MultiCraftInternationalJournalofEngineering,ScienceandTechnologyVol.1,No.1,2009,pp.254-271INTERNATIONALJOURNALOFENGINEERING,SCIENCEANDTECHNOLOGY2009MultiCraftLimited.AllrightsreservedAcombinedapproachofcomplexeigenvalueanalysisanddesignofexperiments(DOE)tostudydiscbrakesquealM.Nouby1*,D.Mathivanan2*,K.Srinivasan11AU/FRGInstituteforCAD/CAM,AnnaUniversity,Chennai-600025,India2DirectorofCAEInfotech,Chennai-600020,IndiaE-mails:((M.Nouby),(D.Mathivanan)；*Correspondingauthors)AbstractThispaperproposesanapproachtoinvestigatetheinfluencingfactorsofthebrakepadonthediscbrakesquealbyintegratingfiniteelementsimulationswithstatisticalregressiontechniques.Complexeigenvalueanalysis(CEA)hasbeenwidelyusedtopredictunstablefrequenciesinbrakesystemsmodels.Thefiniteelementmodeliscorrelatedwithexperimentalmodaltest.Theinput-outputrelationshipbetweenthebrakesquealandthebrakepadgeometryisconstructedforpossiblepredictionofthesquealusingvariousgeometricalconfigurationsofthediscbrake.Influencesofthevariousfactorsnamely；Youngsmodulusofbackplate,backplatethickness,chamfer,distancebetweentwoslots,slotwidthandangleofslotareinvestigatedusingdesignofexperiments(DOE)technique.Amathematicalpredictionmodelhasbeendevelopedbasedonthemostinfluencingfactorsandthevalidationsimulationexperimentsproveditsadequacy.ThepredictedresultsshowthatbrakesquealpropensitycanbereducedbyincreasingYoungsmodulusofthebackplateandmodifyingtheshapeoffrictionmaterialbyaddingchamferonbothsidesoffrictionmaterialandbyintroducingslotconfigurations.ThecombinedapproachofmodelingbrakesquealusingCEAandDOEisfoundtobestatisticallyadequatethroughverificationtrials.Thiscombinedapproachwillbeusefulinthedesignstageofthediscbrake.Keywords:Discbrakesqueal,finiteelementanalysis,experimentalmodalanalysis,designofexperiments1.IntroductionBrakesquealisanoiseproblemcausedbyvibrationsinducedbyfrictionforcesthatcaninduceadynamicinstability(Akay,2002).Duringthebrakingoperation,thefrictionbetweenthepadandthedisccaninduceadynamicinstabilityinthesystem.Usuallybrakesquealoccursinthefrequencyrangebetween1and20kHz.Squealisacomplexphenomenon,partlybecauseofitsstrongdependenceonmanyparametersand,partly,becauseofthemechanicalinteractionsinthebrakesystem.Themechanicalinteractionsareconsideredtobeverycomplicatedbecauseofnonlinearcontacteffectsatthefrictioninterface.Theoccurrenceofsquealisintermittentorevenrandom.Undercertainconditions,evenwhenthevehicleisbrandnew,itoftengeneratessquealnoise,whichhasbeenextensivelystudiedwiththegoalofeliminatingthenoise.However,mechanisticdetailsofsquealnoisearenotyetfullyunderstood(Joeetal.,2008).Severaltheorieshavebeenformulatedtoexplainthemechanismsofbrakesqueal,andnumerousstudieshavebeenmadewithvariedsuccesstoapplythemtothedynamicsofdiscbrakes(Kinkaidetal.,2003).Thereasonfortheonsetofinstabilityhasbeenattributedtodifferentreasons.Someofthemajorreasonsarethechangeofthefrictioncharacteristicwiththespeedofthecontactpoints(Ibrahim,1994；Ouyangetal.,1998；Shinetal.,2002)thechangeoftherelativeorientationofthediskandthefrictionpadsleadingtoamodificationofthefrictionforce(Millner,1978),andaflutterinstabilitywhichisfoundevenwithaconstantfrictioncoefficient(Chowdharyetal.,2001；Chakrabotryetal.,2002；VonWagneretal.,2003；VonWagneretal.,2004).Infact