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CivilComp Proceedings
ISSN 17593433 CCP: 89
PROCEEDINGS OF THE SIXTH INTERNATIONAL CONFERENCE ON ENGINEERING COMPUTATIONAL TECHNOLOGY Edited by: M. Papadrakakis and B.H.V. Topping
Paper 19
Stabilized Finite Elements for Elastohydrodynamic Lubrication Problems W. Habchi^{1}, D. Eyheramendy^{2}, P. Vergne^{1} and G. MoralesEspejel^{3}
^{1}LaMCoS, INSALyon, CNRS UMR5259, France
W. Habchi, D. Eyheramendy, P. Vergne, G. MoralesEspejel, "Stabilized Finite Elements for Elastohydrodynamic Lubrication Problems", in M. Papadrakakis, B.H.V. Topping, (Editors), "Proceedings of the Sixth International Conference on Engineering Computational Technology", CivilComp Press, Stirlingshire, UK, Paper 19, 2008. doi:10.4203/ccp.89.19
Keywords: finite elements, elastohydrodynamic lubrication, artificial diffusion, fullsystem approach.
Summary
Nowadays, roller bearings are essential components in any mechanical system that
includes rotating parts. In
order to further improve the functioning of these components, they are lubricated. It is
important for the good functioning of a bearing to have a
reliable tool to estimate minimum film thickness and frictional contact losses.
In this work, we are mainly interested in a particular lubrication regime known as elastohydrodynamic (EHD). In this regime, the contacting bodies are separated by a full lubricant film. The pressure generated in the film is high enough to induce a significant elastic deformation of the contacting bodies. Therefore a strong coupling between hydrodynamic and elastic effects is involved. Here we present a finite element fullsystem approach to model the lubricant flow in such contacts. The elastic problem is modelled by applying the classical linear elasticity equations to a structure with large enough dimensions compared to the contact size. As for the hydrodynamic problem, the Reynolds [1] equation for thin film Newtonian flows is solved on a part of the boundary of the structure corresponding to the contact area. This equation is a simplified version of the NavierStokes equations dedicated to thin film flows where the pressure gradient across the film thickness can be neglected. It is highly nonlinear since the rheological properties of lubricants show a high dependence on pressure. The two problems are solved simultaneously by means of a Newtonlike procedure. This leads to high convergence rates of the solution especially when compared to semisystem approach based models where the two problems are solved separately and an iterative procedure is established between them. At the exit of the contact, a free boundary problem arises. It is handled by applying the penalty method. For highly loaded contacts, the standard Galerkin solution of the Reynolds equation exhibits an oscillatory behaviour. This is explained by writing the Reynolds equation as a convectiondiffusion equation as a function of pressure. When the load is highly increased, this equation becomes convection dominated and requires streamline upwinding techniques (Streamline Upwind PetrovGalerkin [2] / Galerkin Least Squares [3]) in order to stabilize the solution. Finally, the nonNewtonian behaviour of the lubricant is taken into account along with the heat generation that takes place in the lubricant film due to both shear forces and the lubricant's compressibility. References
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