BALKANTRIB O5 5 th INTERNATIONAL CONFERENCE ON TRIBOLOGY JUNE Kragujevac, Serbia and Montenegro

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1 BALKANTRIB O5 5 th INTERNATIONAL CONFERENCE ON TRIBOLOGY JUNE5-8 5 Kragujevac, Seria and Montenegro THE TEMPERATURE DISTRIBUTION IN THE WHEEL/BRAKE SHOES CONTACT C Popescu Wagon Depot of Craiova Romania ATudor - Politehnica University of Bucharest- Romania Astract An analytical solution for the temperature in wheel-rail and wheel-rake shoe was otained The friction heat sources appear simultaneously The steady-state temperature distriution in a wheel of locomotive or wagon undergoing uniform heating in rail and four rake shoes and nonuniform cooling is presented The conduction of heat from the sliding contact zones in the axial direction of the rake shoes and the radial direction of the wheel, as well as the heat loss y convection from the sides and periphery of the disc, are taken into account The analysis shows that the temperature friction can e well evaluated y knowledge of the rolling heat for wheel/rail contact and sliding wheel/rake shoe contacts Key words: Wheel/rake shoe contact; Temperature friction; Heat partition INTRODUCTION The thermal aspect around the contact region can e studied y examining the heat transfer etween stationary reak shoe and a moving ody (relative to the heat source) The slip etween wheel and raking system causes friction heating of oth odies When a rake is working, the transformation of kinetic energy of moving masses into thermal energy takes place This kinetic energy is dissipated etween two odies and apprecialy raises their temperature at the area of the sliding contact Two aspects are special importance in this analysis - the nature and distriution of heat partition into each ody at the interface and the resultant temperature fields in the two odies oth at the interface and with respect to dept While the time for reaching the quasi-steadystate conditions can e very short for a moving ody, it can e relatively long for a stationary ody Thus, it may require a long time to arrive at steady-state conditions for sliding In this case, the heat partition fractions for the two odies may also vary for a long time efore reaching steady-state value Many analytical investigations have een conducted in the past for prediction of the flash temperature and the heat partition [,,] While railway wheels are heating y friction in the contact patch and in the contact rakes, there is also heat loss due to conduction through the contact patch into the rail and into rake shoe A literature survey revealed that considerale attention has een devoted to the cooling and heating of rolling elements [4,5,6] In this paper, an analytical solution is proposed, for the temperature distriution in the rake shoes, when wheel is heating y rolling in rail contact and suject to four surfaces heating y sliding in rake shoes THE FRICTION HEAT TRANSFER MODEL The wheel is considered that a short rotating cylinder This wheel, sujected to heating y rolling and sliding friction and nonuniform convective cooling at aritrary angles (β c ) along the circumference, is shown in Fig The relative positions of the rail and the rake shoes will e analyzed y the angular location Heating is assumed to e provided y means of rolling friction in the angular (γ a ) and

2 means of sliding friction in the four intervals γ, γ, γ and γ (Fig ) External cooling is assumed to e provided The thermal properties of the wheel and the rake shoes are independent of temperature and remained uniform C 6 C 5 q C 7 C 8 ε q ω ε q C 4 q w C 9 ε q ε q C γ C ε q β C q q O C q r Fig y means of airflow convective heat transfer (convection coefficient h) in the interval (C, C ) and (C, C 4 ) and y forced convection heat transfer (convection coefficient h+h o ) in the interval (C 6, C 7 ), (C 8, C 9 ) and (C, ) We seek to determine the cyclically steadystate temperature distriution in the wheel and rake shoes ased on the following assumptions: The temperature of wheel varies along its radius and circumference; the wheel is considered as the disc with constant radius and thickness The heat conduction in the axial direction is neglected, ecause the thickness of disc is small compared with its radius 4 The heat loss y convection occurs from the exposed periphery and from the sides of the wheel; there is also heat loss y convection from side of the rake shoes 5 The entire surface of the rake shoes is in contact with the wheel 6 The convention coefficients are constant and Biot s numers are 7 The temperature of the wheel is equal to that of the rail in the contact zone 8 The temperature of the wheel is equal to that of the rake shoes in the contact zone 9 There is no phase change occurring in the rake shoe or the wheel material at the friction surface The periodic heating at the wheel periphery causes a steady oscillation in temperature in thin annular part of the wheel

