大传动比微型活齿传动系统非线性共振研究
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摘要
为了实现活齿传动在精密传动领域的应用,设计了一种大传动比微型活齿传动系统。基于行星齿轮传动的线弹性动力学理论建立了活齿传动系统的动力学模型,考虑啮合齿数变化引起的非线性效应,建立了活齿传动系统非线性动力学方程。运用谐波平衡法和正规摄动法推导出系统的非线性幅频关系及非线性共振响应方程。利用给出的任意两组活齿传动系统算例参数,分析了活齿传动系统幅频曲线随系统参数的变化规律,给出了系统在不同倍频下的共振响应。结果表明:阻尼系数ζ和啮合活齿数f对幅频曲线的影响最大,系统在ωe≈ω1和ωe≈1/2ω1时共振显著。因此,为了减小活齿传动系统振动及提高系统平稳性,应尽量减小活齿数量和波发生器偏心距。研究结果为活齿传动系统结构改进和传动效率的提高奠定理论基础。
In order to apply the movable tooth drive in precision drive field,a mini type large transmission ratio movable tooth system is designed.Based on an elastic dynamic theory of planetary gear drive,the dynamic model of movable tooth system is established.Considering the nonlinear effect caused by the changing of meshing tooth number,the nonlinear dynamic equations of the movable tooth system are built.The nonlinear amplitude-frequency relationship and resonance equations are deduced with the harmonic balance method and the the perturbation method.Besides,the amplitude-frequency curve changes with parameters and the resonance response laws under different multiplicity frequency are analyzed with the two sets given parameters.Results show that the damping coefficientζand the amount of meshing movable teeth f have a large impact on an amplitude-frequency curve,and the system resonance is prominent whenω_e≈ω_1 andω_e≈1/2ω_1.So,in order to reduce vibration and improve stationarity of the system,a small number of the movable tooth and small offset of wave generator is necessary.The results lay a theoretical foundation for modifying the structure and improving transmission efficiency of the movable tooth system.
In order to apply the movable tooth drive in precision drive field,a mini type large transmission ratio movable tooth system is designed.Based on an elastic dynamic theory of planetary gear drive,the dynamic model of movable tooth system is established.Considering the nonlinear effect caused by the changing of meshing tooth number,the nonlinear dynamic equations of the movable tooth system are built.The nonlinear amplitude-frequency relationship and resonance equations are deduced with the harmonic balance method and the the perturbation method.Besides,the amplitude-frequency curve changes with parameters and the resonance response laws under different multiplicity frequency are analyzed with the two sets given parameters.Results show that the damping coefficientζand the amount of meshing movable teeth f have a large impact on an amplitude-frequency curve,and the system resonance is prominent whenω_e≈ω_1 andω_e≈1/2ω_1.So,in order to reduce vibration and improve stationarity of the system,a small number of the movable tooth and small offset of wave generator is necessary.The results lay a theoretical foundation for modifying the structure and improving transmission efficiency of the movable tooth system.
引文
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[12]Xu Lizhong,Li Huaiyong.Dynamics for an electromechanical integrated harmonic piezodrive system[J].International Journal of Applied Electromagnetics and Mechanics,2014,46(3):709-726.
[13]Xu Lizhong,Li Chong.Coupled dynamics for an electromechanical integrated harmonic piezodrive system[J].Arabian Journal for Science and Engineering,2014,39(12):9137-9159.
[2]Yi Yali,An Zijun.Research on digital design and manufacture technology of rolling swing movable teeth transmission[J].Applied Mechanics and Materials,2011,86:370-373.
[3]苏建.二齿差钢球活齿传动的分析与设计[D].北京:北京工业大学,2012:1-7.
[4]Zhou Jianjun,Chen Zichen.Creative design of movable tooth gear drives[J].Chinese Journal of Mechanical Engineering:English Edition,2004,17(S):98-101.
[5]赵纯可,梁尚明,张杰.二齿差摆杆活齿传动的齿形分析与仿真[J].四川大学学报:工程科学版,2015,47(S1):151-157.Zhao Chunke,Liang Shangming,Zhang Jie.Tooth profile analysis and simulation of the two-tooth defference swing-rod movable teeth transmission[J].Journal of Sichuan University:Engineering Science Edition,2015,47(S1):151-157.(in Chinese)
[6]刘大伟,任廷志,章裕琳.非匀速活齿机构的传动原理及典型结构[J].机械工程学报,2014,50(1):47-54.Liu Dawei,Ren Tingzhi,Zhang Yulin.Transmission theory and typical structure of nonuniform mechanism with movable teeth[J].Journal of Mechanical Engineering,2014,50(1):47-54.(in Chinese)
[7]李剑锋,苏健,陈兴,等.二齿差钢球活齿传动的齿廓方程及齿廓干涉分析[J].北京工业大学学报,2014,40(5):641-647.Li Jianfeng,Su Jian,Chen Xing,et al.Tooth profile equation and interference analysis of the two-tooth difference steel ball movable tooth transmission[J].Journal of Beijing University of Technology,2014,40(5):641-647.(in Chinese)
[8]李冲,许立忠.压电谐波电机驱动系统非线性主共振分析[J].振动、测试与诊断,2016,36(3):575-579.Li Chong,Xu Lizhong.Non-linear primary resonance of driving system for a harmonic piezoelectric motor[J].Journal of Vibration,Measurement&Diagnosis,2016,36(3):575-579.(in Chinese)
[9]梁尚明,张均富,徐礼钜,等.摆动活齿传动系统振动的动力学模型[J].振动工程学报,2003,16(3):285-289.Liang Shangming,Zhang Junfu,Xu Liju,et al.Dynamic model of swing movable teeth transmission system vibration[J].Journal of Vibration Engineering,2003,16(3):285-289.(in Chinese)
[10]金向阳,于广滨,关祥毅.航空用微小型正弦活齿系统扭振动力学分析[J].中北大学学报:自然科学版,2007,28(4):299-303.Jin Xiangyang,Yu Guangbin,Guan Xiangyi.Torsion dynamics of aviation micro cylinder sine oscillating tooth system[J].Journal of North University of China:Natural Science Edition,2007,28(4):299-303.(in Chinese)
[11]安子军,高飞.摆杆活齿传动扭转振动分析与建模研究[J].机械设计与研究,2007,23(3):79-81.An Zijun,Gao Fei.Torsion vibration analysis and modeling research on swing-rod movable teeth transmission[J].Machine Design and Research,2007,23(3):79-81.(in Chinese)
[12]Xu Lizhong,Li Huaiyong.Dynamics for an electromechanical integrated harmonic piezodrive system[J].International Journal of Applied Electromagnetics and Mechanics,2014,46(3):709-726.
[13]Xu Lizhong,Li Chong.Coupled dynamics for an electromechanical integrated harmonic piezodrive system[J].Arabian Journal for Science and Engineering,2014,39(12):9137-9159.