Vol. 9, No. 3, 2014

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ISSN: 1559-3959
Sliding of a cup-shaped die on a half-space: influence of thermal relaxation, convection and die temperature

Louis Milton Brock

Vol. 9 (2014), No. 3, 347–363
Abstract

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.

Keywords
thermoelasticity, 3D, relaxation, multiple connectivity, critical temperature, convection, 3D dynamic, sliding, transverse isotropy, contact zone geometry
Milestones
Received: 15 April 2014
Accepted: 7 July 2014
Published: 4 October 2014
Authors
Louis Milton Brock
Department of Mechanical Engineering
University of Kentucky
265 RGAN
Lexington, KY 40506-0503
United States