A novel method for integrating first- and second-order differential equations in elastohydrodynamic lubrication for the solution of smooth isothermal, line contact problems

This paper contains details of recent developments in the analysis of elastohydrodynamic lubrication problems using the Þnite element method. A steady state isothermal Þnite element formulation of the smooth line contact problem with Newtonian lubricant behaviour is presented containing both Þrst- and second-order formulations of the hydrodynamic equation. Previous problems with the limited range of applicability of both Þrst- and second-order Þnite di¤erence solutions have been overcome by summing both the Þrst- and second-order equationsÕ weighted contributions. Application of the method to a range of problems unattainable by either single Þrst- or second-order formulations is presented. Copyright