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 [Formula: see text], dissipated energy [Formula: see text], damping loss factor [Formula: see text], and normal contact damping [Formula: see text] are deduced in detail, and the influence of fractal parameters and dynamic friction coefficient [Formula: see text] on them are simulated. The simulation curves show that strain energy [Formula: see text], dissipated energy [Formula: see text], damping loss factor [Formula: see text], and normal damping [Formula: see text] increase with the increase in the fractal roughness G; the influence of fractal dimension D on [Formula: see text] is more changeable, first [Formula: see text] decreases with the increase in D and then increases. [Formula: see text], [Formula: see text], and [Formula: see text] increase with the increase in D and [Formula: see text], respectively; the effect of [Formula: see text] on [Formula: see text] is not obvious, so simple change in [Formula: see text] has no significant change in [Formula: see text]; 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.
Highlights
Mechanical joint surfaces is widely existed in all kinds of mechanical systems, such as the joint surfaces of spindle and guide rail of high-end CNC machine tool, joint surface of robot’s moving pairs and rotating pairs, bolted joint surfaces, and so on
According to the research,1 .90% of the total damping of the machine tool are contributed by joint surfaces, that is, the contact damping on the joint surfaces is much higher than the structure damping of material
This article is based on the literatures above, by considering the influence of dynamic friction coefficient, elastic–plastic deformation mechanism, and three-dimensional fractal dimension, the normal contact damping fractal model of dry-friction joint surfaces based on Hertz theory and fractal theory is derived in detail
Summary
Mechanical joint surfaces is widely existed in all kinds of mechanical systems, such as the joint surfaces of spindle and guide rail of high-end CNC machine tool, joint surface of robot’s moving pairs and rotating pairs, bolted joint surfaces, and so on. Since the contact damping model is based on two-dimensional fractal, it is not reasonable[15,16] in theory to describe the three-dimensional surface topography based on two-dimensional fractal curve, and the elastic–plastic transition mechanism of asperities is not considered. This article is based on the literatures above, by considering the influence of dynamic friction coefficient, elastic–plastic deformation mechanism, and three-dimensional fractal dimension, the normal contact damping fractal model of dry-friction joint surfaces based on Hertz theory and fractal theory is derived in detail. According to the classical Hertz elastic contact theory, the normal load of a single asperity in the elastic deformation zone is feðvÞ. Substituting equation (13) into equations (22) and (23), respectively, which can be simplified as ðvÞ=
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