Numerical modeling of disc brake system in frictional contact.pdf

8/10/2019 Numerical modeling of disc brake system in frictional contact.pdf

1/18

49

Vol. 36, No. 1 (2014) 4966

TribologyinIndustry

www.tribology.fink.rs

NumericalModelingofDiscBrakeSystem

inFrictionalContact

A. Belhocinea, A.R. Abu Bakarb, M. Bouchetara a

aDepartmentofMechanicalEngineering,USTOOranUniversity,L.P1505ElMnaouer,USTO31000Oran,Algeriab

DepartmentofAutomotiveEngineering,UniversitiTeknologiMalaysia,81310UTMSkudai,Malaysia.

Keywords:

Brakedisc

Heatflux

Heattransfercoefficient

Thermalanalysis

Finiteelement

Stress

A B S T R A C T

Safetyaspectinautomotiveengineeringhasbeenconsideredasanumber

onepriority indevelopmentofnewvehicle.Eachsinglesystemhasbeen

studied and developed in order tomeet safety requirement. Instead of

having air bag, good suspension systems, good handling and safe

cornering,there isonemostcriticalsystem inthevehiclewhich isbrake

systems. The objective of this work is to investigate and analyse the

temperature distribution of rotor disc during braking operation using

ANSYSMultiphysics.Theworkusesthefiniteelementanalysistechniques

topredict the temperaturedistributionon thefullandventilatedbrake

disc and to identify the critical temperature of the rotor by holding

account certainparameters such as; thematerial used, thegeometric

designofthediscandthemodeofbraking.Theanalysisalsogivesus,the

heatfluxdistributionforthetwodiscs.

2014 Published by Faculty of Engineering

Corresponding author:AliBelhocine

Faculty of Mechancal Engineering,

USTOOranUniversity,

L.P.1505ElMnaouer,USTO,

31000OranAlgeria

Email:[email protected]

1. INTRODUCTION

Braking 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 energythrough friction between the brake pads and therotor faces. High temperatures can also lead tooverheating of brake fluid, seals and othercomponents. The stopping capability of brakeincreases by the rate at which heat is dissipated

due to forced convection and the thermalcapacity of the system [1]. Tracing of thermal

effects in any given part of the brake is possibleby numerical simulations, but it requires a valid

model to be constructed. The verification of suchmodel 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 the

optimization were only boosted with the adventof modern computational resources in the late

R

ESEARCH


2/18

A.Belhocineetal.,TribologyinIndustryVol.36,No.1(2014)4966

50

eighties [5]. Currently, although of not simpleusage and requiring previous understanding ofthe basics of fluid mechanics and heat transfercoupled with knowledge of flows numericalmodeling, CFD has significantly gainedpreference in the automotive industry designprocess as tool for predicting complex flow andheat transfer behaviour in regions whereotherwise very laborious and time consuming bya combination of nodetosurface and surfacetosurface contact elements [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 combinedeffect of load, speed, friction coefficient, and the

thermo physical and durability properties of thematerials of a frictional couple. Experimentsshowed that the friction coefficient in generaldecreased with increasing sliding speed andapplied load, but increased with increasing disctemperature up to 300 C and then decreasedabove this temperature. The specific wear ratewas found to increase with increasing slidingspeed and disc temperature [8].

Nouby et al [9] introduced a nontraditionalevaluation tool to examine the effects ofdifferent materials, in practical applications, thatare used in fabricating disc brake componentsfor commonly used or special requirements suchas heavyduty performance and racing cars. Anextension of the FE models discussed earlier isan experimental set up work would be needed.As result, brake disc convective cooling analysisand optimization is nowadays mostly carried outusing CFD commercial codes, e,g. [10].

Many investigations of analysis of heat flow

through the ventilated disc brakes are reportedin the literature. Michael and Roland [11]discussed the airflow patterns in the disc rotors.Wallis et al [12] carried out a numerical studyusing Fluent on disc rotor blades to examine theeffects of local heat and mass transfer of theaxial gap distances for a single and corotatingdisc. 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 contactsurfaces due to moving heat surfaces, there aremore 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 understand

thermal 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 generatedbetween two sliding bodies causes thermoelasticdeformation, which alters the contact pressuredistribution. This coupled thermomechanicalprocess is referred to as frictionallyexcitedthermoelastic instability (TEI) [19]. Abu Bakarand Ouyang [20] adjusted the surface profilesusing measured data of the surface height andproduced a more realistic model for brake pads.Direct contact interaction between disc brakecomponents is represented threedimensionalFE model of the disc brake corner thatincorporates a wheel hub and steering knucklethat was developed and validated at bothcomponents and assembly levels to predict discbrake squeal. In addition, the real pad surfacetopography, negative frictionvelocity slope, andfriction damping were considered to increasethe prediction accuracy of the squeal. Brake

squeal is a high frequency noise produced whendriver decelerates and/or stops the vehiclemoving at low speed. It is the noise caused byselfexcited vibration generated by the frictionforce variation between the friction material androtor. It is a phenomenon of dynamic instabilitythat 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 velocityand the nature of the involved surfaces [21]. Theinterface temperature has momentous influence


