In this paper a finite element formulation for transient analysis of journal bearings is described. The formulation can be used for partial or full-arc bearings with oil-supply hole and oil-feed grooves, with tapered or misaligned journal, and with elliptical or eccentric bearings. An important feature of this analysis is relatively low computing cost. The analysis is followed by an illustrative example in which 17 different cases of a connecting-rod bearing are solved.

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.

Analytical solutions are not available for spherical bearing problems except for very specialized cases. However, the finite element method presented here can be used to analyze virtually any such bearing having an incompressible lubricant between surfaces which are smooth, rigid, and impermeable. The method can be easily extended to account for permeable surfaces and lubricants with variable viscosity and density. Triangular finite elements with linear interpolation functions are used to model the lubricant film. For complete films an elimination method solves the resulting system of equations; for incomplete films an iteration scheme incorporates Reynolds boundary conditions. The method is extended from “direct” (explicit) problems of specified planar motion to “indirect” (implicit) problems with specified planar loads and can be further extended to solve these problems with general spatial motion and loads. The results for spherical bearings are similar in trend to those for cylindrical journal bearings and suggest the former as possible alternatives, especially if axial as well as radial forces are present.

The mobility method of solution is frequently used for analyzing dynamically loaded journal bearings. Curve fits of journal-bearing solutions are used in this method. All the currently available curve fits are lacking in one or more of three important features—the solution accuracy, the solution detail, and the solution time. A new set of analytical curve fits is presented in this paper. The set includes: the two components of mobility vectors, location and magnitude of maximum film pressure, and the starting and finishing angles of the pressure curve. For an ideal journal bearing, the new curve fits give accuracy and solution detail comparable to an expensive finite-element analysis, while keeping the solution time comparable to that required for the short-bearing approximation. An example is presented to demonstrate the use of the new curve fits.

The finite element formulation for regular cylindrical bearings is extended to include irregular (noncylindrical) bearing surfaces. The optimum bearing shape is sought for a specific duty cycle with a constant load and sinusoidal angular displacement. The optimization is done with a view to maximizing the minimum film thickness. For the purpose of optimization a one-dimensional cylindrical bearing is considered. The optimum among all elliptical shapes is found to combine a specifically elliptical sleeve and a perfectly circular journal. For this optimum noncylindrical bearing the absolute minimum film thickness is about a factor of 36 higher than that for the corresponding regular bearing. The absolute maximum pressure for the optimum bearing is about a factor of 5 lower than that for the regular bearing.