双侧双级双圆弧螺旋锥齿轮章动减速器动力学分析

Dynamics analysis of nutation drive with two-stage bilateral meshing double circular arc spiral bevel gears

以双侧双级双圆弧螺旋锥齿轮章动减速器为研究对象,综合考虑时变啮合刚度、啮合阻尼、传递误差、齿侧间隙等因素,采用集中参数法建立该类传动系统的12自由度弯-扭耦合非线性动力学模型.以四阶变步长Runge-Kutta法求解该系统的动态响应,并分析激励频率、支承刚度对系统动载荷系数的影响.结果表明,随着激励频率的变化,系统相继呈现出7倍周期、拟周期和混沌响应现象.无量纲激励频率为0.5和1.0时,动载荷系数出现峰值.在支承刚度的0.5~3.5倍范围内,随着支承刚度增大,系统动载荷系数降低.研究结果为后续的章动传动系统动态优化设计提供了理论依据.

This paper focuses on the nutation drive system with two-stage bilateral meshing double circular arc spiral bevel gears.Considering the factors of time-varying meshing stiffness,meshing damping,transmission error and backlash,a translation-torsion coupled nonlinear dynamic model with 12 degrees of freedom is established by utilizing the lumped parameter method.Using the fourth-order Runge-Kutta method with variable time step,the dynamic response of the nutation drive system is obtained.Moreover,the influence of excitation frequency and support stiffness on dynamic load coefficient is analyzed.The results show that seven-period,quasi-period and chaos response appear in the system with the change of excitation frequency.When the dimensionless excitation frequency is 0.5 and 1.0,the dynamic load coefficient appears two peak values.In the range of 0.5~3.5 times of the support stiffness,the dynamic load coefficient of the system can be reduced with the increase of the support stiffness.The results provide theoretical foundation for the later dynamic optimization design of the nutation drive.