Effects of angle misalignment error and center distance deviation on time-varying mesh stiffness of a spur gear pair

Angle misalignment error and center distance deviation are inevitable imperfections in gear transmission systems. These two faults frequently coexist, directly affecting the time-varying mesh stiffness (TVMS) and, consequently, the vibrational response of the gear system. Establishing a gear TVMS model that accounts for the coupling effect between angle misalignment error and center distance deviation is crucial for the early design and subsequent fault diagnosis of gear transmission systems. This paper establishes a gear TVMS model that accounts for the coupling between angle misalignment error and center distance deviation. The accuracy of the proposed model is validated through finite element simulations. Using the proposed stiffness model, we investigate the respective influence of each individual fault on the meshing stiffness. The variation trend of meshing stiffness with backup ratio under fault conditions is quantitatively analyzed, and a design strategy is proposed—setting the backup ratio between 2.5 and 3.5—to mitigate the effects of these faults. A comparative study was conducted on the influences of the coupled fault and the individual single faults on the mesh stiffness. The results show that the influence of the coupled fault on the meshing stiffness of the system is manifested as a nonlinear combination of the influences of single faults. Furthermore, this nonlinear characteristic becomes more pronounced as the severity of the faults increases. In the case study in this paper, the difference between them reaches 18.71%. This study provides a theoretical foundation for optimizing the design and fault diagnosis of gear transmission systems.