Heat transfer analysis of the ungrooved disk of a cooled, multiplate clutch

Abstract

A one-dimensional analysis is presented to determine the transient response of a disk due to a time varying heat flux boundary condition. The boundary condition alternates with a step change between a heating flux and a cooling flux which can occur over different time periods (simulating coolant grooves in the adjacent disk). For a multiplate clutch where the driving and reaction disks are of different materials, an approximation of the amount of the heat generated at the sliding interface which enters each disk is presented. Results are given to illustrate the effects of materials, heating and cooling fluxes, and time period on the transient temperature response. Increasing (reducing) the heating (cooling) flux, increasing (reducing) the time period of the heating (cooling) flux, decreasing the disk thickness or increasing the disk thermal diffusivity increases the disk temperature during the clutch engagement period. Nomenclature c = specific heat d 0 , d m , e m = variables in Fourier series approximation to the time-dependent heat flux boundary condition; Eqs. (15), (16), and (17), respectively / = fraction of heat generation at interface which enters disk a h = convection coefficient in coolant channel / 0 , /" = integrals defined in Eq. (10) / = integer from zero to some finite value used in boundary condition; Eq. (4) k = thermal conductivity L = disk thickness m, n = indices of infinite series P N = normal pressure applied to rotating disks q = heat flux q l9 q 2 = heat fluxes in time-dependent boundary condition r = radius or radial direction s = dummy integration variable T = temperature due to a constant boundary condition T = temperature due to a time varying boundary condition T f = fluid temperature Th = temperature due to a constant boundary condition and an initial condition of zero temperature Th' = temperature due to a time varying boundary condition and an initial condition of zero temperature Tj = initial temperature distribution TJ = uniform initial temperature t = timê = time period used in periodic boundary condition x = axial direction a = thermal diffusivity, k/(pc) = function of time used in solution A<£ = angular difference 0 = dimensionless temperature, Th'l(q,Llk) + d 0 at/L 2 \ n = (n7r)IL H s = coefficient of sliding £ = function of x used in solution 77 = numerical constant p = density T = time period used in periodic boundary condition Y = torque per unit area <f > = angular direction if/ -function of x and t used in solution a) = difference between rotational speeds of two disks in sliding contact a*! = angular speed of the reaction disk a) 2 -angular speed of the driving disk Subscripts a = disk defined between x = 0 and x = -L a b = disk defined between x = 0 and x = L h i = initial value 0 = disk defined between x = L and x = 2L

Finite element implementation of the eigenfunction series solution for transient heat conduction problems with low Biot number

“…Under these conditions, the heat lost by convection from the exposed surfaces during a single engagement is often a negligible proportion of that generated by frictional dissipation, so that the temperatures reached are largely determined by the ratio between the total heat input and the thermal capacity of the components. Heat loss by convection then occurs during the intervening idle periods and a significant factor in the design of transmission clutches for systems such as earth moving machines that experience frequent engagements is that the temperature should not accumulate to excessive values over time [3,4].…”