In order to identify gear crack failure, modelling the mesh stiffness of a cracked tooth is crucial. In this study, an analytical model of the mesh stiffness for cracked helical gears considering the axial mesh stiffness components and the deflection of the gear body has been proposed. Based on the analytical model, the comparison of the mesh stiffness with and without the axial mesh stiffness components or the deflection of the gear body was carried out. Mesh stiffness of three crack propagation scenarios with different crack sizes has been investigated. Simultaneously, a method to detect the crack length has been deduced based on the time period of the mesh stiffness. Simulation has been conducted using a six-degrees-of-freedom helical gear dynamic model in order to study the effect of tooth crack propagation on the dynamic response. Statistical indicators extracted in the time domain and frequency domain were adopted to evaluate the crack propagation level. The results indicated that the analytical model that has been proposed is able to provide a relatively accurate mesh stiffness, taking into consideration the axial mesh stiffness components and the deflection of the gear body. Mesh stiffness reduced with the propagation of the crack size in either the direction of the crack depth or the crack length. Through analysis of the time period of the residual signal from the dynamic transmission error, the crack length was able to be accurately identified. The shape factor in the selected statistical indicators is most sensitive to the tooth crack propagation in the frequency domain.

中文翻译：

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带齿裂纹扩展的斜齿轮啮合刚度建模与动力学仿真

为了识别齿轮裂纹故障，对裂纹齿的啮合刚度建模至关重要。在这项研究中，已经提出了考虑轴向啮合刚度分量和齿轮体挠度的裂纹斜齿轮啮合刚度分析模型。在分析模型的基础上，对有和没有轴向啮合刚度分量或齿轮体挠度的啮合刚度进行了比较。研究了具有不同裂纹尺寸的三种裂纹扩展场景的网格刚度。同时，推导出了一种基于网格刚度时间段的裂纹长度检测方法。使用六自由度斜齿轮动态模型进行了仿真，以研究齿裂纹扩展对动态响应的影响。采用时域和频域提取的统计指标来评价裂纹扩展程度。结果表明，所提出的分析模型能够提供相对准确的啮合刚度，同时考虑了轴向啮合刚度分量和齿轮体的挠度。网格刚度随着裂纹尺寸在裂纹深度或裂纹长度方向上的扩展而降低。通过分析动态传输误差产生的残差信号的时间段，能够准确识别裂纹长度。所选统计指标中的形状因子对频域中的齿裂纹扩展最为敏感。