General contact mechanics theory for randomly rough surfaces with application to rubber friction

TL;DR

This paper extends contact mechanics and rubber friction theories to rough surfaces with diverse material properties, providing a comprehensive model that predicts contact behavior and frictional forces under various conditions.

Contribution

It introduces a generalized theory for contact mechanics and rubber friction applicable to surfaces with roughness and various material properties, including layered and viscoelastic materials.

Findings

Roughness influence diminishes with increasing sliding speed.

The model accurately predicts contact area and friction forces.

At typical tire speeds, roughness effects can be neglected.

Abstract

We generalize the Persson contact mechanics and rubber friction theory to the case where both surfaces have surface roughness. The solids can be rigid, elastic or viscoelastic, and can be homogeneous or layered. We calculate the contact area, the viscoelastic contribution to the friction force, and the average interfacial separation as a function of the sliding speed and the nominal contact pressure. We illustrate the theory with numerical results for a rubber block sliding on a road surface. We find that with increasing sliding speed, the influence of the roughness on the rubber block decreases, and for typical sliding speeds involved in tire dynamics it can be neglected.