3/18


51

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 smooth and reliable functioning. In fact, itinfluences the thermoelastic instabilities, whichin turn alter the friction performance at thebraking junctions [22]. In the front wheel, forexample, disc brake pads absorb a major amount(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]. At such high temperatures, pads

suffer from a loss of effectiveness called fadebecause 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 thefriction coefficient to the operating temperaturelevel for the coupled friction surfaces is probablythe most critical point in designing safe andeffective braking systems and it is not surprisingthat many researchers pay their attention totheoretical models for surface temperatureevaluation as well as to surface temperaturemeasurements. A lot of studies about heattransfer at the coupled interfaces are reported inliterature which takes into account thesuperposition of several phenomena, eachdescribed by a number of simplifyingassumptions: experimental, analytical andnumerical methods are attempted to understandand to predict wear effects. From anexperimental standpoint, the system relativemotion, its geometry and the high thermal

gradients which are typically attained makeexperimental temperature detection a complexmatter if one wishes to use thermocoupleslocated directly at the friction interface [2527].Therefore, noncontact measurementsincluding optical or infrared methods could bethe solution and early works are appearing inthis sense [2831]. The latter technique seems tobe the most effective and valuable due to itsability to perform continuous temperature maprecording with relatively high resolutions whencompared to other traditional methods but it isto consider that the area to focus on is hiddenby the coupled surfaces. Due to the described

difficulties in the experimental approach, inrecent years, the finite element method [32] hasbecome the preferred method for studying theproblem at hand while few analytical models arealso available [33]. However, a critical analysis ofthe above mentioned works allows to clearlyconcluding that, often, numerical predictions fortemperature distribution arent adequatelyvalidated by experimental tests. Spulber andVoloaca [34] proposed a new simulation methodof a disc brake thermal stress resistance, fordifferent temperatures, by interactive processingof images obtained by thermography.Temperature evaluation for different workingregimes can be made by recording and processingthermograms of a disc brake heated inside thelaboratory by an external heating source. Taken

pictures along the temperature variation, from theambient value to a value close to real one obtainedon the usual experiments, are processed usingimage analyse softwares.

In the work of Mosleh et al. [35] a brake dustgenerated in vehicle brakes causes discolorationof wheels and, more importantly, the emission ofparticles 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 asize of 350 nm had the highest percentage in theparticle size distribution plots, regardless of themagnitude of the nominal contact pressure andthe sliding speed. The precise calculation foreach of the rate of wear [3638] and the internalenergy of friction clutch will lead to Knowledgethe lifetime of friction material with highaccuracy. Due to their predominantlysubmicrometer size, a significant amount ofbrake dust particles may be inhalable in

environmental 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 contactpressure is presented to indicate the importanceof the contact stiffness between contact surfaces.According to Altuzarra et al. [40], if the slidingspeed is high, the resulting thermomechanicalfeedback is unstable, leading to the developmentof nonuniform contact pressure and local high


4/18


52

temperature with important gradients calledhot spots. The formation of such localized hotspots is accompanied by high local stresses thatcan lead to material degradation and eventualfailure [41]. Also, the hot spots can be a source ofundesirable frictional vibrations, known in theautomotive disc brake community as hotroughness or hot judder [42].

The ventilated disc is lighter than the solid disc,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, brake fade and vapor lock [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 that of the solid disc, 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 oftemperature distribution for dry friction system(flywheel, clutch disc and pressure plate) 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 and minimum at outer radius) based ontheory of clutch design. The effect of convection

is 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 andpressure plate (one bad central and two bands)and compared with case of full contact betweensurfaces for single engagement and repeatedengagements. Furthermore, their work showseffect of pressure capacity on the temperaturefield, when the pressure is a function of time ,three kinds of pressure variation with time(constant , linear and parabolic) are presented.

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; the strategy of calculation is based on thesoftware ANSYS 11. This last is comprehensivemainly for the resolution of the complex physicalproblems. 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 thestresses on disc surface.

2.

NUMERICAL

PROCEDURE

In braking process, the temperature fieldchanges input heat flux and heat exchangeconditions. The input heat flux is mainly relevantto friction coefficient disc, the angular velocity ofbrake disc while heat exchange is connectedwith the friction pair materials and externalenvironmental factors.

Based on the first law of Thermodynamics,during braking, kinetic energy is converted tothermal energy. Due to friction between themain components of disc brake (pads and disc)

the conversion of energy takes place.

Initially the generated thermal energy istransferred by conduction to the components incontact and next by convection to environment.

The initial heat flux qointo the rotor face is directlycalculated using the following formula [48]:

01

2 2o

d p

m g V z q

A

(1)

Where z=a/g is the braking effectiveness, a is the

deceleration of the vehicle [m/s2], is the ratedistribution of the braking forces between thefront and rear axle, Ad disc surface swept by abrake pad [m2],Vois the initial speed of the vehicle[m/s], pis the factor load distribution on the discsurface, m is themass of the vehicle [kg] and g isthe acceleration of gravity (9.81) [m/s2].

The disc rotor vane passage and a sector chosenfor the numerical analysis are shown in Fig. 1the dimension for the baseline study with an

outer diameter of 262 mm and inner diameter of66 mm and 36 vanes. The geometric model wascreated using ANSYS Worbench11.


5/18


53

Fig.

1.Geometrical characteristics of the ventilated disc.

The loading corresponds to the heat flux on thedisc surface. The dimensions and the parametersused in the thermal calculation are recapitulatedin Table 1.

Table1.Input parameters.

Description Values

Inner disc diameter, mm 66

Outer disc diameter, mm 262

Disc thickness (TH), mm 29Disc height (H), mm 51

Vehicle mass m, kg 1385

Initial speed Vo , km/h 28

Deceleration a, m/s2 8

Effective rotor radius Rrotor, mm 100.5

Rate distribution of the braking forces ,% 20

Tire radius Rtire, mm 380

Factor of charge distribution of the disc p 0.5

Surface disc swept by the padAd, mm2 35993

The material of brake disc is gray cast iron (GF)with high carbon content, with goodthermophysical characteristics, thermoelasticcharacteristics of which adopted in this simulationof the rotor are recapitulated in Table 2.

