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中英文翻译在全接触条件下盘式制动器摩擦激发瞬态热弹性不稳定的研究.doc中英文翻译在全接触条件下盘式制动器摩擦激发瞬态热弹性不稳定的研究.doc

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编号:201311171034015449    类型:共享资源    大小:457.00KB    格式:DOC    上传时间:2013-11-17
  
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Frictionallyexcitedthermoelasticinstabilityindiscbrakes—TransientprobleminthefullcontactregimeAbstractExceedingthecriticalslidingvelocityindiscbrakescancauseunwantedformingofhotspots,non-uniformdistributionofcontactpressure,vibration,andalso,inmanycases,permanentdamageofthedisc.Consequently,inthelastdecade,agreatdealofconsiderationhasbeengiventomodelingmethodsofthermoelasticinstability(TEI),whichleadstotheseeffects.Modelsbasedonthefiniteelementmethodarealsobeingdevelopedinadditiontotheanalyticalapproach.TheanalyticalmodelofTEIdevelopmentdescribedinthepaperbyLeeandBarber[Frictionallyexcitedthermoelasticinstabilityinautomotivediskbrakes.ASMEJournalofTribology1993;115:607–14]hasbeenexpandedinthepresentedwork.Specificattentionwasgiventothemodificationoftheirmodel,tocatchthefactthatthearclengthofpadsislessthanthecircumferenceofthedisc,andtothedevelopmentoftemperatureperturbationamplitudeintheearlystageofbreaking,whenpadsareinthefullcontactwiththedisc.Awayisproposedhowtotakeintoaccountbothoftheinitialnon-flatnessofthediscfrictionsurfaceandchangeoftheperturbationshapeinsidethediscinthecourseofbraking.Keywords:Thermoelasticinstability;TEI;Discbrake;Hotspots1.IntroductionFormationofhotspotsaswellasnon-uniformdistributionofthecontactpressureisanunwantedeffectemergingindiscbrakesinthecourseofbrakingorduringengagementofatransmissionclutch.Iftheslidingvelocityishighenough,thiseffectcanbecomeunstableandcanresultindiscmaterialdamage,frictionalvibration,wear,etc.Therefore,alotofexperimentaleffortisbeingspenttounderstandbetterthiseffect(cf.Refs.)ortomodelitinthemostfeasiblefashion.Barberdescribedthethermoelasticinstability(TEI)asthecauseofthephenomenon.LaterDowandBurtonandBurtonetal.introducedamathematicalmodeltoestablishcriticalslidingvelocityforinstability,wheretwothermoelastichalf-planesareconsideredincontactalongtheircommoninterface.ItisinaworkbyLeeandBarberthattheeffectofthethicknesswasconsideredandthatamodelapplicablefordiscbrakeswasproposed.LeeandBarber’smodelismadeupwithametalliclayerslidingbetweentwohalf-planesoffrictionalmaterial.OnlyrecentlyaparametricanalysisofTEIindiscbrakeswasmadeorTEIinmulti-discclutchesandbrakeswasmodeled.TheevolutionofhotspotsamplitudeshasbeenaddressedinRefs.Usinganalyticalapproachortheeffectofintermittentcontactwasconsidered.Finally,thefiniteelementmethodwasalsoappliedtorendertheonsetofTEI(seeRef.).Theanalysisofnonlineartransientbehaviorinthemode,whenseparatedcontactregionsoccur,isevenaccomplishedinRef.Asinthecaseofotherengineeringproblemsofinstability,itturnsoutthatamoreaccuratepredictionbymathematicalmodelingisoftenquestionable.Thisismainlyimpartedbyneglectingvariousimperfectionsandrandomfluctuationsorbytheimpossibilitytodescribeallpossibleinfluencesappropriately.Therefore,someeffortarousedtointerpretresultsofcertainexperimentsinadditiontoclassicalTEI(see,e.g.Ref).ThispaperisrelatedtotheworkbyLeeandBarber[7].Usingananalyticalapproach,ittreatstheinceptionofTEIandthedevelopmentofhotspotsduringthefullcontactregimeinthediscbrakes.ThemodelproposedinSection2enablestocoverfinitethicknessofbothfrictionpadsandtheribbedportionofthedisc.Section3isdevotedtotheproblemsofmodelingofpartialdiscsurfacecontactwiththepads.Section4introducesthetermof‘‘thermalcapacityofperturbation’’emphasizingitsassociationwiththevalueofgrowthrate,ortheslidingvelocitymagnitude.Ananalysisofthediscfrictionsurfacesnon-flatnessanditsinfluenceoninitialamplitudeofperturbationsisputforwardintheSection5.Finally,theSection6offersamodeloftemperatureperturbationdevelopmentinitiatedbythementionedinitialdiscnon-flatnessinthecourseofbraking.Themodelbeinginuseherecomesfromadifferentialequationthatcoversthevariationofthe‘‘thermalcapacity’’duringthefullcontactregimeofthebraking.2.ElaborationofLeeandBarbermodelThebrakediscisrepresentedbythreelayers.Themiddleoneofthickness2a3standsfortheribbedportionofthediscwithfullsidewallsofthicknessa2connectedtoit.Thepadsarerepresentedbylayersofthicknessa1,whichareimmovableandpressedtoeachotherbyauniformpressurep.ThebrakediscslipsinbetweenthesepadsataconstantvelocityV.WewillinvestigatetheconditionsunderwhichaspatiallysinusoidalperturbationinthetemperatureandstressfieldscangrowexponentiallywithrespecttothetimeinasimilarmannertothatadoptedbyLeeandBarber.Itisevidencedintheirwork[7]thatitissufficienttohandleonlytheantisymmetricproblem.TheperturbationsthataresymmetricwithrespecttothemidplaneofthedisccangrowatavelocitywellabovetheslidingvelocityVthusbeingmadeuninteresting.Letusintroduceacoordinatesystem(x1;y1)fixedtooneofthepads(seeFig.1)thepointsofcontactsurfacebetweenthepadanddischavingy1=0.Furthermore,letacoordinatesystem(x2;y2)befixedtothediscwithy2=0forthepointsofthemidplane.Wesupposetheperturbationtohavearelativevelocityciwithrespecttothelayeri,andthecoordinatesystem(x;y)tomovetogetherwiththeperturbatedfield.ThenwecanwriteV=c1-c2;c2=c3;x=x1-c1t=x2-c2t,x2=x3;y=y2=y3=y1+a2+a3.Wewillsearchtheperturbationoftheuniformtemperaturefieldintheformandtheperturbationofthecontactpressureintheformwheretisthetime,bdenotesagrowthrate,subscriptIreferstoalayerinthemodel,andj=-1½istheimaginaryunit.Theparameterm=m(n)=2pin/cir=2pi/L,wherenisthenumberofhotspotsonthecircumferenceofthedisccirandLiswavelengthofperturbations.ThesymbolsT0mandp0mintheaboveformulaedenotetheamplitudesofinitialnon-uniformities(e.g.fluctuations).Bothperturbations(2)and(3)willbesearchedascomplexfunctionstheirrealpartdescribingtheactualperturbationoftemperatureorpressurefield.Obviously,ifthegrowthrateb<0,theinitialfluctuationsaredamped.Ontheotherhand,instabilitydevelopsifB〉0.2.1.TemperaturefieldperturbationHeatfluxinthedirectionofthex-axisiszerowhentheribbedportionofthediscisconsidered.Next,letusdenoteki=Ki/Qicpicoefficientofthelayeritemperaturediffusion.ParametersKi,Qi,cpiare,respectively,thethermalconductivity,densityandspecificheatofthematerialfori=1,2.Theyhavebeenre-calculatedtotheentirevolumeofthelayer(i=3)whentheribbedportionofthediscisconsidered.TheperturbationofthetemperaturefieldisthesolutionoftheequationsWithanditwillmeetthefollowingconditions:1,Thelayers1and2willhavethesametemperatureatthecontactsurface2,Thelayers2and3willreachthesametemperatureandthesameheatfluxinthedirectiony,3,AntisymmetricconditionatthemidplaneTheperturbationswillbezeroattheexternalsurfaceofafrictionpad(If,instead,zeroheatfluxthroughexternalsurfacehasbeenspecified,weobtainpracticallyidenticalnumericalsolutionforcurrentpads).Ifwewritethetemperaturedevelopmentinindividuallayersinasuitableformweobtainwhereand2.2.ThermoelasticstressesanddisplacementsForthesakeofsimplicity,letusconsidertheribbedportionofthedisctobeisotropicenvironmentwithcorrectedmodulusofelasticitythough,actually,thestiffnessofthislayerinthedirectionxdiffersfromthatinthedirectiony.Suchsimplificationis,however,admissibleastheyieldingcentrallayer3practicallydoesnottakeeffectonthediscflexuralrigidityunlikefullsidewalls(layer2).Givenathermalfieldperturbation,wecanexpressthestressstateanddisplacementscausedbythisperturbationforanylayer.Thethermoelasticproblemcanbesolvedbysuperimposingaparticularsolutiononthegeneralisothermalsolution.Welookfor
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