7. numerical modeling of disc brake system in frictional...

49

Vol.36,No.1(2014)49‐66

TribologyinIndustry

www.tribology.fink.rs

NumericalModelingofDiscBrakeSysteminFrictionalContact

A.Belhocine

a,A.R.AbuBakarb,M.Bouchetara

aa

DepartmentofMechanicalEngineering,USTOOranUniversity,L.P1505El‐Mnaouer,USTO31000Oran,Algeriab

DepartmentofAutomotiveEngineering,UniversitiTeknologiMalaysia,81310UTMSkudai,Malaysia.

Keywords:

BrakediscHeatfluxHeattransfercoefficientThermalanalysisFiniteelementStress

ABSTRACT

Safetyaspectinautomotiveengineeringhasbeenconsideredasanumberonepriority indevelopmentofnewvehicle.Eachsinglesystemhasbeenstudied and developed in order tomeet safety requirement. Instead ofhaving air bag, good suspension systems, good handling and safecornering,there isonemostcriticalsystem inthevehiclewhich isbrakesystems. The objective of this work is to investigate and analyse thetemperature distribution of rotor disc during braking operation usingANSYSMultiphysics.Theworkusesthefiniteelementanalysistechniquestopredict the temperaturedistributionon the fullandventilatedbrakedisc and to identify the critical temperature of the rotor by holdingaccount certain parameters such as; thematerial used, the geometricdesignofthediscandthemodeofbraking.Theanalysisalsogivesus,theheatfluxdistributionforthetwodiscs.

©2014PublishedbyFacultyofEngineering

Correspondingauthor:

AliBelhocineFaculty of Mechancal Engineering,USTOOranUniversity,L.P.1505El‐Mnaouer,USTO,31000OranAlgeriaE‐mail:[email protected]

1. INTRODUCTIONBraking system is one of the important safetycomponents of a vehicle. Braking system ismainly used to decelerate vehicles from aninitial speed to a given speed. Friction basedbraking systems are the common device toconvert kinetic energy into thermal energythroughfrictionbetweenthebrakepadsandtherotor faces. High temperatures can also lead tooverheating of brake fluid, seals and othercomponents. The stopping capability of brakeincreasesbytherateatwhichheatisdissipateddue to forced convection and the thermalcapacity of the system [1]. Tracing of thermal

effectsinanygivenpartofthebrakeispossiblebynumericalsimulations,butitrequiresavalidmodeltobeconstructed.Theverificationofsuchmodel can be performed on the basis of realtemperature measurements, using the imagesequences recorded by a thermal camera. Theanalysis of recorded temperature distributionmay help to identify the worn out brakecomponents[2].Brake disc convective cooling has beenhistorically studied by means of experimentaland theoretical methods [3,4] and theoptimizationwereonlyboostedwiththeadventof modern computational resources in the late

RESEARCH

A.Belhocineetal.,TribologyinIndustryVol.36,No.1(2014)49‐66

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eighties [5]. Currently, although of not simpleusage and requiring previous understanding ofthe basics of fluidmechanics and heat transfercoupled with knowledge of flows numericalmodeling, CFD has significantly gainedpreference in the automotive industry designprocessas tool forpredictingcomplex flowandheat transfer behaviour in regions whereotherwiseverylaboriousandtimeconsumingbyacombinationofnode‐to‐surfaceandsurface‐to‐surfacecontactelements[6].Gao and Lin [7] stated that there wasconsiderable evidence to show that the contacttemperature is an integral factor reflecting thespecific power friction influence of combinedeffectof load,speed,frictioncoefficient,andthethermophysicalanddurabilitypropertiesofthematerials of a frictional couple. Experimentsshowed that the friction coefficient in generaldecreased with increasing sliding speed andapplied load,but increasedwith increasingdisctemperature up to 300 °C and then decreasedabove this temperature. The specific wear ratewas found to increase with increasing slidingspeedanddisctemperature[8].Nouby et al [9] introduced a nontraditionalevaluation tool to examine the effects ofdifferentmaterials,inpracticalapplications,thatare used in fabricating disc brake componentsforcommonlyusedorspecialrequirementssuchas heavy‐duty performance and racing cars. Anextension of the FEmodels discussed earlier isan experimental set upworkwould beneeded.Asresult,brakediscconvectivecoolinganalysisandoptimizationisnowadaysmostlycarriedoutusingCFDcommercialcodes,e,g.[10].Many investigations of analysis of heat flowthrough theventilateddiscbrakesare reportedin the literature. Michael and Roland [11]discussedtheairflowpatternsinthediscrotors.Wallis et al [12] carried out a numerical studyusingFluentondiscrotorbladestoexaminetheeffects of local heat and mass transfer of theaxial gap distances for a single and co‐rotatingdisc. The study of single rotating disc showedthat heat and mass transfer coefficient areenhanced considerably by decreasing the hubheight. In the sliding contact process, atemperature variation in the contacting bodiesthat resulted from frictional heating will causemany related engineering problems, such as

