Fully coupled high-order finite difference methods for elastohydrodynamic lubrication line and point contact problems

Purpose Elastohydrodynamic lubrication (EHL) commonly occurs in highly stressed tribological pairs of mechanical components, such as rolling gears and bearings, where it reduces the friction and wear between contact surfaces. For example, EHL theory has been applied in railway engineering to analyze the wheel–rail contact behavior of high-speed trains under water-lubricated conditions. The combination of high contact pressures and water’s low viscosity significantly influences both elastic deformation and the numerical convergence of the Reynolds equation. Therefore, a robust and accurate numerical method for EHL contact problems is essential. Design/methodology/approach In this paper, a high-order finite difference method is proposed to solve the EHL line and point contact problems, whose cavitation conditions are treated by the penalty method. The highly nonlinear equations resulting from the high-order finite difference discretization are solved by the trust-region dogleg algorithm. A high-order biased upwind finite difference scheme is also presented in order to reduce the numerical dissipation and dispersion arising from the high-order upwind finite difference scheme. Findings Numerical examples demonstrate that this method achieves more accurate solutions using fewer nodes compared to other numerical methods. Furthermore, the biased upwind finite difference scheme has better accuracy than the upwind one. Originality/value In this paper, high-order centered and (biased) upwind finite difference methods combined with a state-of-the-art nonlinear solver, i.e. the trust-region dogleg algorithm, are constructed to solve the EHL line and point contact problems.