Wear 257 (2004) 1250–1256 Characterisation of the 3D waviness and roughness motifs S. Mezghani a,b , H. Zahouani a,b,∗ a Laboratoire de Tribology et Dynamique des Syst` emes, UMR CNRS 5513, Institut Europ´ een de Tribologie, Ecole Centrale de Lyon, 36 Avenue Guy de Collongue, 69131 Ecully cedex, France b Ecole Nationale d’Ing´ enieurs de St Etienne, 58 rue Jean Parot, 42000 St Etienne, France Received 15 January 2004; received in revised form 3 March 2004; accepted 28 May 2004 Abstract The surface summits and their waviness envelope constitute the boundary surface of contact area during the tribological life of solids. The form, scale and orientation of the three-dimensional motifs play an important role on flatness behaviour of engineered surfaces, contact mechanics, adherence, friction, lubrication and leakage problems. The basic idea of this work considers that the three-dimensional motifs of the surface are a key elements of surface topography in regard to different field of tribology. The 2D motif is defined as the part of profile which associates tow peaks separated a deep valley (pit). The extension of the 2D motif definition to the 3D morphology needs the simultaneous assessment of waviness and roughness. The approach developed in this work is based on a geomorphologic definition of 3D motif. The approach is improved by a new algorithm of waviness envelope construction and a morphologic filter using the waviness envelope as a low-frequency surface of filtering. © 2004 Elsevier B.V. All rights reserved. Keywords: Waviness; Lubrication; 2D motifs 1. Introduction In tribological point of view, the fluid flow phenomena between contacting rough surfaces are interesting for the lu- brication mechanisms and sealing problems. For example, the metal to metal sealing parts are sometimes used as sepa- rable fluid connectors. It is well known that the surface mor- phology of contacting parts governs the pressure distribution and the leakage across the metal seals essentially the local morphology plays an important role on contact mechanics and the leakage rate. Different recent works have shown the importance of the surface waviness related to the summits envelope in friction and adherence, the pressure supported by the summits during an elastic contact and the size of the motifs in the mixed or hydrodynamic lubrication. This paper concerns the development of two approaches of surface morphology assessment in regard to the tribolog- ∗ Corresponding author. Tel.: +33 72186000; fax: +33 78433383. E-mail address: hassan.zahouani@ec-lyon.fr (H. Zahouani). ical performances. The method consists in a morphologi- cal decomposition of the surface topography as a local 2D or 3D motifs [1–4]. The first method defines the motifs as a combination of the summits and pits for a mono- and multi-directional morphology. Three parameters are neces- sary to define an oriented motifs: ρ, λ, θ. The depth ρ com- puted as the difference between the summits and pits, the width λ defined as the Cartesian distance between the sum- mits and θ the orientation of the motif. The 3D morpho- logical tree can be represented by the density of the mo- tifs oriented in each θ direction at different scales ρ and wavelength λ. This multi-scale representation is very use- ful in tribology. The fluid reservoir can be characterised by the multi-scale aspect of the motifs size and their orienta- tion. The second approach developed is based on a geomor- phologic definition of 3D motif. A 3D motif is considered as a catchment basin surrounded by watershed lines. A new algorithm of waviness envelope construction has been devel- oped. 0043-1648/$ – see front matter © 2004 Elsevier B.V. All rights reserved. doi:10.1016/j.wear.2004.05.024