英文资料.pdf

FIELDCHENHOISTTHEHEATTHETEMPERATUREC2112008ELSEVIERLTDALLRIGHTSRESERVEDISAPROCESSENERGYHOISTSITUATIONON13,6,10,11ISFIXEDTIONOFTEMPERATUREPERTURBATIONSINMULTIDISKCLUTCHESANDBRAKESDURINGOPERATIONNAJI12ESTABLISHEDONEDIMENSIONALMATHEMATICALMODELTODESCRIBETHETHERMALBEHAVIOROFABRAKESYSTEMYEVTUSHENKOANDIVANYK13DEDUCEDTHETRANSIENTTEMPERATUREFIELDFORANAXISYMMETRICALHEATCONDUCTIVITYPROBLEMWITH2DCOORDINATESITISDIFFICULTFORTHESEMODELSTOREFLECTTHEREALTEMPERATUREFIELDOFBRAKESHOEWITH3DGEOMETRY2THEORETICALANALYSIS21THEORETICALMODELFIG1SHOWSTHESCHEMATICOFHOISTSBRAKINGFRICTIONPAIRINORDERTOANALYZEBRAKESHOES3DTEMPERATUREFIELD,THECYLINDRICALCOORDINATESR,U,ZISADOPTEDTODESCRIBETHEGEOMETRICSTRUCTURESHOWNINFIG2,WHERERISTHEDISTANCEBETWEENAPOINTOFBRAKESHOEANDTHEROTATIONAXISOFBRAKEDISCUISTHECENTRALANGLEZCORRESPONDINGAUTHORTEL8613805209649FAX8651683590708APPLIEDTHERMALENGINEERING292009932937CONTENTSLISTSAVAILABLEEMAILADDRESSPENGYUXINGHOTMAILCOMYXPENGEMERGENCYBRAKING,SOTHEREISMOREINTENSETEMPERATURERISEINBRAKESHOETHEBRAKESHOEISKINDOFCOMPOSITEMATERIAL,ANDTHETEMPERATURERISERESULTINGFROMFRICTIONALHEATENERGYISTHEMOSTIMPORTANTFACTORAFFECTINGTRIBOLOGICALBEHAVIOROFBRAKESHOEANDTHEBRAKINGSAFETYPERFORMANCE510THEREFORE,ITISNECESSARYTOINVESTIGATETHEBRAKESHOESTEMPERATUREFIELDWITHRESPECTTOINVESTIGATINGBRAKEPADSCURRENTTHEORETICALMODELSOFBRAKESHOESTEMPERATUREFIELDAREBASEDONONEDIMENSIONORTWOAFFERRANTE11BUILTATWODIMENSIONAL2DMULTILAYEREDMODELTOESTIMATETHETRANSIENTEVOLUMETHODISANANALYTICSOLUTIONMETHOD,ITISDIFFICULTTOSOLVETHEEQUATIONOFHEATCONDUCTIONWITHCOMPLICATEDBOUNDARIESTHEREFORE,THEANALYTICSOLUTIONCALLEDINTEGRALTRANSFORMMETHODISADOPTED19,BECAUSEITISSUITABLEFORSOLVINGTHEPROBLEMOFNONHOMOGENEOUSTRANSIENTHEATCONDUCTIONINORDERTOMASTERTHECHANGERULESOFBRAKESHOESTEMPERATUREFIELDDURINGHOISTSEMERGENCYBRAKINGANDIMPROVETHESAFERELIABILITYOFBRAKING,A3DTRANSIENTTEMPERATUREFIELDOFTHEBRAKESHOEWASSTUDIEDBASEDONINTEGRALTRANSFORMMETHOD,ANDTHEVALIDITYISPROVEDBYNUMERICALSIMULATIONANDEXPERIMENTALRESEARCH1INTRODUCTIONTHEHOISTSEMERGENCYBRAKINGMECHANICALENERGYINTOFRICTIONALHEATEMERGENCYBRAKINGPROCESSOFMININGOFHIGHSPEEDANDHEAVYLOAD,ANDTHISINGCONDITIONOFVEHICLE