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Abstract

In this two-part paper we consider the elastohydrodynamic lubrication (EHL) of soft-layered solids representing elliptical contacts. The problem has not previously attracted much attention, partly due to the lack of an effective numerical procedure to solve the coupled non-linear system of equations, but it is essential to the proper design of bearings with soft elastomeric liners and the full understanding of synovial joint lubrication.

In Part 1, the elasticity analysis for the surface deformation of a low elastic modulus layer on a hard-backing half-space under various forms of normal loadings is considered, by means of both the rigorous Hankel transform method and various simplifications. For layers of compressible materials (v ≤ 0.4), a generalized foundation model described by a second-order differential equation is proposed to represent the relationship between the surface deformation and the applied pressure. The empirical equation developed in this study is valid for a very wide range of the aspect ratio of the contact and provides an alternative way of modelling the elastic deformation without recourse to the often tedious integration in the numerical analysis of the EHL problem. The simplest form (constrained column model) of the equation, where the surface deformation is directly proportional to the local applied pressure, was found to be reasonably accurate for compressible thin layers (the aspect ratio 2b/h_t ≥ 5 and Poisson's ratio v ≤ 0.4).

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Elastohydrodynamic Lubrication of Soft-Layered Solids at Elliptical Contacts: Part 1: Elasticity Analysis

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