The edges of rollers in needle and roller bearings are crowned (i.e., rounded) in order to prevent large stress concentrations. At present, the crowning radius is determined empirically. In this paper, a numerical solution for the stress concentration in crowned elastic rollers is found. Using this method the true contact region, the load-vs.-compliance relationship, and the peak normal pressure can be determined for any roller geometry. The influence of crown radius on stress concentration is illustrated through numerical examples. This method may profitably be used in the stress analysis and design of a variety of machine elements such as gears, cams, and toothed couplings.

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