3 t' Adopting a fixed Eulerian reference frame, the steady state heat transfer equation in cylindrical coordinates for the wheel is T T T h' + + = T r r r r p δ () γ R d x z α where T is the temperature rise and (r, φ) the coordinate system fixed to the wheel The oundary conditions and the solution are otained in our papers [, 4, 5] HEAT SLIDING FRICTION DISTRIBUTION COEFFICIENT IN THE BRAKE SHOE α Fig g Considering the heat transfer y conduction along the length of the rake shoe and y convection from the periphery (Fig ), the differential equation for the temperature distriution at any axis distance z is given T α p (T To ) z A (6) where is thermal conductivity of the rake shoe material, T the temperature in the rake shoe at any axial distance z, T o the amient temperature and, α the heat transfer coefficient for the rake shoe, p, A the perimeter and cross-sectional area of the rake shoe Sustituting T =T-T o and m =(α p / A ) /, the general solution of equation (5) is given y mz mz T = Ae + Be, A and B are the constants which are defined y oundary conditions With the oundary conditions T =, z = g (7) T = q = ( ε ) q z z= (8) and T = Ts, z = (9) the solution of equation (6) ecomes: Ts sinh{ m (g z) } T (z) = sinh(m g ) (4) The sliding frictional power dissipation rate in the contact patch of wheel and rake shoe is proportional to the pressure q = µ v op (x) We assume that friction coefficient (µ ) and pressure p (x) are constants and that all the frictional power dissipation is transformed in heat Using equations (4) and (8) can e calculated the surface rake shoe temperature ( ε ) q Ts = tanh( m g ) m (4) Dimensionless temperature of rake shoe surface Ts d q d θs = = ( ε ) tanh( mg ) = qr q mr qa = ( ε) tanh( mg) = C εc q mr (4) with q a C = tanh(m g ) and a m R q q a =, a = q d The partition coefficient ε will e calculated with equations () and (4) γ θ, β + = C ε C (4) It is generally assumed that every wheel has four rake shoes The partition heat coefficient for every rake shoe (ε, ε, ε and ε ) are calculated y conditions that the temperature for the wheel and rail, left rake shoe and right rake shoe are respectively equal [,4]

4 4 SURFACE BRAKE - SHOES TEMPERATURE The surface rake shoes dimensionless temperature can e otained y numerical solution Thus, for example, the Figures, 4, 5 and 6 show the dimensionless temperature for the,,, rake- shoes (UIC 54) respectively The curve is otained for following parameters: - relative heat flux: q a = q a = q a = q a = 4; - convection heat transfer coefficient, h = Wm - o C - ; The curve is otained for following parameters: - relative heat flux: q a = q a = q a = q a =, - convection heat transfer coefficient, h = Wm - o C - ; The curve is otained for following parameters: - relative heat flux: q a = q a = 4 and q a = q a = 4 (inequal efficiency of rale-shoes); - convection heat transfer coefficient, h = Wm - o C - Dimensionless temperature Angular position of rake- shoe Fig 4 The maximum temperatures predicted for the rail and left and right rake shoes are summarized in Tale These temperatures are calculated y the normal conditions for wheel/rail and rake/shoe contact [6,7] ( q = 5x 6 W/m, q a = q a = q a = q a = x 6 W/m, h o = W/m K for high speed, and h o = W/m K for low speed) Dimensionless temperature Angular position of rake- shoe Fig Dimensionless temperature Fig5 Angular position of rake- shoe 4

