By taking into account steady-state heat transfer, and surface distortion due to thermal and elastic deformations, a two-dimensional thermoelastic model is developed for rough surface asperity contact, where the thermal influence function connecting the thermal deformation and the contact pressure is derived based on the Dundurs’ theorem. The model has been shown to be accurate at low as well as high frictional heating conditions by comparison with published results. As an application of this model, the contact problem of a cylinder on a random rough surface is studied in detail.

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