Research on the Dynamic Response of a Cracked-Spur Gear System with Parameter Uncertainty

In this paper, the time-varying mesh stiffness (TVMS) of a gear is meticulously derived using the potential energy method (PEM) and an analytical expression for it is obtained. Subsequently, calculations are performed to determine the effects of crack depth and crack angle on the TVMS. The validation is carried out using the finite element method (FEM). Then, a discussion is carried out on the dynamic characteristics of a spur gear system with a crack. Moreover, uncertainty is an objective reality in gear systems, arising from various factors such as the material properties and working environment. To enable a more reasonable evaluation of the dynamic characteristics of the spur gear system, this paper presents a deviation of an uncertainty interval analysis method based on Chebyshev polynomials. A dynamic model of the spur gear system with uncertain parameters is then proposed. The dynamic response of a gear transmission system with these uncertain parameters is investigated in detail. Additionally, the interval response of a gear system with root cracks under uncertainty is further investigated. The experimental results confirm the inherent presence of uncertainty in the gear system and validate the effectiveness of the proposed uncertainty analysis method.