Lundberg-Palmgren Fatigue Theory: Considerations of Failure Stress and Stressed Volume

Load ratings and fatigue life prediction of rolling bearings is based on the Lundberg-Palmgren theory first published in Sweden in 1947. The basic equation of this theory includes the stressed volume of material in the bearing raceway subsurfaces as a major parameter. This volume of material is simplistically determined to have a nearly rectangular subsurface cross-sectional area bounded by the length of the maximum contact area ellipse and the depth at which the maximum failure-causing stress occurs. The latter stress is assumed to be effective over this area. In fact, a distribution of stress occurs, and in this investigation it is demonstrated that the subsurface volume with a potential for fatigue cracking is substantially different from that used by Lundberg and Palmgren. This difference in volume, particularly in the presence of surface shear stresses, can have a profound effect on the method and prediction of bearing fatigue lives.