Scale-invariant analysis of wear particle surface morphology I: Theoretical background, computer implementation and technique testing

Reliable numerical characterization of wear particle surface morphology is an important and still unresolved engineering problem. Since the shape and surface topography of wear particles often exhibits a fractal nature, fractal methods are frequently employed in their characterization. However, the fractal methods used in the particle analysis ignore the fundamental property that fractal objects can be described by a small set of mathematical rules. Finding those rules that describe a particular fractal image is a difficult problem and no general solution exists to date. In this paper, a new method for the characterization of wear particle morphology is proposed and described. The method is based on a partitioned iterated function system (PIFS) which is a collection of contractive affine transformations. Each affine transformation converts one part of a wear particle image onto another part of the same image. PIFSs were constructed for both computer-generated and scanning electron microscope images of wear particles. Results obtained in this study clearly demonstrate that the morphology of wear particles can be effectively characterized by the PIFS method.