On the Short Wavelength Cutoff Limit in Persson's Hysteresis Friction Theory

Abstract The kinetic friction of rubber sliding on a rough surface has been modeled using multiscale roughness friction theories by Persson and Klüppel. Both theories calculate the hysteresis friction due to the viscoelastic energy dissipation of rubber over a wide range of frequencies corresponding to several length scales of roughness. In Persson's theory, the lower limit of the length scale (or the short wavelength cutoff) is a free parameter whereas Klüppel's theory explicitly calculates this limit. In this study, equations from Klüppel's theory were adapted to derive an expression for the lower limit of the length scale for Persson's friction model. This newly derived expression eliminates the need for any experimental calibration in determining the short wavelength cutoff limit when estimating hysteresis friction of rubber sliding on rough surfaces using Persson's theory.