基于谐波平衡法的摆线钢球行星传动等速输出机构非线性动态特性研究

摘要

In order to reveal the nonlinear dynamics behavior of the equal speed output mechanism of cycloid ball planetary transmission,a pure torsion strongly nonlinear dynamics model was established in consideration of different number of balls,input excitation,different stiffness and different engagement state.Expressing the vice engagement preload function in a polynomial form and the vice engagement gap function in a describing function form,the harmonic balance method was used to convert the differential equations into nonlinear algebraic equations,which were solved by MATLAB,and the steady-state response of the system at foundamental frequency was obtained.The nonlinear dynamic characteristics were analyzed by changing the influential parameters such as the number of balls,axial compression and mesh stiffness.The results show that only two frequency orders of resonances of the preload system are stimulated.The nonlinear degree of the system decreases with the increase of the number of steel balls,the mesh stiffness and the preload. Preload is the most prominent factor affecting the degree of nonlinearity.The number of resonant frequencies of the gap system is related to the number of steel balls.The amplitude-frequency response curve shows the typical non-linear characteristics,and also shows the appearance of unilateral and bilateral impacts.The harmonic balance method based on polynomial function provides an effective method for the further study of the dynamic characteristics of cycloid ball planetary drives.%为揭示摆线钢球行星传动等速输出机构的非线性动力学行为，建立考虑机构钢球数目、输入激励、啮合副啮合状态及啮合刚度的纯扭转强非线性动力学模型。将啮合副预紧函数表现为多项式的形式，将啮合副间隙函数表达为描述函数的形式，通过谐波平衡法将微分方程组转化为非线性代数方程组，利用 MATLAB 进行求解，得到系统的基频稳态响应。通过改变钢球数、轴向压缩量与啮合刚度，分析参数变化对系统非线性特性的影响。结果表明，预紧系统只有两阶频率激发共振，系统非线性程度随钢球数、啮合刚度和预紧量的增加而减弱，预紧量是影响系统非线性程度的主要因素；间隙系统激发共振频率的阶数与钢球数目有关，幅频响应曲线出现典型非线性特征，出现单边冲击与双边冲击现象。基于多项式函数的谐波平衡法为深入研究摆线钢球行星传动系统的动态特性提供了一种有效方法。