On the effect of wear on asperity heigth distributions, and the corresponding effect in the mechanical response

TL;DR

This paper investigates how wear alters asperity height distributions, revealing that wear can produce bimodal distributions affecting contact mechanics, and challenges the assumption that surfaces are Gaussian.

Contribution

It demonstrates that wear modifies asperity height distributions to Gaussian tails with different parameters, complicating the Gaussian surface assumption.

Findings

Wear can cause bimodal asperity height distributions.

The tail of asperity distribution remains Gaussian after wear.

Surface Gaussianity is an oversimplification.

Abstract

Since the time of the original Greenwood & Williamson paper, it was noticed that abrasion and wear lead to possibly bimodal distribution of asperity height distribution, with the upper tail of asperities following from the characteristics of the process. Using a limit case solution due to Borucki for the wear of an originally Gaussian distribution, it is shown here that the tail is indeed always Gaussian, but with different equivalent parameters. Therefore, if the wear process is light, one obtains a bimodal distribution and both may affect the resulting contact mechanics behaviour. In this short note, we illustrate just the main features of the problem. We conclude that it is an oversimplification to consider surfaces Gaussian.