Analysis of the Elastic Contact of a Hollow Ball With a Flat Plate

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Abstract
This paper presents the analysis of the stress field in a hollow sphere in the vicinity of the contact area. The sphere is subjected to a normal load applied through a flat plate. The elastic contact shape and extent are developed for a load of 1000 lb applied to a 1-in-dia hollow ball with a 0.08-in-thick wall. Hollow ball shell bending stresses have a significant effect upon the subsurface stress field. Fatigue life estimates for the hollow ball vary significantly depending upon the selection of decisive stress amplitude. Comparison of the maximum value and location of the reversing orthogonal subsurface shear stress with solid ball data according to the Lundberg-Palmgren dynamic life theory predicts a 91.6 percent life reduction for the hollow ball contact. The use of the unidirectional subsurface shear stress results in a prediction of hollow ball contact life over 30 times the solid ball contact life.

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