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ABSTRACTACOMPACTANDEFFICIENTFLYWHEELENERGYSTORAGESYSTEMISPROPOSEDINTHISPAPERTHESYSTEMISASSISTEDBYINTEGRATEDMECHANICALANDMAGNETICBEARINGS,THEFLYWHEELACTSASTHEROTOROFTHEDRIVESYSTEMANDISSANDWICHEDBETWEENTWODISKTYPESTATORSTOSAVESPACETHECOMBINEDUSEOFACTIVEMAGNETICBEARINGS,MECHANICALBEARINGSANDAXIALFLUXPMSYNCHRONOUSMACHINEASSISTSTHEROTORFLYWHEELTOSPINANDREMAININMAGNETICLEVITATIONINTHEVERTICALORIENTATION,WHILECONSTRAINSTHEOTHERFOURDEGREESOFFREEDOMINRADIALDIRECTIONSMECHANICALLYTHEMATHEMATICALMODELOFTHEPROPOSEDSYSTEMHASBEENDERIVEDTHREEDIMENSIONALFINITEELEMENTMETHODISAPPLIEDFORSTUDYINGTHEPERFORMANCESANDVERIFYINGTHEMATHEMATICALMODELOFTHESYSTEMTHEANALYSISRESULTSSUPPORTTHEFEASIBILITYOFTHESYSTEMIINTRODUCTIONNMODERNPOWERINDUSTRIES,WITHTHEADVANCESOFHIGHSTRENGTHANDLIGHTWEIGHTCOMPOSITEMATERIAL,CONTROLTECHNOLOGYANDPOWERELECTRONICS,THEFLYWHEELENERGYSTORAGESYSTEMFESSISBECOMINGAVIABLEALTERNATIVETOTRADITIONALCHEMICALBATTERYSYSTEMS,WITHITSADVANTAGESSUCHASHIGHERENERGYSTORAGEDENSITY,LOWERRISKOFOVERCHARGEANDOVERDISCHARGE,EASIERDETECTIONOFTHEDEPTHOFDISCHARGE,OPERATIONOVERAWIDERTEMPERATURERANGE,LONGERLIFESPANANDENVIRONMENTALFRIENDLINESS14ASARESULT,FESSISNOWCONSIDEREDAPROMISINGTECHNOLOGYFORMANYAPPLICATIONSINCLUDINGSPACEFLIGHT,TRANSPORTATION,POWERINDUSTRY,MILITARY,ANDBUILDINGSERVICESINGENERAL,AFLYWHEELENERGYSTORAGESYSTEMISCOMPOSEDOFAFLYWHEEL,MAGNETICORMECHANICALBEARINGSTHATSUPPORTTHEFLYWHEEL,AMOTORGENERATORTODRIVETHEFLYWHEELANDINTERCONVERTTHEMECHANICALENERGYANDELECTRICALENERGY,CONTROLANDPOWERELECTRONICDEVICES,ANDTOUCHDOWNBEARINGSTHISSEPARATEDRIVINGMOTORGENERATORINADDITIONTOMAGNETICBEARINGSMAKESTHEROTORLONGANDAPTTOPRODUCEBENDINGVIBRATIONSANDTHELARGEMOTORBEARINGSYSTEMMAKESITDIFFICULTFORMINIATURIZATION5TOOVERCOMETHESEPROBLEMS,ASELFBEARINGPERMANENTMAGNETMOTORISINTRODUCEDTHEMOTORCOMBINESMAGNETICBEARINGANDMOTORINGFUNCTIONALITYINTOASINGLEMAGNETICACTUATORSUCHDESIGNSCANREDUCETHEOVERALLLENGTHOFAMOTORBECAUSELESSMECHANICALBEARINGSAREREQUIRED,THUSINCREASINGPOWERDENSITY,REDUCINGWEIGHT,ANDLOWERINGSUSCEPTIBILITYTOROTORDYNAMICVIBRATIONS6ASSHOWNINFIG1,THEREARETHREEDIRECTIONSALONGX,YANDZAXESWITHINTHEFLYWHEEL,SUCHTHATSIXDEGREESOFFREEDOMDOFWHICHARETHEDISPLACEMENTANDROTATIONOFEVERYAXISSHOULDBECONTROLLEDWITHTHEHELPOFMECHANICALORMAGNETICBEARINGSMECHANICALBEARINGSHAVETHEADVANTAGESOFSIMPLESTRUCTUREANDEASYOPERATION,BUTTHEFRICTIONALLOSSANDTHEREBY,THEUSEOFLUBRICATIONSHOULDALWAYSBETAKENINTOCONSIDERATIONESPECIALLY,THEFRICTIONOCCURRINGONTHEBEARINGWHICHISALONGTHEDIRECTIONOFTHEGRAVITY,IE,THEDIRECTIONALONGZAXISINFIG1,ISMUCHGREATERTHANTHOSEINTHEOTHERDIRECTIONSFORTHISREASON,ITISNOTPRACTICALTOUSEMECHANICALBEARINGSALONGTHISAXIS,WHILEFORTHEOTHERAXES,THEYCANSTILLBETOLERATEDACTIVEMAGNETICBEARINGSHAVEMANYADVANTAGESOVERTHECONVENTIONALBEARINGSSUCHBENEFITSINCLUDEHIGHERENERGYEFFICIENCY,LOWERWEAR,LONGERLIFESPAN,ABSENCEOFNEEDOFLUBRICATIONANDMECHANICALMAINTENANCE,ANDWIDERRANGEOFOPERATINGTEMPERATURESTHEREAREMANYSTUDIESCONCERNINGMAGNETICBEARINGS,BUTMOSTOFTHEMTREATTHEBEARINGINWHICHATLEASTFIVEDOFOFTHEOBJECTARECONTROLLEDSINCETHECONTROLOFEACHDOFREQUIRESASENSOR,ANACTUATORANDACONTROLLER,THEENTIRESYSTEMBECOMESCOMPLEXINTERMSOFTHEDESIGNOFITSMECHANICAL/ELECTRICALPARTANDTHECONTROLSYSTEM7CONSIDERINGTHIS,THISPAPERPRESENTSANEWCONCEPTOFMAGNETICBEARING,INWHICHONLY2DOFOFANAXIS,NAMELY,THETRANSLATIONANDROTATIONALONGANDABOUTAXIALDIRECTIONSRESPECTIVELY,AREACTIVELYCONTROLLEDTHEMOTIONSINOTHERDIRECTIONSAREENTIRELYRESTRICTEDBYMECHANICALBEARINGSTHECOMBINEDUSEOFACTIVEMAGNETICBEARINGSANDMECHANICALBEARINGSCANCUTDOWNTHECOMPLEXITYOFCONTROLANDMAKETHESYSTEMMORESTABLE,VIABLEANDCOSTEFFECTIVECURRENTLY,AXIALFLUXPERMANENTMAGNETMOTORSAFPMUSEDINMANYAPPLICATIONSHAVEBECOMEANAPPEALINGRESEARCHFIELD89THEYHAVESEVERALUNIQUEFEATURESSUCHASHIGHEFFICIENCY,HIGHPOWERANDTORQUEDENSITIES,LOWROTORLOSSESANDSMALLMAGNETICTHICKNESSHOWEVER,THEDISADVANTAGEISTHATTHEDISTRIBUTEDWINDINGSHAVEENDWINDINGSOFSIGNIFICANTLENGTHCOMPAREDTOTHEACTIVEPARTOFTHECOILCONDUCTORSTHISFEMANALYSESFORTHEDESIGNANDMODELINGOFANOVELFLYWHEELENERGYSTORAGESYSTEMASSISTEDBYINTEGRATEDMAGNETICBEARINGCZHANG,STUDENTMEMBER,IEEE,PWU,STUDENTMEMBER,IEEEANDKJTSENG,SENIORMEMBER,IEEECENTREFORADVANCEDPOWERELECTRONICS,NANYANGTECHNOLOGICALUNIVERSITYBLKS2,NANYANGAVENUE,SINGAPORE639798,REPUBLICOFSINGAPOREIFIG1THREEMOTIONDIRECTIONSOFFLYWHEEL0780389875