317

Vol.35,No.4(2013)317‐329

TribologyinIndustry

www.tribology.fink.rs

EffectofBandContactontheTemperatureDistributionforDryFrictionClutch

O.I.Abdullah

a,J.Schlattmanna

a

SystemTechnologyandMechanicalDesignMethodology,HamburgUniversityofTechnology,Germany.

Keywords:

BandcontactDryfrictionclutchFrictionalheatingTemperaturefield2DFEM

ABSTRACT

Inthisstudy,thetwodimensionalheatconductionproblemforthedryfriction clutch disc ismodeledmathematically analysis and is solvednumericallyusingfiniteelementmethod,todeterminethetemperaturefieldwhenband contactsoccursbetween the rubbing surfacesduringtheoperation ofanautomotive clutch.Temperature calculationhavebeenmade for contact area of different bandwidth and the resultsobtainedcomparedwiththeseattainedwhencompletecontactoccurs.Furthermore, the effects of slipping timeand sliding velocity functionareinvestigatedaswell.Bothsingleandrepeatedengagementsmadeatregularintervalareconsidered.

©2013PublishedbyFacultyofEngineering

Correspondingauthor:

OdayI.AbdullahSystemTechnologyandMechanicalDesignMethodology,HamburgUniversityofTechnology,Hamburg,Germany.E‐mail:oday.abdullah@tu‐harburg.de

1. INTRODUCTIONExperience shows that most premature clutchfailures can be attributed to excessive surfacetemperature generated during slipping. And topreventclutchfailurebeforeexpectedlifecycleitis necessary to know the maximum surfacetemperature and how this depends on knownconditions of loading, physical properties anddimensions of the clutch disc and degree of aircooling.Newcomb [1] derived the equations duringslipping period to determine the energydissipatedandthetemperaturesreachedatanyinstant during a single engagement of a clutch

when its torque capacity is a function of time.Twotypicaltorque‐timevariationsarediscussedand a comparison is made with the case whenthetorqueisassumedtobeconstant.Anderson [2] introduced and discussed fourautomotivefrictionsystemhotspottypes.Theseare asperity, focal, distortional, and regional.Friction material and metal counter surfacewearconsequencesarediscussed,astheyrelateto the different hot spotting types. Focal hotspots are emphasized. These may formmartensiteonthecastirondrumordiskrubbingsurface. Such hot spots, if not prevented, canprovide a root cause for unacceptableperformanceordurabilityinautomotivefriction

RESEARCH

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systems. Computer studies, using a two‐dimensionalmodel,areusedtocomplementtheexperimental studies of critical hot spots anddetermine hot spot thermal flux limits. Surfacemelting and known requirements for theformation of martensite are used to establishboundsfromthecomputeranalysis.Lee and Barber [3] investigated thethermoelastic instability in automotive diskbrake systems and focusing on the effect of afinitediskthickness.Afinitelayermodelwithananti‐symmetric mode of deformation canestimate the onset of instability observed inactual disk brake systems. Also some effects ofsystem parameters on stability are found toagreewelltoexperimentalobservations.Lee and Barber [4] investigated thermoelasticinstability in an automotive disk brake systemexperimentally under drag braking conditions.The onset of instability is clearly identifiablethrough the observation of non‐uniformities intemperature measured using embeddedthermocouples. A stability boundary isestablished in temperature/speed space, thecritical temperature being attributable totemperature dependence of the brake padmaterialproperties.Itisalsofoundthattheformof the resultingunstableperturbationsoreigenfunctions changes depending upon the slidingspeedandtemperature.Yevtushenko e al [5] were applied one‐dimensional transient heat conductivity to studythe contact problem of a sliding of two semi‐spaces, which induces effects of friction, heatgeneration and water during braking. In thepresent temperature analysis the capacity of thefrictional source on the contact plane dependentonthetimeofbraking.TheproblemsolvedexactlyusingtheLaplacetransformtechnique.Numericalresults for the temperature are obtained for thedifferent values of the input parameter, whichcharacterize the duration of the increase of thecontactpressureduringbraking fromzero to themaximum value. An analytical formula for theabrasivewearof the contactplane isobtained inthe assumption, that the wear coefficient is thelinearfunctionofthecontacttemperature.Decuzzi and Demelio [6] studied the thermo‐mechanicaldamageofclutchesandbrakesduetothermoelastic instability (TEI), which leading to

