Mechanical Model of Contact Between a Sphere-Based Fractal Rough Surface and a Rigid Flat Surface

To investigate mechanical properties of point contact between rough surfaces and improve the bearing capacity of contact component, the Weierstrass-Mandelbrot function is used to simulate a three-dimensional sphere-based fractal rough surface, and then a mechanical model of contact between a sphere-based fractal rough surface and a rigid plane is developed. The truncated size distributions for asperities with different frequency indexes in different contact zones are derived. The relation between real contact area and total contact load is obtained, and the contact pressure distribution on the contact half width is obtained. The results show that the mechanical properties of sphere-based fractal rough surface are mainly affected by the range of frequency index. When the relation between the minimum frequency index nmin and the elastic critical frequency index nec is nmin+5≤nec, the sphere-based fractal rough surface exhibits elastic property in a complete contact process. When the relation between the nmin and the elasto-plastic critical frequency index nepc is nmin>nepc, the sphere-based fractal rough surface exhibits inelastic property during the entire contact process. The value of contact half width of the sphere-based fractal rough surface mainly depends on the radius of base circle. With the same ratio of interference, the peak contact pressure is proportional to the value of the minimum frequency index. In elastic and elasto-plastic deformation process, the contact pressure reaches the maximum at the center of contact zone, and decreases from center to edge of the contact zone. In plastic deformation process, the contact pressure exhibits approximately uniform distribution in whole contact zone. © 2019, Editorial Office of Journal of Xi'an Jiaotong University. All right reserved.