Asymmetric Asperity Height Distributions in a Scale-Dependent Model for Contact and Friction

Abstract

The effect of an asymmetric distribution of asperity heights is accounted for in a recently developed scale-dependent multiasperity model of contact and friction. A Weibull distribution of asperity heights is used which allows the skew and kurtosis to be varied, but not independently of each other. The contact and friction model used includes the effects of adhesion and of scale-dependent friction. The results obtained demonstrate that positive/negative skew decreases/increases both the friction coefficient and its dependence on the magnitude of the normal load.

Height-Dependent Asperity Radii of Curvatures in a Contact and Friction Model

“…It is interesting to note that in all three cases shown (Figs. 4a,b,c), an e of -0.95 decreases friction and dramatically reduces the load-dependence of friction which was predicted in [19]- [20] for constant radii of curvature. Similarly for e = 1.0, friction is highest and so is its dependence on normal load.…”

“…However, when an asperity breaks free of its mating surface during unloading, its undeformed location may still bring it within the distance h in which there are attractive forces using the Maugis model of adhesion. The effect of these attractive forces on the applied normal force was neglected in [19]- [20], but are accounted for here.…”

“…Three key dimensionless parameters representing the surface roughness, the friction regime of the contacts, and the surface energy of adhesion, were seen to influence the value of the friction coefficient. In [20], Adams and Müftü included the effect of an asymmetric distribution of asperity heights using a Weibull function to account for skew and kurtosis.…”

Improvements to a scale-dependent model for contact and friction

“…In this paper, three effects are included in the AMM scale-dependent contact and friction model [1]. A Weibull distribution is used, which allows the skew and kurtosis of the asperity height distribution to be varied, but not independently of each other [27]. The effect of non-constant radii of curvature of the asperity summits, with the curvature varying with asperity height, is examined [28].…”