localized surface burning of frictional materials,permanent distortions ofmetal plates, vibrationsandnoise.Inthiswork,theanalyticalformulationproposed before, rephrased in dimensionlessform,isemployedtoestimatetheinfluenceofthematerialpropertiesontheminimumcriticalspeedofslidingsystems.Twocasesofpractical interestare considered, an automotive multi‐disc clutch(dissimilar materials case) and a carbon–carbonbrake/clutch for high speed applications (similarmaterials case). In both cases the relativeimportanceinalteringtheminimumcriticalspeedand thedirection of change of eachparameter isexamined and a comparison with previousavailable solutions is performed. A simple andsufficiently accurate relation is found to holdbetweentheslidingVorrotatingΩcriticalspeedandthearbitrarymaterialparameterξ,

n

oooV

V

minmin

Thiscanbeemployed inestimating theoptimumsetofmaterialpropertiesforslidingsystems.Yun [7] used finite elementmethod to solve theproblem involving thermoelasto dynamicinstability(TEDI)infrictionalslidingsystems.Theresulting matrix equation contains a complexeigenvaluethatrepresentstheexponentialgrowthrate of temperature, displacement, and velocityfields. Compared to the thermoelastic instability(TEI)inwhicheigenmodesalwaysdecaywithtimewhen the sliding speed is below a critical value,numerical results from TEDI have shown thatsome of the modes always grow in the timedomainatanyslidingspeed.Asaresult,whentheinertial effect is considered, the phenomenon ofhot spotting canactuallyoccurat a sliding speedbelowthecriticalTEIthreshold.Thefiniteelementmethod presented here has obvious advantagesover analytical approaches and transientsimulationsoftheprobleminthatthestabilitiesofthe system can be determined for an arbitrarygeometry without extensive computationsassociated with analytical expressions of thecontact condition or numerical iterations in thetimedomain.Grze[8]investigatedthetemperaturefieldsofthesoliddiscbrakeduringshort,emergencybraking.The standard Galerkin weighted residualalgorithmwasusedtodiscretizetheparabolicheattransfer equation. The finite element simulation

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fortwo‐dimensionalmodelwasperformedduetothe heat flux ratio constantly distributed incircumferentialdirection.Twotypesofdiscbrakeassembly with appropriate boundary and initialconditionsweredeveloped.Resultsofcalculationsfor the temperatureexpansion inaxialandradialdirectionsarepresented.Theeffectoftheangularvelocity and the contact pressure evolution ontemperatureriseofdiscbrakewasinvestigated.Itwasfoundthatpresentedfiniteelementtechniquefor two‐dimensional model with particularassumptioninoperationandboundaryconditionsvalidateswithsofarachievementsinthisfield.Jing et al [9] studied the disadvantages of thethermo‐elastic instability (TEI) due to frictionalheat energy at the rough sliding interfaces. Themainshortcomingofexistingliteraturesis, inouropinion, that it do not deduce theoreticalmathematicsmodel taken intoaccount the roughsurface profile with the heat convection andradiation boundary conditions in temperaturefield. We now present our finite element modelthatwebelievecanmuchreducethisshortcoming.In the full paper, we explain ourmodel in somedetail;inthisabstract,wejustaddsomepertinentremarks to naming the two topics. Topic 1 is:contactmodelofroughsurfaceprofile.Topic2is:temperaturefieldmodelofbrakedisks.FinallyweperformsimulationsinANSYS.Theresults,shownin the full paper, show the importance of theroughness in the temperature field and thepracticabilityofthemodel.Hwang et al [10] determined the temperaturedistribution,thermaldistortion,andthermalstressinasoliddiscby threedimensionalmodeling forrepeatedbraking.Brakingisappliedfourtimesinthepresentstudy;thevehicleisdeceleratedfrom100to50kphwith0.6g,afterwhichthevelocityisagainacceleratedto100kph.Inordertosimulatethe friction heat behavior accurately in repeatedbraking,themovingheatsource,whichisdefinedby time and space variable, is applied on thefrictional surface. The temperature field andthermalstressinthediscpresentanon‐uniformitycharacteristicbecauseof themovingheat source.Temperature and thermal stress of the point onthe frictional surface of the brake disc presentfluctuation in the braking operation. The coningangledue to thenon‐uniform radial temperaturedistribution varies with temperature. Thermalfatigueisalsodiscussedinthisarticle.

