Reduced Scale Thermal Characterization Of Automotive Disc .
This is a repository copy of Reduced scale thermal characterization of automotive discbrake.White Rose Research Online URL for this : Accepted VersionArticle:Alnaqi, AA, Barton, DC orcid.org/0000-0003-4986-5817 and Brooks, PC (2015) Reducedscale thermal characterization of automotive disc brake. Applied Thermal Engineering, 75.pp. 658-668. ISSN 2014.10.001ReuseItems deposited in White Rose Research Online are protected by copyright, with all rights reserved unlessindicated otherwise. They may be downloaded and/or printed for private study, or other acts as permitted bynational copyright laws. The publisher or other rights holders may allow further reproduction and re-use ofthe full text version. This is indicated by the licence information on the White Rose Research Online recordfor the item.TakedownIf you consider content in White Rose Research Online to be in breach of UK law, please notify us byemailing eprints@whiterose.ac.uk including the URL of the record and the reason for the withdrawal terose.ac.uk/
Accepted ManuscriptReduced scale thermal characterization of automotive disc brakeAbdulwahab A. Alnaqi, David C. Barton, Peter C. hermaleng.2014.10.001Reference:ATE 6015To appear in:Applied Thermal EngineeringReceived Date: 22 April 2014Revised Date:20 September 2014Accepted Date: 1 October 2014Please cite this article as: A.A. Alnaqi, D.C. Barton, P.C Brooks, Reduced scale thermalcharacterization of automotive disc brake, Applied Thermal Engineering (2014), doi: 10.1016/j.applthermaleng.2014.10.001.This is a PDF file of an unedited manuscript that has been accepted for publication. As a service toour customers we are providing this early version of the manuscript. The manuscript will undergocopyediting, typesetting, and review of the resulting proof before it is published in its final form. Pleasenote that during the production process errors may be discovered which could affect the content, and alllegal disclaimers that apply to the journal pertain.
ACCEPTED MANUSCRIPTReduced scale thermal characterization of automotive disc brake1Alnaqi, Abdulwahab A.*;1Barton, David C.; 1Brooks, Peter C.1University of Leeds, United KingdomIPT* Corresponding author. Tel: 44-7423278626.E-mail address: mnaaal@leeds.ac.uk (A.A. Alnaqi).AbstractThe thermal behaviour of a disc brake is a critical factor that needs to be considered at theCRdesign phase. Most researchers utilise a full size brake dynamometer or a simple pin-on-discrig to experimentally evaluate the performance of a friction pair (disc and pad). In the currentMANUSpaper, a scaling methodology is proposed to evaluate the thermal performance of a disc brakeat a reduced scale. The resulting small scale disc brake has the advantage of low cost andreduced development time. The proposed scaling methodology was validated by comparingthe results for the full and small scale discs using a conventional brake dynamometer. Inaddition, a two dimensional axisymmetric transient thermal finite element model wasdeveloped using Abaqus software to assist in the validation of the scaling methodology. Thenumerical simulations confirmed the equivalence between the full and small scale discDthermal performance using the proposed scaling methodology and also gave good agreementwith the experimental results. It is concluded that the scaling methodology is an importantTEtool with which to evaluate the thermal performance of disc brakes in the early design phase.NotationEPKeywords: Disc brake, thermal performance, dynamometer, small scale.Thermal diffusivity[ m2 / s ]γThe ratio of heat flux into the pad to the total heat flux[---]µaThe viscosity of the airρMaterial density[ kg / m ]ρaThe density of the air[ kg / m ]ωRig rotational speed[ rad / s ]τTorque[ Nm ]ACCα[ kg / ms ]331
ACCEPTED MANUSCRIPTPad area[m2 ]AFFull scale pad area[m2 ]ASSmall scale pad area[m2 ]cpSpecific heat capacity[ J / kg .K ]doBrake disc outer diameterdtWheel rolling diameterFnNormal forcehConvective heat transfer coefficientkThermal conductivity coefficientkaThermal conductivity coefficient of the air[ W / m.K ]mdDisc mass[ kg ]γHeat partition ratioQHeat energy quantityq ′x′Heat flux per unit area′q ′radRadiation heat flux per unit arearmMean rubbing radius of disc brake[ m]rmFMean rubbing radius of full scale disc brake[ m]rmSMean rubbing radius of small scale disc brake[m]ReReynolds number[---]SScaling factor[---]tdBrake disc thickness[ m]IPTA[m]CR[ m]MANUS[N][ W / m 2 .K ][ W / m.K ]D[---]TE[J ]EP[W / m2 ]ACC[W / m2 ]2