wear, fusion, and deformation. Since Blok [13]and Jaeger and Carslaw [14] pioneered thestudies of temperature rise at the contactsurfacesdue tomovingheat surfaces, therearemore researches aimed at studying thetemperature rise and distribution. Vick andFurey [15] deduced the base theory of thefrictional heat and calculated a set of regularlyarranged contact areas’ temperaturedistribution; Chen et al. [16] used the classictheory to calculate the local temperature risethat greatly influences the glue,wear, and localplastic deformation. Chen and Li [17]established a wear model to simulate slidingprocesses in order to analyse the frictionalheating. Bogdanovich and Tkachuk [18]presented some experiments to understandthermal phenomena in a sliding contact,revealing that asperities in contact were foundto undergo the pulse effect of the temperatureapproaching the melting point of one of thefriction members. The friction heat generatedbetweentwoslidingbodiescausesthermoelasticdeformation, which alters the contact pressuredistribution. This coupled thermo‐mechanicalprocess is referred to as frictionally‐excitedthermoelastic instability (TEI) [19]. Abu Bakarand Ouyang [20] adjusted the surface profilesusing measured data of the surface height andproducedamorerealisticmodelforbrakepads.Direct contact interaction between disc brakecomponents is represented three‐dimensionalFE model of the disc brake corner thatincorporates awheel hub and steering knucklethat was developed and validated at bothcomponentsandassembly levels topredictdiscbrake squeal. In addition, the real pad surfacetopography,negativefriction–velocityslope,andfriction damping were considered to increasethe prediction accuracy of the squeal. Brakesquealisahighfrequencynoiseproducedwhendriver decelerates and/or stops the vehiclemoving at low speed. It is the noise caused byself‐excited vibration generated by the frictionforcevariationbetweenthefrictionmaterialandrotor.It isaphenomenonofdynamicinstabilitythat occurs at one or more the naturalfrequencies of the brake system. The clutchtribological behaviours depend significantly onthe dynamic contact temperature of thefrictional surfaces, which in turn is related tonormal pressure load, relative sliding velocityandthenatureoftheinvolvedsurfaces[21].Theinterfacetemperaturehasmomentousinfluence


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on friction and wear effects, with potentialfailures caused by high thermal levels andthermo mechanical stresses. It is well knownthat the temperature sensitivity of frictionmaterials is a critical aspect wishing to ensuretheir smoothand reliable functioning. In fact, itinfluencesthethermo‐elasticinstabilities,whichin turn alter the friction performance at thebraking junctions [22]. In the front wheel, forexample,discbrakepadsabsorbamajoramount(up to 80 %) of the total kinetic energy of anautomobile. This causes the generation of hightemperature up to 370 °C on the disc. Theseverity of such temperature rise is furthermanifested in the form of a very high flashtemperature up to 600 °C at the contactingasperities[23].Atsuchhightemperatures,padssuffer from a loss of effectiveness called “fade”because of a reduction in the kinetic frictioncoefficient. High interfacial temperatures canlead to a decrease in shear strength of the padand consequently a decrease in frictional forcewhich induces fade [24]. Thus, correlating thefrictioncoefficienttotheoperatingtemperaturelevelforthecoupledfrictionsurfacesisprobablythe most critical point in designing safe andeffectivebrakingsystemsanditisnotsurprisingthat many researchers pay their attention totheoretical models for surface temperatureevaluation as well as to surface temperaturemeasurements. A lot of studies about heattransferatthecoupledinterfacesarereportedinliterature which takes into account thesuperposition of several phenomena, eachdescribed by a number of simplifyingassumptions: experimental, analytical andnumericalmethodsareattemptedtounderstandand to predict wear effects. From anexperimental standpoint, the system relativemotion, its geometry and the high thermalgradients which are typically attained makeexperimental temperature detection a complexmatter if one wishes to use thermocoupleslocateddirectlyatthe frictioninterface[25‐27].Therefore, “non‐contact measurements”including optical or infrared methods could bethe solution and early works are appearing inthissense[28‐31].Thelattertechniqueseemstobe the most effective and valuable due to itsability toperformcontinuous temperaturemaprecordingwithrelativelyhighresolutionswhencompared toother traditionalmethodsbut it istoconsiderthattheareatofocusonis“hidden”by the coupled surfaces. Due to the described

difficulties in the experimental approach, inrecentyears,thefiniteelementmethod[32]hasbecome the preferred method for studying theproblemathandwhilefewanalyticalmodelsarealsoavailable[33].However,acriticalanalysisofthe above mentioned works allows to clearlyconcluding that, often, numerical predictions fortemperature distribution aren’t adequatelyvalidated by experimental tests. Spulber andVoloaca [34] proposed a new simulationmethodof a disc brake thermal stress resistance, fordifferent temperatures, by interactive processingof images obtained by thermography.Temperature evaluation for different workingregimescanbemadebyrecordingandprocessingthermograms of a disc brake heated inside thelaboratory by an external heating source. Takenpicturesalongthetemperaturevariation,fromtheambientvaluetoavalueclosetorealoneobtainedon the usual experiments, are processed usingimageanalysesoftwares.In the work of Mosleh et al. [35] a brake dustgeneratedinvehiclebrakescausesdiscolorationofwheelsand,moreimportantly,theemissionofparticles suspected of health hazard in theenvironment. Laboratory testing of brake padmaterials against cast iron discs revealed thatthe majority of wear particles aresubmicrometer in size. Wear particles with asizeof350nmhadthehighestpercentageintheparticlesizedistributionplots,regardlessofthemagnitudeof thenominal contactpressureandthe sliding speed. The precise calculation foreachoftherateofwear[36‐38]andtheinternalenergyof frictionclutchwill lead toKnowledgethe lifetime of friction material with highaccuracy. Due to their predominantlysubmicrometer size, a significant amount ofbrake dust particles may be inhalable inenvironmental and occupational exposuresituations.Abdullah et al. [39] used the finite elementmethod to study the contact pressure andstresses during the full engagement period ofthe clutches using different contact algorithms.Moreover, sensitivity study for the contactpressureispresentedtoindicatetheimportanceofthecontactstiffnessbetweencontactsurfaces.According to Altuzarra et al. [40], if the slidingspeed is high, the resulting thermo‐mechanicalfeedbackisunstable,leadingtothedevelopmentof non‐uniform contact pressure and local high


