Dynamic Modeling and Sensitivity Analysis of Stiffness Modulations Induced by Pitting Evolution in Spur Gear

In this study, a six-degree dynamic model considering torsion and bending is proposed for a single-stage spur gear reducer. The objective is to study the effect of progressive pitting on the dynamic behavior of the system. The evolution of mesh stiffness over time is modeled using an energy-based approach that takes into account the geometric characteristics of pitting defects, including their depth, width, and location on the gear teeth. The equations of motion are obtained using the Lagrangian method and subsequently solved numerically using the Runge-Kutta scheme. Vibration responses are analyzed in the time, frequency, and time-frequency domains for both healthy and damaged gears. The results show that the onset of pitting leads to a significant loss of stiffness, amplitude modulation, and the appearance of spectral sidebands near the mesh frequency. A quantitative parametric sensitivity analysis reveals that the apparent contact velocity plays a predominant role at low speeds and in the early stages of damage. In contrast, at high speeds and advanced degradation levels, pit depth and width become dominant. The proposed methodology provides valuable comprehension into the propagation mechanisms of pitting faults and offers practical guidance for early failure detection and condition-based maintenance of gear drive systems.