,TRAINANDSOWORKFOCUSEDONTHEBRAKEPADSTEMPERATUREESPECIALLY,BECAUSETHEBRAKESHOE13594311/SEEFRONTMATTERC2112008ELSEVIERLTDALLDOI101016/JAPPLTHERMALENG200804022OFTRANSFORMINGOFBRAKEPAIRTHEHASTHECHARACTERISTICISWORSETHANBRAKTHEPREVIOUSFIELD14,10,12,13DURINGTHEPROCESSOFTHEMETHODSSOLVINGBRAKEPADS3DTRANSIENTTEMPERATUREFIELDCONCENTRATEDONFINITEELEMENTMETHOD13,1417,APPROXIMATEINTEGRATIONMETHOD4,18,GREENSFUNCTIONMETHOD12ANDLAPLACETRANSFORMATIONMETHOD9,13,ETCTHEFORMERTHREEMETHODSARENUMERICALSOLUTIONMETHODSANDAREOFLOWRELATIVEACCURACYFOREXAMPLE,FINITEELEMENTMETHODCANSOLVETHECOMPLICATEHEATCONDUCTIONPROBLEM,BUTTHEACCURACYOFCOMPUTATIONALSOLUTIONISRELATIVELYLOW,WHICHISAFFECTEDBYMESHDENSITY,STEPLENGTHANDSOONTHOUGHTHELAPLACETRANSFORMATIONINTEGRALTRANSFORMMETHODEMERGENCYBRAKINGWITHEXPERIMENTALDATA,THATTHE3DTRANSIENTTEMPERATUREFIELDMODELOFBRAKESHOEISVALIDANDPRACTICAL,ANDANALYTICSOLUTIONSOLVEDBYINTEGRALTRANSFORMMETHODISCORRECTTHREEDIMENSIONALTRANSIENTTEMPERATUREEMERGENCYBRAKINGZHENCAIZHU,YUXINGPENG,ZHIYUANSHI,GUOANCOLLEGEOFMECHANICALANDELECTRICALENGINEERING,CHINAUNIVERSITYOFMININGANDTECHNOLOGY,ARTICLEINFOARTICLEHISTORYRECEIVED22NOVEMBER2007ACCEPTED27APRIL2008AVAILABLEONLINE6MAY2008KEYWORDSBRAKESHOETHREEDIMENSIONALTRANSIENTTEMPERATUREFIELDABSTRACTINORDERTOEXACTLYMASTERBRAKING,THETHEORETICALMODELACCORDINGTOTHETHEORYOFOPERATINGCONDITIONOFMININGDEDUCEDBYADOPTINGINTEGRALTRANSFORMFIELDWERECARRIEDOUTANDENTWEREOBTAINEDATTHESAMEFORMEASURINGBRAKESHOESAPPLIEDTHERMALJOURNALHOMEPAGEWWWELSEVIRIGHTSRESERVEDOFBRAKESHOEDURINGHOISTSXUZHOU221116,CHINACHANGERULESOFBRAKESHOESTEMPERATUREFIELDDURINGHOISTSEMERGENCYOFTHREEDIMENSIONAL3DTRANSIENTTEMPERATUREFIELDWASESTABLISHEDCONDUCTION,THELAWOFENERGYTRANSFORMATIONANDDISTRIBUTION,ANDTHEHOISTSEMERGENCYBRAKINGANANALYTICSOLUTIONOFTEMPERATUREFIELDWASMETHODFURTHERMORE,SIMULATIONEXPERIMENTSOFTEMPERATUREVARIATIONREGULARITIESOFTEMPERATUREFIELDANDINTERNALTEMPERATUREGRADITIME,BYSIMULATINGHOISTSEMERGENCYBRAKINGCONDITION,THEEXPERIMENTSWEREALSOCONDUCTEDITISFOUND,BYCOMPARINGSIMULATIONRESULTSATSCIENCEDIRECTENGINEERINGERCOM/LOCATE/APTHERMENGISTHEDISTANCEBETWEENAPOINTOFBRAKESHOEANDTHEFRICTIONSURFACEASFORTHEGEOMETRICSTRUCTUREANDPARAMETERSSHOWNINFIG2,ITSSEENTHATA6R6B,06U6U0,06Z6LITISCLEARTHATTHEBRAKESHOESTEMPERATURETISTHEFUNCTIONOFTHECYLINDRICALCOORDINATESR,U,ZANDTHETIMETACCORDINGTOTHETHEORYOFHEATCONDUCTION,THEDIFFERENTIALEQUATIONOF3DTRANSIENTHEATCONDUCTIONISGAINEDASFOLLOWSO2TOR21ROTOR1R2O2TOU2O2TOZ21AOTOT1WHEREAISTHETHERMALDIFFUSIVITY,AK/QC1CKISTHETHERMALCONDUCTIVITYQISTHEDENSITYCISTHESPECIFICHEATCAPACITY22BOUNDARYCONDITION221HEATFLOWANDITSDISTRIBUTIONCOEFFICIENTITISDIFFICULTFORFRICTIONHEATGENERATEDDURINGEMERGENCYBRAKINGTOEMANATEINASHORTTIME,SOITISALMOSTTOTALLYABSORBEDBYBRAKEPAIRASTHEBRAKESHOEISFIXED,THETEMPERATUREOFTHEFRICTIONSURFACERISESMUCHSHARPLY,ANDTHISEVENTUALLYAFFECTSITSTRIBOLOGICALBEHAVIORMORESERIOUSLYINORDERTOMASTERTHEREALTEMPERATUREFIELDOFTHEBRAKESHOEDURINGEMERGENCYBRAKING,THEHEATFLOWANDITSDISTRIBUTIONCOEFFICIENTOFFRICTIONSURFACEMUSTBEDETERMINEDWITHACCURACYACCORDINGTOTHEOPERATINGCONDITIONOFEMERGENCYBRAKING,SUPPOSETHATTHEVELOCITYOFBRAKEDISCDECREASEDLINEARLYWITHTIME,THEHEATFLOWISOBTAINEDWITHTHEFORMQSRTKC1LC1PC1V0C11C0TT0KC1LC1PC1W0C1R1C0TT02WHEREQISTHEHEATFLOWOFFRICTIONSURFACEPISTHESPECIFICPRESSUREBETWEENBRAKEPAIRV0ANDW0ISTHEINITIALLINEARANDANGULARVELOCITYOFTHEBRAKEDISCLISTHEFRICTIONCOEFFICIENTBETWEENBRAKEPAIRT0ISTHEWHOLEBRAKINGTIME,KISTHEDISTRIBUTIONCOEFFICIENTOFHEATFLOWSUPPOSETHEFRICTIONALHEATISTOTALLYTRANSFERREDTOTHEBRAKESHOEANDBRAKEDISK,ANDTHEDISTRIBUTIONCOEFFICIENTOFHEATFLOWISOBTAINEDACCORDINGTOTHEANALYSISOFONEDIMENSIONALHEATCONDUCTIONFIG3SHOWSTHECONTACTSCHEMATICOFTWOHALFPLANESUNDERTHECONDITIONOFONEDIMENSIONALTRANSIENTHEATCONDUCTION,THETEMPERATURERISEOFFRICTIONSURFACEZ0ISOBTAINEDWITHTHEFORMDTQKPP4ATPQPQCKP4TP3WHEREQISTHEHEATFLOWABSORBEDBYHALFPLANEANDTHEHEATFLOWISGAINEDFROMEQ3PPRESPECTIVELYACCORDINGTOEQ5,THEDISTRIBUTIONCOEFFICIENTOFZCZHUETAL/APPLIEDTHERMALENGINEERING292009932937933FIG1SCHEMATICOFHOISTSBRAKINGFRICTIONPAIRFIG23DGEOMETRICALMODELOFBRAKESHOEHEATFLOWENTERINGBRAKESHOEISOBTAINEDWITHTHEFORMKQSQAQSQSQD1C0QDQSQD1C01QSQD11C011QSCSKSQDCDKDC16C17126222COEFFICIENTOFCONVECTIVEHEATTRANSFERONTHEBOUNDARYWITHREGARDTOTHELATERALSURFACEANDTHETOPSURFACEOFTHEBRAKESHOE,THEIRCOEFFICIENTSOFCONVECTIVEHEATTRANSFERAREOBTAINED,RESPECTIVELY,ACCORDINGTOTHENATURALHEATCONVECTIONBOUNDARYCONDITIONOFUPRIGHTPLATEANDHORIZONTALPLATEHL142DTLLL147AHU059DTULU147BQPQCKDT4T4SUPPOSETHETWOHALFPLANESHASTHESAMETEMPERATURERISEONTHEFRICTIONSURFACE,ANDTHENTHERATIOOFHEATFLOWENTERINGTHETWOHALFPLANESISGIVENASQSQDPQSCSKSPDT4TPPQDCDKDPDT4TPQSCSKSPQDCDKDP5WHERETHESUBSCRIPTSANDDMEANTHEBRAKESHOEANDBRAKEDISC,FIG3CONTACTSCHEMATICOFTWOHALFPLANESENGINEERINGWHERETHESUBSCRIPTLANDUREPRESENTTHELATERALSURFACEANDTHETOPSURFACE,RESPECTIVELYHISTHECOEFFICIENTOFCONVECTIVEHEATTRANSFERONTHEBOUNDARY,DTISTHETEMPERATUREDIFFERENCEBETWEENTHEBOUNDARYANDTHEAMBIENT,LISTHESHORTERDIMENSIONOFTHEBOUNDARY223INITIALANDBOUNDARYCONDITIONCONTACTSURFACEBETWEENBRAKESHOEANDBRAKEDISCISSUBJECTEDTOCONTINUOUSHEATFLOWQSDURINGEMERGENCYBRAKINGPROCESSBRAKESHOESBOUNDARIESAREOFNATURALCONVECTIONWITHTHEAIRTHEBOUNDARYANDINITIALCONDITIONCANBEREPRESENTEDBYC0KOTORH1TH1T0F1TRATP006U6U006Z6L8AKOTORH2TH2T0F2TRBTP006U6U006Z6L8BC0KOTOZH3TQSH3T0F3TZ0TP006U6U0A6R6B8CKOTOZH4TH4T0F4TZLTP006U6U0A6R6B8DC0K1ROTOUH5TH5T0F5TU0TP006Z6LA6R6B8EK1ROTOUH6TH6T0F6TUU0TP006Z6LA6R6B8FTRUZTT0T0A6R6B06U6U006Z6L8GWHERET0ISTHEINITIALTEMPERATUREOFTHEBRAKESHOEATT023INTEGRALTRANSFORMSOLVINGMETHODINTEGRALTRANSFORMMETHODHASTWOSTEPSFORSOLVINGTHEPROBLEMFIRSTLY,ONLYBYMAKINGSUITABLEINTEGRALTRANSFORMFORSPACEVARIABLE,THEORIGINALEQUATIONOFHEATCONDUCTIONCOULDBESIMPLIFIEDASTHEORDINARYDIFFERENTIALEQUATIONWITHREGARDTOTHETIMEVARIABLETTHEN,BYTAKINGINVERSETRANSFORMWITHREGARDTOTHESOLUTIONOFTHEORDINARYDIFFERENTIALEQUATION,THEANALYTICSOLUTIONOFTHETEMPERATUREFIELDWITHREGARDTOTHESPACEANDTIMEVARIABLESCOULDBEOBTAINEDINTEGRALTRANSFORMMETHODISAPPLIEDTOSOLVEEQ1WITHBOUNDARYCONDITIONEQ8BYINTEGRALTRANSFORMWITHREGARDTOTHESPACEVARIABLESZ,U,RINTURN,THEIRPARTIALDIFFERENTIALCOULDBEELIMINATED”WRITINGFORMULASTOREPRESENTTHEOPERATIONOFTAKINGTHEINVERSETRANSFORMANDTHEINTEGRALTRANSFORMWITHREGARDTOZ,THESEAREDEFINEDBYTRUZTX1M1ZBMZNBMTRUBMT9TRUBMTZL0ZBMZ0C1TRUZ0TDZ010934ZCZHUETAL/APPLIEDTHERMALWHERETRUBMTISTHEINTEGRALTRANSFORMOFTR,U,Z,TWITHREGARDTOZZBM,ZISTHECHARACTERISTICFUNCTION,ZBM,ZCOSBMLC0ZBMISTHECHARACTERISTICVALUE,BMTANBMLH3,ANDH3H3KNBMISTHENORM,1NBM