An analytical solution of the Reynolds equation for finite, hydrodynamic, fixed-incline slider bearings in dynamic operation

A new analytical solution of the Reynolds equation with Dirichlet boundary conditions (zero boundary pressure) for finite, hydrodynamic, fixed-incline slider bearings is derived. It includes transient effects from either film-thickness or load temporal variation, which is a new feature in the literature. It is much simpler than the three solutions published since Michell's pioneering study in 1905. The new solution is based on transformations and classic methods in the theory of differential equations. It is expressed by a finite series with optimal convergence radius and is validated against quality numerical data with excellent agreement, including its comparison with the exact solution for the infinitely long bearing. Analytical expressions are derived for bearing performance parameters, namely the load, frictional forces, centre of pressure, flow rates, thermal power and/or power loss, and temperature rise by viscous heating. A condition is proved to check for backflow at the bearing inlet. An example of transient effects and comparison with the results of the “steady-state” approach is included. Finally, a table lists major performance parameters, their exact equations and precise approximants derived by regression with the aid of a single parameter, allowing calculations with just a spreadsheet or a scientific calculator.