Statistical approaches to description of rough engineering surfaces at nano and microscales

Abstract

Statistical models of rough surfaces are widely used in tribology. These models include models based on assumption of normality of the asperity heights or similar assumptions that involve Gaussian distributions, models based solely on properties of the power spectral density of the surface heights along with models based on assumption of fractal character of roughness. It is argued that models describing surface roughness solely by its fractal dimension or its autocorrelation function (or its power spectral density) do not reflect tribological properties of surfaces. Then typical experimental data obtained for rough engineering surfaces prepared by grinding have been studied at nano and microscales. The heights of the micro-asperities were determined by a profilometre (stylus), while the data for nano/atomic scale was obtained by AFM (Atomic Force Microscopy). The assumption of the normal distribution for the roughness heights has been studied by application of various modern tests of normality. It was found that the height distribution of the surfaces under investigation were not Gaussian at both nano and microscales. Hence, the statistical models of rough surfaces under consideration cannot be used for description of the surfaces and there is a need in critical re-examination of the current statistical approaches.

Adhesive Strength of Contacts of Rough Spheres

“…In the simulation, we assume L = R and put q 0 = q min and q 1 = q max . Note that the roughness produced in the described way does not necessarily represent real surfaces, which normally show strong phase correlation (Borodich et al, 2016). However, we consider the described generator as a way for producing well-defined comparable rough topography.…”

Roughness of Deposited Carbon-Based Coatings and Its Statistical Characteristics at Nano and Microscales

“…A review of statistical approaches to surface roughness was given by Borodich et al (2016). The first attempt to use the random process approach in tribology is due to Linnik and Khusu (1954a,b).…”

“…Hence, the explicit or implicit assumption of the Gaussian distribution of heights is employed also in almost all established models of contact between rough adhesive surfaces. This is related to both non-adhesive models of contact and the classic models of adhesive contact between rough surfaces such as developed by Fuller and Tabor (1975), Maugis (2000), Galanov (2011), Fuller (2011), Galanov and Valeeva (2016); see also a review in Borodich et al (2016).…”

“…Thus, if it is established that the surface roughness is Gaussian, then one can use the classic models of contact. Very recently, we tested the hypothesis of normality using mathematically rigorous approach (Borodich et al, 2016;Pepelyshev et al, 2018) on grinded surfaces. We showed that the asperities of grinding surfaces are not normal at both nano and microscales whilst intact surfaces of replicas of polishing papers are normal.…”

Combined effect of surface microgeometry and adhesion in normal and sliding contacts of elastic bodies

“…[28]. The limitations of the fractal approach to describe the roughness of real surfaces were discussed by Borodich et al [29,30].…”