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Remarks on the Reynolds problem of elastohydrodynamic lubrication

Published online by Cambridge University Press:  26 September 2008

José-Francisco Rodrigues
José-Francisco Rodrigues
Affiliation:
C.M.A.F.-I.N.I.C. and University of Lisbon, Av. Prof. Gama Pinto, 2 – 1699 Lisboa Codex, Portugal
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Abstract

The mathematical model of the flow of a viscous lubricant between elastic bearings leads to the study of a highly non-linear and non-local elliptic variational inequality. We discuss the existence of a solution by using an a prioriL∞-estimate. This method allows us to solve a large class of problems, including those arising from the linear Hertzian theory, and yields new existence results for the cases of a pressure-dependent viscosity or the inclusion of a load constraint. For small data the uniqueness of the solution holds, and we show that in the cylindrical journal bearing problem with small eccentricity ratio, the free boundary is given by two disjoint differentiable arcs close to the free boundary of the first-order approximate solution.

Type
Research Article
Information
European Journal of Applied Mathematics , Volume 4 , Issue 1 , March 1993 , pp. 83 - 96
Copyright
Copyright © Cambridge University Press 1993

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