52

temperature with important gradients called‘hot spots’. The formation of such localized hotspotsisaccompaniedbyhighlocalstressesthatcan lead to material degradation and eventualfailure[41].Also,thehotspotscanbeasourceofundesirable frictional vibrations, known in theautomotive disc brake community as ‘hotroughness’or‘hotjudder’[42].Theventilateddiscislighterthanthesoliddisc,and additional convective heat transfer occurson the surface of the vent hall. Thus, theventilated disc can control its temperature riseand minimize the effects of thermal problemssuch as the variation of the pad frictioncoefficient,brakefadeandvaporlock[43,44].The ventilated disc, however, may increasejudder problems by inducing an uneventemperature field around the disc. Also, thethermal capacity of the ventilated disc is lessthan thatof thesoliddisc, and the temperatureof the ventilated disc can rise relatively fasterthan that of the solid disc during repetitivebraking [45]. Therefore, thermal capacity andthermal deformation should be carefullyconsidered when modifying the shape of theventilated disc. Recently, Abdullah andSchlattmann [46] carried out detailed oftemperaturedistributionfordryfrictionsystem(flywheel,clutchdiscandpressureplate)duringrepeated engagements. The finite elementmethod used to compute the temperature fieldfor clutch disc under different pressuredistributions. Two types of pressuredistributions were applied between contactsurfaces uniform pressure and the linearpressure with disc radius (maximum at innerradius andminimum at outer radius) based ontheoryofclutchdesign.Theeffectofconvectionis considered in both cases. The same authors[47] applied the finite element method tocalculate the heat generated on the surfaces offriction clutch and temperature distribution forcase of bands contact between flywheel andclutch disc, and between the clutch disc andpressureplate(onebadcentralandtwobands)andcomparedwithcaseoffullcontactbetweensurfaces for single engagement and repeatedengagements. Furthermore, their work showseffect of pressure capacity on the temperaturefield,when thepressure is a function of time ,three kinds of pressure variation with time(constant,linearandparabolic)arepresented.

In this study, we will make a modeling of thethermal behaviour of the dry contact betweenthe discs of brake pads at the time of brakingphase;thestrategyofcalculationisbasedonthesoftware ANSYS 11. This last is comprehensivemainlyfortheresolutionofthecomplexphysicalproblems. As a current study of this problemANSYS Simulations with less assumption andless program restrictions have been performedfor the thermo mechanical case. Temperaturedistribution obtained by the transient thermalanalysis is used in the calculations of thestressesondiscsurface.2. NUMERICALPROCEDURE

In braking process, the temperature fieldchanges input heat flux and heat exchangeconditions.Theinputheatfluxismainlyrelevanttofrictioncoefficientdisc,theangularvelocityofbrake disc while heat exchange is connectedwith the friction pair materials and externalenvironmentalfactors.Based on the first law of Thermodynamics,during braking, kinetic energy is converted tothermal energy. Due to friction between themaincomponentsofdiscbrake (padsanddisc)theconversionofenergytakesplace.Initially the generated thermal energy istransferredbyconductiontothecomponentsincontactandnextbyconvectiontoenvironment.Theinitialheatfluxqointotherotorfaceisdirectlycalculatedusingthefollowingformula[48]:

01

2 2od p

m g V zq

A

(1)

Wherez=a/gisthebrakingeffectiveness,aisthedeceleration of the vehicle [m/s2], ɸ is the ratedistribution of the braking forces between thefront and rear axle, Ad disc surface swept by abrakepad[m2],Voistheinitialspeedofthevehicle[m/s],εpisthefactorloaddistributiononthediscsurface,m is the massof thevehicle [kg]andg istheaccelerationofgravity(9.81)[m/s2].Thediscrotorvanepassageandasectorchosenfor the numerical analysis are shown in Fig. 1the dimension for the baseline study with anouterdiameterof262mmandinnerdiameterof66mmand36vanes.ThegeometricmodelwascreatedusingANSYSWorbench11.


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Fig.1.Geometricalcharacteristicsoftheventilateddisc.

The loadingcorrespondstotheheat fluxonthediscsurface.ThedimensionsandtheparametersusedinthethermalcalculationarerecapitulatedinTable1.Table1.Inputparameters.

Description Values

Innerdiscdiameter,mm 66

Outerdiscdiameter,mm 262

Discthickness(TH),mm 29

Discheight(H),mm 51

Vehiclemassm,kg 1385

InitialspeedVo , km/h 28

Decelerationa,m/s2 8

EffectiverotorradiusRrotor,mm 100.5

Ratedistributionofthebrakingforcesɸ,% 20

TireradiusRtire,mm 380

Factorofchargedistributionofthediscεp 0.5

SurfacediscsweptbythepadAd,mm2 35993

Thematerial of brake disc is gray cast iron (GF)with high carbon content, with goodthermophysical characteristics, thermoelasticcharacteristicsofwhichadoptedinthissimulationoftherotorarerecapitulatedinTable2.Table2.Materialpropertiesofbrakedisc.

