A Fractal Theory of the Interfacial Temperature Distribution in the Slow Sliding Regime: Part I—Elastic Contact and Heat Transfer Analysis

The frictional temperature rises at the microcontacts of rough surfaces are analyzed by characterizing the surfaces as fractals and assuming Hertzian contacts of spherical asperity tips. The maximum temperature rise of a fractal surface domain in the slow sliding regime, where transient effects are negligible, is expressed as a function of thermomechanical properties, sliding speed, friction coefficient, real and apparent contact areas of the fractal domain, and fractal parameters. The distribution density function of the temperature rise at the real contact area is also determined based on the statistical temperature rise distributions of individual microcontacts and the maximum temperature rise of a fractal domain. This function characterizes the fractions of the real contact area subjected to different temperature rises, and can be used to analyze tribological interactions on dry and boundary-lubricated sliding surfaces.