Journal of Jilin University(Engineering and Technology Edition) ›› 2023, Vol. 53 ›› Issue (2): 364-375.doi: 10.13229/j.cnki.jdxbgxb20220644

Previous Articles     Next Articles

Dynamic stability analysis of a amplitude⁃limited vibration system with multiple rigid constraints

Yan YANG1,2(),Yu-qing SHI1,2,Xiao-rong ZHANG2,Guan-wei LUO2   

  1. 1.School of Mechatronic Engineering，Lanzhou Jiaotong University，Lanzhou 730070，China
    2.Gansu Provincial Key Laboratory of System Dynamics and Reliability of Rail Transport Equipment，Lanzhou 730070，China
  • Received:2022-05-25 Online:2023-02-01 Published:2023-02-28

RICH HTML

 1   

PDF (PC)

95

Abstract:

The mechanical model of a two-degree-of-freedom amplitude-limited vibration system with multiple rigid constraints is established. Combined with the periodic and impact Poincaré mapping， the pattern types of periodic impact motions and their occurrence domains are identified in a two-parameter system. With the irreversible mutual transition of adjacent one-periodic impact motions， there are a series of singularities， hysteresis and tongue-shaped transition domains on the critical line of the distribution domains. Based on the sampling range of dynamic parameter， the dynamic response of the vibration system under extreme mass distribution conditions is analyzed. The simulation results show that the non-smooth bifurcation behaviors such as Grazing bifurcation and Sliding bifurcation leads to the one-periodic impact motion sequence transits to incomplete and complete chattering-impact motions. Excessive energy loss in instantaneous impact leads to sticking phenomenon， which changes the original structure of the vibration system and reduces the degree of freedom of the system. Due to the simultaneous action of complete chattering-impact at multiple rigid constraints， the transient static state appears in extreme control parameter domain.

Key words: mechanical design, amplitude-limited vibration, bifurcation, transition domain, chattering-impact

CLC Number: 

  • TH113.1

Fig.1

Limiting vibration system with multiple rigid constraints"

Fig.2

Modes and distribution domains of periodic-impact motions in the （ω，δ）parameter system"

Fig.3

Descriptions about transition domains between adjacent p/1 and （p+1）/1 period 1 motions"

Fig.4

One-parameter bifurcations of the tongue-shaped domain between adjacent 4/1 and 3/1 motions， δ=0.3"

Fig.5

Phase plane portraits and Poincaré mapping diagrams of mass blocks M1， δ=0.3"

Fig.6

Modes and distribution domains of periodic motions in the （ω，δ） parameter system when μm =0.05"

Fig.7

Chattering impact bifurcation at constraint A2A3， μm =0.05， ω=1.5"

Fig.8

Time trajectories of chattering impact motions， μm =0.05， ω=1.5"

