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

Abstract

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 Ee, dissipated energy Ep, damping loss factor Δ, and normal contact damping Cn are deduced in detail, and the influence of fractal parameters and dynamic friction coefficient μ on them are simulated. The simulation curves show that strain energy Ee, dissipated energy Ep, damping loss factor Δ, and normal damping Cn increase with the increase in the fractal roughness G; the influence of fractal dimension D on Ee is more changeable, first Ee decreases with the increase in D and then increases. Ep, D, and Cn increase with the increase in D and μ, respectively; the effect of μ on Ee is not obvious, so simple change in μ has no significant change in Ee; 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.