基于MATLAB的齿轮传动系统振动与分岔理论分析

Analysis of the Bifurcation and Theory Vibration of the Gear Transmission System based on the MATLAB

在考虑直齿轮各零件部件基础上,建立了三自由度齿轮传动系统动力学模型。借助数学软件MATLAB,利用Runge-kutta法对所构建的齿轮动力学方程进行求解,得到其动力学响应曲线,并分析了齿轮传动系统在激励频率变化下的分岔与稳定性。通过分析发现了强非线性齿轮传动系统存在着复杂的分岔结构和普适规律,为深入研究齿轮系统非线性动力学行为提供参考。

Based on the consideration of various parts of spur gear,the three degree of freedom dynamics model of gear transmission system is established. With the help of the mathematical software MATLAB,the gear dynamics equation constructed by using the Runge- kutta method is solved,the dynamics response curve is got,and the bifurcation and stability of the gear transmission system under different excitation frequency are analyzed. Through the analysis found the complex bifurcation structure and general rule are exist in the strongly nonlinear gear system,a reference for further study of gear system nonlinear dynamics is provided.