Three-dimensional fractal model of normal contact damping of dry-friction rough surface

According to the influence of the normal contact damping of joint surfaces on the dynamic characteristics of high-precision machinery (machine tool, robot, etc.), in this article, a three-dimensional fractal model of normal contact damping of dry-friction rough joint surfaces based on Hertz theory and fractal theory is established. The three-dimensional surface topography is constructed, according to the modified double variable Weierstrass-Mandelbrot function. The fractal model of strain energy E-e, dissipated energy E-p, damping loss factor Delta, and normal contact damping C-n are deduced in detail, and the influence of fractal parameters and dynamic friction coefficient mu on them are simulated. The simulation curves show that strain energy E-e, dissipated energy E-p, damping loss factor D, and normal damping C-n increase with the increase in the fractal roughness G; the influence of fractal dimension D on E-e is more changeable, first Ee decreases with the increase in D and then increases. E-p, Delta, and C-n increase with the increase in D and mu, respectively; the effect of mu on E-e is not obvious, so simple change in mu has no significant change in E-e; a comparative analysis of the theoretical calculation of normal damping and experimental results show that their general trend is consistent, and they increase with the increase in total normal contact load P, the relative error is 5%-25%. The theoretical model can provide reference for the design of normal contact damping of the joint surfaces.