Dynamic Analysis of Transmission Gears With Combined Tooth Wear and Root Crack Failures

Compound faults present a considerable challenge in fault diagnosis for gear transmission systems, as existing studies predominantly focus on individual failure modes. To address this limitation, the present study proposes a novel dynamic response analysis model that simultaneously considers tooth profile wear and root crack faults. A numerical model for tooth profile wear is developed based on the Archard wear law, which allows for the calculation of wear progression over multiple operating cycles. The potential energy method is then employed to derive a time‐varying mesh stiffness model, capturing the interactive effects of tooth wear and root cracks on system stiffness and dynamic behavior. A six‐degree‐of‐freedom dynamic model of the gear transmission system is constructed using the lumped mass method, with time‐varying mesh stiffness as an input. The dynamic response is solved using the fourth‐order Runge–Kutta method to simulate the system under various levels of cracks and wear. Experimental validation confirms the model’s effectiveness in representing the complex dynamics of compound faults, demonstrating its superiority over traditional models that focus on single failure modes. This model provides an innovative theoretical framework and dynamic support for fault diagnosis in gear transmission systems subject to multiple failure modes.