A Finite Element Approach of the Fully Coupled Elastohydrodynamic Problem

Up to now, most of the numerical works dealing with the modelling of the isothermal elastohydrodynamic problem were based on a weak coupling resolution of the Reynolds and elasticity equations (semi-system approach). The latter were solved separately using 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 non-linear 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 complexity is the same as for classical algorithms, but with an improved convergence rate, a reduced size of the problem and a regular sparse Jacobian matrix. This method is applied to the case of a Generalized Newtonian lubricant using a powerful shear-thinning model. The results are compared with experimental data.