A unified estimation method for gear fatigue P-S-N curves and fatigue limits based on ensemble learning and data augmentation

P-S-N curve and fatigue limit are crucial indicators for evaluating the fatigue reliability of gears and serve as the essential foundation for gear anti-fatigue design. However, the isolation of the current estimation methods for both results in a large number of test samples with a long test cycle and high costs. Thus, this study proposes a unified estimation method for gear fatigue P-S-N curves and fatigue limits, which utilizes a few group data of fatigue tests carried out under constant loads to predict fatigue limit based on ensemble learning and data augmentation methods. Moreover, a multi-objective optimization algorithm is applied to establish a formula for the evaluation of gear bending fatigue limits considering stress and life distributions. Validation of this formula is conducted on several gear bending fatigue test cases covering different materials, manufacturing processes, and gear sizes. The results indicate that the gear fatigue limit prediction error of the formula is 4.92% on average and 8.79% at maximum. The overall sample size and test time are reduced by approximately 50% and 60%, respectively, in comparison to the group method and the staircase method in ISO 12107 utilized for obtaining the P-S-N curve and fatigue limit.