Effects of gear center distance variation on time varying mesh stiffness of a spur gear pair

Gear center distance variation is one of the most common defects of gear transmission systems. The changes in the gear center distance as well as other faults (e.g. tooth crack, pitting) have a direct influence on the Time Varying Mesh Stiffness (TVMS) which further modifies gear vibration behaviors. Accurately estimating gear TVMS under fault conditions is crucial in gear vibration dynamic simulation. Common methods used to evaluate TVMS are generally based on the assumption that the gear pair is perfectly mounted and that all mesh points are at their theoretical positions. This assumption prevents these methods from modeling deviations in gear center distance. To address this shortcoming, this paper proposes a new gear mesh kinematic model that can evaluate the actual contact positions of tooth engagement with time varying gear mesh center distance. With the proposed kinematic model, the actual TVMS of both healthy and cracked gear teeth are computed under conditions of perfect mounting, constant gear center distance deviation, and also time-varying gear center distance. Numerical simulations indicate that gear center distance variation has a significant effect on gear TVMS. Comparison between the effect of multiple faults and summed individual effects on TVMS indicates that the TVMS modification due to multiple-faults do not appear to combine in a linear manner. The proposed model for actual TVMS enables gear system dynamic models to be used to study the effects of assembly errors, gear run-out errors, shaft bending, and bearing deformation on the vibration behavior of gear transmission systems.