Elastohydrodynamically Lubricated Ball Bearings with Couple-Stress Fluids, Part I: Steady-State Analysis

Conventional elastohydrodynamic lubrication (EHL) analysis of point contacts is extended to include couple-stress effects in lubricants blended with polymer additives. A transient pressure differential equation, generally referred to as a modified Reynolds equation, is derived from the Stokes microcontinuum theory and solved using the finite difference method with a successive over-relaxation scheme. The solution is obtained under isothermal conditions, assuming a suitable exponential relation of pressure-viscosity variation. A nondimensional couple-stress parameter, which can be considered the molecular length of the additives in the lubricant, is used in the analysis. From the results obtained, the influence of the couple-stress parameter on the EHL point contacts is apparent and cannot be neglected. Lubricants with couple stresses provide an increase in the load-carrying capacity and reduction in friction coefficient as compared to Newtonian lubricants. Empirical formulas for the calculation of central and minimum film thicknesses of lubricated point contacts with couple-stress fluids are derived with the nonlinear least-squares curve-fitting technique using different numerically evaluated data. This may help to avoid the time-consuming numerical calculations.