DYNAMICAL ANALYSIS ON A KIND OF SEMI-ACTIVE VIBRATION ISOLATION SYSTEMS WITH DAMPING CONTROL 1)

doi:10.6052/0459-1879-20-147

Abstract

Abstract:

A series of single-degree-of-freedom semi-active nonlinear vibration isolation system with cubic stiffness based on relative velocity feedback on-off control is studied. By using the averaging method, the approximate analytical solutions of the primary resonance of the system are obtained, which is controlled by the acceleration and relative velocity based acceleration drive damping control, the velocity and relative velocity based sky-hook damping control, and the displacement and relative velocity based ground-hook damping control, respectively. A further comparison between the numerical solutions and the approximate analytical solutions under different control strategies is fulfilled. And such comparison results suggest that the approximate analytical results are quite consistent with the numerical solutions, which verifies the effectiveness of the approximate analytical solutions. Moreover, the stability conditions of the steady-state solution of the system under different control strategies are analyzed by Lyapunov theory, and the influences of system parameters on the control effect are discussed. In order to compare the control performances in the three different control approaches, the amplitude-frequency response equation is conducted. The results show that the similar expressions can be found in the switching conditions in the process of the analytical analysis of the three relative velocity feedback control strategies. In the aspect of suppressing resonance response amplitude, the sky-hook damping control strategy based on velocity and relative velocity feedback has the best damping effect in low frequency band, while the acceleration drive damping control strategy based on acceleration and relative velocity feedback has the best damping effect in high frequency band. The sky-hook damping control strategy also shows good performance in reducing the amplitude response of transient response. This analytical research method can also be applied to the system with other semi-active on-off control strategies, and it provides an effective way for the control strategy research of semi-active vibration isolation system.

Key words: vibration isolation system, semi-active control, primary resonance, averaging method, approximate analytical solution

CLC Number:

O322
O328

Zhang Wanjie, Niu Jiangchuan, Shen Yongjun, Yang Shaopu, Wang Li. DYNAMICAL ANALYSIS ON A KIND OF SEMI-ACTIVE VIBRATION ISOLATION SYSTEMS WITH DAMPING CONTROL ¹⁾[J]. Chinese Journal of Theoretical and Applied Mechanics, 2020, 52(6): 1743-1754.

Figures/Tables 14

Fig. 1 Model of a single-degree-of-freedom semi-active vibration isolation system

Fig. 2 Amplitude-frequency response with acceleration driven damper control ($c_{on} =1500 $N$\cdot$s/m, $c_{off} =50$ N$\cdot$s/m, $A =0.06$ m)

Fig. 3 Amplitude-frequency response with sky-hook control ($c_{on} =1000 $N$\cdot$s/m, $c_{off} =50$ N$\cdot$s/m, $A =0.05$ m)

Fig. 4 Amplitude-frequency response with ground-hook control ($c_{on} =1000 $N$\cdot$s/m, $c_{off} =50$ N$\cdot$s/m, $A =0.04$ m)

