Planar Hertz Contact With Heat Conduction

Abstract

The paper discusses the planar Hertz contact problem when the bodies are not only pressed together but also exchange heat by conduction. The nature of the problem and the results depend strongly on the direction of heat flow. If heat flows into the material with the larger distortivity, the common boundary conditions are sufficient to achieve a solution which satisfies the inequalities associated with a contact problem. For heat flowing in the opposite direction, the common boundary conditions by themselves lead to contradictions, but the difficulties can be overcome by introducing a zone of imperfect contact. The formulation is based on a suitable Green’s function, and the problem is reduced to a singular integral equation which must be solved numerically.