ACCEPTED MANUSCRIPTTTemperature[oC ]ViInitial forward vehicle velocity[ m/ s ]vSliding velocity[ m/ s ]IPT1. IntroductionThe foundation brake is one of the most important systems in a road vehicle as it plays amajor part in slowing the vehicle by converting the kinetic energy of the vehicle to heatCRenergy that is dissipated through the disc brake and pads. To find an optimum design, thedevelopment process for disc brakes involves a number of steps and many aspects of thebraking system need to be considered to ensure that it meets both legal and customer criteria.MANUSThe conventional design process using full scale dynamometer testing is expensive and timeconsuming because to achieve the desired goal there are complicated experimentalprocedures which need to be carried out. One key aspect of these procedures is to assess themaximum temperature reached by the brake discs and pads during critical braking eventssince these temperatures not only affect the friction performance of the system but alsoultimately the structural integrity of the brake. Thermal modelling using theoreticalDconsiderations and finite element software is another approach which can be used in thedesign process to save time and cost to investigate the thermal performance of disc brakesTEunder different loading conditions [1-4].The brake dynamometer is an excellent research platform as the test conditions and brakingEPparameters can be carefully controlled. There are two major types of dynamometer: theinertial dynamometer and the CHASE dynamometer. The inertial dynamometer is used toACCevaluate full sized brakes but this is a very time consuming and expensive process. Incontrast, the CHASE dynamometer uses a small amount of friction material rubbing against adrum and it requires a shorter testing time than the inertial dynamometer [5].A small scale test rig presents an alternative way to potentially reduce the cost and time ofdisc brake design [6], since it involves lower material overheads than full scale testing and soincreases the potential for rapid back-to-back testing [7]. A reduced scale testing system hasbeen used in the past for different applications, such as screening for friction stability usingthe FAST machine and monitoring drum lining material using the CHASE machine [8, 9].Furthermore, reduced scale testing can improve the accuracy and reproducibility of results by3
ACCEPTED MANUSCRIPTreducing spurious effects such as caliper and bracket deflection and pressure fluctuations [6].Moreover, one of the areas that needs to be considered carefully is convective cooling as thecooling rates of the reduced scale and full size configuration are not equivalent because of thedifferent physical geometries [6]. Therefore, scaling is a complex process and careful tuningof the scaled parameters is needed in order to obtain comparable results [10].IPTA pin-on-disc type rig has been utilised as an experimental setup in the literature [10-12] toinvestigate friction materials. This uses a single pad pushed against one side of a rotatingdisc. Other studies use two brake pads attached 180 degrees from each other, again pressedCRagainst one side of a rotating disc [6, 7]. However, none of the previous small scale studieshas tried to implement a realistic brake caliper, which allows the pads to be applied to bothMANUSsides of the disc simultaneously to represent the real world configuration of an automotivebrake.In the present research, the main goal is to develop a scaling methodology that can be used toinform the design of a reduced scale brake dynamometer especially with regard to the thermalperformance. This paper firstly outlines the assumptions underlying the scaling processbefore deriving the equations required to give equivalent thermal performance between theDsmall and full scale brake. An existing conventional brake dynamometer is then described,followed by the derivation of the design parameters of the equivalent small scale system. TheTEpaper proceeds to compare the measured disc surface temperatures between the full size andsmall scale discs for two different drag brake events. Finally the results of finite elementEPsimulations of the two differently scaled brake rotors are compared with the experimentaldata to demonstrate the validity of the scaling approach adopted.ACC2. Thermal analysis of solid brake rotorUnderstanding the thermal performance of an automotive disc brake is the key factor indeveloping a scaling methodology that replicates real world conditions. In this section thethermal analysis of a disc brake is presented in brief. In order to predict the temperaturedistribution of the disc brake, the heat flux generated by friction between the pad and disc isrequired. The following assumptions apply: The kinetic energy of the vehicle is converted to thermal energy due to friction at thesliding interface without any other energy loss during the braking event.4
ACCEPTED MANUSCRIPT The heat flux generated by friction at the interface between the pad and the disc istransferred to the brake pads and disc according to their respective thermal properties. Heat loss by radiation from the disc is included in this study along with heat transferby convection and conduction. All brake parts are in a steady state condition before braking commences.IPTA one dimensional schematic model of a disc brake is illustrated in Figure 1. This model wasused to derive the finite difference equation required to evaluate the thermal performance ofthe disc. The numerical equations for the one dimensional disc brake model were derivedCRfrom the energy balance equation and the heat diffusion equation with assumed constantEPTEDMANUSthermal conductivity [13-15].XACCYFigure 1: One dimensional thermal model for a brake discThe heat diffusion equation or heat equation with constant thermal conductivity is as follows: 2T 2T 2T q 1 T x 2 y 2 z 2 k α t5(1)
