Effects of pressure-dependent viscosity variation on the squeeze film lubrication between a sphere and a rough flat plate with couple stress fluids

In this paper, a theoretical study of the combined effects of surface roughness and the variation of viscosity with pressure on the squeeze film lubrication between sphere and a flat plate is presented. Based on the Christensen’s stochastic theory for the hydrodynamic lubrication of rough surfaces, two types of one-dimensional surface roughness (radial and azimutal) patterns are considered. The generalized averaged Reynold’s equation for Stokes couple stress fluids accounting for the pressure dependent viscosity is mathematically derived for the problem under consideration. The standard perturbation technique is used to solve the averaged nonlinear Reynold’s equation and an approximate analytical solution for the fluid film mean pressure is obtained for the two types of one-dimensional roughness patterns. It is found that, the effects of couple stresses and pressure dependent viscosity variation are to improve the squeeze film characteristics.