Role of Fractal Geometry in Roughness Characterization and Contact Mechanics of Surfaces

A proper characterization of the multiscale topography of rough surfaces is very crucial for understanding several tribological phenomena. Although the multiscale nature of rough surfaces warrants a scale-independent characterization, conventional techniques use scale-dependent statistical parameters such as the variances of height, slope and curvature which are shown to be functions of the surface magnification. Roughness measurements on surfaces of magnetic tape, smooth and textured magnetic thin film rigid disks, and machined stainless steel surfaces show that their spectra follow a power law behavior. Profiles of such surfaces are, therefore, statistically self-affine which implies that when repeatedly magnified, increasing details of roughness emerge and appear similar to the original profile. This paper uses fractal geometry to characterize the multiscale self-affine topography by scale-independent parameters such as the fractal dimension. These parameters are obtained from the spectra of surface profiles. It was observed that surface processing techniques which produce deterministic texture on the surface result in non-fractal structure whereas those producing random texture yield fractal surfaces. For the magnetic tape surface, statistical parameters such as the r.m.s. peak height and curvature and the mean slope, which are needed in elastic contact models, are found to be scale-dependent. The imperfect contact between two rough surfaces is composed of a large number of contact spots of different sizes. The fractal representation of surfaces shows that the size-distribution of the multiscale contact spots follows a power law and is characterized by the fractal dimension of the surface. The surface spectra and the spot size-distribution follow power laws over several decades of length scales. Therefore, the fractal approach has the potential to predict the behavior of a surface phenomenon at a particular length scale from the observations at other length scales.