A simplified version of Persson's multiscale theory for rubber friction due to viscoelastic losses

TL;DR

This paper demonstrates that Persson's multiscale theory for rubber friction due to viscoelastic losses can be accurately approximated by simpler, single-scale models, simplifying the understanding and application of the theory.

Contribution

The paper shows that the complex multiscale model can be replaced by a simpler single-scale approximation without significant loss of accuracy.

Findings

Multiscale model closely matches simpler models.

Dependence on roughness spectrum is largely unnecessary.

The critical parameter is the cutoff, which acts as a fitting parameter.

Abstract

We show the full multiscale Persson's theory for rubber friction due to viscoelastic losses can be approximated extremely closely to simpler models, like that suggested by Persson in 1998 and similarly by Popov in his 2010 book (but we don't make any use of the so-called "Method of Dimensionality Reduction"), so it is essentially a single scale model at the so called large wavevector cutoff. The dependence on the entire spectrum of roughness is therefore only confusing, and we confirm this with actual exact calculations and reference to recent Lorenz et al (2015) data. The multiscale aspect is irrelevant with respect to the real critical issue: the choice of the "free parameter" best fit truncation cutoff, which shows the models are mainly fitting equations. In this sense, we provide at least a very simple one.