The purpose of this paper is to establish a three-dimensional model of sliding friction and to study the influence of surface topography fractal parameters on the model. Firstly, the analysis of the contact between two asperities is completed, for according to the classical molecular-mechanical friction theory, the sliding friction among rough surfaces should be the sum of mechanical force and molecular adhesion. Then based on the fractal theory, the three-dimensional fractal model of sliding friction is deduced. Finally, the influence of the maximum contact area of asperity al, the fractal roughness G and the fractal dimension D on the sliding friction is analyzed by a simulation example, and the analysis results show that the sliding friction F has positive correlation with al and G, and there is an optimal fractal dimension D which minimizes F. The study of the paper can be used to explain the existing experimental results and the friction theory reasonably.
According to the influence of the normal contact damping of joint surfaces on the dynamic characteristics of highprecision 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 threedimensional 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 D, and normal contact damping C n are deduced in detail, and the influence of fractal parameters and dynamic friction coefficient m 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 E e decreases with the increase in D and then increases. E p , D, and C n increase with the increase in D and m, respectively; the effect of m on E e is not obvious, so simple change in m 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.
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