含摩擦的风电齿轮传动系统非线性动力学分析

Nonlinear Dynamics Analysis of the Wind Turbine Gear Transmission System Considering Friction Effect

建立了含摩擦的风电齿轮传动系统的纯扭转非线性动力学模型,引入时变啮合刚度、综合啮合误差等因素,考虑了齿侧间隙与摩擦转矩等非线性因素的影响,进行量纲一化处理后得到了系统的动力学方程组;采用Runge-Kutta法对其进行求解,得出风电齿轮传动系统的非线性动态响应;计算了摩擦因数分别为0和0.07时系统随啮合频率变化的分岔图,并通过庞加莱截面、功率谱和关联维数等定性和定量工具对系统的非线性动力学特性进行了研究。结果表明,摩擦激励会使系统的周期响应中含有较多的次谐成分,诱发更多频率成分;摩擦激励会使得低频区域混沌区间减少,较快进入周期或拟周期运动状态;高频区域周期区间减少,拟周期区间、混沌区间加长,系统运动更为复杂。研究可为风电齿轮传动系统的故障机制研究、结构设计和更优工况的选择提供理论指导。

A torsional nonlinear dynamics model of the wind turbine gear transmission system is established,with the friction effect taken into account.The time-varying meshing stiffness and meshing error are analyzed and introduced,and the influence of nonlinear factors such as backlash and friction torque is considered.After nondimensionalization,the dynamics differential equations are obtained.Runge-Kutta methods are adopted to solve equations and the nonlinear dynamic response of the wind turbine gear transmission system is acquired.The bifurcation diagram of the system changing with meshing frequency is plotted when the friction coefficients are 0 and 0.07.The nonlinear dynamic characteristics of the system are studied by qualitative and quantitative methods such as the Poincare section,power spectrum and correlation dimension.The results show that there are many subharmonic components in the periodic response of the system under friction excitation.Friction excitation induces more frequency components than when the friction is not introduced.Friction excitation reduces the chaotic interval of the low frequency region and makes it enter the periodic or quasi-periodic motion state more quickly.Friction excitation which makes the system motion more complicated can also reduce the period interval of the high frequency region and lengthen the quasi-period interval and chaotic interval.The theoretical guidance is provided for the fault mechanism research,structure design and optimal working condition selection of the wind turbine gear transmission system.