Table

2.

Material properties of brake disc.

Material Properties Disc

Thermal conductivity, k(W/m C) 57

Density, (kg/m3) 7250

Specific heat,C(J/Kg C) 460

Poissons ratio, v 0.28

Thermal expansion, (106/K) 10.85

Elastic modulus, E(GPa) 138

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

It is relatively hard and resists wear.

It is cheaper than steel or aluminum.

It absorbs and dissipates heat well tocool the brakes.

It is very difficult to exactly model the brakedisc, in which there are still researches are goingon to find out transient thermal behaviour of

disc brake during braking applications. There isalways a need of some assumptions to modelany complex geometry. These assumptions aremade, keeping in mind the difficulties involvedin the theoretical calculation and the importanceof the parameters that are taken and thosewhich are ignored. In modeling, we alwaysignore the things that are of less importance andhave little impact on the analysis. Theassumptions are always made depending uponthe details and accuracy required in modeling.

Due to the application of brakes on the car Discbrake 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 hasto be carried out. The thermal loading as well asstructure is axissymmetric. Hence axissymmetric analysis can be performed, but in thisstudy we performed 3D analysis, which is anexact representation for this thermal analysis.

Thermal analysis is carried out and with theabove load structural analysis is also performedfor analysing the stability of the structure.

TH

HClampholes Coolingfin

Discheight Discthickness

10

6


6/18


54

To simplify the analysis, several assumptionshave also been made as follows [50]

All kinetic energy at disc brake rotor surfaceis converted into frictional heat or heat flux.In other words, a high amount of kinetic

energy is converted into heat energy atinterfaces according to the first law ofthermodynamics during the slipping periodand the heat generated between contactsurfaces will be dissipated by conductionbetween friction clutch components and byconvection to the environment.

The heat transfer involved for this analysisonly conduction and convection process.This heat transfer radiation can beneglected in this analysis because of small

amount which is 5 % to 10 % [51]. Indeed,the heat radiation only plays an importantrole at high temperature and low speeds.

The disc material is considered ashomogeneous and isotropic, becauseYoungs modulus, Poissons ratio, and thethermal expansion coefficient are assumedto be constant for isotropic.

The domain is considered as axissymmetric. The temperature field issymmetry with respect to the central plane

of the brake disc

Inertia and body force effects are negligibleduring the analysis. Here, a transientanalysis calculates the effects of thermalloading on a structure, while ignoringinertia and damping effects.

The disc is stress free before the application of

brake. Due to the application of brakes of therotor, heat generation takes place due tofriction and this temperature so generated hasto be conducted across the disc across section.

In this analysis, the ambient temperature andinitial temperature has been set to 20 C.

All other possible disc brake loads areneglected, for example, the effects of wearor other atmospheric factors.

Only certain parts of disc brake rotor will

apply with convection heat transfer such ascooling vanes area, outer ring diameter areaand disc brake surface on which, eachsurface of the rotor was subjected to

different values of convection heat transfercoefficient obtained from this calculations.

Uniform pressure distribution by the brakepad onto the disc brake surface. Uniformpressure distribution in the contact regionis often valid when the pad is new.

The thermal conductivity and specific heat are afunction of temperature, Figs. 2 and 3.

0 100 200 300 400 500 600 700 800 900

35

40

45

50

55

60

ThermalconductivityW/mC

Temperature C Fig.2.Thermal conductivity versus temperature.

0 100 200 300 400 500 600 700

450

500

550

600

650

700

750

800

SpecificheatJ/kgC

Temperature C Fig.3.Specific heat versus temperature.

3. FINITE ELEMENT FORMULATION FOR

HEATCONDUCTION

The unsteady heat conduction equation of each bodyfor an axisSymmetric problem described in thecylindrical coordinate system is given as follows:

1r z

T T Tc rk k

t r r r z z

(2)

With the boundary conditions and initial condition:

*

0T T on (3)

1( )nq h T T on (4)

*

2n nq q on

(5)


7/18


55

0 0T T at time

(6)

where , c, krand kzare the density, specific heatand thermal conductivities in r and z direction ofthe material, respectively. Also, T* is theprescribed temperature, h the heat transfercoefficient, qn* the heat flux at each contactinterface due to friction, T the ambienttemperature, T0the initial temperature and 0, 1and 2are the boundaries on which temperature,convection and heat flux are imposed, respectively.

Using Galerkins approach, a finite elementformulation of unsteady heat Eq. (3) can bewritten in the following matrix form as:

T TC T KH T R

(7)

Where CT is the capacity matrix, KHT is theconductivity matrix. T and R and are the nodaltemperature and heat source vector, respectively.

The most commonly used method for solving Eq.(7) is the direct integration method based on theassumption that temperature Tt at time t andtemperature Tt+tat time t+t have the followingrelation:

1t t t t t t T T T T t

(8)

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

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)

Where the variable b1and b2are given by:

1 2, 1b t b t

(10)

For different values of the wellknownnumerical integration scheme can be obtained[52] in this study, 0.5 1.0was used, whichis an unconditionally stable scheme.

4. PREPARATION OF THE GEOMETRY AND

THE

MESH

4.1Fluidfield

Considering symmetry in the disc, one took only

the quarter of the geometry of the fluid field (Fig.4) by using software ANSYS ICEM CFD.

Fig.4..

Fig.4.Definition of surfaces of the fluid field.

4.2

Preparation

oftheMesh

This stage consists in preparing the mesh of thefluid field. In our case, one used a lineartetrahedral element with 30717 nodes and179798 elements (Fig. 5).