Grze [11] developed a transient thermal analysistoexaminetemperatureexpansioninthediscandpadvolumeundersimulatedoperationconditionsofsinglebrakingprocess.Thiscomplexproblemoffrictional heating has been studied using finiteelement method (FEM). The Galerkin algorithmwasusedtodiscretizetheparabolicheattransferequation for the disc and pad. FE model ofdisc/padsystemheatingwithrespect toconstantthermo‐physical properties of materials andcoefficientoffrictionwasperformed.Thefrictionalheating phenomenon with special reference tocontactconditionswasinvestigated.An axisymmetric model was used due to theproportionalrelationbetweentheintensityofheatfluxperpendiculartothecontactsurfacesandtherateofheattransfer.Thetimerelatedtemperaturedistributions in axial and radial directions arepresented. Evolution of the angular velocity andthecontactpressureduringbrakingwasassumedtobenonlinear.Presentedtransientfiniteelementanalysis facilitates to determine temperatureexpansioninspecialconditionsofthermalcontactinaxisymmetricmodel.Fanetal[12]developedathree‐dimensionalfiniteelement model for thermal‐structure couplinganalysis of a type of disc brake was established.And using the direct‐coupling technique in finiteelementmethod, an emergentworking conditionof braking process was analyzed, getting thedistribution laws of the stress field and thetemperature field, and the interacting lawsbetweenthestressfieldandthetemperaturefield.The results correspond to the actual application,thusprovidingguidanceforthedesigningandthefatigueanalysisofdiscbrakes.In this paper a finite element method has beenapplied to calculate the heat generated on thesurfaces of friction clutch and temperaturedistribution for case of bands contact betweenflywheel and clutch disc, and between the clutchdiscandpressureplate(onebadcentralandtwobands) and compared with case of full contactbetween surfaces for single engagement andrepeated engagements. Furthermore, this papershows effect of pressure capacity on thetemperaturefield,whenthepressureisafunctionoftime,threekindsofpressurevariationwithtime(constant,linearandparabolic)arepresented.

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2. MATHMATICALMODELConsiderthebasicpowertransmissionshowninFig.1,consistingoftwoinertiasI1andI2initiallyrotatingatunequalangularvelocitiesΩ1andΩ2and at any instant time t, rotating at differentangular velocities ω1 and ω2 respectivelythroughouttheclutchengagement.ThemomentofinertiasforinputandoutputareI1andI2.AndT1 is input torque and T2 is output torque.Duringslippingthetorquecapacityoftheclutchvariesasafunctionoftimeϕ(t).Itassumedthatthe torques T1 and T2 are constant since anyvariation in these values is likely to be smallcompared to the uncertainty of theirmeasuredvalues. Then the equations of motion for thesystemareexpressedasfollows[1]:

dt

dItT 1

11 )( (1)

dt

dITt 2

22)( (2)

Fig.1Basicpowertransmissionsystem.Integrating Eq (1) and Eq (2), and using theinitially conditions (at t=0, ω1=Ω1 and ω2=Ω2),whereΩ1andΩ2aretheangularvelocityinitiallyforflywheelandoutputendofshaftrespectively:

1

011

11 )(

1

t

dttI

tI

T (3)

2

022

22 )(

1

t

dttI

tI

T (4)

Andtherelativeangularvelocity(ωr=ω1‐ω2)is:

ro

t

r dttPtM 0

)( (5)

where:

2

2

1

1

I

T

I

TM , )

11(

21 IIP and 21 ro

If there is no external torques (M=0), then theeq.(5)willbe:

ro

t

r dttP 0

)( (6)

The slipping period ts determined by putting(ωr=0)ineq.(6)yield:

t

ro dttP0

)( (7)

