Competitive Failure for Fatigue Reliability Analysis of Transmission Gears Based on Copula Function

To address automotive transmission failures associated with long‐term, fatigue‐related gear damage, a competitive failure reliability framework is developed to support safer vehicle operation. As critical components in gear‐shifting systems, gears are primary load‐bearing elements whose reliability strongly influences transmission performance. This study specifically focuses on the competition between tooth root breakage (driven by bending fatigue) and tooth flank wear (driven by sliding friction and modeled via Archard's law). These modes may occur simultaneously and exhibit a competitive relationship, in which the mode that occurs first governs the gear service life. Based on the Walker crack growth model and the Archard wear model, marginal reliability models are established for tooth root bending fatigue and tribological wear, respectively. The statistical dependence between these two failure modes is modeled using a Copula function, from which the reliability function for competitive gear failure is derived. The reliability life is evaluated based on a specified reliability level within the proposed competitive failure framework.