Evaluation of Discretisation and Integration Methods for the Analysis of Hydrodynamic Bearings With and Without Surface Texturing

Abstract

Surface texturing has been demonstrated to improve tribological performance of hydrodynamic bearings. Because the texturing increases complexity of a surface, numerical methods are required. However, no comparison study has so far been conducted to determine which methods are most accurate with the least number of grid/mesh points. Knowing this would allow for the analysis and optimisation of bearings with complex geometries. In this work, performance of four discretisation methods (finite difference, finite element, finite volume and spectral element (SE)) in approximating the pressure function and three integration methods (Newton–Cotes formulas and Gauss quadrature) in approximating the load capacity, coefficient of friction and film height was evaluated in a systematic manner. Three slider bearing geometries were used: inclined surface without texturing and two parallel surfaces textured with trapezoidal and quadratic dimples. For the evaluation, pressure function, load capacity, coefficient of friction were calculated analytically using the Reynolds equation. Differences between the analytical values and their approximations produced by the numerical methods were calculated versus the number of grid/mesh points. The numbers of points were determined for the differences below 5, 1 and 0.1 %. Results showed that the SE method and the Gauss quadrature were most accurate regardless of the bearing geometry and used up to 28 times fewer points as compared to other methods.