Friction force model and rolling dynamics for a ball on a rough surface with presliding displacement taken into account

• Published in: Mechanics of solids Vol. 48; no. 1; pp. 47 - 56
• Main Author: Plotnikov, P. K.
• Format: Journal Article
• Language: English
• Published: Heidelberg Allerton Press, Inc 2013
• Subjects: Classical Mechanics; Physics; Physics and Astronomy; ball; modeling; rolling friction; slip; presliding displacement; spinning; tribological conjunction pair; characteristic
• ISSN: 0025-6544; 1934-7936
• DOI: 10.3103/S0025654413010056

A model of sliding and spinning friction forces for a ball in the form of finite relations obtained by integrating the tangential stresses over the contact area whose parameters are determined by Hertz’s theory for the “ball-rough horizontal surface” tribological conjunction pair is supplemented with a model of rolling friction torques. The combined model is peculiar in that the presliding displacement effect in rolling and spinning friction torques is taken into account. It is shown that the ball motions in the presliding displacement zone are of quasilinear character and, under shock perturbations, have the form of damping vibrations in the three orientation angles. The numerical parameters of the rolling and spinning friction model are experimentally determined for the presliding displacement zones, while the sliding friction parameters and partly the spinning friction parameters are calculated. Mathematical modeling permits one to discover new properties of the ball, namely, its deceleration in rolling, the onset of damping vibrations at the beginning and end of motion, and the transient process parameters.