Development of a texture averaged Reynolds equation

The application of textured bearing surfaces results in a more complex lubricant flow pattern compared to smooth bearing surfaces. In order to capture the more complex flow pattern and possible inertia effects in the vicinity of the surface pockets, the Navier–Stokes equations should be used to model the flow between textured surfaces instead of the Reynolds equation. In this paper a multi-scale method is presented where the fluid flow in a single micro-scale texture unit cell is modelled using the Navier–Stokes equations, the results of which are then averaged to flow factors to be used in a novel texture averaged Reynolds equation on the macro-scale bearing level. Depending on the local flow conditions the non-linear inertia effects in the flow can either contribute or detract from the local load capacity of the lubricant film. Some results from the micro-scale calculations are presented, followed by the method developed to average these results to the macro-scale. The resulting flow-factors are presented and a load correction term is introduced. Although the method presented does not put restrictions to the texture dimensions, the texture unit cell dimensions are chosen equal to those in an experimental polymer water lubricated bearing. In a follow-up paper these results will be used to determine the efficiency of surface texturing in a lubricated journal bearing application.