两自由度减振镗杆系统的安全盆侵蚀与分岔

PDF(1757 KB)

振动与冲击 ›› 2018, Vol. 37 ›› Issue (22) : 238-244.

论文

两自由度减振镗杆系统的安全盆侵蚀与分岔

石建飞1，苟向锋1,2, 张艳龙1

作者信息 +

Erosion and bifurcation of the safe basin of a two-degree-of-freedom damping boring bar system

SHI Jianfei1,2， GOU Xiangfeng1,2， ZHANG Yanlong2

Author information +

文章历史 +

摘要

建立了考虑橡胶圈和阻尼液非线性因素的两自由度减振镗杆系统的动力学模型，研究了系统的安全盆侵蚀与分岔过程。用数值方法得到初值对系统安全性的影响以及系统参数对安全盆侵蚀演变的影响。在一定的参数条件下，系统安全盆出现了边界分形侵蚀和边界光滑侵蚀两种不同的侵蚀过程。根据系统安全盆在侵蚀过程中的最大Lyapunov指数分析了安全盆边界分形侵蚀与边界光滑侵蚀的区别。结果表明，当安全盆出现边界分形侵蚀时，其相应最大Lyapunov指数大于零，系统出现混沌运动；而当安全盆出现边界光滑侵蚀时，其相应最大Lyapunov指数始终小于零，系统在安全盆侵蚀过程中并没有出现混沌运动，只是振动幅值增大并跳出安全区域。研究结果对减振镗杆系统的参数选择具有一定的指导意义。

Abstract

The dynamic model of a two-degree-of-freedom damping boring bar system was established considering the nonlinear factors of rubber ring and damping fluid.The erosion of the safe basin and bifurcation process of the system were studied.The influences of initial values on the system security and the evolution of the system parameters during the safe basin erosion were examined by numerical methods.Under the condition of certain parameters, two kinds of erosion processes of the safe basin mamely the fractal boundary erosion and smooth bound-ary erosion would occur in the system.The difference between the fractal boundary erosion and smooth boundary erosion was analyzed by the Top Lyapunov Exponent of the system during the erosion process of the safe basin.The results show that the Top Lyapunov Exponent of system will be more than zero, and the chaotic motion of the system will occur when the fractal boundary erosion appears.When the smooth boundary erosion appears, the corresponding Top Lyapunov Exponent will be always less than zero, and the chaotic motion of the system does not occur in the process of the safe basin erosion, however, the amplitude of the system vibration will increase and finally jump out of the safe area.The results are helpful to select the system parameters.

导出引用

石建飞1，苟向锋1,2,张艳龙1. 两自由度减振镗杆系统的安全盆侵蚀与分岔[J]. 振动与冲击, 2018, 37(22): 238-244

SHI Jianfei1,2， GOU Xiangfeng1,2， ZHANG Yanlong2. Erosion and bifurcation of the safe basin of a two-degree-of-freedom damping boring bar system[J]. Journal of Vibration and Shock, 2018, 37(22): 238-244

