Jacobian free Newton-GMRES method for the solution of elastohydrodynamic grease lubrication in line contact using wavelet based pre-conditioners

Jacobian Free Newton-GMRES (JFN-GMRES) method is used in the present study for the analysis of isothermal, steady and incompressible elastohydrodynamic lubrication line contact problem. The lubricant is grease, described by Herschel–Bulkley constitutive equation. The problem is investigated for smooth surface as well as surface with asperity. Governing equations are discretized on uniform grid. The resulting system of algebraic equations is solved using JFN-GMRES method for wide range of parameters of interest. For the convergence of restarted GMRES wavelet based pre-conditioners are used. Pressure profiles, film shapes and details of Petrusevich pressure spikes are given for moderate to high load and speed. The proposed scheme is stable and fast converging. Results presented in tables and graphs confirm these findings. The minimum film thickness increases for decrease in n, a parameter characterizing grease lubricant, with other parameters held constant. There is a noticeable decrease (in height as well as spread) of pressure spike for small values of n, which arrests bearings fatigue life.