Dynamic modeling and analysis of a two-stage gearbox with a crack defect

Abstract Crack is a common defect form that can emerge and cause unpredicted failure during operation in a gearbox. To investigate the corresponding dynamic response and enrich the limited knowledge of the crack defect gearbox, this paper aims to establish an analytical model of the holistic system. Firstly, a time-varying meshing stiffness (TVMS) calculation model is proposed, where the influence of crack defect is incorporated by modifying the tooth geometry properties, like the section area and the inertia moment. Afterwards, an 11-DOF dynamic model of a two-stage gearbox is established. The defect is considered quantitatively by changing the gear contact force. Then, FEM analysis is conducted to validate the accuracy of the established analytical model, with the largest relative error of the proposed model, about 4.8%, in describing the peak values and the impulse period matching well with the rotation time of the defect gear tooth undergoing a meshing cycle. Finally, parameter analysis of the crack defect is achieved utilizing the proposed model, whose results can further help to better understand the gearbox response in different crack conditions.