An approach is presented for simplified analytical, graphical, and numerical solutions to extremely general problems of dynamically loaded bearings. A series of examples illustrates the application of the method to problems of varying complexity.

A mass-conserving model is presented for the transient evolution of cavitation in lubrication analysis. Algorithms are given for its finite element implementation in both direct problems (specified motion) and indirect problems (specified load). Numerical examples demonstrate capabilities and applications of the model and algorithm (s).

A specific numerical calculation procedure is outlined for a general turborotor-bearing system in which distributed inertia and elasticity are consistently represented. Bearings are represented by up to sixteen linear cross coupled coefficients each for stiffness and for damping. Discrete (as well as distributed) masses are allowed. As an example, for stability analysis (free response) a non-dimensional parameter study is made for the special case of a simple rotor supported on two short (Ocvirk) fluid film bearings. A comparison of discrete and distributed parameter rotor representations shows that the discrete parameter model predicts onset of instability at a lower speed ratio and is, therefore, more conservative. For unbalanced response (forced response), comparison is made to Prohl’s method, which represents mass discretely. A considerable reduction in the number of degrees of freedom necessary for accurate system representation is observed with the finite element formulation.

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 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.