On an extension of the fatemi and socie equation for rolling contact in rolling bearings

Abstract

Rolling contact in bearings provides under the raceway surface a non-proportional multiaxial stress distribution. Knowing the stress-state under the location of highest contact stress between rolling elements and raceways, the fatigue life prediction of the bearing is calculated using the Fatemi and Socie lifetime criterion. With the load distribution between rolling elements and raceways, contact stresses are computed, and the location of highest contact stress between rolling elements and raceways in the bearing is identified. This location is considered as the main fatigue failure location in the bearing. On this position, the time-dependent subsurface stress tensors (formula presented) are computed. To calculate the damage and the crack initiation lifetime of the bearing, the plane of maximum shear stress amplitude (formula presented) (critical plane) as well as the maximum normal stress (formula presented) perpendicular to this plane are determined for each time-dependent stress tensor (formula presented). The maximum shear stress amplitude (formula presented) is found between two distinct time-moments, i.e. within a time-interval (formula presented). For the maximum normal stress determination, two approaches are evaluated in this paper: the first approach (A1) is a global approach which does not limit the maximum normal stress determination in the time-interval (formula presented). Instead of this, the second approach (A2) limits the determination only within the time-interval (formula presented) where the maximum shear stress amplitude (formula presented) was found. The purpose of this paper is to investigate the influence of these two approaches on the damage and crack initiation lifetime calculated with the Fatemi and Socie criterion applicate to rolling contact. These two approaches are applicated to the crack initiation lifetime calculation of a rolling bearing. Results from the two approaches concerning crack initiation lifetime and crack orientation are compared together and with conventional results from the standard DIN ISO 281 lifetime calculation.