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.

Optimization of Textured Surface in 2D Parallel Bearings Governed by the Reynolds Equation Including Cavitation and Temperature

“…The ultimate goal is to develop a unified computational approach for the optimization of 3D hydrodynamic and elastohydrodynamic lubrication contacts for any geometry of texture shapes and any lubricant rheology. The initial work conducted on 1D [7] and 2D bearings governed by the Reynolds equation is the first step towards this development.…”

“…One-dimensional (1D) optimal textured surfaces were already established either analytically [4] or through numerical parametric search [5,6]. A unified computational approach that allows finding optimal 1D textured surfaces for a wide range of hydrodynamic bearings governed by the Reynolds equation, accounting for non-Newtonian lubrication and temperature effects was developed previously by the authors of this work and presented in [7].…”

Frictional and load-carrying behaviours of micro-textured sector shape pad thrust bearing incorporating the cavitation and thermal effects

“…Benefits of surface textures on the bearing performance characteristics have been explored and amply highlighted in the recent past . It is observed that the researchers have mainly studied the conformal contacts formed between the parallel and almost parallel surfaces keeping the textures on the stationary surfaces. Significant increase in the load‐carrying capacity and considerable reduction in the friction force/coefficient of friction have been reported in the presence of textures.…”

“…Attempts have also been made by the investigators to understand the performance behaviours of the dimple geometries and their distributions over the bearings' surfaces. Influences of number of dimples, shapes of dimples, dimples’ locations/distributions, dimple area density, dimple depth, size of dimple and aspect ratio of dimple on the bearing performance have been explored intensively. It is highlighted that non‐optimised dimples' shape, size and location in texture may prove detrimental …”

Shape Optimization of A 3D Slider with Dimples

“…Substantial increase in load carrying capacity could be achieved. Gusek et al [10] used a unified approach to optimize texture shapes of parallel slider bearings. The approach works for bearings with fluid flow governed by the Reynolds equation.…”