5 Dimensionless temperature CONCLUSIONS Fig6 An analytical solution is presented for the temperature distriution of rake shoes in contact with rotating wheel (cylinder) The maximum temperature occurs towards nearly exit of heating contact for the left or right rake shoe It is shown that the maximum dimensionless contact temperatures of wheel and rake-shoes are induced in the rake shoe heating contact When the rake shoes haven t similary efficiency (inequal friction), the temperature field of the all rake-shoes is modified Temperature [ o C] 6 REFERENCES Tale Maximum -Left rake shoe -Left rake shoe -Right rake shoe -Right rake shoe [] R Komandury, ZB Hou, Analysis of heat partition and temperature distriution in sliding systems WEAR, Vol 5,, pp Angular position of rake- shoe Low Speed ( m/s) High Speed (9 m/s) [] HS Carslaw, JC Jaeger, Conduction of haet in solids nd edn, Clarendon Press, Oxford, 959 [] A Tudor, C Radulescu, Analysis of heat friction partition in wheel-rail and wheel-rake shoe contact An analytical approach, UPB Sci Bull, Series D, Vol 64, No,, p5-46 [4] A Tudor, C Radulescu, Temperature distriution due to frictional heat generated in wheel rake shoe contact, UPB Sci Bull, Series D, Vol 64, No4,, p47-58 [5] M El-Shering and TP Newcom, The Temperature Distriution due to Frictional Heat Generated etween a Stationary Cylinder and a Rotating Cylinder, WEAR, Vol 4(), 977, pp [6] PUlyse and MM Khonsari, Thermal Response of Rolling Components under Mixed Boundary Conditions: An Analytical Approach, J Heat Transfer, Vol 5, 99, pp [7] K Knothe and S Lieelt, Determination of Temperatures for Sliding Contact with Applications for Wheel-Rail Systems, WEAR, Vol 89, 995, pp 9-99 [8] M Ertz and K Knothe, A Comparasion of Analytical and Numerical Methods for the Calculation of Temperatures in Wheel / Rail Contact, WEAR, Vol 5,, pp NOMENCLATURE A = cross- sectional area of rake shoe, m Bi = Biot numer = hr/κ, dimensionless Bi o = Biot numer of in oth supplementary cooling zones = h o R/k Bi s = Biot numer of in lateral cooling zones = h R /(δ k) g = rake shoe thickness, m h = convection heat transfer coefficient in main frontal zone, Wm - o C - h o = convection heat transfer coefficient in supplementary cooling, Wm - o C - h = convection heat transfer coefficient in lateral zones, Wm - o C - k = thermal conductivity, Wm o C P = rake shoe perimeter, m Pe =Peclet numer = a H v/(κ), dimensionless q,,,, = heat source of strength,, and, Wm q a,,, = relative heat source of strength,, and = q,,, /q, dimensionless r = radial coordinate 5

6 R = mean radius, m t = time, s t = width of rake shoe, m T = temperature rise in excess of amient temperature, o C T w = surface wheel temperature, o C z = normal to surface coordinate dimensionless β = polar coordinate for heat source or cooling zone rad β c = polar coordinate for eginning supplementary cooling zone (C 6 point, Fig), rad γ,,,, = angular length of heat source, respectively, rad δ = half of wheel length, m ε,,, = heat partitioning factor in regions,, and κ = thermal diffusivity,m s µ = friction coefficient ψ = angular location, rad θ = dimensionless temperature = kt/(q R) θ w = dimensionless surface wheel temperature = kt w /(q R) 6

Friction at high sliding speed of WC-6Co pin versus steel disc AISI 1045: estimation of the contact temperature

Int. Jnl. of Multiphysics Volume 3 Number 2 29 141 Friction at high sliding speed of WC-6Co pin versus steel disc AISI 145: estimation of the contact temperature T. KAGNAYA 1,2, C. BOHER 1, L. LAMBERT