisloadingbecauseitisgenerallylessstiffthanthesteelandwill,therefore,contributeadditionalloadingagainsttheinsideedgeofthepolepiece.Therefore,theequivalentmagnetmass,inFig.3,mustbethesumofboththesteelpolepieceandthemagnet(theshadedportionofFig.3).Thebondedmagnetmaterialdoesnotprovideanysignificantbondingbetweenmagnetandsteeland,therefore,doesnottransmitforcefromtheyoketothepolepieces.Thechallengethenreducestomodelingthebridges,andthisislargelydependentonthespecificbridgeshape.Ifthebridgesareprincipallystraight,thenbeambendingapproximationsareappropriate.WhenmultiplelayersareconsideredasinFig.4,eachlayercanbeconsideredasbeingindependentlyloadediftheinter-cavitysteelsectionsarewideenoughtodistributeanystressconcentrationsbetweenadjacentbridges.Theloadoneachbridgeisthentheendloadintheradialdirectionduetotheinertialloadingontheremainingsectionofthepolepiecebetweenthebridgeunderconsiderationandtheaxis.Ifthebridgesoneachlayerhavethesamedimensions,thebridgeattheendofthelongestcavitywillbeunderthehigheststress.IfthecavityendsareroundedasshowninFig.5,thentheeffectivelengthofeach“beam”isreduced,andthesimplebeamapproximationsdescribedabovearenolongerreasonable.EachtaperedbridgenowresemblesaroundnotchstressconcentrationelementundersideloadingasshowninFig.5.Thepreciselocationofthepeakstresswithineachbridgeconfigurationwouldrequiresignificantanalysistodeterminewithoutresortingtonumericalsolutions.Inparticular,theequivalentmounting(fixedorsimple)attheendsofeach“beam”forthestraight-bridgemodelisnotclearlydefined.Iftheendsofeachbridgeexperienceminimalbendingcomparedtotherestofthebridge,itisreasonabletoassumethatthepeakstresswillbefoundattheends.Incontrast,thepeakstressintheroundedcavitystructuralmodelwouldbeexpectedattherootofthestressconcentration,correspondingtothemidpointofeachbridge.Fig.5.SketchofresultantforcesonanIPMrotorwithmultiplecavitylayerswithroundedtips.Atthisstage,somegeneralobservationscanbemadeaboutIPMrotordesigndecisionsthatwouldworsenorimprovethemechanicalstressconditions.MaximumrotorspeedA10%reductioninthemechan-icaldesignpointspeedwouldreducethepeakVonMisesstressbyalmost20%.RotorODSimilarly,a10%reductionintheradiusattherotorsurface,wherethebridgesarelocated,wouldalsoreducethestressbya20%factor.RoundedbridgesThe“beam”stressesarereducedasthe“beam”getsshorterwithallotherdimensionsequal.Basedonthecharacteristicsofthenotchstressconcen-trationmodel,acircularlyroundedbridgeshapeshouldnearlyminimizethepeakstress.SmallerpolepiecesA10%reductionofthedeflectingpolepiecemassperunitaxiallengthwillreducethestressalmostlinearly.Thiscanbeachievedbyreducingthefrac-tionofthepolepitchthatthecavitiesspan.Increasingthenumberofmachinepolescanproducethesameeffect.StrengtheningribAddingaribredistributesthecen-trifugalloadfromthepolepieceresultinginasignificantimprovementinthestressstate.Aribthatisaddedtothelaminationgeometryacrosstheaxisofeachcavityresiststhecentrifugalmotionofthepolemassesthroughtensionratherthanbending.Anotherfactorintheresultantforcescausedbytheinertialloadingistheeffectthattheradialdeflectionoftheentirerotorhasonthemagnitudeofthetensilecomponentofhoopstress.Thehooptensioninthebridgeisduetostretchingastherotorexpandsintotheairgapathigherspeeds.TheimplicitboundaryconditionsinhoopstresscalculationsarethattherotorIDandODboundariesareunconstrained.Asaresult,reductionofthedeflectionateitherboundarywillreducetheexpansionoftherotoratthebridgeradiusandthereforealsoreducethehoopstresscomponentofloading.ConstrainingtherotorODisproblematicsinceitwouldre-quireamaterialsubstantiallystifferthansteeltodecreasetheradialdeflectionunderinertialload.Furthermore,addinganyLOVELACEetal.:CONVENTIONALLYLAMINATED,HIGH-SPEED,IPMSYNCHRONOUSMACHINEROTORS809Fig.6.RotorhubdesignusingdovetailedjointsbetweenthehubandrotorID.Fig.7.Rotorhubdesignusingaxialboltsthroughthestacktoanendplate.materialintheairgapthatadverselyaffectstheelectromagneticsaliencyoftheoriginalrotorwoulddegradetheperformanceofthemachine.ConstrainingtherotorIDisamorefeasiblesolutionforimprovingthestructuralintegrityoftherotor.Sincethereisalreadyahubthatmustattachtherotortothecrankshaft,thereisanopportunitytospeciallydesignthehubtoretaintherotorradially.Typically,ahubisonlydesignedtotransmitthetorqueinthecircumferentialdirectionaswouldoccurwithahubthatispressfitinsidetherotor.Apressfit,though,doesnothingtoconstraintherotorIDandsowouldnotmitigatethemaximumstressatthemechanicaldesignpoint.IftherearenospaceconstraintsinsidetherotorID,avarietyofdifferenthubfixturesmightbeconsidered.Aweldedhubmayworkbutcouldalterthemagneticpropertiesofthecore.OnealternativeisanaxialcylinderthatmateswiththerotorIDusingdovetailedsurfacesasshowninFig.6.Anotheralternativeistoconstructanendplatewithstudsdistributedaroundthecircumferenceoftheendplate(oneperpole)asshowninFig.7.Thelaminationswouldbecutwithaholealongeachaxiswherethecoreiswidest(i.e.,therenocavitiesalongtheaxis),andthenassembledontothestuds.Thisboltedsystemisonlypracticalifsufficientbolttensioncanbedevelopedandmaintainedsothattheradialloadistakenupbytheendplate.Ifadequatebolttensionisnotdeveloped,therewillbesignificantside-loadingonthestudsthatwouldlikelyresultinshearingoffthestudsatthesurfaceoftheendplate.Theadvantageofthedovetailfixture(Fig.6)oranyfixturealongtherotorIDsurfaceisthatitisstructurallyrobustandnearlysymmetriciftheradialplateportionofthehubislo-catedaxiallynearthemidpointoftherotorstack.Itschiefdis-advantageisthatthehubcylinderhasafinitethicknessthatmaymakeitnecessarytoreducetheavailablespacefortherotorlaminations.Incontrast,theadvantageofanendplatestructure(Fig.7)isthattheradialplateisattheendofthestackanddoesnotuseanyinternalrealestateinsidetheIDthatmightotherwisebere-servedforaclutchortorqueconverter.Asaresult,thisapproachmayyieldthemostcompactISGconfiguration.Furthermore,theabsenceoftheinternalhuballowstherotortobedesignedwiththesmallestpossibleIDandOD,whichwillreducethepeakstress(squaredimpactonstress).However,anyendplateapproachmustsolvethepracticalinstallationproblemsassoci-atedwithheavilyloadedstudsandcompressedlaminations.InSectionIII,theend