MaterialProperties Disc

Thermalconductivity,k(W/m°C) 57

Density,ρ(kg/m3) 7250

Specificheat, C (J/Kg°C) 460

Poisson’sratio,v 0.28

Thermalexpansion,α(10‐6/K) 10.85

Elasticmodulus,E(GPa) 138

Rotors are made of cast iron for threereasons[49]:

Itisrelativelyhardandresistswear.

Itischeaperthansteeloraluminum.

It absorbs and dissipates heat well tocoolthebrakes.

It is very difficult to exactly model the brakedisc,inwhichtherearestillresearchesaregoingon to find out transient thermal behaviour ofdiscbrakeduringbrakingapplications.There isalways a need of some assumptions to modelany complex geometry. These assumptions aremade, keeping inmind the difficulties involvedinthetheoreticalcalculationandtheimportanceof the parameters that are taken and thosewhich are ignored. In modeling, we alwaysignorethethingsthatareoflessimportanceandhave little impact on the analysis. Theassumptions are always made depending uponthedetailsandaccuracyrequiredinmodeling.DuetotheapplicationofbrakesonthecarDiscbrake rotor, heat generation takes place due tofriction and this thermal flux has to beconducted and dispersed across the Disc Rotorcross section. The condition of braking is verymuch severe and thus the thermal analysis hastobecarriedout.Thethermalloadingaswellasstructure is axis‐symmetric. Hence axis‐symmetricanalysiscanbeperformed,butinthisstudy we performed 3‐D analysis, which is anexact representation for this thermal analysis.Thermal analysis is carried out and with theaboveloadstructuralanalysisisalsoperformedforanalysingthestabilityofthestructure.

TH

HClampholes Coolingfin

Discheight Discthickness

10

6


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To simplify the analysis, several assumptionshavealsobeenmadeasfollows[50]

Allkineticenergyatdiscbrakerotorsurfaceisconvertedintofrictionalheatorheatflux.In other words, a high amount of kineticenergy is converted into heat energy atinterfaces according to the first law ofthermodynamicsduringtheslippingperiodand the heat generated between contactsurfaces will be dissipated by conductionbetween frictionclutchcomponentsandbyconvectiontotheenvironment.

Theheat transfer involved for thisanalysisonly conduction and convection process.This heat transfer radiation can beneglected in this analysis because of smallamountwhich is5%to10%[51]. Indeed,the heat radiation only plays an importantroleathightemperatureandlowspeeds.

The disc material is considered ashomogeneous and isotropic, becauseYoung’s modulus, Poisson’s ratio, and thethermal expansion coefficient are assumedtobeconstantforisotropic.

The domain is considered as axis‐symmetric. The temperature field issymmetrywithrespecttothecentralplaneofthebrakedisc

Inertiaandbodyforceeffectsarenegligibleduring the analysis. Here, a transientanalysis calculates the effects of thermalloading on a structure, while ignoringinertiaanddampingeffects.

Thediscisstressfreebeforetheapplicationofbrake.Due to theapplicationofbrakesof therotor, heat generation takes place due tofrictionandthistemperaturesogeneratedhastobeconductedacrossthediscacrosssection.

Inthisanalysis,theambienttemperatureandinitialtemperaturehasbeensetto20°C.

All other possible disc brake loads areneglected, for example, the effects of wearorotheratmosphericfactors.

Only certain parts of disc brake rotor willapplywithconvectionheattransfersuchascoolingvanesarea,outerringdiameterareaand disc brake surface on which, eachsurface of the rotor was subjected todifferentvaluesof convectionheat transfercoefficientobtainedfromthiscalculations.

Uniformpressuredistributionbythebrakepad onto the disc brake surface. Uniformpressure distribution in the contact regionisoftenvalidwhenthepadisnew.

Thethermalconductivityandspecificheatareafunctionoftemperature,Figs.2and3.

0 100 200 300 400 500 600 700 800 900

35

40

45

50

55

60

Th

erm

al c

ond

uct

ivit

y W

/m°C

Temperature °C Fig.2.Thermalconductivityversustemperature.

0 100 200 300 400 500 600 700

450

500

550

600

650

700

750

800

Sp

ecif

ic h

eat

J/k

g°C

Temperature °C Fig.3.Specificheatversustemperature.3. FINITE ELEMENT FORMULATION FORHEATCONDUCTION

Theunsteadyheatconductionequationofeachbodyfor an axis‐Symmetric problem described in thecylindricalcoordinatesystemisgivenasfollows:

1r z

T T Tc rk k

t r r r z z

(2)

Withtheboundaryconditionsandinitialcondition:

*0T T on (3)

1( )nq h T T on (4)

*2n nq q on

(5)


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0 0T T at time

(6)

whereρ,c,krandkzarethedensity,specificheatand thermalconductivities inrandzdirectionofthe material, respectively. Also, T* is theprescribed temperature, h the heat transfercoefficient, qn* the heat flux at each contactinterface due to friction, T∞ the ambienttemperature,T0 the initial temperatureandΓ0,Γ1andΓ2aretheboundariesonwhichtemperature,convectionandheatfluxareimposed,respectively.Using Galerkin’s approach, a finite elementformulation of unsteady heat Eq. (3) can bewritteninthefollowingmatrixformas:

