Theory of Rolling Friction for Spheres

Abstract

A theory of rolling friction featuring the importance of elastic hysteresis losses is presented. A simple model of retarded elasticity is chosen to represent the physical properties of the material. A prediction resulting from the theory is that the coefficient of friction for a relatively hard sphere rolling on a softer base material should vary with speed so as to go through a maximum. This relationship resembles closely the variation of mechanical loss with frequency. The results are not restricted to rolling but also apply to well-lubricated sliding where shearing forces have been minimized. Although the theory is developed for a material with idealized physical properties, it nevertheless affords a basis for comparing real materials and for predicting their frictional properties in cases where deformation losses are predominant.

Performance of diamond-like carbon-protected rubber under cyclic friction. II. Influence of substrate viscoelasticity on the friction evolution

“…(13). Approximated equations describing these limits can be found, 7,8 but in the present work these points have been identified numerically.…”

“…We will base our approach on the work from Flom and Bueche, 7 further revised and expanded by Moore. 8 First, a Voigt model 6 is assumed to simulate the rubber behavior, and a "mattress approach" is used for calculating the contact areas.…”

“…(19). In the previous analysis, 7,8 only the first pass of the ball on the rubber was considered. Although they provide valuable information about the effect of material parameters and test conditions, no information was given about the evolution of the CoF with time (i.e., in the case of consecutive laps).…”

“…2(c)). In previous works, 7,8 the asymmetry of the contact area was only described in terms of frontÀback (i.e., a x ! jx 0 j) caused by the delayed response of the substrate.…”

Viscoelastic characterization of an EPDM rubber and finite element simulation of its dry rolling friction

“…The exact analytical calculation of the observed strains during mechanical loading of rubbery elements is a great challenge due to the complexity of the viscoelastic material models. Although some simplified analytical methods were developed to evaluate for example the friction resistance or internal heat generation in viscoelastic materials during rolling contact, they failed for more complex stress states or for repeated stresses [1][2][3][4][5][6][7][8][9]. On the other hand the finite element (FE) method is able to handle complex viscoelastic material models owing to the permanent advancement of the software and hardware background.…”