Fig.5.Mesh of the fluid field.

At the time of the braking process, a part of the

frictional heat escapes into the ambient air byconvection and radiation. Consequently, thedetermination of the heat transfer coefficients isessential. Their exact calculation is, however,rather difficult, because these coefficientsdepend on the location and the construction ofthe braking system, the speed of the vehicle andconsequently, on the air circulation. Since theprocess of heat transfer by radiation is not toosignificant, we will determine using ANSYS CFX11.0 code only the convection coefficient (h) ofthe disc. This parameter will be exploited to

determine the threedimensional distribution ofthe temperature of the disc.

InterfaceFluidsolid

Exit of the air

DSYM1

DR1

DV1

Entry 1of the air

Entry 2of the air


8/18


56

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. 6 and 7).

Fig.6.Meshing of the full disc (Number of elements272392).

Fig.

7. Meshing of the ventilated disc (Number of

elements 27691).

4.3ModelinginANSYSCFX

For the preparation of the mesh of CFD model,one defines initially, various surfaces of the discin integrated computer engineering andmanufacturing (ICEM) CFD as shown in Fig.8;we used a linear tetrahedral element with 30717nodes and 179798 elements. In order not toweigh down calculation, an irregular mesh is

used in which the mesh is broader where thegradients are weaker (nonuniform mesh),

Fig.8.Definition of surfaces of the full disc.

Table.3Boundary conditions.

BoundaryBoundarycondition

Parameters

Inlet Pressure inletAtmospheric pressure

and temperature

Outlet Pressure outlet

Atmospheric pressure

and temperatureDomain

edgesSymmetry Symmetry

Disc surface Wall800K temperature,

thermal properties ofgrey cast iron

a) Physical modelIn 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 the

analysis.

b)

Definition of the domainsInitially, one valid the elaborated models andone activate in the option "Thermal Energy thecalculation of heat transfer Heat Transfer ".Fluid domain: Speed entry: Vent non.st= Vent Va.tDisc domain: Entering flux: FLUXnon.st= (CF) (Ventnon.st),

CF = 149893.84Vent non.st= Vent Va.t

FLOWnon.st:Non stationary flux entering.Vent non.st: Non stationary speed entering of the air.

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

d)

Definition of the boundary conditionsThe first step is to select the Inlet and Outletfaces of the heat flux. These options are found in

the insertion menu Boundary Conditions in theCFX Pre.


9/18


57

The boundary conditions concerning the padswill be also defined. One selects the optionsWall and "Symmetry ", because there will bethe possibility of adjusting a certain number ofparameters in the boundary conditions such asflux entering the disc.

e) Application of the interfaces domainsThe areas of interfaces are commonly used tocreate the connection or linkage areas. Surfaceslocated between the interactions regions (airdisc) are reported as solidfluid interface.

f)

Temporary ConditionSince in this study is to determine thetemperature field in a disc brake during thebraking phase of a vehicle of average class, we

take the following temporal conditions: Braking time= 3.5 [s]

Increment time = 0.01 [s]

Initial time = 0 [s]

Before starting the calculation and the analysiswith ANSYS CFX PRE, it can be ensured that themodel does not contain any error.

The airflow through and around the brake discwas analyzed using the ANSYS CFX softwarepackage. The ANSYSCFX solver automaticallycalculates heat transfer coefficient at the wallboundary. Afterwards the heat transfercoefficients considering convection werecalculated and organized in such a way, that theycould be used as a boundary condition inthermal analysis. Averaged heat transfercoefficient had to be calculated for all disc usingANSYS CFX Post as it is indicated in Fig. 9.

Fig.

9. Distribution of heat transfer coefficient on afull disc in the steady state case (FG 15).

g) Results of the calculation of the heattransfer coefficient (h)

The heat transfer coefficient is a parameterrelated to velocity of air and the shape of brakedisc, and many other factors. In different velocityof air, the heat transfer coefficient in differentparts of brake disc changes with time [53]. Heattransfer coefficient will depend on air flow in theregion of brake rotor and vehicle speed, but itdoes not depend on material. In this simulation,it is determined the average value of thecoefficient h Wall heat Transfer Coefficient,variable with time (Figs. 10 and 11).

-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

Heattransfercoefficienth[W

m-C-]

Time [s] Fig. 10. Variation of heat transfer coefficient (h) ofvarious surfaces for a full disc in transient case (FG 15).

-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

250SC1

SC2

SC3

SF1

SF3

SPV1

SPV2

SPV3

SPV4

ST1

ST2

ST3

ST4

SV1

SV2

SV3SV4H

eat

transfercoefficienth[Wm

-2

C-1]

Time [s] Fig.

11. Variation of heat transfer coefficient (h) ofvarious surfaces for a ventilated disc in transient case(FG 15).

4.4Determinationofthedisctemperature

The modeling of the disc temperature is carried

out by simulating a stop braking of a middleclass car (braking of type 0).


10/18


58

The characteristics of the vehicle and of the discbrake are listed in Table 1.

The vehicle speed decreases linearly with timeuntil the value 0 as shown in Fig. 12. Thevariation of the heat flux during the simulationtime is represented on the Fig. 13.

0 10 20 30 40

0

10

20

30

Speed[ms-

1]

Time [s]

Sp ee d [m s-1]

Fig.

12.Speed of braking versus time (Braking of type 0).

0 10 20 30 40

0

1x10

6

2x106

3x106

4x106

5x106

HeatFlux[Wm

-2]

Time [s]

H ea t Fl ux

Fig.

13.Heat Flux versus time.

