Derivation of dynamic couple-stress Reynold’s equation of sliding-squeezing surfaces and numerical solution of plane inclined slider bearings

Deriving a general dynamic Reynold’s equation of sliding-squeezing surfaces with non-Newtonian fluids is necessary for the assessment of dynamic characteristics of a lubricating system. Taking into account the transient squeezing-action effect and considering the effects of couple stresses resulting from the lubricant blended with various additives, the non-Newtonian dynamic Reynold’s equation applicable to the general film shape is derived by using the Stokes micro-continuum theory. As an application, the numerical analysis of a two-dimensional plane inclined slider bearing is illustrated. Based upon the small perturbation technique, two Reynold’s-type equations responsible for both the steady performance and the perturbed characteristics are obtained. The steady and perturbed pressures are then numerically calculated by using the conjugate gradient method. From the results obtained, the effects of couple stresses provide an improvment on both the steady-state performance and the dynamic stiffness and damping characteristics especially for the bearing with a higher value of aspect ratio.