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

Since the time of the original Greenwood and 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 not complete, 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.