2B2MH23LB2MH23H3SUBMITEQ10INTOEQS1AND8,THEFOLLOWINGEQUATIONSISOBTAINEDO2TOR21ROTOR1R2O2TOU2F3KCOSLC1BMC0B2MC1TRUBMT1AOTRUBMTOT11AC0KOTORH1TC22F1TRATP006U6U011BKOTORH2TC22F2TRBTP006U6U011CC0K1ROTOUH5TC22F5TU0TP0A6R6B11DK1ROTOUH6TC22F6TUU0TP0A6R6B11ETRUBMTZL0ZBMZ0C1T0DZ0T0A6R6B06U6U011FINTHESAMEWAY,THEINVERSETRANSFORMANDTHEINTEGRALTRANSFORMWITHREGARDTOUANDRAREDEFINEDBYTRUBMTX1N1UVNUNVNETRVNBMT12ETRVNBMTZU00U0C1UVNU0C1TRU0BMTDU013WHEREETRVNBMTISTHEINTEGRALTRANSFORMOFTRUBMTWITHREGARDTOUUVN,UISTHECHARACTERISTICFUNCTION,UVN,UVNC1COSVNUH5C1SINVNUVNISTHECHARACTERISTICVALUE,TANVNU0VNH5H6V2NC0H5H6H5H5KH6H6KNVNISTHENORM,1NVN2V2NH25C1U0H6V2NH26C16C17H5HIC01ETRVNBMTX1I1RVCIRNCIETVCIVNBMT14ETVCIVNBMTZBARVCIR0C1ETR0VNBMTDR015WHEREETVCIVNBMTISTHEINTEGRALTRANSFORMOFETRVNBMTWITHREGARDTORRVCI,RISTHECHARACTERISTICFUNCTION,RVCI,RSVC1JVCIC1RC0VVC1YVCIC1R,JVCIC1RANDYVCIC1RARETHEBESSELFUNCTIONSOFTHEFIRSTANDSECONDKINDWITHORDERV,WHERESVCIC1Y0VCIC1BH2C1YVCIC1BUVCIC1J0VCIC1AC0H1C1JVCIC1AVVCIC1J0VCIC1BH2C1JVCIC1BWVCIC1Y0VCIC1AC0H1C1YVCIC1ACIISTHECHARACTERISTICVALUEWHICHSATISFIESTHEEQUATIONUVC1SVC0WVC1VV0NCIISTHENORM,1NCIP22C2IU2VB2C1U2VC0B1C1V2V,WHEREB1H21C2I1C0VCIA2C138ANDB2H22C2I1C0VCIB2C138FINALLY,ACCORDINGTOTHEABOVEINTEGRALTRANSFORM,EQS1AND8CANBESIMPLIFIEDASFOLLOWSDETVDTAB2MC2IETVACIVNBMTT016AVV292009932937ETCIVNBMTET0T016BWHEREACI,VN,BM,TG1G2G3,G1AC1BC1RVCIBKC1EC22F2AC1RVCIAKC1EC22F1C18C19G2ZBAVKC1C22F5C1R2C1RVCIRDRZBAVC1COSVNU0H5C1SINVNU0KC1C22F6C1R2C1RVCIRDRG3ZBAF3KC1COSLC1BMC1SINVNBMH5V1C0COSVNBMC20C21C1RC1RVCIRDRTHESOLUTIONETVCIVNBMTCANBEGAINEDBYSOLVINGTHEEQ16BYTAKINGTHEINVERSETRANSFORMWITHREGARDTOETVCIVNBMTACCORDINGTOEQS9,12AND14,THEANALYTICSOLUTIONOFBRAKESHOES3DTRANSIENTTEMPERATUREFIELDISOBTAINEDTRUZTX1M1X1N1X1I1ZBMZNBMUVNUNVNRVCIRNCIEC0AB2MC2ITC1ETV0ZT0EC0AB2MT0ACIVNBMTDT0243517FIELDISCARRIEDOUTWITHT0723STHECHANGERULESOFTEMPERATUREFIELDANDINTERNALTEMPERATUREGRADIENTAREANALYZEDWHATSSHOWNINFIGS59AREPARTIALSIMULATIONRESULTSWHATISSHOWNINFIG5ISBRAKESHOES3DTEMPERATUREFIELDWHENTIMEIS723SITISSEENFROMFIG5THATTHEHIGHESTTEMPERATUREOFTHEBRAKESHOEIS396534KAFTERBRAKING,ANDITSLOWESTTEMPERATUREIS293KANDTHEHEATENERGYISMAINLYCONCENTRATEDFIG53DTEMPERATUREFIELDOFBRAKESHOET723SFIG6THECHANGEOFTEMPERATUREONFRICTIONSURFACEWITHTIMETZCZHUETAL/APPLIEDTHERMALENGINEERING292009932937935FIG4HALFSECTIONVIEWOFBRAKESHOESSAMPLETABLE1BASICPARAMETERSOFBRAKEPAIRANDTHEEMERGENCYBRAKINGCONDITIONQKGMC03CJKGC01KC01KWMC01KC01T0KV0MSC01PMPAL3SIMULATIONANDEXPERIMENTFIG4SHOWSTHEHALFSECTIONVIEWOFBRAKESHOESAMPLELINECANDDARETHECENTERLINEANDBOTTOMLINEOFTHECROSSSECTION,RESPECTIVELYTHESAMPLEDIMENSIONISA1375MM,B1625MM,U01/6RAD,L6MMTHEMATERIALOFBRAKESHOEANDBRAKEDISCAREASBESTOSFREEAND16MN,RESPECTIVELYTHEIRPARAMETERSANDTHECONDITIONOFEMERGENCYBRAKINGARESHOWNINTABLE1SUPPOSETHATTHEFRICTIONCOEFFICIENTANDTHESPECIFICPRESSUREARECONSTANTDURINGEMERGENCYBRAKINGPROCESSBASEDONTHEABOVEANALYTICMODEL,SIMULATIONOFBRAKESHOES3DTEMPERATUREBRAKESHOE2206253002952931013804BRAKEDISC7866473532125158FIG7THECHANGEOFTEMPERATUREONLINEDWITHTIMETCREASESALLTHETIMEWHENZP00006MONCETHEZISUPTO0002M,THEDIFFERENCEINTEMPERATUREDURINGBRAKEISLESSTHAN3KITINDICATESTHATTHEHEATENERGYFOCUSESONTHETHERMALEFFECTLAYER,ANDITSTHICKNESSISABOUT0002MINORDERTOPROVETHEANALYTICMODEL,EXPERIMENTSWERECARRIEDOUTONTHEFRICTIONTESTERINFIG10THEEXPERIMENTALPRINCIPLEISASFOLLOWSWHENTHEBRAKEBEGINS,TWOBRAKESHOESAREPUSHEDTOBRAKETHEDISCWITHCERTAINPRESSUREPANDTHETEMPERATUREOFPOINTEONTHEFRICTIONSURFACEISMEASUREDBYTHERMOCOUPLEBECAUSETHESPECIMENTHICKNESSISTOOTHINANDTHESTRUCTUREOFTHEFRICTIONTESTERISLIMITED,ITISDIFFICULTTOFIXTHETHERMOCOUPLEINTHEBRAKESHOETHEREFORE,THETHERMOCOUPLEISFIXEDDIRECTLYONTHEBRAKEDISCWHICHISCLOSEDTOPOINTESHOWNINFIG10FIG11SHOWSTHETEMPERATURESCHANGERULESATPOINTEUNDERTWOSITUATIONSOFEMERGENCYBRAKINGFROMFIG11,ITISOBSERVEDTHATTHETEMPERATUREATPOINTEINATFIRST,THENDECREASESTHEHIGHESTTEMPERATUREBYSIMULAISLOWERTHANANDALSOLAGSBEHINDTHEEXPERIMENTALDATAIN11A,THESIMULATIONTEMPERATUREREACHESTHEMAXIMUMKAT36SWHILETHEEXPERIMENTALDATACOMESUPTOTHE43565KAT38SINFIG11B,THESIMULATIONRESULTTHEMAXIMUM46955KAT45SWHILETHEEXPERIMENTALCOMESUPTO47968KAT5SITISSEENFROMFIG11,THETEMPERMEASUREDBYEXPERIMENTISLOWERTHANSIMULATIONRESULTSATENGINEERING292009932937FIG8THECHANGEOFTEMPERATUREGRADIENTONLINECWITHTIMET936ZCZHUETAL/APPLIEDTHERMALONTHELAYEROFFRICTIONSURFACENAMEDTHERMALEFFECTLAYER,WHICHINDICATESTHETHERMALDIFFUSIBILITYOFTHEBRAKESHOEISPOORINORDERTOMATERTHETEMPERATURECHANGERULESOFFRICTIONSURFACEDURINGEMERGENCYBRAKINGPROCESS,THEVARIATIONOFFRICTIONSURFACESTEMPERATUREWITHTIMETISSIMULATEDWHATISSHOWNINFIG6REVEALSTHATTHETEMPERATUREOFFRICTIONSURFACEINCREASESFIRSTLY,THENDECREASESTHISISBECAUSETHATTHESPEEDOFBRAKEDISCISHIGHINTHEBEGINNINGANDTHISRESULTSINLARGEHEATFLOWWHILETHECOEFFICIENTOFCONVECTIVEHEATTRANSFERISLOWONTHEBOUNDARYATTHEMOMENT,SOTHETEMPERATUREINCREASESATTHELATESTAGEOFBRAKETHEHEATFLOWDECREASESWITHTHESPEEDWHILETHECOEFFICIENTOFCONVECTIVEHEATTRANSFERISHIGHDUETOLARGEDIFFERENCEINTEMPERATUREONTHEBOUNDARY,WHICHLEADSTODECREASINGINTEMPERATUREFIGS6AND7REFLECTTHETEMPERATURECHANGERULESINTHERADIALDIMENSIONTHETEMPERATUREATTHEOUTSIDEOFBRAKESHOEISHIGHERTHANTHATINSIDE,ANDTHEOUTSIDETEMPERATURECHANGESMOREGREATLYFIG8DEMONSTRATESTHECHANGERULESOFTHETEMPERATUREGRADIENTALONGTHEDIRECTIONZTHEHIGHESTTEMPERATUREGRADIENTOFTHEFRICTIONLAYERISUPTO3739C2105K/MANDDECREASESSHARPLYALONGTHEDIRECTIONZTHELOWESTVALUEISONLY4597C210C011K/MINTHEBEGINNINGTHETEMPERATUREGRADIENTOFTHERMALEFFECTLAYERISTHEHIGHESTWHILETHETEMPERATUREISCLOSETOTHESURROUNDINGTEMPERATUREASTHEBRAKEGOESON,THETEMPERATUREGRADIENTDECREASESGRADUALLYUNTILTHEENDFIG9SHOWSTHECHANGEOFTEMPERATUREATDIFFERENTDEPTHONTHELINECWITHTIMETTHETEMPERATUREDECREASESSHARPLYWITHTHEINCREASINGZ,ANDTHEBOUNDARYCONDITIONHASLITTERINFLUENCEONTHEINNERTEMPERATURETHETEMPERATUREINTHENITINVERSESTHISISBECAUSETHETHERMOCOUPLEITSELFABHEATENERGYFROMTHEBRAKESHOEINTHEBEGINNING,THENRETOTHEBRAKESHOEWHENTHETEMPERATUREDECREASESONBETWEENTHEEXPERIMENTALDATAANDTHESIMULATIONREINDICATESTHATTHESIMULATIONSHOWSGOODAGREEMENTWITHTHENT,ANDTHEERRORSOFTHEIRHIGHESTTEMPERATUREARE199FIG9THECHANGEOFTEMPERATUREATDIFFERENTDEPTHONTHELINECWITHTIMETFIG10SCHEMATICOFFRICTIONTESTERCREASESTIONFIG42714MAXIMUMREACHESDATAATUREFIRST,SORBSLEASESCOMPARISSULTSEXPERIMEFIG11ATEMPERATURESCHANGERULESATPOINTEWITHTIMETP138MPA,V010M/SBEGINNINGTHETEMPERATUREGRADIENTOFTHERMALEFFECTLAYERCHANGERULESOFBRAKESHOES3DTRANSIENTTEMPERATUREFIELDDURINGEMERGENCYBRAKINGACKNOWLEDGEMENTSTHISPROJECTISSUPPORTEDBYTHEKEYPROJECTOFCHINESEMINISTRYOFEDUCATIONGRANTNO107054ANDPROGRAMFORNEWCENTURYEXCELLENTTALENTSINUNIVERSITYGRANTNONCET040488ZCZHUETAL/APPLIEDTHERMALENGINEERING292009932937937WASTHEHIGHEST,THETEMPERATUREINCREASEDSWIFTLYASTHEBRAKINGPROCESSGOINGON,THETEMPERATUREGRADIENTDECREASEDWHILETHETEMPERATUREINCREASEDTHEBOUNDARYAND216,RESPECTIVELYITINDICATESTHATTHEANALYTICSOLUTIONOF3DTRANSIENTTEMPERATUREFIELDISCORRECT4CONCLUSION1THETHEORETICALMODELOF3DTRANSIENTTEMPERATUREFIELDWASESTABLISHEDACCORDINGTOTHETHEORYOFHEATCONDUCTIONANDTHEEMERGENCYBRAKINGCONDITIONOFMININGHOISTTHEINTEGRALTRANSFORMMETHODWASAPPLIEDTOSOLVETHETHEORETICALMODEL,ANDTHEANALYTICSOLUTIONOFTEMPERATUREFIELDWASDEDUCEDITINDICATESTHATINTEGRALTRANSFORMMETHODISEFFECTIVETOSOLVETHEPROBLEMOF3DTRANSIENTTEMPERATUREFIELDWITHREGARDTOCYLINDRICALCOORDINATES2BASEDONTHEANALYTICSOLUTIONOFTHETHEORETICALMODEL,THENUMERICALANALYSISWASADOPTEDTOSIMULATETHECHANGERULESOFTEMPERATUREDISTRIBUTIONUNDERTHEEMERGENCYBRAKINGCONDITIONSIMULATIONRESULTSSHOWEDTHETEMPERATUREOFFRICTIONSURFACEINCREASEDFIRSTLYANDTHENDECREASEDINTHEFIG11BTEMPERATURESCHANGERULESATPOINTEWITHTIMETP158MPA,V0125M/SCONDITIONHADLITTERINFLUENCEONTHEINTERNALTEMPERATURERISETHEHEATENERGYWASCONCENTRATEDONTHETHERMALEFFECTLAYERANDITSTHICKNESSISABOUT2MM3THEEXPERIMENTALDATAHASGOODAGREEMENTWITHTHESIMULATIONRESULTS,ANDTHEERRORSOFTHEIRHIGHESTTEMPERATUREAREABOUT2,WHICHPROVETHECORRECTNESSOFTHEINTEGRALTRANSFORMMETHODSOLVINGTHETHEORETICALMODELOF3DTRANSIENTTEMPERATUREFIELDTHEANALYTICALMODELCANREFLECTTHEREFERENCES1YYANG,JMZHOU,NUMERICALSIMULATIONSTUDYOF3DTHERMALSTRESSFIELDWITHCOMPLEXBOUNDARY,JOURNALOFENGINEERINGTHERMOPHYSICS27320074874892LLI,JSONG,ZYGUO,STUDYONFASTFINITEELEMENTSIMULATIONMODELOFTHERMALANALYSISOFVEHICLEBRAKE,JOURNALOFSYSTEMSIMULATION171220052869287228773CHGAO,XZLIN,TRANSIENTTEMPERATUREFIELDANALYSISOFABRAKEINANONAXISYMMETRICTHREEDIMENSIONALMODEL,JOURNALOFMATERIALSPROCESSINGTECHNOLOGY1291320025135174JYLI,JRBARBER,SOLUTIONOFTRANSIENTTHERMOELASTICCONTACTPROBLEMSBYTHEFASTSPEEDEXPANSIONMETHOD,WEAR2653420084024105ZYSHI,ZCZHU,GACHEN,EXPERIMENTALSTUDYONFRICTIONBEHAVIORSOFBRAKESHOESMATERIALSFORHOISTWINDERDISCBRAKES,LUBRICATIONENGINEERING12200