The simplest torques (under uniform wearcondition)variationwithtimeduringslipping[1]:1.Constanttorque(orpressure)Thepressureforthiscaseis:

optp maxmax )( (8)

then:

oioio CrrrtpTt )()()( 22max (9)

where: )( 22max ioioo rrrpC

AnditcanbefoundtheslippingtimetsfromEq.(7),andrelativeangularvelocityωrformEq.(6):

o

ros TPt

(10)

)1()(s

ror t

tt (11)

2. PressureincreasinglinearlyThepressurefunctionis:

)/()( maxmax so ttptp (12)

then:

)/()()/(

)/()(22

max soioiso

so

ttCrrrttp

ttTt

(13)

Bythesameproceduresinitem(1)itcanbefundtheslippingtimeandrelativeangularvelocity:

o

ros TPt

2 (14)

2

1)(s

ror t

tt (15)

T1

p p

T2

ω1

I1 I2

ω2

T

T

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(t/ts)

(w/w

ro)

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 10

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

Constant TorqueLinear TorqueParabolic Torque

3.PressureparabolicallyincreasingThepressurefunctionis:

)/(2)/()( maxmax sso ttttptp (16)

then,

)/(2)/(

)()/(2)/(

)/(2)/()(22

max

sso

ioisso

sso

ttttC

rrrttttp

ttttTt

(17)

Theslippingtimeandrelativeangularvelocityare:

o

ros TPt

2

3 (18)

1

2

3

2

1)(

23

ssror t

t

t

tt (19)

During the slipping period, the thermal heatfluxeswithtimeontheclutchatanyinstantperunitarea(W/m2)is[11]:

ic rttpftq )()()( (20)

where fc is the heat partition ratio whichimposes division of heat entering the clutch,pressure plate and flywheel (assume the samematerial properties for the flywheel andpressureplate),andisgivenasfollows[12].

pppccc

ccc

fffccc

cccc

cKcK

cK

cKcK

cKf

(21)

where k is the thermal conductivity, ρ is thedensityandc isthespecificheat.Allvaluesandparameters, which refer to the axial cushion,frictionmaterial, flywheelandpressureplate inthe following considerations, will have bottomindexescu,c,fandprespectively.Then,theheatfluxontheclutchdiscforconstantpressureis:

)1()( maxs

irooc t

trpftq (22)

Theheatfluxontheclutchdiscforlinearpressureis:

3

max)(ss

irooc t

t

t

trpftq (23)

Andtheheatfluxontheclutchdiscforparabolicpressureis:

54

32

max

2

1

2

5

32

*)(

ss

sss

irooc

t

t

t

t

t

t

t

t

t

t

rpftq

(24)

The maximum heat fluxes occur at (t=0),

)}3/({ stt and (t=0.467 ts) corresponding to

the constant pressure, linear pressure andparabolicpressurerespectively.Figs.2,3and4showsthepressure,relativeslipspeedandheatfluxvarieswithtimeduringtheslipping.

Fig. 2. Variation of [pmax(t)/pmaxo] with time forconstant,linearlyandparabolicallyincreasingtorque.(tsistheslippingtimewhenthetorqueisconstant).

Fig.3Variationof[ωr(t)/ωro]with(t/ts)forconstant,linearlyandparabolicallyincreasingtorque.

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2

(t/ts)

C o ns t a nt T o rq ue

Line a r T o rq ue

P a ra b o lic T o rq ue

[ pmax (t)/pmaxo

 ] 

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Fig.4Variationof[q(t)/fcμpmaxoωrori]with(t/ts)forconstant,linearlyandparabolicallyincreasingtorque.The total thermal energy dissipated during asingleengagementforconstantpressureis:

srooicTc tpArfQ max2

1 (25)

where,A )]([ 22io rrnA isthetotalareafor

contact and n number of contact surfaces. Thetotalthermalenergyduringasingleengagementforlinearpressureis:

srooicTl tpArfQ max4

1 (26)

And the total thermal energy during a singleengagementforparabolicpressureis:

srooicTp tpArfQ max3

1 (27)

Whentheengagementprocessstarts forclutch,the heat will generated between the surfacesdue to the slipping (result of the difference invelocities between the driving shaft and drivenshaft). The heat generatedwill dissipate by theconductionbetween friction clutch componentsandbyconvectiontoenvironment.Duetoshorttime for slipping process the radiation isneglected.Itcanbeobtained,thatthetemperaturedistribution by building two‐dimensional modelstopresentthefrictionalheatingprocessforfrictionclutch. The starting point for the analysis of thetemperature field in the friction clutch is theparabolic heat conduction equation in thecylindricalcoordinatesystem{r‐radialcoordinate(m),θ‐circumferentialcoordinate(rad),andz‐axialcoordinate(m)}[13],whichiscenteredintheaxisofthediscandzpointstoit’sthickness(Fig.5‐a).

