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

杨荣刚 安子军

振动与冲击 ›› 2017, Vol. 36 ›› Issue (2) : 153-158.

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振动与冲击 ›› 2017, Vol. 36 ›› Issue (2) : 153-158.
论文

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

  • 杨荣刚  安子军
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Nonlinear dynamic characteristics of the equal speed output mechanism of cycloid ball planetary transmission based on harmonic balance method

  • YANG Ronggang,AN Zijun
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摘要

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。

Abstract

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.

关键词

摆线钢球行星传动 / 等速输出机构 / 谐波平衡法 / 幅频特性 / 轴向预紧 / 非线性振动

Key words

cycloid ball planetary transmission / equal speed output mechanism / harmonic balance method / amplitude-frequency characteristics / axial preload / nonlinear vibration

引用本文

导出引用
杨荣刚 安子军. 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[J]. 振动与冲击, 2017, 36(2): 153-158
YANG Ronggang,AN Zijun. Nonlinear dynamic characteristics of the equal speed output mechanism of cycloid ball planetary transmission based on harmonic balance method[J]. Journal of Vibration and Shock, 2017, 36(2): 153-158

参考文献

[1] 王国彪,赖一楠,范大鹏,等. 新型精密传动机构设计与制造综述. 中国机械工程,2010, 21(16):1891-1897.
Wang Guobiao, Lai Yinan, Fan Dapeng, et al. Summary of New Type Precision Transmission Design and Manufacture[J]. China Mechanical Engineering, 2010, 21(16):1891-1897.
[2] 徐盛林,陈  耿. 精密超精密定位技术及其应用[J]. 中国机械工程,1997, 8(4):73-75.
Xu shenglin, Chen Geng. Precision Ultra-precision Positioning Technology and Its Applications[J]. China Mechanical Engineering, 1997, 8(4):73-75.
[3] 安子军,张  鹏,杨作梅. 摆线钢球行星传动系统参数振动特性研究[J]. 工程力学,2012,29(3):244-251.
An Zijun, Zhang Peng, Yang Zuomei. Research on Properties for Parametric Vibration of Cycloid Ball Planetary Transmission System[J]. Engineering Mechanics, 2012, 29(3):244-251.
[4] 张  鹏,安子军. 摆线钢球行星传动动力学建模与固有特性分析[J]. 中国机械工程,2014,25(2):157-162.
Zhang Peng, An Zijun. Dynamics Model and Natural Characteristics of Cycloid Ball Planetary Transmission[J]. China Mechanical Engineering, 2014, 25(2):157-162.
[5] 陈思雨,唐进元,谢耀东. 齿轮传动系统的非线性冲击动力学行为分析[J]. 振动与冲击,2009,28(4):70-75,204.
CHEN Siyu, TANG Jinyuan, XIE Yaodong. Analysis of nonlinear impact dynam ic behavior for agear pair system with tim e-varying stiffness and friction[J]. Journal of vibration and shock,2009,28(4):70-75,204.
[6] AL-SHYYAB A,KAHRAMAN A. A non-linear dynamic model for planetary gear sets[J]. Proceedings of the Institution of Mechanical Engineers,Part K-Journal of Multi-body Dynamics,2007,221(4):567-576.
[7] 孙涛,沈允文,孙智民,等. 行星齿轮传动非线性动力学方程求解与动态特性分析[J]. 机械工程学报,2002,38(3):11-15.
SUN Tao,SHEN Yunwen,SUN Zhimin,et al. Study on nonlinear dynamic behavior of planetary gear train solution and dynamic behavior analysis[J]. Journal of Mechanical Engineering,2002,38(3):11-15.
[8] 巫世晶,刘振皓,王晓笋,等. 基于谐波平衡法的复合行星齿轮传动系统非线性动态特性[J]. 机械工程学报,2011,47(1):55-61.
WU Shijing,LIU Zhenhao,WANG Xiaosun,et al. Nonlinear Dynamic Characteristics of Compound Planetary Gear Train Sets Based on Harmonic Balance Method[J]. Journal of Mechanical Engineering,2011,47(1):55-61.
[9] 刘志峰,张志民,张敬莹,等. 基于多项式的等高齿锥齿轮时变啮合刚度建模[J]. 吉林大学学报(工学版),2013,43(4): 139-144.
LIU Zhifeng,ZHANG Zhimin,ZHANG Jingying,et al. Modelling of high-spiral bevel gear mesh stiffness based on polynomial[J]. Journal of Jilin University(Engineering and Technology Edition). 2013,43(4):139-144.
[10] THEODOSSIADES S, NATSIAVAS S. Non-lineal dynamics of dear-pair systems with periodic stiffness and backlash[J]. Journal of Sound and Vibration, 2000,229(2): 287-310.
[11] 马锐,陈予恕. 含裂纹故障齿轮系统的非线性动力学研究[J]. 机械工程学报, 2011,47(21):84-90.
MA Rui, CHEN Yushu. Nonlinear Dynamic Research on Gear System With Cracked Failure[J]. Journal of Mechanical Engineering, 2011,47(21):84-90.
[12] 刘志峰,郭春华,杨文通,等. 基于分段间隙函数的螺旋锥齿轮时变啮合参数分析[J]. 振动与冲击,2013,32(4):153-157,162.
LIU Zhifeng,GUO Chunhua,YANG Wentong,et al. Time-varying meshing parameters analysis for spiral bevel gear based on sub-clearance function[J]. Journal of vibration and shock,2013,32(4):153-157,162.

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