A Schur-Complement Model-Order-Reduction Technique for the Finite Element Solution of Transient Elastohydrodynamic Lubrication Problems
The current work presents reduced order finite element modeling framework for the solution of transient elastohydrodynamic lubrication (EHL) problems. The model order reduction technique is based on a Schur-complement method, applied to the elastic part within EHL problems. As such, it is exact and introduces no additional errors to the solution, with respect to the standard non-reduced finite element model. The technique reduces by one, the dimension of the linear elasticity part within the EHL problem. The use of the Schur-complement method however leads to a semi-dense Jacobian matrix. This is why the technique is complemented with a splitting procedure, allowing it to retrieve a standard finite-element-like sparsity pattern. In terms of computational performance, it is shown through a set of numerical experiments that the proposed reduced model offers a speed-up in computational times of the order of 15:1, compared to the equivalent full model, without any compromise on the accuracy of the solution.
Equivalent geometry of a transient EHL line contact