0,0,20,

;111

2

2

2

2

22

2

tzrrrt

T

z

TT

rr

T

rr

T

oi (28)

whereαisthethermaldiffusivity,α=k/ρc,riandroaretheinnerandouterradiusforoftheclutchdisc.Hencethedistributionofheatflowwillbeuniform in circumferential direction, whichmeans that, the temperature andheat flowwillnot vary in θ direction, and thus the heatconductionequationreducesto:

0,0,

;11

2

2

2

2

tzrrrt

T

z

T

r

T

rr

T

oi (29)

Fig.(5‐a).Thefrictionclutchdisc(axisymmetric).Theboundaryandinitialconditionsaregivenasfollowsforallcasesduringengagement:

0,20

];),,([0

ttz

TtzrThr

TK

cu

aorrcu (30)

whereTaistheambienttemperatureandhistheconvectionheattransfercoefficient.

0,)2/()2(

];),,([0

tttzt

TtzrThr

TK

ccucu

aorrc (31)

0,)2(,)2(

];),,([

tttzt

TtzrThr

TK

ccucu

airrc i (32)

Theinitialtemperatureis,

)2/(0,

;)0,,,(

cucoi

i

ttzrrr

TzrT

(33)

(t/ts)0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

Constant TorqueLinear TorqueParabolic Torque

[ q(t)/f c μ p

maxo ω

ro r i

 ] 

riro

r

z Flywheelside

Pressureplateside

Axialcushion

z

θ riro

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0),2(0;0

ttzr

Tcurr i

(34)

0,;00

trrrz

Toiz (35)

Theboundary condition for contact surface, forthefirstcase(fullcontactarea)is(Fig.5‐b),

soi

cttzc

ttrrr

tqz

TK

ccu

0,

);()2/( (36)

Fig.(5‐b).FEmodelwithboundaryconditionsforcase(1).Forthesecondandthirdcases(onecentralbandofcontact), theboundaryconditions forcontactsurfaceare(Fig.5‐c),

soi

ttzc

ttrrrrrrz

TK

ccu

0,

;0

21

)2/( (37)

s

cttzc

ttrrr

tqz

TK

ccu

0,

);(

21

)2/( (38)

Fig. (5‐c). FE model with boundary conditions forcases(2&3).For the fourth and fifth cases (two band ofrubbing contact), the boundary conditions forcontactsurfaceare(Fig.5‐d),

soi

cttzc

ttrrrrrr

tqz

TK

ccu

0,,

);(

21

)2/( (39)

s

ttzc

ttrrrz

TK

ccu

0,

;0

21

)2/( (40)

Fig. (5‐d). FE model with boundary conditions forcases(4&5).ThedetailsofeachthecaseisoutlinedinTable(1). Table1.Descriptionofr1andr2forallcases.

CaseNo.

DescriptionContactarea%

1 Fullcontact:r1=‐,r2=‐ 100

2

Onebandofcontact:

2

2

1oii rrr

r

,2

2

1oio rrr

r

50

3

Onebandofcontact:

8

54 22

1ioio rrrr

r

8

45 22

2ioio rrrr

r

75

4

Twobandsofcontact:

221 75.025.0 io rrr

222 25.075.0 io rrr

50

5

Twobandsofcontact:

8

53 22

1io rr

r

8

35 22

2io rr

r

100

3. FINITEELEMENTFORMULATIONThe object of this section is to developapproximate time‐stepping procedures foraxisymmetric transient governingequations. Forthistohappen,thefollowingboundaryandinitialconditionsareconsidered:

