Generalized fractal analysis and its applications to engineering surfaces

Fractal analysis previously developed for surface characterization is generalized and an intrinsic length unit a in this analysis has been taken as lateral resolution of the measuring instrument η. This generalized analysis allows the surface characterization in terms of two fractal parameters-fractal dimension D and amplitude coefficient C , which, in theory, are instrument independent and unique for each surface . A powerful technique is developed for the simulation of fractal surface profiles. Based on the generation of random surfaces of various D and C values, we note that D primarily relates to relative power of the frequency contents and C to the amplitude of all frequencies. A number of engineering surfaces-particulate magnetic tapes, thin-film rigid disks, steel disks, plastic disks and diamond films, all of varying roughnesses were measured to validate the generalized fractal analysis. We have obtained D and C parameters for each engineering surface from the measurements made using two instruments with significantly different resolutions. The variation in C within each surface is attributed to the simplified assumption of lateral resolution as the intrinsic length unit. We found that for a given surface with varying roughnesses, D essentially remains constant and to a first order C varies monotonically with variance of surface heights ( σ 2 ) for a given instrument. Simulated σ shows similar trends to the measured σ for small scan lengths. Coefficient of friction of all surfaces has reasonable correspondence with C . Based on this study, the fractal parameter C may better represent the variance for tribological surfaces.