Using idealized assumptions, the stress condition in the semi-infinite body of the Hertzian contact region can be calculated for various geometries as a function of the surface pressure (normal force), the friction (tangential force at the surface), and the residual stresses in the material. Equivalent stresses can be formed from the coordinate stresses using various stress hypotheses (distortion energy hypothesis, shear stress hypothesis, and alternating shear stress hypothesis). The effects of friction, residual stresses, and contact geometry on the location and magnitude of the equivalent stresses appearing in the material have been investigated, the stress hypotheses being evaluated in terms of the extent to which they take account of these effects in an appropriate form. These investigations show clearly that the distortion energy hypothesis is the best representation of the extent of material stress in the case of dynamically loaded rolling elements. The shear stress hypothesis can be considered as a good approximation whereas the alternating shear stress hypothesis is only capable of providing useful conclusions to a limited extent.

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