Tp onTT (41)

ha onTThq )( (42)

qcu onqq (43)

r

HeatFlux

Insulated, h=0

ConvectionConvection

r Insulated,h=0

ConvectionHeatFlux

h=0 h=0

r1

r2

z

Convection

z

r Insulated,h=0

Convection HeatFlux

h=0 HeatFlux

r1

r2

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0 ttimeonTT o (44)

whereTpistheprescribedtemperature,ΓΤ,Γh,Γq,are arbitrary boundaries onwhich temperature,convectionandheatfluxareprescribed.Inordertoobtainmatrix formofEq. (25)theapplicationof standard Galerkin’s approach was conducted[15]. The temperature was approximated overspaceasfollows:

n

iii tTzrNtzrT

1

)(),(),,( (45)

where:Niareshapefunctions,nisthenumberofnodes in an element, Ti(t) are time dependentnodal temperatures. The standard Galerkin’sapproach of Eq. (25) leads to the followingequation:

01

2

2

2

2

dt

TC

z

T

r

T

rr

TNK i (46)

UsingintegrationbypartsofEq.(42)weobtain,

0dnz

TNKdl

r

TNK

d

t

TCN

r

T

r

N

z

T

z

N

r

T

r

N

K

ii

i

iii

(47)

Integralformofboundaryconditions:

q h

haiqi

ii

dTThNdqN

dnz

TNKld

r

TNK

)((48)

Substituting Eq. (44) and spatial approximationEq.(41)toEq.(43)weobtain:

h

q

hai

qijj

i

jjijiji

dTThN

dqNdTt

NNC

dTr

N

r

N

z

N

z

N

r

N

r

NK

0)(

(49)

where,iandjrepresentthenodes.Equation(45)canbewritteninmatrixform:

RTKt

TC

(50)

Where[C] istheheatcapacitymatrix,[K] istheheatconductivitymatrix,and{R}isthethermalforcematrix,or:

jjijj

ij RTKt

TC

(51)

where,

dNNCC jiij

dNNh

d

Tr

N

r

N

Tz

N

z

NT

r

N

r

N

KK

ji

jji

jji

jji

ij

hq

haiqii dThNdNqR

orinmatrixform,

dNNCC T ][][

dNNhdBDBKK TT

hq

hT

aqT dNThdNqR

Table2.Thermophysicalpropertiesofmaterialsandoperationsconditionsforthethermalanalysis.

Parameters ValuesInnerradius,ri [m] 0.085Outerradius,ro [m] 0.135Momentsofinertiafortheengine[kg‐m2] 1Momentsofinertiaforthetransmission/vehicle[kg‐m2]

5

TorqueT[Nm] 587.47Thicknessoffrictionmaterial,tc[m] 0.002Thicknessoftheaxialcushion,tcu[m] 0.001Maximumpressure,pmaxo [MPa] 0.25Coefficientoffriction,μ 0.4Numberoffrictionsurfaces,n 2Maximumangularslippingspeed,ωro(rad/sec)

220

Conductivityforfrictionmaterial,Kc(W/mK) 0.75Conductivityforpressureplate&flywheel,Kp&Kf(W/mK)

56

Densityforfrictionmaterial,ρc(kg/m3) 1300Densityforpressureplate&flywheel,ρp&ρf(kg/m3)

7200

Specificheatforfrictionmaterial,cc(J/kgK) 1400Specificheatforpressureplate&flywheel,cp&cf(J/kgK)

450

Timestep,Δt(s) 0.002Theslippingtime(constantpressure),ts1 0.3121Theslippingtime(linearpressure),ts2 0.624Theslippingtime(parabolicpressure),ts3 0.468

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(t/ts)

Tem

pera

ture

[K]

0 0.2 0.4 0.6 0.8 1300

310

320

330

340

350

360

370

380

Constant PressureLinear PressureParabolic Pressure

Time [s]

Tem

pera

ture

[K]

