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<p class="noindent">A rigid, cup-shaped die translates at constant subcritical speed on a thermoelastic half-space that exhibits thermal relaxation and convection. The die surface is held at a temperature different from ambient temperature, and sliding friction exists in a contact zone that is not simply connected. A three-dimensional dynamic steady state model is assumed and, based on an approximation for inversion of integral transforms, a solution in analytic form is obtained. Auxiliary conditions for sliding contact are satisfied; in particular, contact zone traction is stationary with respect to compression force. Among other results, it is found that a dynamic steady state is precluded if die-ambient temperature difference is too large. Similar results are known, but only for die temperatures that exceed the ambient value. </p>

Sliding of a cup-shaped die on a half-space: influence of thermal relaxation, convection and die temperature