´ski***D.Kozanecka*,Z.Kozanecki**,J.Łagodzin
InstituteofTurbomachinery,TechnicalUniversityofLodz,219/223WolczanskaSt.,93-005Lodz,Polandarticleinfoabstract
Inrotordynamics,thebearingcharacteristicsexertsadecisiveinfluenceondynamicsoftherotatingshaft.Theresearchandapplicationexperiencehaveledtoactivemagneticbearings(AMBs),whichallowforuniqueapplicationsinrotatingsystems.Thepaperpre-sentstheinvestigationsconcerningoptimizationofthemagneticbearingconstruction.Anactivemagneticbearingoperatesasaradial,auxiliarydamper,whichcooperateswiththelong,flexibleshaftline(aircraftindustryapplications)andmodifiesitsdynamicproperties.InthedevelopedconceptofAMBsforaviationpurposes,anecessityofincreasingitsbear-ingloadcapacityanddampinghasoccurred.Thesecondimportantcriterionisaweightreduction.Thisadvancedproblemleadstospecificrequirementsonthedesignandmate-rialsfortheAMB.Toachievethesegoals,somesimulationshavebeenperformed.Theexperimentalresultsarepresentedaswell.Ó2010ElsevierB.V.Allrightsreserved.Articlehistory:Availableonline23May2010Keywords:ActivemagneticdamperElectromagnetOptimizationNumericalanalysis1.IntroductionAwiderangeofnon-conventionalapplicationsintoday’saeroindustryisaseriouschallengeforengineersasfarasspe-cificperformanceandreliabilityissuesareconcerned.Inordertosatisfydemandsimposedbyavarietyofcomplexworkingconditions,itisnecessarytoemploythelatestavailablenumericaltechnologyallowingforoptimizationandsimulationpro-cedures,whichhelptoevaluatethefeasibilityofapplicationofanoveldesignattheearlystage.Then,aprototypecanbebuiltandaseriesoflabtestsmaybeconducted[2,10].Thepresentpaperaimsatshowinganapplicationofthemagneticbearingasavibrationdamperinthetorquetransmis-sionsystemtoarearrotoroftheconventionalhelicopter[5,7].Magneticbearingsofferanovelwayofsolvingclassicalprob-lemsofrotordynamicsbysuspendingaspinningrotorwithnocontact,wearandlubrication,andcontrollingitsdynamicbehavior[1,3,4].Thepaperpresentstheinvestigationsconcerningoptimizationofthismagneticsupportconstruction.Anactivemagneticbearingoperatesasaradial,auxiliarydamper,whichcooperateswiththelong,flexibleshaftline,appliedintheaircraftindustry,andmodifiesitsdynamicproperties.2.ConceptofmodificationInastandardhelicopter,apowertransmissionsystemiscomposedofseveralshortsegmentsoftheshaftsupportedbyrollingbearingsandconnectedtogetherwithaseriesofelasticmembranecouplings(Fig.1a).Duetoasignificantnumberofsupportsappliedatarelativelyshortdistancealongtheshaft,thementionedsystemissubcritical,whichimpliesvarious*Correspondingauthor.**Correspondingauthor.***Correspondingauthor.´ski).E-mailaddresses:dkozan@p.lodz.pl(D.Kozanecka),zkozan@p.lodz.pl(Z.Kozanecki),jakub.lagodzinski@p.lodz.pl(J.Łagodzin1007-5704/$-seefrontmatterÓ2010ElsevierB.V.Allrightsreserved.doi:10.1016/j.cnsns.2010.04.0442274D.Kozaneckaetal./CommunNonlinearSciNumerSimulat16(2011)2273–2278Fig.1.Helicopterpowertransmissionsystemscheme.(a)Classicalsolution.(b)Novelconceptwithanovercriticalflexibleshaftsupportedbytheactivemagneticdamper.performancelimitations.Thesolutioniscommoninthehelicopterdesignbutitscrucialdisadvantageisitsweightandstruc-turalcomplexity[2].AconceptoftheproposedactivevibrationdampingsystemispresentedinFig.1b,inwhichamagneticbearinghasbeenmountedonthe5400mmlong,single-segmentshaft.Thus,thepowertransmissionsystemcanbesimplifiedanditsweightreduced.Oneofthedisadvantagesofthesystemisthatithastoundergothroughaseriesofcriticalfrequenciesuntilthenominalpowerisreachedduringitsstart-up,duetoasinglesupportoftheshaftand,hence,itsrelativelyhighflexibility.Anapplicationoftheactivemagneticbearingcombinedwithitsdynamicpropertiescontrolabilityallowsforsafepassingthroughthosefrequenciesandobtaininganovercriticaloperationmodeofthepowertransmissionsystem,whichisfavor-ablefromtheviewpointofoperationproperties[6].Agenerationofthemagneticdampingforcebytheactivebearingfortheparticularapplicationmentionedaboveisacomplexissue.Apartfromthecontrolsystemdesign,itisvitaltoestablishnoveloptimizationproceduressupportingthedesignofgeometryofelectromagnetsofthebushofthebearing,amaterialselectionofthebushandthejournal,andamod-elingprocessofthejournal–bushsystem.Itisalsonecessarytoanalyzetheoptimizationofthedesignfromtheviewpointofforcesgeneratedbyelectromagnetswithsimultaneoussatisfactionoftheminimummasscondition[5,10].3.BearingmodelsandanumericalanalysisForthepurposeofanumericalanalysis,twogeometriesoftheradialmagneticbearingwereconsidered–hetero-andhomopolar(Fig.2),betweenwhichaprincipaldifferenceisthelosslevelduetohysteresisandeddycurrents.Forthesetwogeometryvariants,anumericalanalysisoftheinductiondistributioninthebushandjournalelements,whichcooperatewithapairofelectromagnets,wascarriedout[9]withtheANSYSWorkbenchtoolanditsMaxwellLaws-basedmodule–ANSYSMagnetostatic.Thenumericalanalysiswasconductedwiththesamecorematerial–ARMCOiron,forwhichthemagnetizationcurveB–Hwasestablishedusingthematerialsavailableinpublicdomain[10].Thecalculatedresultantmagneticforceactingonthebushatitscentralpositionwasacomparativecriterionforallthecasesunderinvestigation.Thecurrentvaluesincoilsandalsothedimensionoftheradialgapinthebearingwerekeptconstant.Aseriesofthenumericalanalysesdescribedaboveallowedfortheelectromagnetpoleshapeanddimensionoptimization.Thenumericalmodelofthebearingwasthenboundedbytheair-propertiedcuboidofthedimensionsthatweregreaterineachdirectionXYZfromthemodelby60mm.TheDrichletboundaryconditionwassetoneachcuboidsurface.Atthestageofthesurfaceshapeandpoleoptimization,atransversesymmetrysurfaceofthemodel,perpendiculartotheshaftaxis,wasusedtosettheNeumanboundarycondition[9].Fig.2.Bearingmodels:heteropolarandhomopolar.D.Kozaneckaetal./CommunNonlinearSciNumerSimulat16(2011)2273–22782275Fig.3.Exemplarymodelmesh–cores,poles,abushandanairgap.Foreachsimulation,meshgenerationsettings(elementsizeandtype,meshqualityintheairgap)werekeptconstant.Dependingupontheanalyzedcase,themodelmeshwascomposedof150–200elements,withaparticularcaretoasatis-factorynumberofelementsintheairgaps,wherethemagneticfieldishighlynonlinear(Fig.3).Duetothisphenomenon,usingaGAPtool(GapAspectratio3:1,GapDensity:Coarse),themeshbetweenthepolesandthebushmountedontheshaftwasrefined.Additionally,withaSIZINGCONTROLtool,anaveragemeshelementsizeinelectromagnetscoreandthebushwassetto5mm.Thereasonforthatwastoobtainafinemodeldescriptionand,hence,moreaccurateresults,attheexpenseofsignificantlyextendedcomputationtime,however.Fig.4presentsanumericallycomputeddistributionofthemagneticinductionforapairofpolesforboththehetero-andhomopolarbearing.Ithasbeenobservedthattheheteropolargeometryallowsforabettercorematerialutilization.Themaximumlevelofinductioninthissolutionwas1.4T,whichguaranteesgenerationoftheforceiftheshaftisconcentricallylevitatinginthesupportbush.Thisisa2.4timesgreaterelectromagneticforceifcomparedtothehomopolarmodel,inwhichthegeneratedforceisequalto42.5N.Inthefollowingstage,aseriesofparametricalanalysesfortheheteropolarbearingwereconductedtooptimizethepolegeometryasafunctionoftheelectromagneticforcegeneratedbyelectromagnets.Bothorthogonalandroundpoleswereanalyzed(seeSection4).Inthepracticalrealization,roundpolesofthediameterD=28mmwereused.Forsuchaconcept,thegeneratedmagneticforceisequalto122.4N(seeFig.5).Itisthehighestvaluethatcanbeachievedundertheassumedconditions,which,ifcom-paredtotheorthogonalpoles,guaranteestheminimumweightofthebearing.4.InvestigationresultsToverifythefeasibilityofthemodificationsintroduced,ahelicoptertailbeamteststandwasprepared(Fig.6).Forthepurposeoftheexperiment,asteelbushwasmountedontheshortpower-transmittingshaft,whichendsjustbehindtheFig.4.Magneticinductiondistributioninhetero-andhomopolarbearingmodels.2276D.Kozaneckaetal./CommunNonlinearSciNumerSimulat16(2011)2273–2278Fig.5.Heteropolarbearingmodel:magneticforcevs.polediameter.Fig.6.Magneticforcemeasurementteststand.Theaangle(unscaled)coversthewholerangeoftheshaftmovementslimitedbytheradialclearanceinthedamper.magneticdamper.Thisshortshaftwasusedbeforeatdifferentstagesoftheinvestigations,toadjustthecontrolsystemoftheactivebearing.Atthattime,acomparativecriterionforbothgeometries(hetero-andhomopolar)wasavalueofthecur-rentsrequiredtoelevatetheshaftanditsbushtotheupperboundingposition[8].Asignificantproblemtodealwithwasaproperinterpretationofsimilaritiesbetweenthepracticalexperimentconditionsandthoseassumedduringthenumericalsimulations.Inthesimulations,thebushwassituatedideallyconcentrically(e=0)andwasabletomovetransversely,keepingthusitsaxisandthemagneticdamperaxisparallel.Intherealobject,thebushperformsa‘pendulum’movementwithrespecttotherotationalaxiscrossingthecenteroftheelasticclutchmembraneconnectingthepowerunitwiththeshaft.Takingintoconsiderationadistancebetweentheclutchmembraneandthedamper,andalsoaradialclearancebetweenthebushandpolesoftheanglea=0°304000,itisconcludedthattheaxesofthebushandthedamperarepracticallyparallel.Hence,ithasbeenagreedthatthemethodofforcemeasurementsintherealmodeliscomparablewiththeoneinthenumericalsimulations.InFig.7aelectromagnetscoils,whichwerefedduringtheexperiment,areshown.TheresultantforceoftheupperpairofelectromagnetsFXTwasactingalongtheXaxis,whereastheresultantFYTwasactingalongtheYaxis.ThetotalresultantforceFwwasactingupwardsalongtheverticalaxis,equalizingtheweightoftheshaftMw.Fig.7.(a)Bearingscheme(viewfromthefreeendoftheshaft).(b)Realactivemagneticdamperteststand.D.Kozaneckaetal./CommunNonlinearSciNumerSimulat16(2011)2273–22782277Fig.8.Experimentaldynamiccharacteristicsrecordedduringactivevibrationcontrolofthehelicopterpower-transmittingsystemprototype.Initiallyduringtheexperiment,theshaftwaslyingfreelyunderitsweightonthelowerelectromagnetpoles.Next,valuesofthecurrentIXTandIYTintheupperelectromagnetcoilswereincreasedtothemagnitudesFw,atwhichtheweightoftheshaftwithbushMwwasequalizedandtheshaftwaselevated(Fig.7a).DuringtheexperimentboththeelectromagnetsinoperationwerefedwithequalcurrentsIXTandIYT.Acomparisonbetweentherealandnumericalresultsclearlystandsfortheintroducedmodifications.Inthiscase,dy-namicstiffnesscriteria,whichdependbothupontheelectromagnetsandtheappliedcontrolsystem,wereomitted.Measur-ingtheattractionforceoftheelectromagnetsunderconstantbasecurrentIB=3Aandtheequalradialgap,itisfoundthattheheteropolardesignelevatestheshaftatISheter=IYT=IXT=30%PWM(PulseWidthModulation),whilethehomopolardesignre-quires50%ofPWMforthecontrolcurrentIShomo.AssumingtherelationbetweentheforceandthecurrentinthemagneticIShomo%ÁISbearingasFw$I2¼50¼5totheforceratio,avalueofS,itcanbefoundthatafterthesubstitutionofthecurrentratioI330%ÁISSheter25/9=2.77appears.Itishenceseenthatforthesameforcerequiredfortheshaftelevation,theheteropolardesignofthebearingguaranteesalmosta3timeshigherincreaseintheforce.Forthenumericalsimulationresults,theforceratiois122.4/42.5=2.88.Thisinconsistencyisaresultofimperfectionofthenumericalmodel,which,e.g.,doesnottakeintoac-countaninfluenceoftheadjacentpairofelectromagnets.5.ConclusionsWithintheexperimentalscope,aseriesofsimulationswascarriedouttoconfirmtheefficiencyoftheoptimizedbearingdesignasanactivedamperinthepower-transmittingsystem(Fig.7b).Theresultsindicatethatthereisapossibilitytocon-trolvibrationsoftheshaftandtoreducesignificantlythevibrationamplitudewhenthecriticalfrequencypassesthenormalandmaximumrotationalspeed(5000rev/min)atthestart-up.Fig.8presentsexperimentallyacquireddynamicBodecharacteristicsofthe5400mmlonghelicopterpower-transmittingshaftalongwithdampedtrajectoriesoftheshaftinthemagneticsupportwhilepassingthecriticalfrequency.Theresultsconfirmboththeefficiencyofthepresentedmethodandthepossibilityofeffectivevibrationdampingintheconsideredapplication.Inspiteofrelativelyhighvibrationamplitudesinthevicinityofthreesubsequentcriticalfrequen-cies,theshaftremainswithintheassumedclearancesafemarginsandisabletoreachitsnominalandmaximumpowerwithoutanymechanicalcontactwiththemagneticsupport.Withintheentireoperatingenvelope,maximumamplitudesandtrajectoriesdonotexceed50%ofthediametricalclearanceofthebearingdesign,whichwasequalto2mminthedis-cussedcase.Themodificationdescribedinthepaperprovidesasignificantmassreductionofthesystem,whichiscrucialinanyaeroapplications.2278D.Kozaneckaetal./CommunNonlinearSciNumerSimulat16(2011)2273–2278References[1]ChibaA,FukadoT,IchikawaO,OshimaM,TakemotoM,DorrellD.Magneticbearingsandbearinglessdrives.Oxford,London:Elsevier;2005.[2]DeSmidtHA.Robust–adaptiveactivevibrationcontrolofalloyandflexiblematrixcompositerotorcraftdrivelinesviamagneticbearings:theoryandexperiment.PhDdissertation.UniversityPark,Pennsylvania,USA:PennsylvaniaStateUniversity;2005.[3]SchweitzerG,TraxlerA,BleulerH.Magnetlager.Berlin:Springer-Verlag;1993[inGerman].[4]SchweitzerG,MaslenEH,editors.(Contributors:H.Bleuler,M.Cole,P.Keogh,R.Larsonneur,E.H.Maslen,R.Nordmann,Y.Okada,G.Schweitzer,A.Traxler.)Magneticbearings–theory,designandapplicationtorotatingmachinery.Springer-Verlag;2009.[5]KozaneckaD.Dynamicsoftheflexiblerotorwithanadditionalactivemagneticbearing,machinedynamicsproblems,vol.25,No.2.Warsaw,Poland;2001.p.21–38.[6]KozaneckaD,KozaneckiZ,LechT.Modellingthedynamicsofactivemagneticbearingactuators.In:Procworldmulticonferenceonsystemics,cyberneticsandinformatics,SCI2001,July22–25,vol.IX.IndustrialPartsI:USA;2001.p.232–235.[7]KozaneckaD,KozaneckiZ,LechT.Theoreticalandexperimentalinvestigationofdynamicsoftheflexiblerotorwithactivemagneticbearings.AdvVibEng2002;1(4):412–22.[8]KozaneckaD,KozaneckiZ,LechT,KaczmarekA.Identificationoftheexternalloadoftherotatingshaftsupportedinactivemagneticbearings.In:Proc´,December8–11,vol.II.2003.p.797–804.7thconferenceondynamicalsystemstheoryandapplications.Łódz[9]TheoryreferenceforANSYSandANSYSWorkbench11.0.ANSYSInc.:Canonsburg,USA;2007.Availablefrom:www.ansys.com.´skiJ.Modelingofmagneticfieldswiththefiniteelementmethodinmachinediagnosticsystems.SolidStatePhenom2009;147–149:155–60.[10]Łagodzin
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