Jacobian-free Newton Multigrid method for Elastohydrodynamic line contact with grease as lubricant

In this article, a Jacobian-free Newton Multigrid (JFNMG) method is used for the analysis of isothermal, steady state and incompressible Elastohydrodynamic lubrication (EHL) line contact problem. The lubricant is grease and its rheology is described by Hershel-Bulkley constitutive equation. The problem is investigated for smooth contact surfaces. A finite difference scheme, developed after discretizing governing equations on a uniform grid, is used for the solution of the EHL problem. The JFNMG method is applied to the system of algebraic equations, which arise in the scheme, and obtain solution for a wide range of parameters of interest. The proposed scheme not only overcomes the limitations of conventional schemes but is also, stable and fast converging for the investigation of the EHL problems. The JFNMG method approximates Jacobian matrixvector product accurately with much ease without requiring additional storage at each iteration, and avails convergence features of Newton method as well as convergence strategy (up to discretization error) of multigrid. The EHL features, namely, pressure profiles, film shapes and Petrusevich pressure spikes are studied for different parameters of interest. The minimum film thickness decreases for decrease in n, which is a power law index in Hershel-Bulkley model 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.