Micro and Nano Scale Statistical Properties of Rough Surfaces of Significance in Their Friction

The paper is devoted to statistical analysis of rough surfaces and extraction of parameters of significance for modelling of friction between the surfaces. It is known that modern experimental techniques, e.g., techniques based on atomic-force microscopy (AFM) allow the researchers to describe the surface topography up to atomic scale resolution. However, to predict any tribological process one has to understand which parameters of the rough surfaces are the governing parameters for the process under consideration and to be able to predict the changes in the process behaviour when the parameters are varied. Nowadays more than 30 parameters and functions are used in order to characterize the complex structures of rough surfaces. In particular, these parameters include (i) height (amplitude) parameters, e.g. the maximum height of the profile; (ii) horizontal parameters, e.g. the number of intersections of the profile with the mean line; (iii) parameters related to the shape of protuberances, e.g. the root mean square (rms) slope and the rms curvature of the profile; and (iv) parameters associated with spatial extend and amplitude of the roughness, like the high spot count [1, 2]. Whitehouse and Archard [3] suggested to study the surface roughness using the auto-correlation function and its Fourier transform, the power spectral density. The fractal approaches to description of the surface roughness are caused by experimental observations that graphs of the spectral density of the surface topography have often the power-law character [2,4]. However, it was shown that neither fractal dimension nor the power spectral density can be the single parameter or function that may characterise tribological properties of rough surfaces [2,5] and hence the some modern models of contact between rough surfaces that are based solely on their spectral density or fractal dimension, are of little use for practical applications. Hence, new statistical approaches to characterisation of rough surfaces that are connected to surface features related to physical mechanisms of friction have to be explored. It is proposed to split the scales of consideration of the surfaces into nano and micro-scales due to the difference of physical mechanisms acting at these scales. Using several modern statistical approaches including the sliding window techniques and the Kolmogorov-Smirnov statistics for two samples, simpler profiles with equivalent roughness in terms of the height distribution are constructed. The simple profiles obtained earlier can be further simplified by using the sorting techniques. We can say that the mechanical and tribological properties of the simpler profile and the original one are the same.