THREE-DIMENSIONAL CALCULATION OF TEMPERATURE IN A ROTATING DISK SUBJECTED TO AN ECCENTRIC CIRCULAR HEAT SOURCE AND SURFACE COOLING

Abstract

This article derives, for the first time, an appropriate analytical solution for the calculation of three-dimensional temperature distribution inside a rotating disk subjected to an eccentric circular heat source and surface cooling. This problem is encountered in, among others, the pin-on-disk frictional device, thrust ball bearing, or machining in a lathe. In order to obtain this solution under an explicit and simple form, we assume that the cooling occurs over the whole frictional surface of the disk, including the heated region. A numerical study, using the finite-volume method, is also conducted in order to define the limits of validity of the above assumption. It is shown that the analytical solution is accurate for a wide range of heat convection coefficients ( h  ≤ 1,000 W/m²K for high Peclet numbers and h  ≤ 5,000 W/m²K for low ones).