1 Wan Qi, Liu Geng, Song Chun-yu, et al. Study on the dynamic interaction of multiple clearance joints for flap actuation system with a modified contact force model[J]. Journal of Mechanical Science and Technology, 2020, 34(7): 2701-2713.
2 张树培,夏明悦,张玮,等. 考虑非线性刚度的间隙球铰碰撞动力学建模与仿真[J/OL]. [2022-02-07].
3 张发军,张烽,宋钰青,等. 铰碰与臂重激振下串联机械臂参数的抑振优化[J]. 哈尔滨工程大学学报, 2019, 40(5): 1000-1005.
Zhang Fa-jun, Zhang Feng, Song Yu-qing, et al. Parameters optimization based on vibration suppression of manipulator undergoing internal collision of hinges and heavy vibration of arms[J]. Journal of Harbin Engineering University, 2019, 40(5): 1000-1005.
4 Alok S, Chaudhary K, Guha A. A study on critical order of joints with clearances and its effect on kinematic performance of multiloop planar mechanisms[J]. Sadhana-Academy Proceedings In Engineering Sciences, 2020, 45(1): 126.
5 Jiang S, Chen X L. Reducing undesirable effects of clearances on dynamic and wear of planar multi-link mechanism[J]. Nonlinear Dynamics, 2020, 100(3): 1-29.
6 Shin D, Palazzolo A. Nonlinear analysis of a geared rotor system supported by fluid film journal bearings[J]. Journal of Sound and Vibration, 2020, 475: 115269.
7 林何,屈文宽, Rätsch Matthias,等. 齿轮-轴承系统非线性振动混沌吸引子周期轨道控制[J]. 振动与冲击, 2020, 39(13): 1-6, 15.
Lin He, Qu Wen-kuan, Rätsch Matthias, et al. Periodic orbit control of nonlinear vibration chaotic attractors of a gear-bearing system[J]. Journal of Vibration and Shock, 2020, 39(13): 1-6, 15.
8 石怀龙,郭金莹,王勇. 变轨距高速列车的动力学[J]. 机械工程学报, 2020, 56(20): 98-105.
Shi Huai-long, Guo Jin-ying, Wang Yong. Dynamic performance of high-speed gauge-changeable railway vehicle[J]. Journal of Mechanical Engineering, 2020, 56(20): 98-105.
9 Lv Xiao-hong, Gao Quan-fu, Luo Guan-wei. Dynamic characteristics of a mechanical impact oscillator with a clearance[J]. International Journal of Mechanical Sciences, 2020, 178: 105605.
10 申永康,殷珊,徐慧东,等. 碰撞振动系统不连续擦边分岔的线性反馈控制[J]. 应用力学学报, 2018, 35(4): 688-693.
Shen Yong-kang, Yin Shan, Xu Hui-dong, et al.Linear feedback control of the discontinuous grazing bifurcation in a vibro-impact system[J]. Chinese Journal of Applied Mechanics, 2018, 35(4): 688-693.
11 Wei Dao-gao, Wang Wei-jia, Wang Bo, et al. Bifurcation and chaotic behaviors of vehicle brake system under low speed braking condition[J]. Journal of Vibration Engineering and Technologies, 2021, 9(8):2107-2120.
12 Thi H L, Junca S, Legrand M. Periodic solutions of a two-degree-of-freedom autonomous vibro-impact oscillator with sticking phases[J]. Nonlinear Analysis-Hybrid Systems, 2018, 28: 54-74.
13 Alzate R, Piiroinen P T, Bernardo M D. From complete to incomplete chattering: a novel route to chaos in impacting cam-follower systems[J]. International Journal of Bifurcation and Chaos, 2012, 22(5): 1250102.
14 Hős C, Champneys A R. Grazing bifurcations and chatter in a pressure relief valve model[J]. Physica D: Nonlinear Phenomena, 2012, 241(22): 2068-2076.
15 Baranyai T, Várkonyi P L. Zeno chattering of rigid bodies with multiple point contacts[J]. Nonlinear Dynamics, 2017, 92(4): 1857-1879.
16 Costa D, Vaziri V, Kapitaniak M, et al. Chaos in impact oscillators not in vain: dynamics of new mass excited oscillator[J]. Nonlinear Dynamics, 2020, 102: 835-861.
17 王锐,田晓超,杨志刚,等. 压电低频旋转驱动器的设计与实验[J]. 吉林大学学报: 工学版, 2020, 50(4): 1283-1287.
Wang Rui, Tian Xiao-chao, Yang Zhi-gang, et al. Design and experimental of piezoelectric low-frequency driven rotary actuator[J]. Journal of Jilin University(Engineering and Technology Edition), 2020, 50(4): 1283-1287.
18 Oruganti P S, Krak M D, Singh R. Step responses of a torsional system with multiple clearances: Study of vibro-impact phenomenon using experimental and computational methods[J]. Mechanical Systems and Signal Processing, 2018, 99: 83-106.
19 Liu Y, Chávez P J, Guo B Y, et al. Bifurcation analysis of a vibro-impact experimental rig with two-sided constraint[J]. Meccanica, 2020, 55: 2505-2521.
20 Dumanli A, Sencer B. Active control of high frequency chatter with machine tool feed drives in turning[J]. CIRP Annals-Manufacturing Technology, 2021, 70(1): 309-312.
