A novel fractal contact model based on size distribution law

This study develops a new fractal contact model to evaluate contact status on rough surfaces. Specifically, the three-dimensional Weierstrass-Mandelbrot function is used to characterize fractal surfaces, in which the asperity level range is determined by the power spectral density of surface. A novel size distribution law of truncation regions has been proposed based on rough surface truncation in our previous study to overcome the limitation of the law proposed by Mandelbrot. By using the size distribution law, a multi-asperity contact model is established to calculate the contact force and real contact area. The evolution of the asperity level range is considered during the compression process. Furthermore, the elastic or plastic deformation status of each asperity in the level range is determined. In the implementation of the proposed theoretical model, the numerical truncation of fractal surfaces is conducted to obtain the effective asperity level range. Finite element simulation of fractal surface contact and compression experiments of copper specimens are conducted to validate the fractal contact model. The theoretical results of the contact force and total contact area agree well with the simulation and experimental results. The effects of the fractal parameters on the contact behavior are further investigated. The results indicate that the proposed fractal contact model can provide an accurate prediction of rough contact behaviors.