Extended Hertz Theory of Contact Mechanics for Case-Hardened Steels With Implications for Bearing Fatigue Life

The analytical expressions currently available for Hertzian contact stresses are applicable only for homogeneous materials and not for case-hardened bearing steels, which have inhomogeneous microstructure and graded elastic properties in the subsurface region. Therefore, this article attempts to determine subsurface stress fields in ball bearings for graded materials with different ball and raceway geometries in contact. Finite element models were developed to simulate ball-on-raceway elliptical contact and ball-on-plate axisymmetric contact, to study the effects of elastic modulus variation with depth due to case hardening. Ball bearings with low, moderate, and heavy load conditions are considered. The peak contact pressure for case-hardened steel is always more than that of through-hardened steel under identical geometry and loading conditions. Using equivalent contact pressure approach, effective elastic modulus is determined for case-carburized steels, which will enable the use of Hertz equations for different gradations in elastic modulus of raceway material. Nonlinear regression tools are used to predict effective elastic modulus as a weighted sum of surface and core elastic moduli of raceway material and design parameters of ball–raceway contact area. Mesh convergence study and validation of equivalent contact pressure approach are also provided. Implications of subsurface stress variation due to case hardening on bearing fatigue life are discussed.