T TC T KH T R

(7)

Where CT is the capacity matrix, KHT is theconductivity matrix. T and R and are the nodaltemperatureandheatsourcevector,respectively.ThemostcommonlyusedmethodforsolvingEq.(7)isthedirectintegrationmethodbasedontheassumption that temperature Tt at time t andtemperatureTt+Δtattimet+Δthavethefollowingrelation:

1t t t t t tT T T T t

(8)

Eq. (8) can be used to reduce the ordinarydifferential Eq. (7) to the following implicitalgebraicequation:

1 2

2 1

T T t t T T t

t t t

C b KH T C b KH T

b R b R

(9)

Wherethevariableb1andb2aregivenby:

1 2, 1b t b t

(10)

For different values of β the well‐knownnumerical integration scheme can be obtained[52]inthisstudy,0.5β1.0wasused,whichisanunconditionallystablescheme.4. PREPARATION OF THE GEOMETRY ANDTHEMESH

4.1FluidfieldConsideringsymmetryinthedisc,onetookonlythequarterofthegeometryofthefluidfield(Fig.4)byusingsoftwareANSYSICEMCFD.

Fig.4..

Fig.4.Definitionofsurfacesofthefluidfield.4.2PreparationoftheMeshThisstageconsistsinpreparingthemeshofthefluid field. In our case, one used a lineartetrahedral element with 30717 nodes and179798elements(Fig.5).

Fig.5.Meshofthefluidfield.Atthetimeofthebrakingprocess,apartofthefrictional heat escapes into the ambient air byconvection and radiation. Consequently, thedeterminationoftheheattransfercoefficientsisessential. Their exact calculation is, however,rather difficult, because these coefficientsdepend on the location and the construction ofthebrakingsystem,thespeedofthevehicleandconsequently, on the air circulation. Since theprocess of heat transfer by radiation is not toosignificant,wewill determineusingANSYSCFX11.0 code only the convection coefficient (h) ofthe disc. This parameter will be exploited todeterminethethree‐dimensionaldistributionofthetemperatureofthedisc.

InterfaceFluid‐solid

Exitoftheair

DSYM1

DR1

DV1

Entry1oftheair

Entry2oftheair


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For reasons of symmetry of the disc, one tookonly the quarter of the geometry in the case ofthe full and ventilated disc; one kept thetetrahedral form to generate the mesh of thediscs(Figs.6and7).

Fig.6.Meshingofthefulldisc(Numberofelements272392).

Fig. 7. Meshing of the ventilated disc (Number ofelements27691).4.3ModelinginANSYSCFXFor the preparation of themesh of CFDmodel,onedefinesinitially,varioussurfacesofthediscin integrated computer engineering andmanufacturing (ICEM) CFD as shown in Fig.8;weusedalineartetrahedralelementwith30717nodes and 179798 elements. In order not toweigh down calculation, an irregular mesh isused in which the mesh is broader where thegradientsareweaker(nonuniformmesh),

Fig.8.Definitionofsurfacesofthefulldisc.Table.3Boundaryconditions.

BoundaryBoundarycondition

Parameters

Inlet PressureinletAtmosphericpressureandtemperature

Outlet PressureoutletAtmosphericpressureandtemperature

Domainedges

Symmetry Symmetry

Discsurface Wall800Ktemperature,thermalpropertiesof

greycastiron

a) Physicalmodel

In this step, one declares all of the physicalcharacteristics of the fluid and the solid. Afterthe meshing, are defined all the parameters ofthe different models to be able to start theanalysis.

b) DefinitionofthedomainsInitially, one valid the elaborated models andoneactivateintheoption"ThermalEnergy»thecalculationofheattransfer«HeatTransfer".Fluiddomain:Speedentry:Ventnon.st=Vent–Va.tDiscdomain:Enteringflux:FLUXnon.st=(CF)(Ventnon.st),

CF=149893.84Ventnon.st=Vent–Va.t

FLOWnon.st:Nonstationaryfluxentering.Ventnon.st:Nonstationaryspeedenteringoftheair.

c) DefinitionofmaterialsWe introduce into the computer code thephysical properties of used materials. In thisstudy, we selected one cast iron material (FG15).

d) DefinitionoftheboundaryconditionsThe first step is to select the Inlet and Outletfacesoftheheatflux.Theseoptionsarefoundintheinsertionmenu“BoundaryConditions”intheCFXPre.


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The boundary conditions concerning the padswill be also defined. One selects the options“Wall” and "Symmetry ", because there will bethe possibility of adjusting a certain number ofparameters in the boundary conditions such asfluxenteringthedisc.

e) ApplicationoftheinterfacesdomainsThe areas of interfaces are commonly used tocreate theconnectionor linkageareas.Surfaceslocated between the interactions regions (air‐disc)arereportedassolid‐fluidinterface.

f) TemporaryConditionSince in this study is to determine thetemperature field in a disc brake during thebraking phase of a vehicle of average class,wetakethefollowingtemporalconditions:

‐Brakingtime=3.5[s]

‐Incrementtime=0.01[s]

‐Initialtime=0[s]Before starting the calculation and the analysiswithANSYSCFXPRE,itcanbeensuredthatthemodeldoesnotcontainanyerror.The airflow through and around the brake discwas analyzed using the ANSYS CFX softwarepackage. The ANSYS‐CFX solver automaticallycalculates heat transfer coefficient at the wallboundary. Afterwards the heat transfercoefficients considering convection werecalculatedandorganizedinsuchaway,thattheycould be used as a boundary condition inthermal analysis. Averaged heat transfercoefficienthadtobecalculatedforalldiscusingANSYSCFXPostasitisindicatedinFig.9.