4.5Creatingoffiniteelementmeshfordisc

Meshing of the full and ventilated disc has been doneusing ANSYS Multiphysics. The element used of themeshing is of tetrahedral shape (Figs. 14 and 15).

Fig.14.Full type disc mesh model (total number ofnodes 172103 total number of elements 114421).

Fig.15. Ventilated type disc mesh model (totalnumber of nodes 154679 total number of elements94117).

4.6Applyingtheboundaryconditions

The boundary conditions are introduced intomodule ANSYS Workbench [Multiphysics], bychoosing the mode of first simulation of the all(permanent or transitory), and by defining thephysical properties of materials. Theseconditions constitute the initial conditions of oursimulation. After having fixed these parameters,one introduces a boundary condition associatedwith each surface.

Total time of simulation = 45 s

Increment of initial time = 0.25 s Increment of minimal initial time = 0.125 s

Increment of maximal initial time = 0.5 s

Initial temperature of the disc = 20 C

Materials: Grey Cast Iron FG 15.

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 obtainedby flux entering by means of the code CFX.

5. RESULTSANDDISCUSSIONS

The modeling of temperature in the disc brake willbe carried out by taking account of the variation ofa certain number of parameters such as the type ofbraking, the cooling mode of the disc and thechoice of disc material. The brake discs are madeof cast iron with high carbon content; the contact

surface of the disc receives an entering heat fluxcalculated by relation (1).


11/18


59

A model presents a three dimensional solid Discsqueezed by two finitewidth friction materialcalled pads. The entire surface, S, of the Disc hasthree different regions including S1 and S2. OnS1 heat flux is specified due to the frictionalheating between the pads and Disc, and S2 isdefined for the convection boundary. The rest ofthe region, except S1 U S2, is either temperaturespecified or assumed to be calculated: the innerand outer rim area of Disc. Since the axissymmetric model is considered all the nodes onthe hub radius are fixed. So the nodaldisplacements in the hub become zero, i.e. inradial, axial and angular directions.

5.1Influenceofconstructionofthedisc

Figure 16 shows the variation of thetemperature versus time during the total timesimulation of braking for a fall disc and aventilated disc. The highest temperatures arereached at the contact surface of discpads. Thestrong rise in temperature is due to the shortduration of the braking phase and to the speedof the physical phenomenon. For the two typesof discs, one disc has an immediate, fasttemperature rise followed by a fall intemperature after a certain time of braking.

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

Temperature[C]

T im e [s]

V e n t i l a t e d d i s c

F u l l d is c

(a)

(b)Fig.

16. Temperature distribution of a full (a) and

ventilated disc (b) of cast iron (FG 15).

It can be concluded that the geometric design ofthe disc is an essential factor in theimprovement of the cooling process of the discs.

Figures 17 and 18 respectively show thetemperature variation according to the thicknessand radius. It can be noted that there is anappreciable variation of temperature between thetwo types of full and ventilated disc. The influenceof ventilation on the temperature field appearsclearly at the end of the braking (t = 3.5 s).

0 5 10 15 20 25 3050

100

150

200

250

300

350

400

Temperatur

e[C]

Thickness [mm]

Full disc FG 15

Ventilated disc FG 15

Full disc Ventilated disc

Fig.17.Temperature variation through the thicknessfor both designs with same material (FG15).

70 80 90 100 110 120 130 140

150

200

250

300

350

400

Full disc FG 15

Ventilated disc FG 15

Temperature[C]

Radius [mm] Fig.

18.Temperature variation through a radius forboth designs with the same material (FG15).


12/18


60

5.2Influenceofbrakingmode

The disc brake and the wheel are dimensionedaccording to the performance and economicrequirements of the vehicle. They mustsupport increasingly greater mechanical andthermal loads at mean velocities in permanentprogression. Among the parameters having aninfluence on the thermal behaviour of the discbrake is the braking mode, which depends onthe 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 speedversus time (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 beequal to 135 s. This is intended to determine thesaturation temperature disc under a cyclicthermal load. This cycle is repeated severaltimes: the first mode consists of braking andacceleration, and the second consists of braking,cooling and deceleration.

Figure 19 shows a driving cycle of fourteensuccessive braking, in the form of sawtooth.

0 20 40 60 80 100 120

0

5

10

15

20

25

30

Speed[ms-

1]

Time [s] Fig.

19.Driving cycle with fourteen repeated braking(Mode 1).

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

Vitesse[ms-

1]

Time [s]

Fig.20.Cycle braking with phase of idles after eachbraking (mode 2).

Figures 21 and 22 show the threedimensionaldistribution of the maximum temperature

reached in the disc for the two modes of braking,one observes a normal increase in temperaturein the tracks of friction and the external crown.The vanes very strongly warm up and tend todilate and become deformed until the completesolidification of the disc. This deformation willcause the setting in umbrella of the disc.

Fig. 21. Temperature map of the disc in mode ofbraking 1 at the moment t=131.72 [s].

Fig. 22. Temperature map of the disc in mode ofbraking 2 at the moment t=130.45 [s].


13/18


61

Figure 23 shows the comparison of the change intemperature of the disc for a cyclic braking processbetween the first mode and the second mode. 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 themaximum temperatures increase. The initial stateof the disc changes after each cycle; the downtimesallow only one partial cooling. After each coolingphase, the disc begins to warm again. In fact,during successive brakings the capacity of coolingof the disc is insufficient to lower the surfacetemperature to near the initial temperature, whichcauses an accumulation of energy and therefore ahigher surface temperature. These results show,

that the transient thermal behaviour of a discbrake depends on the braking cycle imposed and itis dominating because it dictates the cooling timeof 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 % compared with the first cycle.We conclude that the braking mode with a coolingphase influences the heat transfers in the disc verypositively, which involves a reduction in themaximum temperature of the interface, whichcauses cracking and mechanical wear.

0 20 40 60 80 100 1200

100

200

300

400

500

600

700

800

900

1000

1100

1200

Temperature[C]

Time [s]

Mo de of bra kin g 2

Mo de of bra kin g 1

Fig. 23. Temperature variation of the two brakingmodes versus time.

In addition, this tendency will enable us to ensurethe safety and fatigue life of the brake systemcomponent. Finally, it would be interesting to carryout this calculation on brake test benches in orderto validate these results of the numerical simulation.

5.3Comparisonbetweenfullandventilateddisc

In this part, we presented the cartographies oftotal and directional heat flux and as well as thetemperature distribution in a full and ventilateddisc and of cast iron FG 15 for each moment withbraking. The temperature distribution of the discat the beginning braking (with t=0.25 s) isinhomogeneous. According to experimentaltests' carried out by research , braking oftenbegin with the formation from hot circlesrelatively on the uniform surfaces of the disc inthe circumferential direction, moving radially onthe disc and transforming then into hot points((hotspot)).The appearance of the phenomenonof the hot points is due to the nonuniformdissipation of heat flux.

Concerning the heat flux, it can be notedaccording to Figs. 25 and 28 that the maximumvalue of the total heat flux is located on the levelof the calorific throat at the end of braking (t =3.5 s); this is explained by the increase in thegradients and the thermal concentrations in thiszone. The calorific throat is manufactured so asto limit the heat flux coming from the frictiontracks and moving towards the bowl of the discbrake in order to avoid the excessive heating ofthe rim and the tire. During the heating, the discis tightened to dilate in the hot zones fromwhere creating of compressive stresses withplasticization. On the other hand, during cooling,there is appearance of residual stresses oftraction. The disc is thus subjected during itsrotation to constraints traction/compression.

a. Fulldisc

a : t= 0.25[s] b : t= 1.8839[s]


14/18


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 ofmaterial FG 15.

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.Distribution of total heat flux for a full disc ofmaterial FG 15.

a : According to the axis X

b:According to the axis Y

c :According to the axis Z

Fig.

26. Distribution of directional heat flux at the

moment t= 1.8839 [s] according to three axes (X, Y, Z)for a full disc of a material FG 15.

b. Ventilateddisc

a : t= 0.25 [s] b : t= 1.8506 [s]


15/18


63

c : t= 3.5 [s] d : t= 5 [s]

e : t= 20 [s] f : t= 45 [s]

Fig. 27. Temperature distribution for a ventilateddisc of material FG 15.

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.Distribution of total heat flux for a ventilateddisc of material FG 15.

a : According to the axis X

b : According to the axis Y

c : According to the axis ZFig.

29. Distribution of directional heat flux at themoment t= 1.8506 [s] according to three axes (X, Y, Z)for a ventilated disc of a material FG 15.

5. CONCLUSION

In this study, we have presented a numericalsimulation of the thermal behaviour of a full andventilated disc in transient state. By means ofthe computer code ANSYS 11 we were able tostudy the thermal behaviour of a gray cast iron(FG 15).

In addition to the influence of the ventilation ofthe disc, on the thermal behaviour of the discsbrake, the numerical simulation shows thatradial ventilation plays a very significant role incooling of the disc in the braking phase, we alsostudied the influence of the braking mode on the


16/18


64

thermal behaviour of the disc brake. Throughthe numerical simulation, it could be noted thatthe quality of the results concerning thetemperature field is influenced by severalparameters such as:

Technological parameters illustrated by thedesign.

Numerical parameters represented by the

number of elements and the step of time.

Physical parameters expressed by the typesof materials.

Braking mode implemented.

Regarding the calculation results, it can be saythat they are satisfactorily in agreement withthose commonly found in the literature

investigations. It would be interesting to solvethe problem in thermo mechanical disc brakeswith an experimental study to validate thenumerical results, for example, on test benches,in order to demonstrate a good agreementbetween the model and reality.

Regarding the outlook, there are threerecommendations for the expansion of futurework related to disc brake that can be done tofurther understand the effects of thermo

mechanical contact between the disc and pads,the recommendations are as follows:

1. Experimental study to verify the accuracy ofthe numerical model developed.

2. Tribological and vibratory study of thecontact disc pads;

3.

Study of dry contact sliding under themacroscopic aspect (macroscopic state ofthe surfaces of the disc and pads).

REFERENCES

[1] R. Thundil Karuppa Raj, R. Ramsai, J. Mathew, G.Soniya: Numerical investigationoffluidflowandheattransfercharacteristicsontheaerodynamics

ofventilateddiscbrakerotorusingCFD, ThermalScience, Issue 00, pp. 204204, 2012.

[2] M. Kastek, T. Piatkowski, H. Polakowski, J.Maachowski, K. Damaziak: Thermographicsmeasurementsandnumericalsimulationofacar

breaks, in: 11th International Conference onQuantitativeInfraRedThermography,1114 June

2012, Naples, Italy, ID228, pp. 19.

[3] R. Limpert: The thermal performance ofautomotive disc brakes, SAE paper, Doi:10.4271/750873, 1975.

[4] S. Morgan and R.W. Dennis: A theoreticalprediction of disc brake temperatures and a

comparison with experimental data, SAETechnical Papers, No. 720090, 1972.

[5] M.N. Dhaubhadel: Review:CFDapplicationsintheautomotive industry, Journal of FluidsEngineering, Vol. 118, No. 4, pp. 647653, 1996.

