时变啮合刚度是齿轮系统动力学模型的参数激励，当齿轮出现齿根裂纹时，啮合刚度变化引起的动态响应特征是实现齿轮裂纹故障诊断的重要依据。以非标齿轮为研究对象，针对齿根裂纹故障对其时变啮合刚度的影响，建立考虑基圆与齿根圆不重合的变截面悬臂梁模型，提出利用改进势能法求解齿轮啮合刚度的计算模型，与原势能法和 ISO 6336⁃1⁃2006进行对比分析，并计算齿顶高系数和顶隙系数改变时不同裂纹尺寸的轮齿刚度和齿轮时变啮合刚度；建立非标齿轮传动系统六自由度动力学分析模型，利用4⁃5阶 Runge⁃Kutta 数值法求解故障系统的动态响应。仿真结果表明改进势能法显著提高了非标齿轮时变啮合刚度的求解精度。齿根裂纹的存在使得非标齿轮综合啮合刚度明显减小，系统时域信号中存在周期性冲击响应，频域中出现调制边频带结构，这些均为齿轮系统故障诊断提供了理论依据。%When a tooth crack failure occurs, the dynamic response caused by time⁃varying mesh stiffness changes plays a significant role in monitoring the operating conditions of a gear system and diagnosing its fault. We study a non⁃standard gear and the effect of tooth crack fault on the time⁃varying mesh stiffness. We establish the non⁃uni⁃form cantilever beam model in which the misalignment between base circle and root circle is taken into account. The three gear mesh stiffneses calculated with the improved algorithm, the existing potential energy method and the ISO 6336⁃1⁃2006 Standard are compared to verify the improved potential energy method.The tooth stiffness and time⁃var⁃ying gear mesh stiffness with different crack sizes are calculated when the gear addendum coefficient and the tip clearance coefficient change. The 6⁃degeee⁃of⁃freedom dynamics analysis model of a non⁃standard gear transmission system is established, and the Runge⁃Kutta numerical method is used to analyze the dynamic response. The simula⁃tion results show that when the cracked tooth comes in contact, mesh stiffness decreases greatly and that the dynam⁃ic response presents a periodically impulse amplitude. Besides, modulation sidebands appear in the frequency do⁃main; these results provide a theoretical basis for diagnosing the fault of a gear system.
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