Fig.9. Distribution of heat transfer coefficient on afulldiscinthesteadystatecase(FG15).

g) Results of the calculation of the heattransfercoefficient(h)

The heat transfer coefficient is a parameterrelatedtovelocityofairandtheshapeofbrakedisc,andmanyotherfactors.Indifferentvelocityof air, the heat transfer coefficient in differentpartsofbrakediscchangeswithtime[53].Heattransfercoefficientwilldependonairflowintheregion of brake rotor and vehicle speed, but itdoesnotdependonmaterial.Inthissimulation,it is determined the average value of thecoefficient h “Wall heat Transfer Coefficient”,variablewithtime(Figs.10and11).

-0,5 0,0 0,5 1,0 1,5 2,0 2,5 3,0 3,5 4,0

0

10

20

30

40

50

60

70

80

90

100

110

120 SC1 SC2 SC3 SC4 SF1 SF3 ST2 ST3 ST4 SV1 SV2 SV3 SV4

Hea

t tr

ansf

er c

oeff

icie

nt h

[W

m-2°C

-1]

Time [s] Fig. 10. Variation of heat transfer coefficient (h) ofvarioussurfacesforafulldiscintransientcase(FG15).

-0,5 0,0 0,5 1,0 1,5 2,0 2,5 3,0 3,5 4,00

25

50

75

100

125

150

175

200

225

250 SC1 SC2 SC3 SF1 SF3 SPV1 SPV2 SPV3 SPV4 ST1 ST2 ST3 ST4 SV1 SV2 SV3 SV4H

eat

tran

sfer

coe

ffic

ien

t h [

W m

-2 °

C-1

]

Time [s] Fig.11. Variation of heat transfer coefficient (h) ofvarioussurfacesforaventilateddiscintransientcase(FG15).4.4DeterminationofthedisctemperatureThemodelingofthedisctemperatureiscarriedout by simulating a stop braking of a middleclasscar(brakingoftype0).


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ThecharacteristicsofthevehicleandofthediscbrakearelistedinTable1.The vehicle speed decreases linearly with timeuntil the value 0 as shown in Fig. 12. Thevariation of the heat flux during the simulationtimeisrepresentedontheFig.13.

0 10 20 30 40

0

10

20

30

Spe

ed [

ms-1

]

T im e [s]

Speed [m s-1]

Fig.12.Speedofbrakingversustime(Brakingoftype0).

0 10 20 30 400

1x106

2x106

3x106

4x106

5x106

Hea

t F

lux

[W

m-2

]

T im e [s]

H eat F lux

Fig.13.HeatFluxversustime.4.5CreatingoffiniteelementmeshfordiscMeshingofthefullandventilateddischasbeendoneusingANSYSMultiphysics.Theelementusedof themeshingisoftetrahedralshape(Figs.14and15).

Fig.14. Full typediscmeshmodel (total numberofnodes172103–totalnumberofelements114421).

Fig.15. Ventilated type disc mesh model (totalnumberofnodes154679‐totalnumberofelements94117).4.6ApplyingtheboundaryconditionsThe boundary conditions are introduced intomodule ANSYS Workbench [Multiphysics], bychoosing themode of first simulation of the all(permanent or transitory), and by defining thephysical properties of materials. Theseconditionsconstitutetheinitialconditionsofoursimulation.Afterhavingfixedtheseparameters,oneintroducesaboundaryconditionassociatedwitheachsurface.

Totaltimeofsimulation=45s

Incrementofinitialtime=0.25s

Incrementofminimalinitialtime=0.125s

Incrementofmaximalinitialtime=0.5s

Initialtemperatureofthedisc=20°C

Materials:GreyCastIronFG15.

Convection: One introduces the values ofthe heat transfer coefficient (h) obtainedfor each surface in the shape of a curve(Figs.10,11)

Flux: One introduces the values obtainedbyfluxenteringbymeansofthecodeCFX.

5.RESULTSANDDISCUSSIONSThemodelingoftemperatureinthediscbrakewillbecarriedoutbytakingaccountofthevariationofacertainnumberofparameterssuchasthetypeofbraking, the cooling mode of the disc and thechoiceofdiscmaterial.Thebrakediscsaremadeofcast ironwithhighcarboncontent;thecontactsurface of the disc receives an entering heat fluxcalculatedbyrelation(1).


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AmodelpresentsathreedimensionalsolidDiscsqueezed by two finite‐width friction materialcalledpads.Theentiresurface,S,oftheDischasthree different regions including S1 and S2. OnS1 heat flux is specified due to the frictionalheating between the pads and Disc, and S2 isdefinedfortheconvectionboundary.Therestoftheregion,exceptS1US2,iseithertemperaturespecifiedorassumedtobecalculated:theinnerand outer rim area of Disc. Since the axis‐symmetricmodelisconsideredallthenodesonthe hub radius are fixed. So the nodaldisplacements in the hub become zero, i.e. inradial,axialandangulardirections.5.1InfluenceofconstructionofthediscFigure 16 shows the variation of thetemperature versus time during the total timesimulation of braking for a fall disc and aventilated disc. The highest temperatures arereachedatthecontactsurfaceofdisc‐pads.Thestrong rise in temperature is due to the shortdurationof thebrakingphase and to the speedof the physical phenomenon. For the two typesof discs, one disc has an immediate, fasttemperature rise followed by a fall intemperatureafteracertaintimeofbraking.

