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MultiCraftInternationalJournalofEngineering,ScienceandTechnologyVol.1,No.1,2009,pp.254271INTERNATIONALJOURNALOFENGINEERING,SCIENCEANDTECHNOLOGYwww.ijestng.com©2009MultiCraftLimited.AllrightsreservedAcombinedapproachofcomplexeigenvalueanalysisanddesignofexperimentsDOEtostudydiscbrakesquealM.Nouby1,D.Mathivanan2,K.Srinivasan11AU/FRGInstituteforCAD/CAM,AnnaUniversity,Chennai600025,India2DirectorofCAEInfotech,Chennai600020,IndiaEmailsnoubyluxorgmail.comM.Nouby,mathvanyahoo.comD.MathivananCorrespondingauthorsAbstractThispaperproposesanapproachtoinvestigatetheinfluencingfactorsofthebrakepadonthediscbrakesquealbyintegratingfiniteelementsimulationswithstatisticalregressiontechniques.ComplexeigenvalueanalysisCEAhasbeenwidelyusedtopredictunstablefrequenciesinbrakesystemsmodels.Thefiniteelementmodeliscorrelatedwithexperimentalmodaltest.Theinputoutputrelationshipbetweenthebrakesquealandthebrakepadgeometryisconstructedforpossiblepredictionofthesquealusingvariousgeometricalconfigurationsofthediscbrake.InfluencesofthevariousfactorsnamelyYoungsmodulusofbackplate,backplatethickness,chamfer,distancebetweentwoslots,slotwidthandangleofslotareinvestigatedusingdesignofexperimentsDOEtechnique.Amathematicalpredictionmodelhasbeendevelopedbasedonthemostinfluencingfactorsandthevalidationsimulationexperimentsproveditsadequacy.ThepredictedresultsshowthatbrakesquealpropensitycanbereducedbyincreasingYoungsmodulusofthebackplateandmodifyingtheshapeoffrictionmaterialbyaddingchamferonbothsidesoffrictionmaterialandbyintroducingslotconfigurations.ThecombinedapproachofmodelingbrakesquealusingCEAandDOEisfoundtobestatisticallyadequatethroughverificationtrials.Thiscombinedapproachwillbeusefulinthedesignstageofthediscbrake.KeywordsDiscbrakesqueal,finiteelementanalysis,experimentalmodalanalysis,designofexperiments1.IntroductionBrakesquealisanoiseproblemcausedbyvibrationsinducedbyfrictionforcesthatcaninduceadynamicinstabilityAkay,2002.Duringthebrakingoperation,thefrictionbetweenthepadandthedisccaninduceadynamicinstabilityinthesystem.Usuallybrakesquealoccursinthefrequencyrangebetween1and20kHz.Squealisacomplexphenomenon,partlybecauseofitsstrongdependenceonmanyparametersand,partly,becauseofthemechanicalinteractionsinthebrakesystem.Themechanicalinteractionsareconsideredtobeverycomplicatedbecauseofnonlinearcontacteffectsatthefrictioninterface.Theoccurrenceofsquealisintermittentorevenrandom.Undercertainconditions,evenwhenthevehicleisbrandnew,itoftengeneratessquealnoise,whichhasbeenextensivelystudiedwiththegoalofeliminatingthenoise.However,mechanisticdetailsofsquealnoisearenotyetfullyunderstoodJoeetal.,2008.Severaltheorieshavebeenformulatedtoexplainthemechanismsofbrakesqueal,andnumerousstudieshavebeenmadewithvariedsuccesstoapplythemtothedynamicsofdiscbrakesKinkaidetal.,2003.Thereasonfortheonsetofinstabilityhasbeenattributedtodifferentreasons.SomeofthemajorreasonsarethechangeofthefrictioncharacteristicwiththespeedofthecontactpointsIbrahim,1994Ouyangetal.,1998Shinetal.,2002thechangeoftherelativeorientationofthediskandthefrictionpadsleadingtoamodificationofthefrictionforceMillner,1978,andaflutterinstabilitywhichisfoundevenwithaconstantfrictioncoefficientChowdharyetal.,2001Chakrabotryetal.,2002VonWagneretal.,2003VonWagneretal.,2004.Infact,recentliteraturereviewsKinkaidetal.,2003Papinniemietal.,2002havereportedonthecomplexityandlackofunderstandingofthebrakesquealproblem.Thoughmuchworkwasdoneontheissueofsqueal,itrequirescontinuousstudyandinvestigationtorefinethepredictionaccuracyoffiniteelementmodelsofbrakeassembliestogivebrakedesignengineersappropriatetoolstodesignquietbrakes.Therearetwomaincategoriesofnumericalmethodsthatareusedtostudythisproblem1transientdynamicanalysisHuetal.,Noubyetal./InternationalJournalofEngineering,ScienceandTechnology,Vol.1,No.1,2009,pp.2542712551999AbuBakaretal.,2006and2complexeigenvalueanalysis.Currently,thecomplexeigenvaluemethodispreferredandwidelyusedLiles,1989Leeetal.,1998Blaschkeetal.,2000Bajeretal.,2003AbuBakaretal.,2006Liuetal.,2007Marioetal.,2008Daietal.,2008inpredictingthesquealpropensityofthebrakesystemincludingdampingandcontactduetothequicknesswithwhichitcanbeanalysedanditsusefulnessinprovidingdesignguidancebyanalysingwithdifferentoperatingparametersvirtually.Manyresearchersintheirstudiesonthedynamicsofbrakesystemtriedtoreducesquealbychangingthefactorsassociatedwiththebrakesqueal.ForexampleLiles,1989foundthatshorterpads,damping,softerdiscandstifferbackplatecouldreducesquealwhilstincontrast,higherfrictioncoefficientandwearofthefrictionmaterialwerepronetosqueal.Leeetal.,1998reportedthatreducingbackplatethicknessledtolessuniformofcontactpressuredistributionsandconsequentlyincreasingthesquealpropensity.Huetal.,1999basedontheDOEanalysisfoundthattheoptimaldesignwastheonethatusedtheoriginalfingerlength,theverticalslot,thechamferpad,the28mmthicknessofdisc,andthe10mmthicknessoffrictionmaterial.Brooksetal.,1993foundthatbyshiftingthepistonsawayfromtheleadingedgeofthepadsthesystemcoulddestabilise.Theyalsoreportedthatthepredictedunstablesystemwasduetothecouplingoftranslationalandrotationalmodesofthediscparticularlyathighvaluesofpadstiffness.Fromthesensitivitystudies,theysuggestedthattheeffectivehalflengthofthepad,thepistonmasses,theeffectivemass,inertiaandgroundingstiffnessofthediscandthesecondcircuitactuationstiffnessalsohavepotentialonthediscbrakeinstability.Shinetal.,2002haveshownthatthedampingofthepadandthediscwereimportantinreducinginstability.Theiranalysisalsohasshownandconfirmedthatincreasingdampingofeitherthediscorthepadalonecouldpotentiallydestabilisethesystem.Liuetal.,2007foundthatthesquealcanbereducedbydecreasingthefrictioncoefficient,increasingthestiffnessofthedisc,usingdampingmaterialonthebackofthepadsandmodifyingtheshapeofthebrakepads.Daietal.,2008haveshownthatthedesignofthepadswitharadialchamferpossessestheleastnumberofunstablemodes,whichimplieslessertendencytowardssqueal.Inthepresentstudy,aninvestigationofdiscbrakesquealisdonebyperformingcomplexeigenvalueanalysisusingfiniteelementsoftwareABAQUS/standard.Apositiverealpartofacomplexeigenvalueisbeingseenasanindicationofinstability.ThoughtheFEsimulationscanprovideguidance,itwillratherbetrialanderrorapproachtoarriveatanoptimalconfigurationandalsoonemayneedtorunmanynumberofcomputationallyintensiveanalysestoformulatetheinputoutrelationshipsforpossibleprediction.Hence,inthepresentinvestigation,anovelapproachisproposedbyintegratingthecomplexeigenvalueFEanalyseswithstructuredDOE.Theproposedapproachisaimedtowardspredictionofoptimalpaddesignthroughthevariousfactorsofthebrakepadgeometricalconstruction.Thepaperisorganisedasfollows,itpresentsadetailedliteraturesurveyinthisfieldintherecentperiod.Fromtheliteraturesurveythemainobjectiveswereformed.MethodologytodevelopFEmodelofthediscbrakeispresentedanditwassubsequentlyvalidatedusingexperimentalmodalanalysis.TheCEAapproachispresentedinordertopredictbrakesqueal.ThenDOEapproachforsoftcomputingispresented.Alsoamethodologytotesttheadequacyofthedevelopedstatisticalmodelisdiscussed.2.FiniteelementmodelandcomponentcorrelationAdiscbrakesystemconsistsofadiscthatrotatesabouttheaxisofawheel,acaliper–pistonassemblywherethepistonslidesinsidethecaliperthatismountedtothevehiclesuspensionsystem,andapairofbrakepads.Whenhydraulicpressureisapplied,thepistonispushedforwardtopresstheinnerpadagainstthediscandsimultaneouslytheouterpadispressedbythecaliperagainstthedisc.Figure1ashowsthefiniteelementmodelofthecarfrontbrakeunderconsideration,builtusingtheABAQUSfiniteelementsoftwarepackage.ThebrakemodelusedinthisstudyisasimplifiedmodelconsistingofthetwomaincomponentscontributingtosquealthediscandthepadFigure1b.abFigure1.FiniteelementmodelsofaarealisticbsimplifieddiscbrakemodelNoubyetal./InternationalJournalofEngineering,ScienceandTechnology,Vol.1,No.1,2009,pp.254271256Asimplifiedmodelwasusedinthisstudyforthefollowingreasons1.Forbrakesquealanalysis,themostimportantsourceofnonlinearityisthefrictionalslidingcontactbetweenthediscandthepads.2.ThesimulationincludesgeometrysimplificationstoreduceCPUtime,allowingfarmoreconfigurationstobecomputed.Thediscismadeofcastiron.Thepairofbrakepads,whichconsistoffrictionmaterialandbackplates,arepressedagainstthediscinordertogenerateafrictiontorquetoslowthediscrotation.Thefrictionmaterialismadeofanorganicfrictionmaterialandthebackplatesaremadeofsteel.TheFEmeshisgeneratedusing19,000solidelements.Thefrictioncontactinteractionsaredefinedbetweenbothsidesofthediscandthefrictionmaterialofthepads.Aconstantfrictioncoefficientandaconstantangularvelocityofthediscareusedforsimulationpurposes.Figure2presentstheconstraintsandloadingsforthepadsanddiscassembly.Thedisciscompletelyfixedatthefourcounterboltholesandtheearsofthepadsareconstrainedtoallowonlyaxialmovements.Thecaliper–pistonassemblyisnotdefinedinthesimplifiedmodelofthediscbrakesystem,hencethehydraulicpressureisdirectlyappliedtothebackplatesatthecontactregionsbetweentheinnerpadandthepistonandbetweentheouterpadandthecaliper,anditisassumedthatanequalmagnitudeofforceactsoneachpad.Figure2.ConstraintsandloadingofthesimplifiedbrakesystemForthepurposeofvalidation,themainbrakecomponents,FrequencyResponseFunctionsFRFsweremeasuredatfreefreeboundaryconditionsbyexcitingeachcomponentwithasmallimpacthammerwithsensitivityof10mV/Nandahardtip.Theaccelerationresponsewasmeasuredwithalightsmallaccelerometerwithsensitivityof10mV/gthroughDynamicSignalAnalyzertypeDEWE41TDSA.FRFmeasurementswererecordedforeachcomponentusingSISOconfigurations.Then,theFRF´swereprocessedusingDEWEFRFsoftwareinordertoidentifythemodalparameters,namelyresonancefrequencies,modalshapesanddampingvalues.Figure3showstheexperimentalmodaltestcomponents.Figure3.ExperimentalModalAnalysisComponentsThefrequenciesmeasuredonthediscandcalculatedbythesimulatedmodelformodeswithfreefreeboundaryconditionsareshownintable1.Itcanbeobservedthatthemeasuredandsimulatedfrequenciesareingoodagreement.Figure4showsthemodeshapesofrotorwithnodaldiameters.Inasimilarway,theparametersforthepadsareestimatedbasedonthemeasureddataindicatedinTable2.Themeasuredandsimulatedfrequenciesareingoodagreement.Figure5showsthemodeshapesofthepad.Noubyetal./InternationalJournalofEngineering,ScienceandTechnology,Vol.1,No.1,2009,pp.254271257Table1.ModalresultsoftherotoratfreefreeboundaryconditionsModeshapeExperimentalFrequencyHzFEAFrequencyHzDifferences2ndbending122013036.83rdbending255126363.34thbending400341082.65thbending577455913.16thbending7873779017thbending900892092.2Table2.ModalresultsofthepadatfreefreeboundaryconditionsModeshapeExperimentalFrequencyHzFEAFrequencyHzDifferences1stbending305132315.82ndbending8459838112ndNodalDiameterMode1303Hz3rdNodalDiameterMode2636Hz4thNodalDiameterMode4108Hz5thNodalDiameterMode5591HzFigure4.Modeshapesoftherotoratfreefreeboundaryconditions
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