Scale-invariant analysis of tribological surfaces

Abstract

Surface topography affects wear and lubrication mechanisms occurring between two interacting surfaces. Despite its importance, there is no reliable method fully describing 3-D surface topography features and the results provided by currently used methods are not satisfactory. This is because traditional methods, used to characterize surfaces, such as Fourier transforms, statistical functions and parameters are not able to fully describe intrinsic properties of surfaces, especially those that exist over many different scales. Fractal methods have, therefore, been adapted and applied to overcome these difficulties. In this paper, a partition iterated function system (PIFS) method, recently developed by the authors, is briefly described and applied to 3-D surface topography images of artificial orthopaedic implant surfaces and surfaces of wear particles. This method utilises the ability of fractal geometry to describe complex objects such as clouds, trees and mountains by a few mathematical equations. The complex objects can then be reconstructed back from these equations. When the PIFS method is applied to surface information on 3-D surface topography, it is encoded into a set of affine contractive transformations which fully describe details of the surface topography over different scales. The PIFS method developed appears to be superior to other fractal methods used so far to characterize surface topography. It works well with a wide range of fractal surfaces and it can simultaneously be used to mathematically model the surface topography, calculate the fractal dimension and recognise patterns.