Thermal Analysis of the Transient Temperatures Arising at the Contact Spots of Two Sliding Surfaces

The three-dimensional hyperbolic heat conduction equation is solved to obtain the analytical solution of the temperature rise at the contact area between an asperity and a moving smooth flat. The present analyses can provide an efficient method to avoid the problem of being difficult to give the correct boundary conditions for the frictional heat conduction at an asperity. The mean contact area of an asperity which is needed in the heat transfer analysis is here obtained by a new fractal model. This fractal model is established from the findings of the size distribution functions developed for surface asperities operating at the elastic, elastoplastic and fully plastic regimes. The expression of the temperature rise parameter $T∕f$ (⁠$T$⁠: Temperature rise, $f$⁠: friction coefficient) is thus derived without specifying the deformation style of a contact load. It can be applied to predict the $T∕f$ variations due to the continuous generations of the frictional heat flow rate in a period of time. The combination of a small fractal dimension and a large topothesy of a surface is apt to raise the contact load, and thus resulting in a large $T∕f$ value. A significant difference in the behavior exhibited in the parameters of temperature rise and temperature rise gradient is present between the Fourier and hyperbolic heat conductions; Fluctuations in the thermal parameters are exhibited only when the specimen material has a large value of the relaxation time parameter.