Wear prediction model for a three-dimensional fractal friction surface with multiple-scale asperities

This paper describes a new wear prediction model for a three-dimensional fractal friction surface considering scale dependence. The analytical formulas for critical microcontact area and critical level are derived. According to the truncated area distribution function of asperities at multiple-scale levels, the total real contact area of different deformation stages on the rough surface is obtained respectively. Based on the traditional adhesion theory and fractal theory, and introducing the concept of multi-scale, the wear fractal model of rough friction surface is established. The effects of fractal roughness, fractal dimension, and total contact load on the wear rate are analyzed by numerical simulation. The numerical results show that as the fractal dimension increases, the wear rate decreases first and then increases. There is an optimal fractal dimension to make the wear rate reach the lowest value. With the increase of the fractal roughness, the wear rate will increase. For the fixed surface fractal parameters, the wear rate will increase with the increase of the normal load.