Two-Dimensional Elastohydrodynamic Lubrication Part 1: The Associated Dry Contact Problem

Abstract

Associated with each elastohydrodynamic (EHD) lubrication problem there is a dry contact problem with the same contact zone, |x| a, surface displacement, υ(x), and pressure distribution, p(x).This paper considers the two-dimensional dry contact problem and shows how Poritsky's closed-form solution can be used to derive results of fundamental importance to EHD lubrication. In particular, it is shown that singularities in pressure and pressure gradient arise from discontinuities in dυ/dx and d2υ/dx2. In addition, with υ(x) expressed as a Fourier cosine series of the form υ(x) = ΣnBncos nη (where x = a cos η, 0 ≤ η ≤ π), it follows that at the end points of the contact zone, Reynolds boundary conditions are natural conditions yielding straightforward conditions on the Fourier coefficients, Bn.