参考文献

[1] ANDREN I, Hakansson I. Identification of motion of cutting tool vibration in a continous boring operation correlation to structural properties[J]. Machining Science and Technology, 2004, 18(4): 903-927.
[2] ANDREN I. Identification of dynamic properties of boring bar vibrations in a continuous boring operation[J]. Mechanical systems and Signal Processing, 2004 , 18(4) :869-901.
[3] MEI C . A etive regenerative chatter suppression during boring manufacturing Process. Robotics and Computer Integrated Manufacturing[J].2005,21 (2): 153-158.
[4] Edhi E, Hoshi T. Stabilization of High Frequency Chatter Vibration in Fine Boring by Friction Damper[J]. Precision Engineering, 2001(25)：224-234.
[5] 罗红波,李红梅,程宏伟等. 内置式减振镗杆动力学模型的参数优化[J]. 四川大学学报(工程科学版),2009,41(6):200-204.
LUO Hong-bo, LI Hong-mei, CHENG Hong-wei etc. Parameter optimization of built in damping boring bar kinetic model[J]. Journal of Sichuan University,2009,41(6):200-204.
[6] 赵永成,马飞，闫长罡等. 精镗孔时液膜阻尼减振效果的研究[J].中国机械工程，13(21):1827-1855.
ZHAO Yongcheng, Ma Fei, YAN Changgang, etc. Research on Effect of Decreasing Vibration with Liquid Film Damping in Precise Boring[J]. China Mechanical Engineering, 2002, 13(21) :1827-1829
[7] 秦柏．阻尼动力减振镗杆动态特性仿真与优化设计研究 [D]．黑龙江：哈尔滨理工大学博士学位论文．2009.6
Qin Bai. Study on Dynamic Characteristics Simulation and Optimization Design of Dynamical Vibration Absorption Boring Bar with Damping[D]. Harbin University of Science and Technology. 2009.6
[8] 夏峰,刘战强,宋清华. 约束阻尼型减振镗杆[J]. 航空学报,2014,35(9)：2652-2659.
XIA Feng, LIU Zhanqiang, SONG Qinghua. Boring Bar with Constrained Damping[J]. Acta Aeronautica ET Astronautica Sinica, 2014,35(9)：2652-2659.
[9] 刘立佳,刘献礼,许成阳等. 减振镗杆振动控制研究综述[J]. 哈尔滨理工大学学报,2014,19(2):12-17.
LIU Li-jia, LIU Xian-li, XU Cheng-yang etc. Preview of Damping Boring Bar Vibration Control[J]. Journal of Harbin University of Science and Technology,2014,19(2):12-17.
[10] NAYFEH A H, SANCHEZ N E. Bifurcation in a softening Duffing oscillator[J]. International Journal of Nonlinear Mechanics, 1989,24: 483-497.
[11] SOLIMAN M S. Fractal erosion of basins of attraction in coupled non-linear systems[J]. Journal of Sound and Vibration, 1995,182(5): 729-740.
[12] Yongxiang Zhang, Guanwei Luo. Wada basin boundaries in a two-dimensional cubic map[J]. Physics Letters A, 2013,377:1274-1281.
[13] 戎海武,王向东,徐伟等. 谐和与噪声联合作用下Duffing振子的安全盆分叉与混沌[J]. 物理学报,2007,56(4):2005-2011.
[14] SHANG Hui-Lin. Control of Fractal Erosion of Safe Basins in a Holme-Duffing System via Delayed Position Feedback [J]. CHIN. PHYS.LETT,2011, 28(1): 010502.
[15] 葛根,竺致文,许佳. 形状记忆合金梁在简谐和白噪声联合激励下的混沌及安全盆侵蚀现象[J]. 振动与冲击, 2012, 31(23): 1-11.
GE Gen, ZHU Zhi-wen, XU Jia. Chaos and fractal boundary of safe basin of a shape memory alloy beam subjected to simple harmonic and white noise excitations[J]. Journal of Vibration and Shock, 2012, 31(23): 1-11.
[16] 邵俊鹏，秦柏. 基于ADAMS的动力减振镗杆仿真分析[J]. 机械设计与研究,2008,24(1): 84-88.
Shao Junpeng, Qin Bai. Simulation analysis of dynamical vibration boring bar based on ADAMS[J]. Mechanical Design and Research,2008,24(1): 84-88.
[17] 王靖岳,王浩天,张有强. 用小波函数控制汽车非线性悬架系统中的混沌[J].机械科学与技术，2010, 29(7):953-961.
Wang J Y, Wang H T, Zhang Y Q. Chaos Control of a Vehicle Nonlinear Suspension System by Wavelet Function[J]. Mechanical Science and Technology for Aerospace Engineering, 2008,24(1): 84-88.
[18] 毕凤荣,勾新刚,吴华杰. 减振器非线性阻尼对车身振动的影响分析[J]. 振动工程学报, 2002, 15(2):155-161.
Bi Fengrong, Gou Xingang, Wu Huajie. Influence of Nonlinear Damping of Shock Absorber on Vibration of Automobile Body[J]. Journal of Vibration Engineering, 2002, 15(2):155-161.
[19] 杨绍普,申永军. 滞后非线性系统的分岔与奇异性[M]. 北京：科学出版社，2003
Yang S P, Shen Y J. Bifurcation and singularity of hysteretic nonlinear systems[M]. science press, 2003, 10-
[20] 戎海武,王向东,徐伟. 有界随机噪声激励下软弹簧Duffing振子的安全盆分叉[J]. 物理学报,2005,54(10):4610-4613.
Rong Hai-Wu, Wang Xiang-Dong, Xu Wei etc. Bifurcation of safe basins in softening duffing oscillator under bounded noise excitation[J]. ACTA PHYSICA SINICA,54(10):4610-4613.
[21] Tatlier. Fractal dimension of zeolite surfaces by calculation[J]. Chaos, Solitons and Fractals, 2001,12(6):1145-1155.
[22] 尚慧琳.时滞位移反馈对Helmholtz振子系统的分形侵蚀安全域的控制[J]. 物理学报,2011,60(7):4610-4613.
Shang Hui-Lin. Controlling fractal erosion of safe basins in a Helmholtz oscillator by delayed position feedback[J]. ACTA PHYSICA SINICA, 2011,60(7):61-67.