Time-Varying Meshing Stiffness Calculation and Dynamics Simulation of Multi-Spalling Gear

Spalling alters a gear’s time-varying meshing stiffness (TVMS), thereby affecting its vibration characteristics. However, most studies focus on single-spalling gears and overlook the possibility of multi-spalling gears. Additionally, because most spalls are irregular, traditional analytical models neglect the torsional effects that are caused by asymmetric spalling. In this study, a shape-independent model for calculating the TVMS of multi-spalling gears, which considers torsional stiffness, was developed. A 16-degree-of-freedom dynamic model was established to analyze the dynamic response, incorporating the multi-spalling TVMS. The model was then validated through experiments. The results show that the proposed method accurately calculates the TVMS of a multi-spalling spur-gear system. Changes in the relative position of the spalling can significantly affect the TVMS. Multiple-tooth spalling influences the TVMS over several meshing cycles, while single-tooth multiple spalling affects the TVMS based on the specific spalling parameters. Different spalling patterns lead to substantial differences in the system’s dynamic behavior. Multiple spalling teeth generate several pulses, whereas a single tooth with multiple spalls only generates one significant pulse. This study provides a solid foundation for understanding the dynamic behavior of spalled gear systems, revealing their dynamic characteristics and failure mechanisms.