Viscoelastic contact mechanics between randomly rough surfaces

TL;DR

This paper provides exact numerical analysis of viscoelastic contact mechanics, revealing how friction and contact area depend on surface roughness, sliding speed, and pressure, with results aligning with analytical theories.

Contribution

It offers the first exact numerical results for viscoelastic contact mechanics on fractal rough surfaces, validating analytical models and detailing the influence of sliding speed and pressure.

Findings

Friction force and contact area depend on surface roughness and sliding speed.

Contact area can be described by a universal master curve.

Numerical results agree with analytical contact mechanics predictions.

Abstract

We present exact numerical results for the friction force and the contact area for a viscoelastic solid (rubber) in sliding contact with hard, randomly rough substrates. The rough surfaces are self-affine fractal with roughness over several decades in length scales. We calculate the contribution to the friction from the pulsating deformations induced by the substrate asperities. We also calculate how the area of real contact, $A(v,p) $, depends on the sliding speed $v$ and on the nominal contact pressure $p$, and we show how the contact area for any sliding speed can be obtained from a universal master curve $A(p)$. The numerical results are found to be in good agreement with the predictions of an analytical contact mechanics theory.