A STUDY ON THE SQUEAL OF A DRUM BRAKE WHICH

JournalofSoundandibration(2001)240(5),789}808doi:10.1006/jsvi.2000.3195,availableonlineat:[e-mail]¹urboandPowerMachineryResearchCenter(¹PMRC),SeoulNational;niversity,San56-1,Shinrim-dong,Kwanak-ku,Seoul151-742.Korea,E-mail:[e-mail]chineryandDesign,SeoulNational;niversity,San56-1,Shinrim-dong,Kwanak-ku,Seoul151-742,KoreaANDC.G.AHNResearchInstituteofEngineeringScience,SeoulNational;niversity,San56-1,Shinrim-dong,Kwanak-ku,Seoul151-742,Korea(Received19October1999,andin,nalform25April2000)Astabilityanalysisofadrumbrake,whichhasshoesofnon-uniformcross-section,isperformedtondasimpleande!ectivemethodofreducingthesquealofthedrumbrakebypartiallychangingtheshapesoftheshoes.Thesquealisconsideredasanoiseinducedbytheself-excitedvibrationofthedrumbrakewhichmakesthebrakeunstable.Shoesofnon-uniformcross-sectionareoftenusedforthedrumbrakeofcurrentpassengercarstoreducethesqueal.However,thein#uenceofthisnon-uniformityuponthesquealhasnotbeenanalyzedtheoretically.Inthisstudy,thedrumandtheshoesareassumedasauniformringandnon-uniformarches,respectively,formodellingthebrake.Forareasonablemethodofmodelling,thevibrationcharacteristicsofthebrakeandtheirrelationstothesquealarediscussedbasedontheresultsofmodaltests.Thein#uencesofbrakedesignparametersuponthesquealareinvestigated,andaminorchangeofthecross-sectionisproposedtoreducethesqueal.Thee!ectoftheminorchangeisveriedthroughnoisedynamometertests.Inaddition,thee!ectofasymmetryofthedrum,whichcanbebuiltbymassaddition,ispresented.(2001AcademicPress1.INTRODUCTIONSquealisasignicantnoiseproblemoccurringinvehiclebrakingsystems,masstransitsystems,etc.Kootwijk-Damman[1]andNakaietal.[2]havebeeninvestigatedrailwaywheelsquealofmasstransitsystems,andMcMillan[3]hasdevelopedanon-linearfrictionmodelfortheunderstandingofthephenomenonofrailwaywheelsqueal.Manystudiesonthesquealofvehiclebrakingsystemshavealsobeenperformedsincethe1920s.Earlierstudiesonthebrakesquealfocusedon&&stick}slip''causedbythecoe$cientofstaticfriction,higherthanthatofdynamicfriction.Subsequently,negativefriction}velocity0022-460X/01/100789#20$35.00/0(2001AcademicPressslopeaswellas&&sprag-slip''phenomenonwasconsideredasareasonofthesqueal[4}8].Millnerintroducedanideathatthesquealisaphenomenonofdynamicinstabilitycausedbythecouplinge!ectsbetweenbrakecomponents;thecouplinge!ectsarebuiltbythefrictionalforcevariationsduetothevariationinnormalforcesbetweenthebrakecomponents[9].Heproposedanewtheoreticalmodelofadrumbrake,andOkamuraetal.improvedhismodeltorepresentarealdrumbrakeinmoredetail[10].ThestudyonthesquealhasbeencontinuedbyLangetal,Chenetal.,Zhuetal.,HulteHnandsoforth[11}17].HulteHnproposedamodelofadrumbrakeinwhichthedrumandtheshoeswereassumedtobedistributedmass-springsystems.Inthesestudies,thesquealofdrumbrakeswhichhaveshoesofuniformcross-sectionhasbeeninvestigated.Shoesofnon-uniformcross-sectionareoftenusedforthedrumbrakeofrecentpassengercarstoreducethesqueal.Thenon-uniformcross-sectionisbuiltbychangingtheshapesoftheshoespartially,andthisminorchangeisasimpleande!ectivemethodtoreducethesqueal.Howeverthemethodofchangingtheshapeshasnotasyetbeenanalyzedtheoretically,butdeterminedthroughperceptionandexperiment.Thispaperdealswithatheoreticalanalysisforthesquealofadrumbrakewhichhastheshoesofnon-uniformcross-section.Aminorchangeoftheshoe'scross-sectionwillbeproposedtoreducethesqueal,andthee!ectofthechangewillbeveriedthroughnoisedynamometertests.Inaddition,thee!ectofmassadditiontothedrum,whichwasinvestigatedbyLangetal.[18]throughasimplebinary#uttermodel,willbepresented.2.EXPERIMENTALINVESTIGATIONFORTHEDYNAMICCHARACTERISTICSOFTHEDRUMBRAKEThesquealwasmonitoredduringdrivetestsofapassengercarandmeasuredtohavefrequenciesof3)1and5)1kHz;the3)1kHzsquealwillbemainlydealtwithinthispaper.Thesquealisacomplexphenomenoncausedbythedynamicbehaviorofthebrakepartsandfrictionmechanism.Inthissection,thee!ectsofthedynamiccharacteristicsofthedrumandtheshoesaretobediscussed.Modaltestswereperformedtoinvestigatethedynamiccharacteristics.Fromtheresultsofthemodaltests,itwasfoundthatthedynamiccharacteristicsofthebrakepartsvaryastheyareassembledandthebrakepressureisapplied.Therefore,theexperimentalinvestigationswillbefocusedonthecomparisonofthebrakepartsinfreelysupportedconditionwiththebrakeassemblytowhichthebrakepressureisapplied.2.1.DYNAMICCHARACTERISTICSOFTHEBRAKEPARTSThemodalparametersofthedrumandtheshoe,notassembledtogether,wereestimatedthroughthemodaltests.Figure1isthephotoofthedrumandtheshoeusedinthisstudy,andthepointsofFRFacquisitionduringthemodaltestsareshown.Theshoeconsistsofthewebandtherim;thewebisattachedtotherimtoincreasethesti!nessoftheshoe.ThenumberoftheFRFacquisitionduringthemodaltestsareshown.Theshoeconsistsofthewebandtherim;thewebisattachedtotherimtoincreasethesti!nessofthes