[6] J. Abdo: Experimental Technique to StudyTangential to Normal Contact Load Ratio,Tribology Transactions, Vol. 48, No. 3, pp. 389403, 2005.

[7] C.H. Gao, X.Z. Lin: Transient temperature fieldanalysis of a brake in a nonaxisymmetric

threedimensionalmodel, J. Materials Processing

Technology, Vol. 129, No. 13, pp. 513517, 2002.

[8] B. ztrk, F. Arslan,S. ztrk : EffectsofDifferentKinds of Fibers on Mechanical and Tribological

Properties of Brake Friction Materials,Tribology Transactions, Vol. 56, No. 4, pp. 536545, 2013.

[9] M. Nouby, J. Abdo, D. Mathivanan, K. Srinivasan:Evaluation of Disc Brake Materials for Squeal

Reduction, Tribology Transactions, Vol. 54, No. 4,pp. 644656, 2011.

[10] E. Palmer, J. Fieldhouse, R. Mishra: Optimisation

ofpin shapeand its configurationforapin typevente brake disc using CFD., FISITA, Yokohama,Japan, 2006.

[11] D.H. Michael, L.R. Roland: VentilatedBrakeRotorAir Flow Investigation, SAE, Doi:10.4271/971033, 1997.

[12] L. Wallis, E. Leonardi, B. Milton: Air Flow andHeat Transfer in Ventilated Disc Brake Rotors

with Diamond and TearDrop Pillars, in :Proceedings of International Symposium on

Advances in Computational Heat Transfer,Australia, Vol. 41, pp. 643655, 2002.

[13] H. Blok: Theoretical studyof temperatureriseatsurfaces of actual contact under oiliness

lubricating conditions, in: Proceedings of theInstitute of Mechanical Engineers General

Discussion on Lubrication and Lubricants,London, UK,Vol. 2, pp. 222235, 1937.

[14] J.C. Jaeger, H.S. Carslaw: Conduction of Heat inSolids, Clarendon Press, Oxford, UK, 1959.

[15] B. Vick, M.J. Furey:Abasictheoreticalstudyofthetemperature rise in sliding contactwithmultiple

contacts, Tribology International, Vol. 34, No. 12,pp. 823829, 2001.


17/18


65

[16] H. Chen, W. Hu, H. Wang, W. Wang: Calculationoftemperaturefieldsofbodies inslidingcon tact

without lubrication, Journal of TsinghuaUniversity (Science and Technology), Vol. 47, No.11, pp. 19621964, 2007.

[17] Q. Chen, D.Y. Li: A computational study offrictional heating and energy conversion during

slidingprocesses, Wear, Vol. 259, No. 712, pp.13821391, 2005.

[18] P.N. Bogdanovich, D.V. Tkachuk: Temperaturedistribution over contact area and hot spots in

rubbing solid contact, Tribology International,Vol. 39, No. 11, pp. 13551360, 2006.

[19] K.J. Lee, J.R. Barber: An ExperimentalInvestigation of FrictionallyExcited

Thermoelastic Instability in Automotive Disk

BrakesunderaDragBrakeApplication, Journal of

Tribology, Vol. 116, pp. 409414, 1994.[20] A.R. Abu Bakar, H. Ouyang: Wear predictionof

friction material and brake squeal using the

finiteelementmethod, Wear, Vol. 264, No. 11 12,pp. 10691076, 2008.

[21] G. Cuccurullo, V. Spingi, R. Di Giuda: Thermaleffectsindryslidingcontacts,in: 11thInternationalConference on Quantitative InfraRed

Thermography, Naples, Italy, 1114 June 2012.

[22] J. Bijwe, Nidhi, B.K. Satapathy: Influenceofamountof resin onfade and recovery behaviour of non

asbestosorganic

(nao)

friction

materials, Trans.Indian Inst. Met., Vol. 57, pp. 335344, 2004.

[23]P.Gopal, L.R. Dharani, F.D. Blum: Hybridphenolicfrictioncompositescontainingkevlarpulp:partI.

Enhancement offriction andwearperformance,Wear, Vol. 193, No. 2, pp. 199206, 1996.

[24]W.S. Scholtz: Brakepad technical advice, Articleissued by Safeline, November 2002.

[25]J.Bijwe, Nidhi, N. Majumdar, B.K. Satapathy:Influenceofmodifiedphenolic resinson thefade

andrecoverybehavioroffrictionmaterials, Wear,Vol. 259, No. 712, pp. 10681078, 2005.

[26]H. Feng, M. Yimin, L. Junnchering: Studyonheatfeading of phenolic resin friction material for

microautomobile clutch, in: Proceedings of the2010 International Conference on Measuring

Technology and Mechatronics Automaition,Washington, USA, 2010, pp. 596599.

[27]H.S. Qi: Acontactlengthmodelforgrindingwhellworkpiece contact, PhD. Thesis, Liverpool JhonMoores University, UK, 2002.

[28]O.S. Dinc, C.M. Ettles, S.J. Calabrese, H.A. Scarton:Themeasurement of surface temperature in dry

or lubricatedsliding, Trans. ASME, J. Tribol., Vol.115, No. 1, pp. 7882, 1993.

[29]Anon: Material development using infraredthermography, Metallurgia, Vol. 62, 1995.

[30]G. Cuccurullo, V. DAgostino, R. Di Giuda, A.Senatore, V. Spingi : AnAnalitycalSolutionandan ExperimentalApproachfor Thermal Field at

the Interface ofDry Sliding Surfaces, Meccanica,Springer, Vol. 46, pp. 589595, 2011.

