A modified model of Lundberg-Palmgren rolling contact fatigue formula considering the effects of surface treatments

The Lundberg-Palmgren (L-P) fatigue life formula, as a statistical fatigue theory, has been widely used in the industry. However, its direct applicability is limited to the components treated by surface strengthening technologies. Rolling contact fatigue tests and surface integrity measurements of American Iron and Steel Institute (AISI) 9310 rollers with several surface treatments were performed to address this issue. Based on these results, a modified L-P fatigue model was proposed, enabling the consideration of surface modification including surface roughness, residual stress, and hardening introduced by different surface treatments. Compared with the original L-P fatigue formula, its results are more accurate for surface strengthened specimens. Furthermore, this method can assess the contact fatigue life of gears treated by surface strengthening techniques.