The Newton-Raphson algorithm was used in conjunction with Murty’s algorithm and the finite-element method to analyze the elastohydrodynamic lubrication of a journal bearing under dynamic loading. Cavitation boundary conditions were used. A realistic compliance matrix and load schedule were used in the illustrative example. Solutions for the film pressure, the film thickness and its rate of change with time were obtained as functions of the crank angle.

Finite-element techniques are applied to solve the elastohydrodynamic finite journal bearing problem. Reynolds’ equation for the fluid film and the three-dimensional elasticity equations for the bearing housing are solved simultaneously using a unique iteration scheme. The analysis yields the pressure distribution and the displacement distribution which satisfy the elastohydrodynamic requirements of realistic three-dimensional bearing geometries. From these distributions, important information such as the stresses in the bearing material and the minimum film thickness in the lubricant can be calculated. In the calculations it is assumed that the bearing operates with a constant-property lubricant and a linearly elastic bearing material. The solution procedure is applied to a typical problem and numerical results are presented.

SUMMARYThe elastohydrodynamic lubrication problem, in which the lubricant pressure and film thickness are sensitive to surface deformation, is solved by using a finite element procedure and the Newton method. The numerical procedure is applied to the point contact problem, in which a thin lubricant film is maintained between two balls loaded together by a high load under conditions of pure rolling. The present analysis shows that pressure spikes are formed near the outlet region, a result which has been found in the line contact problem and which has been conjectured in the present problem.

A numerical method has been developed for solving the nonlinear differential equation which arises in the elastohydrodynamic contact of bearing surfaces. This method is based upon the finite element approximation of the governing field equation, the Newton-Raphson algorithm for solving nonlinear systems, and the complementarity formulation of free-boundary problems. The lubricated contact between a sphere and a semi-infinite half-space under dynamic loading is analyzed as an illustrative problem.

The elastohydrodynamic lubrication of an automotive piston was analyzed. The important effects of thermal and pressure distortions were demonstrated by analyzing two piston skirts which have different axial profiles but are otherwise identical. Results show that a significant reduction in friction can be realized.