The morphological tree transform of surface motifs. Incidence in tribology

Abstract

In this paper we show two new developments in the three-dimensional characterisation of rough surfaces. The basic idea is to decompose the three-dimensional roughness as a combination of 3D motifs defined by amplitude, wave length, local and overall direction of various components. The multi-scale approach developed in this work is very useful in tribology, the summit of the morphological tree permits the characterisation of the waviness of the summits envelope, each summit can be characterised by the height and the radius of curvature in x and y direction necessary for the computing of Hertzian pressure. The local slopes of the summits envelope play an important role in Coulombic friction, adherence and leakage. The fluid reservoir can be characterised by the multi-scale aspect of the 3D motifs size and their orientation.