Two Cases of Rapid Contact on a Coupled Thermoelastic Half-Space: Sliding Ellipsoidal Die, Rolling Sphere

Abstract

In one case, a rigid ellipsoidal die translates over the surface of a coupled thermoelastic half-space under compression, and because of sliding friction, shear. In the other, a rigid sphere rolls on the surface under a compressive force. Both motions occur along a straight path at constant sub-critical speed. A dynamic steady state is treated, i.e., the contact zone and its traction remain constant in the frame of the die or sphere. Robust asymptotic expressions in analytic form for contact zone traction, temperature and geometry are derived. Axial symmetry is not required in the solution process. Instead Cartesian coordinate formulations are used, but a system of quasi-polar coordinates is introduced that allow problem reduction to integral equations similar in form to those found in 2D contact.