0 2 4 6 8 1 0

2 2 5

2 5 0

2 7 5

3 0 0

3 2 5

3 5 0

3 7 5

4 0 0

Tem

per

atu

re [

°C]

T im e [s ]

V e n t i la te d d i s c F u l l d i s c

(a) (b)

Fig. 16. Temperature distribution of a full (a) andventilateddisc(b)ofcastiron(FG15).

Itcanbeconcludedthatthegeometricdesignofthe disc is an essential factor in theimprovementofthecoolingprocessofthediscs.Figures 17 and 18 respectively show thetemperaturevariationaccordingtothethicknessand radius. It can be noted that there is anappreciablevariationoftemperaturebetweenthetwotypesoffullandventilateddisc.Theinfluenceof ventilation on the temperature field appearsclearlyattheendofthebraking(t=3.5s).

0 5 10 15 20 25 3050

100

150

200

250

300

350

400

Tem

per

atu

re [

°C]

Thickness [mm]

Full disc FG 15 Ventilated disc FG 15

FulldiscVentilateddisc

Fig.17.Temperaturevariationthroughthethicknessforbothdesignswithsamematerial(FG15).

70 80 90 100 110 120 130 140150

200

250

300

350

400

Full disc FG 15 Ventilated disc FG 15

Tem

per

atu

re [

°C]

Radius [mm] Fig.18. Temperature variation through a radius forbothdesignswiththesamematerial(FG15).


60

5.2InfluenceofbrakingmodeThediscbrakeandthewheelaredimensionedaccording to the performance and economicrequirements of the vehicle. They mustsupport increasingly greater mechanical andthermalloadsatmeanvelocitiesinpermanentprogression.Amongtheparametershavinganinfluenceonthethermalbehaviourofthediscbrake is thebrakingmode,whichdependsonthe driver and the traffic conditions. Certainmodes of braking can involve the destructionof the disc and consequently, cause serioustraffic accidents. A braking mode isrepresented in the form of braking cycles,which describe the variation of vehicle speedversustime(v=f(t)).During vehicle operating, the braking system issubjected to repeated actions of the driver. Inthis study,we considered two types of brakingwhose total simulation time is estimated to beequalto135s.Thisisintendedtodeterminethesaturation temperature disc under a cyclicthermal load. This cycle is repeated severaltimes: the first mode consists of braking andacceleration,andthesecondconsistsofbraking,coolinganddeceleration.Figure 19 shows a driving cycle of fourteensuccessivebraking,intheformofsawtooth.

0 20 40 60 80 100 120

0

5

10

15

20

25

30

Spee

d [m

s-1]

Time [s] Fig.19.Drivingcyclewithfourteenrepeatedbraking(Mode1).Figure 20 shows another mode of brakingwhere after each phase of braking one has anidle.

0 20 40 60 80 100 120

0

5

10

15

20

25

30

Vit

esse

[m

s-1

]

T im e [s]

Fig.20.Cyclebrakingwithphaseof idlesaftereachbraking(mode2).Figures 21 and 22 show the three‐dimensionaldistribution of the maximum temperaturereachedinthediscforthetwomodesofbraking,oneobserves anormal increase in temperaturein the tracksof frictionand theexternalcrown.The vanes very strongly warm up and tend todilateandbecomedeformeduntil the completesolidification of the disc. This deformation willcausethesettinginumbrellaofthedisc.

Fig. 21. Temperature map of the disc in mode ofbraking1atthemomentt=131.72[s].

Fig. 22. Temperature map of the disc in mode ofbraking2atthemomentt=130.45[s].


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Figure23showsthecomparisonofthechangeintemperatureofthediscforacyclicbrakingprocessbetweenthefirstmodeandthesecondmode.Fortwo contours, it can be noted that thetemperatures in the disc rise greatly with eachapplication of the brake, then begin theexponential decline. The more the number ofrepetitions of braking increases, the more themaximumtemperaturesincrease.Theinitialstateofthediscchangesaftereachcycle;thedowntimesallowonly onepartial cooling.After each coolingphase, the disc begins to warm again. In fact,duringsuccessivebraking’sthecapacityofcoolingof the disc is insufficient to lower the surfacetemperaturetoneartheinitialtemperature,whichcausesanaccumulationofenergyandthereforeahigher surface temperature. These results show,that the transient thermal behaviour of a discbrakedependsonthebrakingcycleimposedanditisdominatingbecause itdictatesthecoolingtimeof the disc. According to Fig. 23, it can be notedthat in the case of braking cycle mode 2, areduction of the temperature of approximately535 °C is 45.19% comparedwith the first cycle.Weconcludethatthebrakingmodewithacoolingphaseinfluencestheheattransfersinthediscverypositively, which involves a reduction in themaximum temperature of the interface, whichcausescrackingandmechanicalwear.