ACCEPTED MANUSCRIPTwhere α kis the thermal diffusivity of the disc material. This equation provides theρc ptemperature distribution T ( x, y , z ) as a function of time, which aims in the derivative of thetransient one dimensional numerical simulation of the brake. Considering the onedimensional system in Figure 1, under transient conditions with no internal heat generationIPTand constant properties, equation (1) becomes:(2)CR1 T 2 T α t x 2The central difference approximation to the second order spatial derivative is as follows:Tmp 1 Tmp 1 2Tmp m x 2 x 2MANUS 2T(3)Where the subscript m is used to designate the location of the nodal point in x and thesuperscript p is used to define the time dependence of T where:t p t(4)DThen the finite difference approximation to the time derivative in equation (3) can beTEexpressed as for the one dimensional analysis:EP T tm Tmp 1 Tmp t(5)ACCSubstitution of equations (5) and (3) in equation (2) yields:Tmp 1 where()12 Tmp 1 Tmp 1 1 TmpM M M (6) x 2h xand N α tkEquation (6) is valid for the interior nodes of the disc. The following equation may be usedfor the node on the symmetry adiabatic boundary, with Tmp 1 Tmp 1 :6
ACCEPTED MANUSCRIPTTNp 1 ()12 2TNp 1 1 M M p TN (7)The temperature of the surface node T0p 1 with convection and radiation heat loss, can beEin Eg Eout EstT0p 1 T0pkA Pp′′′′(T1 T0 ) q A qrad A ρcAhA(T T ) x t(8)CRp0IPTderived using the energy equation as follows:where E st is the rate of stored energy (mechanical and thermal), E g is the rate of the thermal energyMANUSgeneration and E in and E out are the rates of the energy entering and leaving the control surface(inflow and outflow energy). Rearranging equation (8) for T0p 1 :p′′ 2 N 2 p 2 NT 2T1 2 xq′′ 2 xqrad TT0p 1 1 0MMkMkMM (9)The condition for mathematical stability must also be satisfied in order to realise a stableDsystem and this requires choosing M to satisfy the following condition [13, 15]:M 2N 2TE(10)The above equations were embedded within a bespoke Matlab m-file and used in theEPdevelopment of the scaling methodology described below [3, 16].ACC3. Scaling methodologyThe scaling factor is the fundamental relationship used in the scaling methodology. Thephysical specification of the small scale test brake was developed by applying the scalingfactor to the full scale disc as explained below. The guiding principle of the scaling exerciseis that both the tribological and thermal conditions at the friction interface should be the samefor the small and full scale brakes. Since the friction coefficient is dependent on contactpressure and sliding speed as well as on temperature, the assumption is that both pressure andsliding velocity should be the same at both scales. Thus, provided the scaling techniqueensures the same interface temperatures, the heat generation and tribological conditionsshould also be comparable between the two scales.7
ACCEPTED MANUSCRIPT3.1 Disc massThe main parameter for the proposed scaling process is the scaling factor ( S ), which isdefined as the ratio between the full scale and small scale brake pad areas. If full scaleparameters are denoted by a subscript F and small scale parameters are denoted by aS AFASThe disc mass was scaled using the energy balance equation:(11)CRwhere AF is the full scale pad area and AS is the small scale pad area.IPTsubscript S , then:MANUSQ m d c p T(12)where Q is the heat flow from or to the disc during a braking event, md is the disc mass, c pis the specific heat and T is the difference between the final and initial temperatures. As it isassumed that the energy density (heat flow per unit pad area) in the full and small scale casesshould be equal, this leads to:TEDQFA F SQSAS(13)Substituting equation (12) into equation (13) leads to:EP(md c p T )F(md c p T )S S(14)One of the main aims of the scaling exercise is to replicate the thermal condition acting onACCthe full scale brake and this means that the temperature rise T should be the same. Thusequation (14) reduces to:(md c p )F(md c p )S S(15)If the specific heat of the material of the full and small scale brake discs is the same, thisequation implies that the disc masses should scale linearly with the pad area ratio S .8
