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Research Papers: Elastohydrodynamic Lubrication

A Full-System Approach of the Elastohydrodynamic Line/Point Contact Problem

[+] Author and Article Information
W. Habchi

 LaMCoS, INSA-Lyon, CNRS UMR5259 F69621, Francewassim.habchi@insa-lyon.fr

D. Eyheramendy

 1-LaMCoS, INSA-Lyon, CNRS UMR5259 F69621, France; 2-ISTIL, Université de Lyon, Université Lyon 1 F69622, France

P. Vergne

 LaMCoS, INSA-Lyon, CNRS UMR5259 F69621, France

G. Morales-Espejel

 SKF Engineering and Research Center, P.O. Box 2350, Nieuwegein, The Netherlands

J. Tribol 130(2), 021501 (Mar 13, 2008) (10 pages) doi:10.1115/1.2842246 History: Received July 16, 2007; Received September 08, 2007; Revised November 03, 2007; Published March 13, 2008

The solution of the elastohydrodynamic lubrication (EHL) problem involves the simultaneous resolution of the hydrodynamic (Reynolds equation) and elastic problems (elastic deformation of the contacting surfaces). Up to now, most of the numerical works dealing with the modeling of the isothermal EHL problem were based on a weak coupling resolution of the Reynolds and elasticity equations (semi-system approach). The latter were solved separately using iterative schemes and a finite difference discretization. Very few authors attempted to solve the problem in a fully coupled way, thus solving both equations simultaneously (full-system approach). These attempts suffered from a major drawback which is the almost full Jacobian matrix of the nonlinear system of equations. This work presents a new approach for solving the fully coupled isothermal elastohydrodynamic problem using a finite element discretization of the corresponding equations. The use of the finite element method allows the use of variable unstructured meshing and different types of elements within the same model which leads to a reduced size of the problem. The nonlinear system of equations is solved using a Newton procedure which provides faster convergence rates. Suitable stabilization techniques are used to extend the solution to the case of highly loaded contacts. The complexity is the same as for classical algorithms, but an improved convergence rate, a reduced size of the problem and a sparse Jacobian matrix are obtained. Thus, the computational effort, time and memory usage are considerably reduced.

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Copyright © 2008 by American Society of Mechanical Engineers
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Figures

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Figure 1

Effect of the cube’s size on the elastic deformation calculation

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Figure 2

Mesh size in the regions away from the contact (left, normal mesh; right, extremely coarse mesh)

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Figure 3

Effect of the mesh size on the elastic deformation calculation

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Figure 4

Heavily loaded line contact problem (M=590, L=7.24) and the effect of stabilization. Left, standard Galerkin; center, SUPG; right, GLS.

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Figure 5

Heavily loaded point contact problem (M=9435, L=9) and the effect of stabilization. Left, standard Galerkin; center, SUPG/GLS; right, SUPG∕GLS+ID.

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Figure 6

Effect of “isotopic diffusion” on the solution of Reynolds equation in the case of a point contact

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Figure 7

Global numerical scheme of the full-system EHD solver

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Figure 8

Overall complexity of the numerical model

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Figure 9

Meshing of the contact area Ωc

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Figure 10

Result for M=200 and L=10: 3D dimensionless pressure profile (left), dimensionless pressure and film thickness profiles along the central line in the X direction (right)

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