0 0.05 0.1 0.15 0.2 0.25 0.3300

310

320

330

340

350

360

370

380

case-1Case-2Case-3

In order to determine temperature distributionof this transient heat conduction problem, thefine mesh element was essential. Moreover,whentheiterativemethodofthegivenproblemis employed, then a relatively short time isneeded for the calculations. In the next step ofthe study, the Crank‐Nicolson method wasselectedasanunconditionallystablescheme.Inthis paper ANSYS software was used toinvestigate transient thermoelastic analysisbehaviour of dry friction clutch. In allcomputationsforthefrictionclutchmodel,ithasbeen assumed a homogeneous and isotropicmaterial and all parameters and materialspropertiesarelistedinTable2.The heat transfer coefficient was changed asfunction of the relative surface velocityaccording to Balazs et al [14], in a stationaryposition,thevaluespecifiedwas(5W/m2K),andat1500 r.p.m15,20 ,35and40W/(m2K) as afunctionoftherelativesurfacespeedinm/s.Theeight‐noded thermal element (PLANE77) wasused in this analysis; the element has onetemperaturedegreeof freedomateachnodeasthe temperature is scalar. A mesh sensitivitystudy was done to choose the optimum meshfromcomputationalaccuracypointofview.4. RESULTSANDDISCUSSIONSInthispaperthetemperaturedistributionofthefriction clutch disc for the bands contact hasbeeninvestigated.Fivecasesinvolvingdifferentregions and percentage area of rubbing incontacthavebeenconsidered,withassumingforeach configuration dissipating the same totalenergy during an engagement. Full contact ofareaofclutchdiscforthefirstcase,50%and75%ofcentralbandcontactareaisconsideredforcase2andcase3respectively,whereasthetwobands of 50% and 75% contact area used forcase4andcase5respectively.Figure 6 presents the variation of temperaturewith time for single engagement and differenttypesofpressure(case‐2)atmeanradiusrm.Itcanbe seen from this figure that themaximumeffect on temperature change occurs whenapplied constant pressure. The maximum ratiofor temperature differences for (Δconst.pressure/Δlinear pressure) and (Δconst. pressure/Δ parabolicpressure)arefoundtobe1.24and1.1respectively.

Fig.6.Variationoftemperaturewithtimeatrm(Case2).Figures7,8and9demonstrate thevariationofsurface temperatures with time for differentcontact area and different types of pressure. Inallfigures,itwasobservedthatthetemperatureincreases when the contact area decreases(pressure increases). The temperature isproportionaltotheappliedpressureandtimeofslipping, and the temperature increases whenthe slipping time and contact area decrease.Whenthecontactareadecreasesfrom100%to50% themaximum increases in the differencetemperatureisapproximately50%foralltypesofpressures.

Fig. 7. Variation of temperature with time at rm(Constantpressure).

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Time [s]

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0.09 0.1 0.11 0.12 0.13290

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Case-1Case-4Case-5

Fig. 8. Variation of temperature with time at ri(Linearpressure).

Fig. 9. Variation of temperature with time at ro(Parabolicpressure).

Fig. 10. Variation of temperature with radius att=0.1545s(constantpressure).

Fig. 11. Variation of temperature with radius att=0.492s(Linearpressure).

Fig. 12. Variation of temperature with radius att=0.333s(parabolicpressure).Figures 10, 11 and 12 exhibit the surfacetemperature in the radial direction (betweeninner radius ri and outer radius ro). It can benoted that the temperature increases in thecontact area of frictionmaterial (band contact)and no change in the other region of nominalfrictionalinterface.Thissituationduetothefactof using low values of thermal conductivity forfrictionmaterials.The thermalvariationwillbejust on the contact area, and which can beneglectedforotherregionsofnominalfrictionalinterfaceincaseofbandcontact.Thenormaloperationof frictionclutchmakesrepeated engagements and the maximum

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0 6 12 18 24 30 36 42 48 54Time [s]

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]

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]

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]

temperature during this operation is veryimportant. Temperature calculation has beenmade for repeated engagements made atregular intervals of time for the same energydissipations. The time between engagementsistaken5seconds.Figures13,14and15showthe variation of temperature with time at rmfordifferenttypesofpressure(constant,linearand parabolic) during 10 repeatedengagements. The maximum temperaturesreached after 10 engagements are 431 K,415.3K and 423.3K corresponding to theconstant pressure, linear pressure andparabolicpressurerespectively.Fig. 13. Variation of temperature with time at rm(Repeatedengagements‐constantpressure‐case2).Fig. 14. Variation of temperature with time at rm(Repeatedengagements‐linearpressure‐case2).

