Iterative calculation of tribo-contact between a roller and a plate

This article deals with the problem of the hydrodynamic contact of a roller with finite size elastic plate. The lubricant viscosity coefficient is assumed to be a function of the pressure. Generally, this problem requires joined solution of the 2-D hydrodynamic Reynolds’ equations and 3-D equations of solid mechanics. Our approach allows one to decouple the task of solid mechanics from the hydrodynamic task. At the first step, we solve the task of solid mechanics and find the compliance matrix, which establishes a functional relationship between surface deflections and pressure distributions along the lubricant layer. Determined ones, this matrix can be used for any pressure distributions along the lubrication layer. At the second step, we implement the obtained compliance matrix for solving the hydrodynamic problem. To find the compliance matrices, we apply the well known ANSYS package based on the finite element method, and also the Fourier series expansion. For suppressing the numerical noise-like small scaled oscillations we introduce regularization factors for the Fourier coefficients. The determined compliance matrices are used for self-consistent calculation of the pressure and surface deflections by the proposed iterative scheme. The particular results of calculations of pressure distributions and surface deformations are presented for different loadings. Fast convergence of the iterations is shown. Number of iterations depends on the loading conditions: An enhancement of the maximal contact pressure leads to increase of the number of the required iteration cycles.