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Mathematical analysis and numerical simulationof a Reynolds-Koiter model for the elastohydrodynamic journal-bearing device

Published online by Cambridge University Press:  15 May 2002

Iñigo Arregui ,
J. Jesús Cendán  and
Carlos Vázquez
Iñigo Arregui
Affiliation:
Departamento de Matemáticas, Facultad de Informática, University of La Coruña, Campus de Elviña, s/n, 15071 La Coruña, Spain. arregui@udc.es. suceve@udc.es. carlosv@udc.es.
J. Jesús Cendán
Affiliation:
Departamento de Matemáticas, Facultad de Informática, University of La Coruña, Campus de Elviña, s/n, 15071 La Coruña, Spain. arregui@udc.es. suceve@udc.es. carlosv@udc.es.
Carlos Vázquez
Affiliation:
Departamento de Matemáticas, Facultad de Informática, University of La Coruña, Campus de Elviña, s/n, 15071 La Coruña, Spain. arregui@udc.es. suceve@udc.es. carlosv@udc.es.
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Abstract

The aim of this work is to deduce the existence of solutionof a coupled problem arising in elastohydrodynamiclubrication. The lubricant pressure and concentration aremodelled by Reynolds equation, jointly with the free-boundaryElrod-Adams model in order to take into account cavitationphenomena. The bearing deformation is solution of Koitermodel for thin shells. The existence of solution to thevariational problem presents some difficulties: the coupledcharacter of the equations, the nonlinear multivaluedoperator associated to cavitation and the fact of writing theelastic and hydrodynamic equations on two different domains.In a first step, we regularize the Heaviside operator.Additional difficulty related to the differentdomains is circumvented by means of prolongation andrestriction operators, arriving to a regularized coupledproblem. This one is decoupled into elastic and hydrodynamicparts, and we prove the existence of a fixed point for theglobal operator. Estimations obtained for theregularized problem allow us to prove the existence ofsolution to the original one. Finally, a numerical method is proposed in orderto simulate a real journal-bearing device and illustrate the qualitative andquantitative properties of the solution.

Keywords

Koiter modelReynolds equationfree boundary problemsfixed point techniques.
Type
Research Article
Information
ESAIM: Mathematical Modelling and Numerical Analysis , Volume 36 , Issue 2 , March 2002 , pp. 325 - 343
Copyright
© EDP Sciences, SMAI, 2002

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