/05/20002005IEEE1157OBVIOUSLYRESULTSINPOORMACHINEPERFORMANCE,ASASIGNIFICANTPARTOFTHEMACHINECOPPERIE,MORETHAN50OFTHETOTALINMOSTMACHINEDESIGNSISPRODUCINGHEATBUTNOTORQUE10CONCENTRATEDWINDINGSCANSOLVETHISPROBLEMFURTHERMORE,THEYHAVESIMPLERDESIGN,EASIERARRANGEMENTANDHIGHEREFFICIENCYTHEFINITEELEMENTMETHODFEMHASPROVEDTOBEPARTICULARLYFLEXIBLE,RELIABLEANDEFFECTIVEINTHEANALYSISANDSYNTHESISOFPOWERFREQUENCYELECTROMAGNETICANDELECTROMECHANICALDEVICES1112THEFEMCANANALYZEPMCIRCUITSOFANYSHAPEANDMATERIALAREMARKABLEADVANTAGEOFFEMANALYSISOVEROTHERAPPROACHESTOANALYSISOFPMMOTORISTHEINHERENTABILITYTOCALCULATEACCURATELYARMATUREREACTIONEFFECTS,ELECTROMAGNETICFORCEANDTORQUEINTHISPAPER,ANOVELFLYWHEELENERGYSTORAGESYSTEMASSISTEDBYINTEGRATEDMAGNETICBEARINGISPROPOSEDTHEMOTORANDGENERATORARECOMBINEDTOBEASINGLEMACHINEANDTHEFLYWHEELFUNCTIONSASTHEROTORINORDERTOSAVESPACEMECHANICALBEARINGSAREUSEDTORESTRICTTHEDISPLACEMENTANDROTATIONALONGRADIALDIRECTIONS,ANDTHEDISPLACEMENTANDROTATIONALONGAXIALDIRECTIONARECONTROLLEDBYACTIVEMAGNETICBEARINGSTHESTRUCTUREANDELECTROMAGNETICDESIGNOFTHEPROPOSEDSYSTEMISPRESENTEDALONGWITHTHEMATHEMATICALMODEL3DFEMANALYSESAREIMPLEMENTEDTOVERIFYTHEMATHEMATICALMODELANDSUPPORTTHEFEASIBILITYOFTHESYSTEMANALYSISRESULTSHAVEBEENOBTAINEDANDAREPRESENTEDINTHISPAPERIICONSTRUCTIONANDGEOMETRYOFTHEPROPOSEDSYSTEMACONFIGURATIONOFTHEENTIRESYSTEMFIG2SHOWSTHECROSSSECTIONALDIAGRAMOFTHEPROPOSEDFLYWHEELENERGYSTORAGESYSTEMITSCOMPONENTSARELISTEDINTABLEIITEMS1AND8ARETHEUPPERANDLOWERSTATORSFIXEDONTHESYSTEMHOUSINGWHICHISDESIGNEDTODISSIPATERADIALKINETICENERGYFROMANYROTORDEBRISANDENSURESAFETYINTHEEVENTOFMECHANICALFAILUREAXIALFLUXPERMANENTMAGNETSYNCHRONOUSMOTORISIMPLEMENTEDTODRIVETHEFLYWHEELWHICHISALSOFUNCTIONINGASAROTORMECHANICALROTATIONALBALLBEARINGSAREMOUNTEDONTHEOUTERRIMOFTHEROTORTOCONSTRAINITSRADIALMOTIONANDASSISTTHEROTATIONOFTHEFLYWHEEL/ROTORTHISARRANGEMENTMAKESTHESTRUCTUREVERYCOMPACTWITHOUTUSINGTHESHAFTBUTTHELARGEDIAMETEROFTHEBOREOFTHEMECHANICALBEARINGLIMITSTHEMAXIMUMSPEEDBYUSINGFLUIDFILMBEARINGS,THEDNVALUEBOREDIAMETERMMSPEEDRPMCANREACH3,000,00013THATMEANSTHEMAXIMUMSPEEDISLESSTHAN20,000RPMWHENTHEBOREDIAMETERIS150MMINHIGHERSPEEDFLYWHEELSYSTEM,TWOMECHANICALBEARINGSCANBEMOUNTEDATTHEENDSOFTHESHAFTWHICHISFIXEDINTHEMIDDLEOFTHEROTORWITHTHISARRANGEMENT,THESPEEDMAYREACHUPTO60,000RPMANDABOVETHEAXIALMOTIONCANBEREALIZEDWITHTHEAIDOF4SLIDINGBALLBEARINGSINSTALLEDORTHOGONALLYONTHERIMOFTHEROTATIONALBALLBEARINGNONCONTACTEDDYCURRENTDISPLACEMENTSENSORANDPHOTOELECTRICALSENSORARESETINTHEHOLLOWCENTEROFTHETWOSTATORSTODETECTTHEDISPLACEMENTANDANGULARPOSITIONALONGZAXISWHENTHEROTORSPINS,ITEMS2AND10INFIG2TOUCHDOWNBEARINGSARENECESSARYDURINGSTARTINGOPERATIONORINTHEEVENTOFMAGNETICBEARINGSFAILURETHETOUCHDOWNBEARINGSSHALLBEMOUNTEDAGAINSTTHEOUTERRIMOFTHEROTORDURINGNORMALOPERATION,THEREISALESSTHAN05MMAIRGAPBETWEENALLROTORSURFACESANDTHETOUCHDOWNBEARINGS,THUSACHIEVINGAMECHANICALLYCONTACTLESSENVIRONMENTBBASICFEATURESOFTHEPROPOSEDSYSTEMFIG3SHOWSTHEBASICFEATURESOFTHEPROPOSEDSYSTEMTHEMOTORANDGENERATORWITHDISKTYPEGEOMETRYARECOMBINEDINTOASINGLEELECTRICMACHINEASSHOWNINFIG3ATHEROTORDOUBLESASTHEFLYWHEELANDISSANDWICHEDBETWEENTWODISKTYPESTATORSTHISDESIGNMAXIMIZESTHETORQUEPRODUCTIONAREAOFTHEDISKTYPEROTORASSHOWNINFIG3B,EACHOFTHEUPPERANDLOWERSTATORSCARRIESASETOFTHREEPHASECOPPERWINDINGSTOBEFEDWITHSINUSOIDALCURRENTSCONCENTRATEDWINDINGSAREIMPLEMENTEDTOREDUCETHEPOWERLOSSIFDISTRIBUTEDWINDINGSAREUSED,THEWINDINGENDSWILLSPANHALFTHECIRCUMFERENCEOFTHEROTORTHEENDSAREMUCHLONGERCOMPAREDTOTHEEFFECTIVEPARTSOFCOILCONDUCTORS,ANDTHECOPPERLOSSOFTHEWINDINGSWILLTHUSBELARGERINTHISPARTICULARDESIGN,THEREARE6COILS,EACHOFWHICHSURROUNDSASTATORTOOTHTHEDISTRIBUTIONOFTHREEPHASESANDDIRECTIONSOFTHETHREEPHASECURRENTSATAPARTICULARINSTANCEARETABLEICOMPONENTSOFTHEPROPOSEDSYSTEMITEMNUMBERITEMNAME1UPPERSTATOR2POSITIONSENSOR3STATORWINDINGS4TOUCHDOWNBEARINGS5ROTATIONALBALLBEARING6SYSTEMHOUSING7ROTORPERMANENTMAGNETS8LOWERSTATOR9NONMAGNETICMATERIALGUARDRING10ROTATIONSENSOR11FLYWHEELROTOR12FASTENERS13SLIDINGBALLBEARINGFIG2CROSSSECTIONALDIAGRAMOFTHEPROPOSEDSYSTEM1158SHOWNINFIG4BESIDESIMPROVEDEFFICIENCY,SIMPLESTRUCTUREANDEASYINSTALLATIONOFTHESTATORWINDINGCANALSOBEREALIZEDINTHISDESIGNPERMANENTMAGNETSAREMOUNTEDONBOTHSURFACESOFTHEROTOR,ASSHOWNINFIG3CTHEARRANGEMENTOFTHESEPMSANDTHEMAGNETICFLUXFLOWINGINTHEMOTORAREDEPICTEDINFIG4PMSARESETTLEDINOPPOSITEDIRECTIONSINUPPERANDLOWERROTORFACES,SOTHATTHEYWOULDATTRACTEACHOTHERANDINCREASETHETOTALFLUXINTHEMAGNETICCIRCUITSAGUARDRINGMADEOFHIGHSTRENGTHNONMAGNETICMATERIALISUSEDTOASSISTTHEPMSINRESISTINGTHECENTRIFUGALFORCE,ASSHOWNINFIG3DMAGNETICBEARINGSCANBEREALIZEDBYUSINGATTRACTIVEFORCESTHEINTERACTIONBETWEENTHESTATORANDROTORFIELDSPRODUCESANAXIALFORCETHATMAKESTHEROTORANDSTATORATTRACTEACHOTHERTHECURRENTSOFEACHSTATORCANBEINDEPENDENTLYADJUSTEDTOCONTROLTHENETFORCESONTHEROTORANDKEEPITINTHEMIDDLEOFTHETWOSTATORSTHENETFORCEALONGTHEAXIALAXISCANBEOBTAINEDAS21FFF1WHERE1FISTHEFORCEBETWEENTHELOWERSTATORANDROTOR2FISTHEFORCEBETWEENTHEUPPERSTATORANDROTORTHEMOTORGENERATORISEQUIVALENTTOTWOMOTORS,THETOTALTORQUETCANBEWRITTENAS12TTT2WHERE1TAND2TARETORQUESGENERATEDBYTHEUPPERANDLOWERMOTORRESPECTIVELYCDIMENSIONSOFTHEMOTORTHESIZEOFAXIALFLUXMOTORCANBETRANSFORMEDTOTHATOFANEQUIVALENTSIZEDRADIALMACHINEBYTHEFOLLOWINGFORMULAS2OIDDD32OIDDL4WHEREODANDIDARETHEOUTERANDINNERDIAMETERSOFTHEAXIALFLUXDISKTYPEMOTOR,DANDLARETHEINNERDIAMETERANDLENGTHOFTHEEQUIVALENTRADIALMACHINEMAXIMUMTORQUEISPRODUCEDWHEN/3ROIKDDFROMOUTPUTEQUATIONOFTHEMOTOR,WECANGET20SQDLCN5ANDTHEN,WECANOBTAIN3320811RORRSQKDKKCN6WHERE0CISTHEOUTPUTCOEFFICIENT,QISTHERATINGOFMACHINEINKVA,SNISTHERATEDSPEEDINRPS301110GAVWCBAK,COSENNNKPQ7WHEREGAVBREPRESENTSTHEAVERAGEFLUXDENSITYOVERTHEAIRGAPOFTHEMACHINE,ALSOKNOWNASMAGNETICLOADINGAISTHEELECTRICLOADINGWKISTHEWINDINGFACTORNP,NANDCOSNREPRESENTRATEDPOWER,EFFICIENCYANDPOWERFACTORRESPECTIVELYEKISTHERATIOBETWE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EALWAYSASSOCIATEDWITHTRANSIENTEXCITATIONSANDNONLINEARMAGNETICMATERIALSTHEFOLLOWINGTHREEMAXWELLEQUATIONSARERELEVANTTOTRANSIENTAPPLICATIONSHJEGGG36/EBTGG370BG38WHEREHGDENOTESTHEMAGNETICFIELDDENSITY,JGISTHEELECTRICCURRENTDENSITY,ISTHECONDUCTIVITYOFTHEDIELECTRIC,ANDEGISTHEELECTRICFIELDINTENSITYFROM36AND37,WECANOBTAIN10BHTGG39THEFORCEANDTORQUECANBECALCULATEDASTHEDERIVATIVEOFTHESTOREDMAGNETICCOENERGYWWITHRESPECTTOASMALLDISPLACEMENTTHECOENERGYCANBEWRITTENAS11610BVWHDBDVGG40THENTHECOMPONENTOFINSTANTANEOUSFORCESFINTHEDIRECTIONOFTHEDISPLACEMENTSISSDWFDS41THEINSTANTANEOUSTORQUETWITHASMALLANGULARROTATIONDISPLACEMENTISREPRESENTEDBY,/ICONSTWIT42BFEMANALYSISTHEPROPOSEDSYSTEMDESCRIBEDINSECTIONIIWASANALYZEDUSINGATIMESTEPPINGTHREEDIMENSIONALFINITEELEMENTSIMULATOR16THEMESHSHAPEOFANALYSISMODELISSHOWNASFIG5ONLYONESTATORANDROTORAREIMPLEMENTEDINFEMANALYSISINORDERTOSAVECOMPUTATIONALTIME,YETITISEFFECTIVETODESCRIBETHEPERFORMANCESOFTHEENTIRESYSTEMWHENTHESTATORISFEDWITH50HZSINUSOIDALCURRENTUNDEROPENLOOPCONDITION,ANDGIVENANINITIALSPEEDOF1500RPM,BOTHTHEFLUXLINKAGEANDINDUCEDVOLTAGEAREQUASISINUSOIDAL,ANDTHESPEEDSETTLESTOTHESYNCHRONOUSSPEEDEVENTUALLYFEMANALYSISRESULTSARESHOWNASINFIG6ITPROVESTHATTHEMOTORCANBEANALYZEDASASINEWAVEMOTOR,ANDTHEMATHEMATICALANALYSISISTENABLEFIG7AANDBSHOWTHEMAGNETICFLUXDENSITYINTHESTATORANDROTORITISOBVIOUSTHATTHEREARE4REGIONSHAVINGHIGHERFLUXDENSITYINTHESURFACESOFTHESTATORANDROTORRESPECTIVELYITREPRESENTS4POLESINTHEMOTORPERMANENTMAGNETSNDFE35WITHTHEREMANENTFLUXDENSITY123RBTAREMOUNTEDONTHESURFACEOFTHEROTOR,SOINTHEREGIONUNDERPMS,THEFLUXDENSITYISDEFINITELYHIGHERTHANTHATATOTHERPLACESCVERIFICATIONOFTHEMATHEMATICALMODELTHREEPHASECURRENTSCANBEDECOUPLEDINTODQCURRENTS,ASSHOWNBELOWCOSSINADQIII43COS120SIN120BDQIII44COS240SIN240CDQIII45WHEREISTHEELECTRICALANGLEOFTHEROTORMAKING0QI,WEOBTAINAVERAGEZEROTORQUEASSHOWNINFIG8AITISEVIDENTTHATTHETORQUEHASNORELATIONSTODIABFIG7MAGNETICFLUXDISTRIBUTIONOFTHESTATORANDROTORAFLUXDENSITYINTHESTATORBFLUXDENSITYINTHEROTOR00020040060080104020020406TIMESFLUXLINKAGEWBFLUXLINKAGEVSTIME00020040060080120015010050050100150200TIMESINDUCEDVOLTAGEVINDUCEDVOLTAGEVSTIMEAB051015202514001450150015501600TIMESSPEEDRPMSPEEDVSTIMECFIG6FEMSIMULATIONRESULTSWHENSTATORFEDWITH50HZSINUSOIDALCURRENTAFLUXLINKAGEBINDUCEDVOLTAGECROTATIONALSPEEDFIG5MESHSHAPEOFANALYSISMODEL1162SIMILARLY,ASSIGNING0DIAND1QI,THEFORCE,TORQUEANDSPEEDCANALSOBEOBTAINEDASSHOWNINFIG8BDTHEFORCEANDTORQUEAREAPPROXIMATELYCONSTANT,ANDTHESPEEDINCREASESLINEARLYITPROVESTHATTHETORQUEISPROPORTIONALTOQIINTHISWAY,BYASSIGNINGQIORDITOZERO,ANDTHENCHANGINGTHEVALUESOFDIORQIACCORDINGLY,WECANGETTHECURVESOFAXIALMAGNETICFORCEANDTORQUEATTHESTARTINGPOINT,ASSHOWNINFIG9SOLIDLINESREPRESENTTHECALCULATIONRESULTSFROM28AND29,ANDTHESTARMARKSARETHEFEMANALYSISRESULTSWHENITISASSIGNEDWITHDI