Investigation of tooth crack opening state on time varying meshing stiffness and dynamic response of spur gear pair

In the traditional calculation model of mesh stiffness, the tooth root crack is commonly assumed to be in a closed state. However, the gear tooth crack will open under the action of mesh force in the meshing process, the mesh stiffness of the cracked tooth and the dynamic response of gear system is thus different from the closed crack case. There almost no studies have been done to investigate the influence of tooth crack open state on mesh stiffness and dynamic response. Thus, this paper presents an improved mesh stiffness calculation model of the cracked gear, in which the effective compression section and the neutral layer of the cracked tooth are re-evaluated considering the crack opening state. Then, the accuracy of the proposed model is verified by the finite element method (FEM), and the differences of mesh stiffness and statistical indicators of the dynamic response between the proposed and traditional models are further studied. The mesh stiffness calculation results show that the proposed model achieves a higher accuracy than the traditional model. And its precision gradually increases as the crack grows, which can be improved by 2.35% in the case of large crack (48.38% crack) when compared to the traditional model. The fault response signal obtained from the traditional model yields a larger amplitude than the actual situation, which will lead to errors of the statistical indicators used for fault diagnosis, in particular, the RMS value can be up to an average percentage difference of 11.98% under the large crack (48.38% crack). It is concluded that the proposed model has a higher accuracy for calculating the mesh stiffness of the cracked gear and can be further used to serve the fault diagnosis and detection of the gear system.