An Assessment of Statistical Theory of Contact Between Macroscopically Conforming Rough Surfaces

Abstract

Most engineering surfaces possess topographies that are anisotropic. Some of the anisotropic surfaces are unintended result of machining process and others are by design for the purpose of lubricant retention or other considerations. Such is the case in problems involving piston liner and mechanical seal performance wherein the conformal contact of two rough surfaces is considered. It becomes critical to component performance to predict average contact pressure and gap between rough surfaces. Two of the well-known asperity-based statistical theories along with a deterministic method, based on Multi Level Multi Summation (MLMS) technique, are used to study the contact of nominally flat rough surfaces. The asperity-based statistical theories are GW model (Greenwood and Williamson, [1]), and its extension proposed by Chang, Bogy and Etsion [2], CEB model, for treating elastic-plastic contact. The contact examined is a set of nominally flat rough surfaces with a smooth flat. This study attempts to address two questions. The first concerns the effectiveness of asperity-based statistical theories in predicting average contact stress of rough surfaces with various degrees of topographic anisotropy. The second question involves the use of directional curvatures to ascertain the appropriateness of plane curvatures when degree of anisotropy is significant. To this end random surfaces are generated for five degrees of anisotropy including correlation length ratios 1, corresponding to an isotropic surface, and 3, 9, 36 and 81, corresponding to an increasing degree of geometric anisotropy. A module of Surface Distress Analytical Toolset (SDAT), for treating dry contact using deterministic approach with MLMS technique, is utilized to compute the contact pressure for these surfaces. This analysis constitutes ten surfaces for each correlation ratio resulting in fifty simulations of SDAT. For each correlation ratio statistical averages and variations of the maximum and mean contact pressures are found. Using the generated random surfaces, GW and CEB models are furnished with the parameters that include the standard deviation of summit height distribution, area summit density and six curvatures associated with asperity summit. These involve four directional curvatures that include curvatures along the x, y, positive diagonal, negative diagonal, and two equivalent curvatures, one based on spherical tip using average of the four diagonal curvatures and the other based on ellipsoidal asperity summit (Fig 1). The study suggests that GW and CEB typically overestimate average contact pressure. The mean pressures predicted using the largest directional summit curvature agrees most favorably with those predicted by SDAT. Surprisingly, agreement is most favorable for highest geometrical anisotropy. Both statistical methods seem effective in predicting mean gap between surfaces for moderate to low nominal pressures.