ACCEPTED MANUSCRIPT3.2 Brake torqueThe brake torque was calculated using the following equation:τ 2µ Fn rm(16)where Fn is the normal force pushing each pad against the disc, µ is the average coefficientIPTof friction and rm is the mean rubbing radius. The contact pressure for small and full scalebrakes was assumed constant in the current scaling methodology in order to give the sameCRtribological conditions, which leads to:FnFF nSAFAS(17)MANUSwhere FnF is the normal force for the full scale pad and FnS is the normal force for the smallscale pad. Substituting equation (16) into equation (17) leads to:τFAF rmF τS(18)AS rmSAssuming the same friction coefficient for both scales (since the sliding velocity, contactpressure and temperature are assumed to be the same) and scaling the rubbing radii with theDsquare root of the pad area ratio S leads to:TE3τF S 2τS(19)EPEquation (19) was used to calculate the brake torque to be generated by the small scale discbrake assembly from the equivalent full scale value.ACC3.3 Rotational speedIn order to obtain the same tribological conditions at the friction interface, the small scale rigsliding velocity is set equal to the full scale sliding velocity v which is derived from theinitial forward speed of the vehicle Vi as follows:v rmF2Vidt(20)where rmF is the full scale mean rubbing radius and dt is the road wheel rolling diameter.The rotational speed of the small scale rig is given by:9
ACCEPTED MANUSCRIPTωS v(21)rmSwhere ωS is the initial rig rotational speed and rmS is the mean rubbing radius for the smallscale case. Equating the sliding velocity in equations (20) and (21), leads to:2Vidt rmF rmS IPTωS (22)Equation (22) defines the small scale rotational speed as a function of the vehicle wheelCRrolling diameter, initial vehicle speed and ratio of the mean rubbing radius for small and fullscale rigs. The mean disc rubbing radius is a linear quantity and thus scales with S 0 .5according to the scaling methodology; this relation is used to evaluate the relation betweenMANUSthe full and small scale rotational speeds by utilising equation (22) as follows:ωF S 0.5ωS(23)In other words, the disc rotational speed should scale with the inverse of the square root ofthe pad area ratio S .D4. Full scale brake dynamometer and full/reduced scale brakesTEA full scale brake dynamometer, shown in Figure 2, was used to test both the small scalebrake designed using the above scaling methodology and the equivalent full scale brake inorder to validate the scaling methodology. A Lorey Somer LSK1604M04 45 kW DC electricEPmotor rotates the main dynamometer shaft via an enclosed belt drive. The main shaft issupported by two roller element bearings between which is mounted a torque meterACC(Torquemaster TM 213) and speed encoder. An ACME screw linear actuator (LMR 01) [17]was used to pressurise the hydraulic system via a standard brake master cylinder. The brakedynamometer was controlled and monitored using an in-house LabVIEW based dataacquisition system.The rotor and brake pad geometries for the full scale brake are shown in Figure 3 and for thesmall scale brake in Figure 4. Note that the full size rotor has the conventional ‘‘top-hat’’structure for connecting the rotor to the hub whereas the small scale rotor is a plain discwithout such a structure. Both discs were manufactured from standard grey cast iron whilstthe pads were made from proprietary friction material supplied by the manufacturer.10
ACCEPTED MANUSCRIPTIn the case of the full scale disc a BENDIX brake caliper (No. 520 1889 794997) was usedwith a Girling Aluminium Master Cylinder unit. A Wilwood PS1 brake caliper (part no. 1208374), was used for the small scale disc with Wilwood Go Kart master cylinder (part no. 2605520) [18]. For both small and full size brakes, K type sliding thermocouples were used tomonitor the rubbing surface temperature of the rotor as shown in Figure 3 and 4. The slidingIPTthermocouple was placed at the mean rubbing radius in both cases. All the sensors andactuators were calibrated before commencing any test in order to ensure that the output dataTorque and speed sensorMotorEPTEDMANUSDisc and caliperCRwere accurate and reliable.ACCSliding thermocouplesLinear actuatorMaster cylinderFigure 2: Brake dynamometer with full scale brake mounted for testing.11
ACCEPTED MANUSCRIPT(b)MANUSCRIPT(a)TED(c)Figure 3: Full scale disc and pad with thermocouple position: (a) disc geometry, (b)ACCEPbrake pad, and (c) brake assembly mounted on dynamometer.12
TEDMANUSCRIPTACCEPTED MANUSCRIPTEPFigure 4: Small scale disc and pad with thermocouple positionThe control and data acquisition system of the brake dynamometer is shown in Figure 5. TheACCuser controls the test rig using LabVIEW software that has been developed in-house in orderto give full control over the braking conditions. The user controls the braking pressurethrough the linear actuator and the speed of the motor by changing the input voltage whils
characterization of automotive disc brake, Applied Thermal Engineering (2014), doi: 10.1016/ j.applthermaleng.2014.10.001. This is a PDF file of an unedited manuscript that has been accepted for publication. As a service to our customers we are providing this early version of the manuscript. The manuscript will undergo copyediting, typesetting, and review of the resulting proof before it is .
CCC-466/SCALE 3 in 1985 CCC-725/SCALE 5 in 2004 CCC-545/SCALE 4.0 in 1990 CCC-732/SCALE 5.1 in 2006 SCALE 4.1 in 1992 CCC-750/SCALE 6.0 in 2009 SCALE 4.2 in 1994 CCC-785/SCALE 6.1 in 2011 SCALE 4.3 in 1995 CCC-834/SCALE 6.2 in 2016 The SCALE team is thankful for 40 years of sustaining support from NRC
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