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.

在传统的网格刚度计算模型中，通常假定齿根裂纹处于闭合状态。然而，在啮合过程中，齿轮齿裂纹在啮合力的作用下会打开，因此，裂纹齿的啮合刚度和齿轮系统的动力响应与闭合裂纹情况不同。几乎没有任何研究来研究牙齿的开裂状态对网孔刚度和动态响应的影响。因此，本文提出了一种改进的裂纹齿轮啮合刚度计算模型，其中考虑了裂纹的打开状态，重新评估了裂纹的有效压缩截面和中性层。然后，通过有限元方法（FEM）验证了所提出模型的准确性，并进一步研究了模型与传统模型之间的网格刚度差异和动态响应统计指标。网格刚度计算结果表明，所提模型比传统模型具有更高的精度。并且其精度随着裂纹的增长而逐渐提高，与传统模型相比，在大裂纹（裂纹率为48.38％）的情况下可以提高2.35％。传统模型获得的故障响应信号幅度大于实际情况，会导致用于故障诊断的统计指标出现误差，特别是在实际情况下，RMS值的平均百分比差可达11.98％。大裂纹（48.38％裂纹）。