时变啮合刚度算法修正与齿根裂纹动力学建模

Time-varying Mesh Stiffness Algorithm Correction and Tooth Crack Dynamic Modeling

当齿轮产生裂纹时,其啮合刚度变化引起的振动响应特征是实现裂纹故障诊断的重要依据。提出一种考虑齿根圆与基圆不重合时的啮合刚度修正方法,建立齿根裂纹动力学模型并进行其振动响应精确求解。分析齿根圆与齿基圆不重合时啮合刚度求解误差,建立考虑齿根圆修正的齿轮裂纹变截面悬臂梁模型,显著提高了采用势能法求解齿轮时变啮合刚度的求解精度;建立含齿根裂纹故障的齿轮传动系统多自由度动力学模型,利用Runge-Kutta法求解齿轮产生裂纹故障时的动力学响应,仿真结果表明当齿根出现裂纹时,其振动响应中会出现明显的冲击响应特征;测试含2 mm齿根裂纹故障试验台的振动信号,利用二代小波包分解进行信号处理,试验结果与数值分析结果相符,为齿轮传动裂纹故障诊断提供了理论基础。

When the gear tooth is cracked, the vibration response characteristics caused by the change of time-varying mesh stiffness plays an important role in crack fault diagnosis. A correction method of time-varying mesh stiffness considering misalign between the root circle and tooth base circle is presented. Then a dynamic model for the tooth crack is established and adequate dynamic response is obtained. Solution error of the mesh stiffness due to misaligned root circle and tooth base circle is analyzed. The established model which simplified the gear tooth as a variable cross-section cantilever beam that took the modified root circle into consideration is used to improve the accuracy of using potential energy method to calculate the time-varying mesh stiffness. A multi-degree of freedom dynamic model is built for gearbox system with cracked tooth, and the Runge-Kutta method is applied to obtain the dynamic response of the system. The simulation results show that vibration response of the system presents an obvious impact response characteristic. An experiment is conducted on a test bench with 2 mm root crack fault, and the second generation wavelet packet decomposition is used to analyze the obtained vibration signal. Results of experiments agree well with those of simulation. A theory basis for the fault diagnosis of gear transmission system is provided with tooth crack fault.