On the optimization of surface textures for lubricated contacts

The pressure field that develops inside a lubricated contact obeys an elliptic equation known as Reynolds equation, with coefficients that depend on the shape of the contacting surfaces. The load-carrying capacity of a contact, defined as the integral of the pressure field, is an important performance indicator that should be as high as possible to avoid wear and damage of the surfaces. In this article, the effect of arbitrary uniform periodic textures on the load-carrying capacity of lubricated devices known as thrust bearings is investigated theoretically by means of homogenization techniques and first-order perturbation analysis. It is shown that the untextured shape is a local optimum for the load-carrying capacity of the homogenized pressure field. This is proved for bearings of general shape and considering both incompressible and compressible models for the lubricant. The homogenization technique however implies an error. Suitable bounds for the effect of this error are provided in a simplified case.