,recentliteraturereviews(Kinkaidetal.,2003；Papinniemietal.,2002)havereportedonthecomplexityandlackofunderstandingofthebrakesquealproblem.Thoughmuchworkwasdoneontheissueofsqueal,itrequirescontinuousstudyandinvestigationtorefinethepredictionaccuracyoffiniteelementmodelsofbrakeassembliestogivebrakedesignengineersappropriatetoolstodesignquietbrakes.Therearetwomaincategoriesofnumericalmethodsthatareusedtostudythisproblem:(1)transientdynamicanalysis(Huetal.,Noubyetal./InternationalJournalofEngineering,ScienceandTechnology,Vol.1,No.1,2009,pp.254-2712551999；AbuBakaretal.,2006)and(2)complexeigenvalueanalysis.Currently,thecomplexeigenvaluemethodispreferredandwidelyused(Liles,1989；Leeetal.,1998；Blaschkeetal.,2000；Bajeretal.,2003；AbuBakaretal.,2006；Liuetal.,2007；Marioetal.,2008；Daietal.,2008)inpredictingthesquealpropensityofthebrakesystemincludingdampingandcontactduetothequicknesswithwhichitcanbeanalysedanditsusefulnessinprovidingdesignguidancebyanalysingwithdifferentoperatingparametersvirtually.Manyresearchersintheirstudiesonthedynamicsofbrakesystemtriedtoreducesquealbychangingthefactorsassociatedwiththebrakesqueal.Forexample(Liles,1989)foundthatshorterpads,damping,softerdiscandstifferbackplatecouldreducesquealwhilstincontrast,higherfrictioncoefficientandwearofthefrictionmaterialwerepronetosqueal.(Leeetal.,1998)reportedthatreducingbackplatethicknessledtolessuniformofcontactpressuredistributionsandconsequentlyincreasingthesquealpropensity.(Huetal.,1999)basedontheDOEanalysisfoundthattheoptimaldesignwastheonethatusedtheoriginalfingerlength,theverticalslot,thechamferpad,the28mmthicknessofdisc,andthe10mmthicknessoffrictionmaterial.(Brooksetal.,1993)foundthatbyshiftingthepistonsawayfromtheleadingedgeofthepadsthesystemcoulddestabilise.Theyalsoreportedthatthepredictedunstablesystemwasduetothecouplingoftranslationalandrotationalmodesofthediscparticularlyathighvaluesofpadstiffness.Fromthesensitivitystudies,theysuggestedthattheeffectivehalflengthofthepad,thepistonmasses,theeffectivemass,inertiaandgroundingstiffnessofthediscandthesecondcircuitactuationstiffnessalsohavepotentialonthediscbrakeinstability.(Shinetal.,2002)haveshownthatthedampingofthepadandthediscwereimportantinreducinginstability.Theiranalysisalsohasshownandconfirmedthatincreasingdampingofeitherthediscorthepadalonecouldpotentiallydestabilisethesystem.(Liuetal.,2007)foundthatthesquealcanbereducedbydecreasingthefrictioncoefficient,increasingthestiffnessofthedisc,usingdampingmaterialonthebackofthepadsandmodifyingtheshapeofthebrakepads.(Daietal.,2008)haveshownthatthedesignofthepadswitharadialchamferpossessestheleastnumberofunstablemodes,whichimplieslessertendencytowardssqueal.Inthepresentstudy,aninvestigationofdiscbrakesquealisdonebyperformingcomplexeigenvalueanalysisusingfiniteelementsoftwareABAQUS/standard.Apositiverealpartofacomplexeigenvalueisbeingseenasanindicationofinstability.ThoughtheFEsimulationscanprovideguidance,itwillratherbetrial-and-errorapproachtoarriveatanoptimalconfigurationandalsoonemayneedtorunmanynumberofcomputationallyintensiveanalysestoformulatetheinput-outrelationshipsforpossibleprediction.Hence,inthepresentinvestigation,anovelapproachisproposedbyintegratingthecomplexeigenvalueFEanalyseswithstructuredDOE.Theproposedapproachisaimedtowardspredictionofoptimalpaddesignthroughthevariousfactorsofthebrakepadgeometricalconstruction.Thepaperisorganisedasfollows,itpresentsadetailedliteraturesurveyinthisfieldintherecentperiod.Fromtheliteraturesurveythemainobjectiveswereformed.MethodologytodevelopFEmodelofthediscbrakeispresentedanditwassubsequentlyvalidatedusingexperimentalmodalanalysis.TheCEAapproachispresentedinordertopredictbrakesqueal.ThenDOEapproachforsoftcomputingispresented.Alsoamethodologytotesttheadequacyofthedevelopedstatisticalmodelisdiscussed.2.FiniteelementmodelandcomponentcorrelationAdiscbrakesystemconsistsofadiscthatrotatesabouttheaxisofawheel,acaliperpistonassemblywherethepistonslidesinsidethecaliperthatismountedtothevehiclesuspensionsystem,andapairofbrakepads.Whenhydraulicpressureisapplied,thepistonispushedforwardtopresstheinnerpadagainstthediscandsimultaneouslytheouterpadispressedbythecaliperagainstthedisc.Figure1(a)showsthefiniteelementmodelofthecarfrontbrakeunderconsideration,builtusingtheABAQUSfiniteelementsoftwarepackage.Thebrakemodelusedinthisstudyisasimplifiedmodelconsistingofthetwomaincomponentscontributingtosqueal:thediscandthepad(Figure1(b).(a)(b)Figure1.Finiteelementmodelsofa(a)realistic(b)simplifieddiscbrakemodelNoubyetal./InternationalJournalofEngineering,ScienceandTechnology,Vol.1,No.1,2009,pp.254-271256Asimplifiedmodelwasusedinthisstudyforthefollowingreasons:1.Forbrakesquealanalysis,themostimportantsourceofnonlinearityisthefrictionalslidingcontactbetweenthediscandthepads.2.ThesimulationincludesgeometrysimplificationstoreduceCPUtime,allowingfarmoreconfigurationstobecomputed.Thediscismadeofcastiron.Thepairofbrakepads,whichconsistoffrictionmaterialandbackplates,arepressedagainstthediscinordertogenerateafrictiontorquetoslowthediscrotation.Thefrictionmaterialismadeofanorganicfrictionmaterialandthebackplatesaremadeofsteel.TheFEmeshisgeneratedusing19,000solidelements.Thefrictioncontactinteractionsaredefinedbetweenbothsidesofthediscandthefrictionmaterialofthepads.Aconstantfrictioncoefficientandaconstantangularvelocityofthediscareusedforsimulationpurposes.Figure2presentstheconstraintsandloadingsforthepadsanddiscassembly.Thedisciscompletelyfixedatthefourcounter-boltholesandtheearsofthepadsareconstrainedtoallowonlyaxialmovements.Thecaliperpistonassemblyisnotdefinedinthesimplifiedmodelofthediscbrakesystem,hencethehydraulicpressureisdirectlyappliedtothebackplatesatthecontactregionsbetweentheinnerpadandthepistonandbetweentheouterpadandthecaliper,anditisassumedthatanequalmagnitudeofforceactsoneachpad.Figure2.ConstraintsandloadingofthesimplifiedbrakesystemForthepurposeofvalidation,themainbrakecomponents,FrequencyResponseFunctions(FRFs)weremeasuredatfree-freeboundaryconditionsbyexcitingeachcomponentwithasmallimpacthammerwithsensitivityof10mV/Nandahardtip.Theaccelerationresponsewasmeasuredwithalightsmallaccelerometerwithsensitivityof10mV/gthroughDynamicSignalAnalyzertypeDEWE-41-T-DSA.FRFmeasurementswererecordedforeachcomponentusingSISOconfigurations.Then,theFRFswereprocessedusingDEWEFRFsoftwareinordertoidentifythemodalparameters,namely；resonancefrequencies,modalshapesanddampingvalues.Figure3showstheexperimentalmodaltestcomponents.Figure3.ExperimentalModalAnalysisComponentsThefrequ