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.

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