Fig. 15. Variation of temperature with time at rm(Repeatedengagements‐parabolicpressure‐case2).5. CONCLUSIONSANDREMARKSInthispaper transientthermalanalysisofdryfriction clutch disc for a single engagementand repeated engagements based on theuniform wear theory was performed. Two‐dimensional model was built to obtain thenumerical simulation for band contact of discclutch during slipping. The results show thatboth evolution of slipping time and contactarea ratio are intensely effect disc clutchtemperature fields in the domain of time.Proposed finite element modeling techniquefor three types of thermal loads depend ontype of pressure (constant, linear andparabolic),anddifferentregionandlocationofbandcontact. It canbe seen, that theresultoftemperature distribution for constantpressuretypeishigherthantheothertypesofpressure, because of the total quantity ofthermal load is applied in short time withcompared to other types of thermal loads.Also, it can be noticed the uniformtemperatureonthecontactsurfacebecauseofthethermalloadisconstantinradialdirection.Themaximumtemperatureforconstant,linearandparabolicpressuresoccurat(t=0.5ts1) (t=0.78ts2)and(t=0.71ts3)respectively.The study of temperature field of contactsurfaces during repeated engagementsoperationisnecessarytogiveindicationaboutthe maximum temperature, because of thetemperaturewillincreaserapidlywhen

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increases number of times of engagements,and finally likely the temperature exceed thesafe temperature, it's to leading the frictionmaterial to failure, before the expectedlifetime of the clutch. The percentage ofincreases inmaximum temperature are found73.2%, 89.1% and 80.2% corresponding tothe constant pressure, linear pressure andparabolic pressure respectively when thenumber of engagement variation from (1 to10), it is clear that the value of percentageincrease of temperature for linear pressuretypeishighertheothertypesofpressure,thisdue to the total time for engagements whenapplied linear pressure is greater than thetotaltimeofengagementsforothertypes.The damaged or incorrectly machinedflywheel (large deformation, thermal cracks...etc) causes many of problems, one of themfocusing the pressure on small regions ofnominal frictional interface (e.g. bands andspots),forthisit’sessentialwhenfittinganewclutch to a vehicle to ensure that the flywheelis inperfectcondition inorder topreventanypossible clutch problems. The minor scoringand grooving marks in flywheel can beremoved by machining, but if the contactsurface isdeeplyscored, the flywheelmustbereplaced.Scoringandgroovingprevent thedrivenplatefrom contacting the flywheel evenly, resultinginclutchshudderandslippingproblems.Thebandcontactinclutchesisconsideredoneof the disadvantages, which produce bydamaged flywheel, this typeof contact lead tofailure for the friction clutch material beforeestimatedtimeof failure.Thefailureoccursinbandcontactduetoconcentrationoffrictionalheating over zone smaller than frictionalinterface;thisleadstoasignificantincreaseinthevaluesofpressure,andthenwillgeneratedtemperatureshigherthantheexpectedvalues.REFERENCES[1] T.P. Newcomb: “Calculation of Surface

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[10] P.Hwang,XWu,Y.B.Jeon:Thermal–mechanicalcoupled simulation of a solid brake disc inrepeated braking cycles, in:Proceedings of theInstitution of Mechanical Engineers, Part J:JournalofEngineeringTribology,Vol.223,PartJ:J.EngineeringTribology,2009.

[11] Piotr GRZEŚ: Finite Element Analysis ofTemperature Distribution in AxisymmetricModel of Disc Brake, acta mechanica etautomatica,Vol.4,No.4,pp.23‐28,2010.

[12] Liuchen Fan, Xuemei Sun, Yaxu Chu and XunYang:”Thermal‐structurecouplinganalysisofdiscbrake”, in: 2010 International Conference onComputer, Mechatronics, Control and ElectronicEngineering(CMCE),24Aug‐26Aug2010,TBDChangchun,China.

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[14] B. Czéla, K. Váradia, A. Albers, M. Mitariub:“Fethermal analysisofa ceramic clutch”, J.Tribology International, Vol. 42, No. 5, pp.714–723,2009.

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