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为探究地铁不同车速阻尼对传动系统非线性动力学响应的影响,建立地铁斜齿轮弯-扭-轴动力学模型,模型考虑了齿轮副啮合过程中产生的时变啮合刚度、啮合误差以及间隙非线性等系统参数,以及地铁运行工况下的外部参数。通过对六自由度系统微分方程的无量刚处理以及方程归一化,运用变步长四阶Runge-Kutta数值积分法对齿轮动力学模型进行数值分析,获得齿轮系统动态响应状态图。借助时间历程图、相平面图、庞加莱截面图和分岔图等系统状态判定标准,定性分析系统激励频率、啮合阻尼比变化下系统周期运动、拟周期运动、分岔和混沌运动等的演化历程。结果表明,当地铁高速运转、啮合阻尼比大时斜齿轮传动系统运动稳定。最后通过实验验证了其正确性。
In order to explore the influence of different speed damping of subway on the nonlinear dynamic response of transmission system, a model of torsion-torsion-shaft dynamics of metro helical gear is established. The model takes into account the time-varying meshing stiffness, meshing error, Linear and other system parameters, as well as the external parameters of the subway operating conditions. Through the immeasurable processing and the normalization of six-degree-of-freedom differential equations, the fourth-order Runge-Kutta numerical integration method with variable step size is used to analyze the gear dynamics model to obtain the dynamic response state diagram of the gear system. With the aid of time history chart, phase plan, Poincaré cross section and bifurcation diagram, the evolution of system excitation frequency, periodic motion, quasi-periodic motion, bifurcation and chaos motion under the change of meshing damping ratio course. The results show that when the local railway runs at high speed and the meshing damping ratio is large, the helical gear drive system moves steadily. Finally, the correctness of the experiment is verified.