A Unified Computational Approach to the Optimization of Surface Textures: One Dimensional Hydrodynamic Bearings

Abstract

In tribological applications, surface textures are used to increase load capacity and reduce friction losses in hydrodynamic lubricated contacts. However, there is no systematic, efficient and general approach allowing for the optimization of surface texture shapes to give an optimal performance. The work conducted is, in most cases, by “trial and error”, i.e. changes are introduced and their effects studied. This is time consuming and inefficient. In this paper, a unified computational approach to the optimization of texture shapes in bearings is proposed. The approach aims at finding the optimal texture shape that supports the maximum load and/or minimizes friction losses in one dimensional hydrodynamic bearings. The texture shape optimization problem is transformed into a nonlinearly constrained mathematical programming problem with general constraints that can be solved using optimal control software. Load-carrying capacity or friction force of a bearing becomes an objective functional that is maximized or minimized, subject to: (i) any Reynolds equations given by first order ordinary differential equations, (ii) pressure boundary conditions and (iii) functions/parameters that define the surface texture shape. This newly developed approach is demonstrated on examples of parallel textured hydrodynamic bearings. The effects of non-Newtonian fluids, cavitation and viscosity varying with temperature are considered.