Rapid Sliding on a Thermoelastic Half-Space: Rigid Die with Two Contact Surfaces

Abstract

A rigid die with two spherical contact surfaces translates, at constant speed, into a thermoelastic half-space. The spherical surfaces are frictionless and have identical radii, and translation is parallel to the line connecting their centers. Sliding speed is subcritical but may be rapid, and a 3D (dynamic) steady state is assumed. An asymptotic approximation gives integral transform inversions in analytic form. The process of imposing the auxiliary conditions for sliding contact is then presented in some detail. Formulas, calculations and plots illustrate the sensitivity of contact zone geometry and temperature change to sliding speed and proximity of the two spheres.