21 陈云,侯亮,刘文志,等.基于时域仿真法的断续铣削颤振预测[J]. 机械工程学报, 2021, 57(3): 98-106.
Chen Yun, Hou Liang, Liu Wen-zhi, et al. Chatter stability prediction in low immersion milling based on time-domain simulation[J]. Journal of Mechanical Engineering, 2021, 57(3): 98-106.
22 Luo G W, Lv X H, Shi Y Q. Vibro-impact dynamics of a two-degree-of freedom periodically-forced system with a clearance: diversity and parameter matching of periodic-impact motions[J]. International Journal of Non-Linear Mechanics,2014,65:173-195.
[1] Yang LIU. Unloading impact simulation and test of luffing jib tower crane [J]. Journal of Jilin University(Engineering and Technology Edition), 2022, 52(6): 1292-1300.
[2] Ya-bing CHENG,Lu-xiang CHEN,Ping-yu GE,Ze-yu YANG,Peng-yu CAO. Dynamic simulation analysis and wear failure of dual-phase timing bush chain [J]. Journal of Jilin University(Engineering and Technology Edition), 2022, 52(4): 781-788.
[3] Yang ZHAO,Yang XIAO,Hao SUN,Wen-hao HUO,Song FENG,Yong LIAO. Numerical simulation of micro pitting damage characteristics of lubricated contact gears based on contour integral [J]. Journal of Jilin University(Engineering and Technology Edition), 2022, 52(4): 799-810.
[4] Long ZHANG,Tian-peng XU,Chao-bing WANG,Jian-yu YI,Can-zhuang ZHEN. Gearbox fault diagnosis baed on convolutional gated recurrent network [J]. Journal of Jilin University(Engineering and Technology Edition), 2022, 52(2): 368-376.
[5] Wei ZHENG,Jian-jun SUN,Chen-bo MA,Qiu-ping YU,Yu-yan ZHANG,Tao NIU. Research status and prospect of automobile wheel hub machining fixture [J]. Journal of Jilin University(Engineering and Technology Edition), 2022, 52(1): 25-36.
[6] Xiao-chao TIAN,Hai-gang WANG,Hu WANG,Zhi-cong WANG,Jian ZHAO,Zhi-gang YANG,Yue WU. Design and test of broadband power generation device with cantilever piezoelectric vibrator [J]. Journal of Jilin University(Engineering and Technology Edition), 2021, 51(6): 1953-1958.
[7] Wei CHEN,Yu-long LEI,Xing-zhong LI,Yao FU,Jian-long HU,Li-guo HOU. Calculation of adhesive wear of involute cylindrical spur gear under low⁃speed conditions [J]. Journal of Jilin University(Engineering and Technology Edition), 2021, 51(5): 1628-1634.
[8] Jing HU,Cong LI,Bang-cheng ZHANG,Xiao-li QIAO,Xin-ming ZHANG,Xiao-ping ZHOU. Oil film stiffness and damping of double⁃decker ball bearing in consideration of centrifugal expansion [J]. Journal of Jilin University(Engineering and Technology Edition), 2021, 51(5): 1601-1611.
[9] Zong-wei YAO,Xu-dong GAO,Gang LIU,Qiu-shi BI. Research on working performance of vertical screw stirring mill based on numerical simulations [J]. Journal of Jilin University(Engineering and Technology Edition), 2021, 51(5): 1642-1650.
[10] Xiao-tao LI,Jin-peng REN,Xiao-xu LI,Hang YANG. Mechanism of a linear actuator driven by dual piezoelectric oscillators in inverse mode [J]. Journal of Jilin University(Engineering and Technology Edition), 2021, 51(2): 468-471.
[11] Gong CHENG,Ke XIAO,Jia-xu WANG,Wei PU,Yan-feng HAN. Gear contact stiffness under mixed lubrication status [J]. Journal of Jilin University(Engineering and Technology Edition), 2020, 50(2): 494-503.
[12] Yan MAO,Kai CHENG. Telescoping path optimization of a single-cylinder pin⁃type multi⁃section boom based on Hopfield neural network [J]. Journal of Jilin University(Engineering and Technology Edition), 2020, 50(1): 53-65.
[13] Zhen GUO,Hong-ying YU,Zhong-xin HUA,Di ZHAO. Kinematic analysis and simulation of folding process for rigid origami mechanisms [J]. Journal of Jilin University(Engineering and Technology Edition), 2020, 50(1): 66-76.
[14] Fu-chun JIA,Xian-jie MENG,Yu-long LEI. Optimal design of two degrees of freedom dynamic vibration absorber based on multi-objective genetic algorithm [J]. Journal of Jilin University(Engineering and Technology Edition), 2019, 49(6): 1969-1976.
[15] Zhi-jiang XIE,Kun WANG,Yang-jun PI,Xiao-yong WU,Ying-wei GUO. Novel method for forward kinematics of 6⁃PSSparallel manipulator [J]. Journal of Jilin University(Engineering and Technology Edition), 2019, 49(6): 1977-1985.
Viewed
Full text