[31]D. Majacherczak, P. Dufrenoy, Y. Berthier:Tribological thermal and mechanical coupling

aspects of dry sliding contact, TribologyInternational, Vol. 40, No. 5, pp. 834843, 2007.

[32]L. Zhang, Q. Yang, D. Weichert, N. Tan: Simulationand Analysis of Thermal Fatigue Based on

ImperfectionModelofBrakeDiscs, in: Proc.Appl.Math.Mech., Beijing Jiaotong University, PAMM,2009, Vol. 9, pp 533 534.

[33] N. Laraqui, N. Alilat, Gar J.M. cia De Maria, A.

Bairi: Termperatureanddivisionofheatinapinondiskfrictionaldeviceexactanalyticalsolution,Wear, Vol. 266, No. 78, pp. 765770, 2009.

[34]C. Spulber, S. Voloaca: Aspectsregardingthediscbrake's thermal stress simulation by using

InfraredThermography, in: Proceedings of2011International Conference on Optimization of the

RobotsandManipulators,Sinaia, Romania, 2628Mai, 2011.

[35]M. Mosleh, B.A. Khemet: A Surface TexturingApproach for Cleaner Disc Brakes, Tribology

Transactions, Vol. 49, No. 2, pp. 279283, 2006.[36] M.A. Chowdhury, D.M. Nuruzzaman, A.H. Mia,

M.L. Rahaman: Friction Coefficient of DifferentMaterialPairsunderDifferentNormalLoadsand

SlidingVelocities, Tribology in Industry, Vol. 34,No. 1, pp. 1823, 2012.

[37] Birleanu, Sucala Felicia: About the tribologicalbehavior of ceramic materials, Tribology inIndustry, Vol. 30, No. 3&4, pp. 1014, 2008.

[38] V. Bria, D. Dima, G. Andrei, I.G. Birsan, A.Circiumaru: TribologicalandWearPropertiesofMultiLayered Materials, Tribology in Industry,Vol. 33, No. 3, pp. 104109, 2011.

[39] O.I. Abdullah , J. Schlattmann , A.M. AlShabibi:Stresses and Deformations Analysis of a Dry

FrictionClutchSystem,Tribology in Industry, Vol.35, No. 2, pp. 155162, 2013.

[40] O. Altuzarra, E. Amezua, R. Aviles, A .Hernandez:Judder Vibration in Disc Brakes Excited by

Thermoelastic Instability, EngineeringComputations, Vol. 19, No. 4, pp. 411430, 2002.

[41] Y.H. Jang, S.H. Ahn: FrictionallyExcitedThermoelastic Instability in functionally Graded

Material, Wear, Vol. 262, No. 910, pp. 11021112, 2007.


18/18


66

[42] B.Y. Yi, J.R. Barber, P. Zagrodzki: Eigen ValueSolutionofThermoelasticInstabilityProblemsusing

Fourier Reduction, in: Proceedings of the RoyalSocietyofLondon, Vol. 456, pp. 279282, 2000.

[43] H. Jacobsson: Aspectsofdiscbrakejudder, Proc.of the Institution of Mechanical Engineers, PartD: Journal of Automobile Engineering, Vol. 217,No. 6, pp. 419430, 2003.

[44] B.K. Choi, J.H. Park, M.R. Kim: Simulation of theBraking Condition of Vehicle for Evaluating

Thermal Performance ofDisc Brake, in: Proc. ofKSAEAutumnConference, pp. 12651274, 2008.

[45] S.P. Jung, T.W. Park, Y.G. Kim:AStudyonThermalCharacteristicAnalysisandShapeOptimizationof

a Ventilated Disc, International Journal ofPrecision Engineering and Manufacturing, Vol.13, No. 1, pp. 5763, 2012.

[46] O.I. Abdullah, J. Schlattmann: Finite ElementAnalysisofTemperatureField inAutomotiveDry

FrictionClutch, Tribology in Industry, Vol. 34, No.4, pp. 206216, 2012.

[47] O.I. Abdullah, J. Schlattmann: Effect of BandContact onthe TemperatureDistributionforDry

FrictionClutch,Tribology in Industry, Vol. 35, No.4, pp. 317329, 2013.

[48] J. Reimpel: Technologie de freinage, VogelVerlag, Wrzburg, 1998.

[49] A.F. Basha Shaik, Ch.L. Srinivas : Structuralandthermal analysis of disc brakewith andwithout

cross drilled rotar of race car, InternationalJournal of Advanced Engineering Research andStudies, Vol. 1, No.4, pp. 39, 2012.

[50] M.K. Khalid, M.R. Mansor, S.I. Abdul Kudus, M. M.Tahir, M. Z. Hassan: PerformanceInvestigationofthe UTeM Eco Car Disc Brake System,International Journal of Engineering andTechnology, Vol. 11, No. 6, pp. 16, 2011.

[51] R. Limpert: BrakeDesignandSafety. 2nd Edition,Warrendale, Pennsylvania: Society ofAutomotive Engineering Inc., pp. 137144, 1999.

[52] M. Omolayo Petinrin, J. Ogheneortega Oji:Numerical Simulation of Thermoelastic Contact

Problem of Disc Brake with Frictional HeatGeneration, New York Science Journal, Vol. 5, No.10, pp. 3943, 2012.

[53] J. Zhang, C. Xia: Research of the TransientTemperatureFieldandFrictionPropertiesonDisc

Brakes: in: Proceedings of the 2012 2ndInternational Conference on Computer and

InformationApplication, ICCIA 2012, pp. 201204.

Documents

Numerical modeling of disc brake system in frictional contact.pdf