Analytical solution of the transient Reynolds equation for finite hydrodynamic slider (pad) bearings monotonically curved in the sliding direction

Abstract

An analytical solution of the classic Reynolds equation for the fluid film lubrication of finite hydrodynamic slider (pad) bearings monotonically curved (convex) in the sliding direction is developed, covering steady and unsteady conditions. It allows for nonzero inlet pressure to account for fluid inertia. Some scarce analytical solutions exist for plane and exponential film shapes but none for generally curved (convex) shapes. The new solution is validated against analytical and numerical results on plane, exponential and parabolic film shapes with excellent agreement. Analytical equations are developed for various performance variables, including the bearing load, the frictional forces, the centre of pressure, the fluid velocity vector, the thermal power or power loss and the temperature rise by viscous heating, the squeeze time, the lift-off speed and the film stiffness. A sufficient condition is proved to check for inlet backflow. A detailed application example with both steady-state and transient analyses is presented to demonstrate the robustness of the method.