Convenient formulas for modeling three-dimensional thermo-mechanical asperity contacts

Frictional heating is a common phenomenon related to friction and rubbing. Modeling the rough-surface contact in a tribological process that involves frictional heating and thermoelastic deformations requires an interactive thermal-mechanical simulation process through a large amount of numerical calculation. A three-dimensional interactive thermal-mechanical asperity contact model has been developed. The model takes into account steady-state heat transfer, asperity distortion due to thermal and elastic deformations, and material yield by means of the elastic-perfectly plastic assumption. The finite-element method (FEM), discrete convolution and fast Fourier transform (DC-FFT), and conjugate gradient method (CGM) are employed as the solution methods. This model is applied to analyze a large number of numerically generated surfaces of a wide range of statistical properties. A group of semi-empirical formulas correlating the maximum asperity flash temperature, contact pressure, real contact area, and the normal approach between the contacting surfaces is derived as a simplified version of the contact model for convenience of use in tribological simulations. These formulas are compared with the results obtained from numerical analyses with satisfactory accuracy.