Spherical Bearings: Static and Dynamic Analysis Via the Finite Element Method

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Abstract
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.

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