精密钢球传动系统动力学建模与模态分析

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摘要为能够准确反映精密钢球传动系统的固有特性。考虑摆线槽曲率和啮合法向力变化对啮合刚度的影响，通过力矩平衡方程和轴向力平衡方程求得啮合副时变啮合刚度。建立精密钢球传动系统平移-扭转耦合动力学模型，推导出系统动力学微分方程，得到系统自由振动特征方程，求解出系统固有频率和振型。研究结果表明，传动系统的各阶固有频率均呈周期性变化，在给定样机参数时，随着转角的增加，在低阶(110阶)、中高阶(2729阶)、中高阶(3034阶)的各自固有频率轨迹接近处发生模态跃迁，在高阶(3942阶)固有频率轨迹相交处等速钢球组1直线振动模式与等速钢球组2直线振动模式之间会发生变化。

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	张悦
	安子军
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	白晓鹏

关键词 ：精密钢球传动, 四点接触, 时变啮合刚度, 模态分析, 轴向预紧

Abstract：In order to reveal the inherent characteristics of a precision ball transmission system accurately,Considering the influence of the curvature of the cycloidal groove and the variation of meshing normal force on the mesh stiffness,the time-varying mesh stiffness of the meshing pair was obtained by the torque balance equation and the axial force balance equation.A translational-torsional coupling dynamics model of the precision ball transmission system was established,the dynamics of differential equations of the system were derived,the characteristic equation of free vibration of the system was obtained and the natural frequencies and vibration modes were solved.The results show that the natural frequencies of the transmission system are changed periodically.When the parameters of the prototype are given,loci veering occurs at the approach of respective natural frequency curves of low-order (1—10 order) and middle-high-order (27—29 order and 30—34 order) and there are changes between the linear vibration mode of the constant speed ball group 1 and the linear vibration mode of the constant speed ball group 2 at the intersection of the high-order (39—42 order) natural frequency curves with the increasing of the rotation angle.

Key words： precision ball transmission four point contact time-varying mesh stiffness modal analysis axial preload

收稿日期: 2017-10-11 出版日期: 2019-02-15

引用本文:

张悦，安子军，刘子强，白晓鹏. 精密钢球传动系统动力学建模与模态分析[J]. 振动与冲击, 2019, 38(4): 166-174.
ZHANG Yue，AN Zijun，LIU Ziqiang，BAI Xiaopeng. A dynamic model and modal analysis of a precision ball transmission system. JOURNAL OF VIBRATION AND SHOCK, 2019, 38(4): 166-174.

链接本文:

http://jvs.sjtu.edu.cn/CN/ 或 http://jvs.sjtu.edu.cn/CN/Y2019/V38/I4/166

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