0 20 40 60 80 100 1200

100

200

300

400

500

600

700

800

900

1000

1100

1200

Tem

pera

ture

[°C

]

Time [s]

Mode of braking 2 Mode of braking 1

Fig. 23. Temperature variation of the two brakingmodesversustime.Inaddition, this tendencywillenableus toensurethe safety and fatigue life of the brake systemcomponent.Finally,itwouldbeinterestingtocarryoutthiscalculationonbraketestbenchesinordertovalidatetheseresultsofthenumericalsimulation.

5.3ComparisonbetweenfullandventilateddiscIn this part, we presented the cartographies oftotalanddirectionalheatfluxandaswellasthetemperaturedistributioninafullandventilateddiscandofcastironFG15foreachmomentwithbraking.Thetemperaturedistributionofthediscat the beginning braking (with t=0.25 s) isinhomogeneous. According to experimentaltests' carried out by research , braking oftenbegin with the formation from hot circlesrelativelyon theuniformsurfacesof thedisc inthecircumferentialdirection,movingradiallyonthe disc and transforming then into hot points((hotspot)).Theappearanceofthephenomenonof the hot points is due to the nonuniformdissipationofheatflux.Concerning the heat flux, it can be notedaccording toFigs.25and28 that themaximumvalueofthetotalheatfluxislocatedonthelevelof thecalorific throatat theendofbraking (t=3.5 s); this is explained by the increase in thegradientsandthethermalconcentrationsinthiszone.Thecalorific throat ismanufacturedsoasto limit the heat flux coming from the frictiontracksandmovingtowardsthebowlofthediscbrake inordertoavoidtheexcessiveheatingoftherimandthetire.Duringtheheating,thediscis tightened to dilate in the hot zones fromwhere creating of compressive stresses withplasticization.Ontheotherhand,duringcooling,there is appearance of residual stresses oftraction. The disc is thus subjected during itsrotationtoconstraintstraction/compression.a. Fulldisc

‐a‐:t=0.25[s]‐b‐:t=1.8839[s]


62

‐c‐:t=3.5[s]‐d‐:t=5[s]

‐e‐:t=20[s]‐f‐:t=45[s]

Fig. 24. Temperature distribution for a full disc ofmaterialFG15.

‐a‐:t=0.25[s]‐b‐:t=1.8839[s]

‐c‐:t=3.5[s]‐d‐:t=5[s]

‐e‐:t=20[s]‐f‐:t=45[s]

Fig.25.DistributionoftotalheatfluxforafulldiscofmaterialFG15.

‐a‐:AccordingtotheaxisX

‐b‐:AccordingtotheaxisY

‐c‐:AccordingtotheaxisZ

Fig. 26. Distribution of directional heat flux at themomentt=1.8839[s]accordingtothreeaxes(X,Y,Z)forafulldiscofamaterialFG15.b. Ventilateddisc

‐a‐:t=0.25[s]‐b‐:t=1.8506[s]


63

‐c‐:t=3.5[s]‐d‐:t=5[s]

‐e‐:t=20[s]‐f‐:t=45[s]

Fig. 27. Temperature distribution for a ventilateddiscofmaterialFG15.

‐a‐:t=0.25[s]‐b‐:t=1.8506[s]

‐c‐:t=3.5[s]‐d‐:t=5[s]

‐e‐:t=20[s]‐f‐:t=45[s]Fig.28.DistributionoftotalheatfluxforaventilateddiscofmaterialFG15.

‐a‐:AccordingtotheaxisX

‐b‐:AccordingtotheaxisY

‐c‐:AccordingtotheaxisZ

Fig. 29. Distribution of directional heat flux at themomentt=1.8506[s]accordingtothreeaxes(X,Y,Z)foraventilateddiscofamaterialFG15.5. CONCLUSIONIn this study, we have presented a numericalsimulationofthethermalbehaviourofafullandventilated disc in transient state. By means ofthe computer code ANSYS 11 we were able tostudy the thermalbehaviourofagraycast iron(FG15).Inadditiontothe influenceof theventilationofthe disc, on the thermal behaviour of the discsbrake, the numerical simulation shows thatradialventilationplaysaverysignificantroleincoolingofthediscinthebrakingphase,wealsostudiedtheinfluenceofthebrakingmodeonthe


64

thermal behaviour of the disc brake. Throughthenumericalsimulation, itcouldbenotedthatthe quality of the results concerning thetemperature field is influenced by severalparameterssuchas:

• Technologicalparametersillustratedbythedesign.

• Numerical parameters represented by thenumberofelementsandthestepoftime.

• Physicalparametersexpressedbythetypesofmaterials.

• Brakingmodeimplemented.Regarding the calculation results, it can be saythat they are satisfactorily in agreement withthose commonly found in the literatureinvestigations. It would be interesting to solvethe problem in thermo mechanical disc brakeswith an experimental study to validate thenumerical results, forexample,on testbenches,in order to demonstrate a good agreementbetweenthemodelandreality.Regarding the outlook, there are threerecommendations for the expansion of futurework related to disc brake that can be done tofurther understand the effects of thermomechanical contact between the disc and pads,therecommendationsareasfollows:

1. Experimentalstudytoverifytheaccuracyofthenumericalmodeldeveloped.

2. Tribological and vibratory study of thecontactdisc–pads;

3. Study of dry contact sliding under themacroscopic aspect (macroscopic state ofthesurfacesofthediscandpads).

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7. numerical modeling of disc brake system in frictional...

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