Estimation of statistical parameters of rough surfaces suitable for developing micro-asperity friction models

• Topography of HDPE measured with optical profilometry at 26.67, 13.34, 6.67 μm.
• Gaussian autocorrelation functions determined for randomly selected profiles.
• Monte Carlo sampling of profiles to obtain distributions of ACF parameters.
• Monte Carlo sampling to obtain spectral moments.
• Reduced sensitivity to resolution measurement compared to statistical approach.

Numerical models of surface micro-topography find applications in the development of multiscale models for friction and wear between two interacting surfaces. Although much work has been dedicated to developing such multiscale models, they have been hampered by the strong dependence of surface statistics on the resolution of surface topography measurements. The objective of this study is to develop a systematic approach to reduce this dependence so that the resulting statistical parameters are suitable for developing micro-asperity based continuum friction models. The approach significantly reduces but does not eliminate the dependence of surface statistics on the measurement resolution. It is based on fitting a Gaussian function to numerically calculated autocorrelation functions for randomly selected profiles from a surface. The use of a Gaussian function filters out very small scale asperities that affect the statistical parameters but are not tribologically significant. The distributions of the resulting parameters allow us to calculate the spectral moments using Monte Carlo simulations. The approach is applied to numerically generated surfaces as well as micro-topography measurements of a high density polyethylene (HDPE) surface. Results show that the proposed approach is considerably less sensitive to the measurement resolution, especially in comparison to standard statistical sampling methods. We argue that the Gaussian autocorrelation function used in our work is a better choice compared to other forms for continuum-level applications.