Homogenization-based microscopic texture design and optimization in hydrodynamic lubrication

Abstract

The aim of this thesis is to develop an optimization framework for the texture optimization in hydrodynamic lubrication using multi-scale homogenization technique. In hydrodynamic lubrication the asperities do not come into contact due to fluid film present between the surfaces and normal load is carried by the viscous fluid. The Reynolds equation can be used with confidence for such problems. For two-scale separation, a basis for optimizing the surface textures is established through an asymptotic expansion based homogenization scheme, which delivers a macroscopic Reynolds equation containing homogenized coefficients. These homogenized coefficients depend on the fluid film thickness directly and by controlling these coefficients a desired macroscopic response can be obtained. Design variables are introduced to control the fluid film thickness indirectly through an intermediate filtering stage. Both microscopic and macroscopic objectives are defined for texture optimization. The quality of the designed textures are evaluated numerically as well as aesthetically and optimization parameters are selected accordingly. Isotropic and anisotropic textures can be designed by using the proposed optimization scheme. For both microscopic and macroscopic objectives optimization surface textures are reconstructed as a sanity check. Texture optimization for prescribed load bearing capacity and maximum load bearing capacity in temporal and spatial variations are then carried out for squeeze film flow and wedge problem, respectively. Finally, to reduce the computational cost, Taylor’s expansion is proposed for the optimization problem. Overall, the methodology developed in this thesis froms a basis for a comprehensive micro-texture design framework for computational tribology.