Elastohydrodynamic lubrication line contact in couple-stress elasticity

By using the couple-stress elasticity theory, this article firstly analyzes the size-dependent elastohydrodynamic lubrication (EHL) line contact between a deformable half-plane and a rigid cylindrical punch. The size effect that emerged from the material microstructures is described by the characteristic material length. It is assumed that the viscosity and density of the lubricant vary with the fluid pressure. An iterative method is developed to deal with the flow rheology equation, film thickness equation, load balance equation and Reynolds equation at the same time. Then, distributions of fluid pressure, in-plane stress and film thickness are determined numerically at the lubricant contact surface. Influences of the size parameter, punch radius, resultant normal load and entraining velocity on the fluid pressure, in-plane stress and lubricant film thickness are discussed. The fluid pressure and film thickness predicted from the couple-stress elasticity theory present significant departures from the classical elasticity results. It is demonstrated that results for micro-/nano-scale EHL contact problems may be underestimated when the classical elasticity theory is employed.