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A mixed dirichlet-neumann problem for a nonlinear reynolds equation in elastohydrodynamic piezoviscous lubrication

Published online by Cambridge University Press:  20 January 2009

J. Durany ,
G. García  and
C. Vázquez
J. Durany
Affiliation:
Department of Applied Mathematics Univeristy of Vigo 36280-Vioo, Spain
G. García
Affiliation:
Department of Applied Mathematics Univeristy of Vigo 36280-Vioo, Spain
C. Vázquez
Affiliation:
Department of Applied Mathematics Univeristy of Vigo 36280-Vioo, Spain
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Abstract

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The aim of this work is to study the existence of solutions for a mathematical model of the displacement of a piezoviscous lubricant between two elastic surfaces. As we deal with a rolling ball contact problem, the deformations are modelled by the linear Hertzian theory. The fluid pressure behaviour is governed by the classical Reynolds equation for thin film displacement. The relevant aspect of cavitation in lubrication is described by means of the Elrod Adams model which leads to a mathematical free boundary problem.

The two main original features of the model problem in relation to previous works are: the supply of lubricant coming from a groove that is transversal to the direction of fluid displacement and the consideration of a piezoviscous law of Barus. Mathematically, the first one leads to a mixed Dirichlet-Neumann problem for the Reynolds equation and the second one involves an additional nonlinearity in a diffusion type term.

Type
Research Article
Information
Proceedings of the Edinburgh Mathematical Society , Volume 39 , Issue 1 , February 1996 , pp. 151 - 162
Copyright
Copyright © Edinburgh Mathematical Society 1996

References

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