Abstract

Cited
  Shared   
  Discussed   
[1] LI Shoutao, LI Yuanchun. Autonomous Mobile Robot Control Algorithm Based on Hierarchical Fuzzy Behaviors in Unknown Environments[J]. 吉林大学学报(工学版), 2005, 35(04): 391 -397 .
[2] Li Hong-ying; Shi Wei-guang;Gan Shu-cai. Electromagnetic properties and microwave absorbing property
of Z type hexaferrite Ba3-xLaxCo2Fe24O41[J]. 吉林大学学报(工学版), 2006, 36(06): 856 -0860 .
[3] Zhang Quan-fa，Li Ming-zhe，Sun Gang，Ge Xin . Comparison between flexible and rigid blank-holding in multi-point forming[J]. 吉林大学学报(工学版), 2007, 37(01): 25 -30 .
[4] Yang Shu-kai, Song Chuan-xue, An Xiao-juan, Cai Zhang-lin . Analyzing effects of suspension bushing elasticity
on vehicle yaw response character with virtual prototype method[J]. 吉林大学学报(工学版), 2007, 37(05): 994 -0999 .
[5] . [J]. 吉林大学学报(工学版), 2007, 37(06): 1284 -1287 .
[6] Liu Han-bing, Jiao Yu-ling, Liang Chun-yu,Qin Wei-jun . Effect of shape function on computing precision in meshless methods[J]. 吉林大学学报(工学版), 2007, 37(03): 715 -0720 .
[7] Yang Qing-fang, Chen Lin . Division approach of traffic control work zone[J]. 吉林大学学报(工学版), 2006, 36(增刊2): 139 -142 .
[8] Li Yue-ying，Liu Yong-bing，Chen Hua . Surface hardening and tribological properties of a cam materials[J]. 吉林大学学报(工学版), 2007, 37(05): 1064 -1068 .
[9] Zhang He-sheng, Zhang Yi, Wen Hui-min, Hu Dong-cheng . Estimation approaches of average link travel time using GPS data[J]. 吉林大学学报(工学版), 2007, 37(03): 533 -0537 .
[10] Qu Zhao-wei，Chen Hong-yan，Li Zhi-hui，Hu Hong-yu，Wei Wei . 2D view reconstruction method based on single calibration pattern
[J]. 吉林大学学报(工学版), 2007, 37(05): 1159 -1163 .
Copyright © Journal of Jilin University(Engineering and Technology Edition), All Rights Reserved.
Tel: +86-431-85095297　Fax: +86-431-85094074　E-mail: xbgxb@jlu.edu.cn
Powered by Beijing Magtech Co. Ltd