Chaos Identification of Two Rotational and One Translational Decoupled Parallel Mechanism Concerning Clearance

Abstract

Abstract:

Taking a two rotational and one translational decoupled parallel mechanism PU-RCRR-CRRR proposed independently as research object, aiming at the clearances existing in the Hooke joints, and combining Lankarani-Nikravesh contact force model and Newton-Euler method, the mechanism dynamics model was established. The dynamic responses were analyzed, in addition, the chaos phenomenon contained in the mechanism was identified with Poincare map and the largest Lyapunov exponent. The results indicate that chaotic phenomena exists in the dynamic responses of the two rotational and one translational decoupled parallel mechanism concerning clearances.

Key words: parallel mechanism, clearance, dynamics, chaos identification

摘要：

以自主提出的PU-RCRR-CRRR两转动一移动解耦并联机构为研究对象，针对虎克铰的运动副间隙，结合Lankarani-Nikravesh接触力模型与牛顿-欧拉法建立了机构动力学模型；分析了机构的动态响应，并通过Poincare映射以及最大李雅普诺夫指数对机构混沌现象予以辨识。研究结果表明，含间隙的两转动一移动解耦并联机构的动力学响应中确实存在混沌现象。

关键词: 并联机构, 间隙, 动力学, 混沌辨识

CLC Number:

TH113

Hou Yulei, Wang Yi, Li Mingyang, Zeng Daxing, Li Huijian. Chaos Identification of Two Rotational and One Translational Decoupled Parallel Mechanism Concerning Clearance[J]. China Mechanical Engineering, 2015, 26(13): 1759-1766.

侯雨雷, 汪毅, 李明洋, 曾达幸, 李慧剑. 一种含间隙两转动一移动解耦并联机构混沌现象辨识[J]. 中国机械工程, 2015, 26(13): 1759-1766.

References

[1]Aline S，Marcelo A. Comparative Analysis of Chaos Control Methods：A Mechanical System Case Study[J]. International Journal of Non-Linear Mechanics，2011，46(8)：1076-1089.
[2]王国庆，刘宏昭，何长安. 非线性接触模型在多间隙机构混沌分析中的应用[J]. 机械科学与技术，2005，24(6)：636-638.
Wang Guoqing，Liu Hongzhao，He Chang-an. Application of Nonlinear Contact Model in Chaos Analysis of a Mechanism with Clearance Joints[J]. Mechanical Science and Technology，2005，24(6)：636-638.
[3]Zukovic M，Cveticanin L. Chaos in Non-Ideal Mechanical System with Clearance[J]. Journal of Vibration and Control，2009，15 (8)：1229-1246.
[4]金国光，李东福，何颖，等. 柔性变胞机构中的混沌现象研究[J]. 天津工业大学学报，2009，28(4)：58-60，67.
Jin Guoguang，Li Dongfu，He Ying，et al. Research of Chaos of Flexible Metamorphic Mechanism[J]. Journal of Tianjin Polytechnic University，2009，28(4)：58-60，67.
[5]王三民，沈允文，董海军. 含间隙和时变啮合刚度的弧齿锥齿轮传动系统非线性振动特性研究[J]. 机械工程学报，2003，39(2)：28-32.
Wang Sanmin，Shen Yunwen，Dong Haijun. Nonlinear Dynamical Characteristics of a Spiral Bevel Gear System With Back Lash and Time-varying Stiffness[J]. Chinese Journal of Mechanical Engineering，2003，39(2)：28-32.
[6]苟向锋，吕小红，陈代林. 单级齿轮传动系统的Hopf分岔与混沌研究[J]. 中国机械工程，2014，25(5)： 679-683，691.
Gou Xiangfeng，Lü Xiaohong，Chen Dailin. Research on Hopf Bifurcation and Chaos of the Single-stage Gear Transmission System[J]. China Mechanical Engineering，2014，25(5)：679-683，691.
[7]Wolf A，Swift J B，Swinney H L，et al. Determining Lyapunov Exponents from a Time Series[J]. Physica D：Nonlinear Phenomena，1985，16(3)：285-317.
[8]Rosenstein M T，Collins J J，De Luca C J. A Practical Method for Calculating Largest Lyapunov Exponents from Small Data Sets[J]. Physica D：Nonlinear Phenomena，1993，65(1)：117-134.
[9]高峰. 机构学研究现状与发展趋势的思考[J]. 机械工程学报，2005，41(8)：3-17.
Gao Feng.Reflection on the Current Status and Development Strategy of Mechanism Research[J]. Chinese Journal of Mechanical Engineering，2005，41(8)：3-17.
[10]王庚祥，刘宏昭. 考虑球面副间隙的4-SPS/CU并联机构动力学分析[J]. 机械工程学报，2014,51(1):43-51.
Wang Gengxiang，Liu Hongzhao. Dynamics Analysis of 4-SPS/CU Parallel Mechanism with Spherical Joint Clearance[J]. Chinese Journal of Mechanical Engineering，2014，51(1):43-51.
[11]王庚祥，刘宏昭，邓培生. 考虑球面副间隙的并联机构动力学模型[J]. 振动与冲击，2014，33(10)：43-49.
Wang Gengxiang，Liu Hongzhao，Deng Peisheng. Dynamic Modeling for a Parallel Mechanism Considering Spherical Joint Clearance[J]. Journal of Vibration and Shock，2014，33(10)：43-49.
[12]Zhang Xuchong，Zhang Xianmin，Chen Zhong. Dynamic Analysis of a 3-RRR Parallel Mechanism with Multiple Clearance Joints[J]. Mechanism and Machine Theory，2014，78(8)：105-115.
[13]Shiau T N，Tsai Y J，Tsai M S. Nonlinear Dynamic Analysis of a Parallel Mechanism with Consideration of Joint Effects[J]. Mechanism and Machine Theory，2008，43(4)：491-505.
[14]窦玉超，曾达幸，李明洋，等. 一种两转动一移动完全解耦并联机器人机构及其特性分析[J]. 中国机械工程，2014，25(2)：241-245.
Dou Yuchao，Zeng Daxing，Li Mingyang，et al. Analysis of a 2T1R Fully Decoupled Parallel Robot Mechanism and Its Characteristics[J]. China Mechanical Engineering，2014，25(2)：241-245.
[15]Lankarani H M，Nikravesh P E. Continuous Contact Force Models for Impact Analysis in Multibody Systems[J]. Nonlinear Dynamics，1994，5(2)：193-207.
[16]Dubowsky S，Gardner T N. Design and Analysis of Muitilink Flexible Mechanisms with Multiple Clearance Connections[J]. Journal of Engineering for Industry，1977，99(7)：88-96.
[17]Flores P，Ambrósio J，Claro J C P，et al. Influence of the Contact-impact Force Model on the Dynamic Response of Multi-body Systems[J]. Proceedings of the Institution of Mechanical Engineers，Part K：Journal of Multi-body Dynamics，2006，220(1)：21-34.
[18]Ambrósio J. Impact of Rigid and Flexible Multibody Systems: Deformation Description and Contact Models[J]. Virtual Nonlinear Multibody Systems， 2003，103：57-81.
[19]陈予恕. 非线性振动系统的分叉和混沌理论[M]. 北京：高等教育出版社，1993.
[20]龚祝平. 混沌时间序列的平均周期计算方法[J]. 系统工程，2010，28(12)：111-113.
Gong Zhuping. The Calculating Method of the Average Period of Chaotic Time Series[J]. Systems Engineering，2010，28(12)：111-113.
[21]吕金虎，陆君安，陈士华. 混沌时间序列分析及其应用[M]. 武汉：武汉大学出版社，2005.