An Engineering Approach to Hertzian Contact Elasticity—Part I

Results given in this paper are threefold. In the case of Hertzian line contact, a new load/deformation relationship is derived analytically and use is made of the thickness of the outer race section. A minor effect of the section thickness is shown. The exponent on the deformation is 1.074 (instead of 1.1 usually accepted). Results calculated with the new relationship are successfully compared to results calculated with other published relationships and also are compared successfully to some available experimental results. For the case of point contact, useful relationships, obtained by curve-fitting, are given to calculate easily the load versus deformation, maximum Hertzian pressure and ellipse contact dimension as a function of a dimensionless load parameter and ratio k of equivalent radii (instead of sum of curvatures and elliptical integrals before). A large range of k is covered, from 0.05 (found at roller rib contact) to 13,000 to cover all bearing cases, from ball bearings to spherical and tapered roller bearings. Finally, an important analytical relationship, based on curve-fitting, also is suggested to describe a smooth transition from point contact to line contact as the load increases. It is recommended to define bearing setting and bearing preload with the suggested relationship.