Fig. 5 Amplitude-frequency responses with different $c_{on}$

Fig. 6 Amplitude-frequency responses with different $c_{off}$

Fig. 7 Amplitude-frequency responses with different $A$

Fig. 8 Amplitude-frequency responses with different control approaches

Fig. 9 Time history of relative displacement

Fig. 10 Time history of relative acceleration

Fig. 11 Phase-portrait of sprung mass

Fig. 12 Road roughness of D grade

Fig. 13 Time history of stochastic relative displacement responses

Table 1 RMS values of relative displacement and acceleration

References 41

[1]	刘兴天, 陈树海, 王嘉登等. 几何非线性摩擦阻尼隔振系统动力学行为研究. 力学学报, 2019,51(2):371-379
	( Liu Xingtian, Chen Shuhai, Wang Jiadeng, et al. Analysis of the dynamic behavior and performance of a vibration isolation system with geometric nonlinear friction damping. Chinese Journal of Theoretical and Applied Mechanics, 2019,51(2):371-379 (in Chinese))
[2]	陆泽琦, 陈立群. 非线性被动隔振的若干进展. 力学学报, 2017,49(3):550-564
	( Lu Zeqi, Chen Liqun, Some recent progresses in nonlinear passive isolations of vibrations. Chinese Journal of Theoretical and Applied Mechanics, 2017,49(3):550-564 (in Chinese))
[3]	Fu B, Giossi RL, Persson R, et al. Active suspension in railway vehicles: a literature survey. Railway Engineering Science, 2020,28(1):3-35 DOI URL
[4]	朱雅辉, 翁泽宇, 耿超等. 半主动控制浮筏隔振系统的开关算法与仿真研究. 机电工程, 2016,33(3):265-270
	( Zhu Yahui, Weng Zeyu, Geng Chao, et al, Switching algorithms and simulation research on semi-active control of floating raft vibration isolation system. Journal of Mechanical & Electrical Engineering, 2016,33(3):265-270 (in Chinese))
[5]	Savaresi SM, Poussot-Vassal C, Spelta C, et al. Semi-active suspension control design for vehicles. Butterworth-Heinemann Publications, 2010
[6]	高雪, 陈前, 刘先斌. 一类分段光滑隔振系统的非线性动力学设计方法. 力学学报, 2016,48(1):192-200
	( Gao Xue, Chen Qian, Liu Xianbin, Nonlinear dynamics design for piecewise smooth vibration isolation system. Chinese Journal of Theoretical and Applied Mechanics, 2016,48(1):192-200 (in Chinese))
[7]	La VD. Semi-active on-off damping control of a dynamic vibration absorber using Coriolis force. Journal of Sound and Vibration, 2012,331(15):3429-3436 DOI URL
[8]	Karnopp D, Crosby MJ, Harwood RA. Vibration control using semi-active force generators. Journal of Engineering for Industry, 1974,96(2):619-626
[9]	Margolis DL, Tylee JL, Hrovat D. Heave mode dynamics of a tracked air cushion vehicle with semiactive airbag secondary suspension. Journal of Dynamic Systems,Measurement, and Control, 1975: 399-407
[10]	Margolis DL. A procedure for comparing passive, active, and semi-active approaches to vibration isolation. Journal of the Franklin Institute, 1983: 225-238
[11]	ValÁŠEk M, NovÁK M, ŠIka Z, et al. Extended ground-hook - new concept of semi-active control of truck's suspension. Vehicle System Dynamics, 1997,27(5-6):289-303
[12]	Sergio MS, Silani E, Bittanti S. Acceleration-driven-damper (ADD)-An optimal control algorithm for comfort-oriented semiactive suspensions. Transactions of the ASME, 2005,127:218-229
[13]	Savaresi SM, Spelta C. Mixed sky-hook and ADD-Approaching the filtering limits of a semi-active suspension. Journal of Dynamic Systems, Measurement, and Control, 2007,129:382-392 DOI URL
[14]	Savaresi SM, Spelta C. Mix-1-sensor: A control strategy for semi-active suspension. IFAC Proceedings Volumes, 2007,40(10):367-374
[15]	Morselli R, Zanasi R. Control of port Hamiltonian systems by dissipative devices and its application to improve the semi-active suspension behaviour. Mechatronics, 2008,18(7):364-369 DOI URL
[16]	Nirala CK, Kumar RP. A new semi-active suspension system based on Jerk Driven Damper (JDD) Control// Proceedings of the International Conference on Computational Methods in Manufacturing (ICCMM 2011), 2011: 562-568
[17]	Poussot-Vassal C, Spelta C, Sename O, et al. Survey and performance evaluation on some automotive semi-active suspension control methods: A comparative study on a single-corner model. Annual Reviews in Control, 2012,36(1):148-160 DOI URL
[18]	Shen Y, Wang L, Yang S, et al. Nonlinear dynamical analysis and parameters optimization of four semi-active on-off dynamic vibration absorbers. Journal of Vibration and Control, 2012,19(1):143-160 DOI URL
[19]	Díaz IM, Reynolds P. On-off nonlinear active control of floor vibrations. Mechanical Systems and Signal Processing, 2010,24(6):1711-1726 DOI URL
[20]	Eslaminasab N, Vahid AO, Golnaraghi F. Nonlinear analysis of switched semi-active controlled systems. Vehicle System Dynamics, 2011,49(1-2):291-309 DOI URL
[21]	申永军, 杨绍普, 陈恩利等. 一类半主动控制非线性系统的动力学分析. 振动工程学报, 2005,18(2):219-222
	( Shen Yongjun, Yang Shaopu, Chen Enli, et al. Dynamic analysis of a nonlinear system under semi-active control. Journal of Vibration Engineering, 2005,18(2):219-222 (in Chinese))
[22]	申永军, 祁玉玲, 杨绍普等. 含时滞的单自由度半主动悬架系统的动力学分析. 振动与冲击, 2012,31(24):38-40
	( Shen Yongjun, Qi Yuling, Yang Shaopu, et al, Dynamic analysis of a SDOF semi-active suspension system with time-delay, Journal of Vibration and Shock, 2012,31(24):38-40 (in Chinese))
[23]	申永军, 赵永香, 田佳雨等. 一类含时滞的半主动悬架系统的动力学分析. 力学学报, 2013,45(5):756-762
	( Shen Yongjun, Zhao Yongxiang, Tian Jiayu, et al, Dynamical analysis on a kind of semi-active suspension with time delay, Chinese Journal of Theoretical and Applied Mechanics, 2013,45(5):756-762 (in Chinese))
[24]	申永军, 田佳雨, 赵永香等. 含时滞半主动天棚悬架系统的解析研究. 振动、测试与诊断, 2014,34(6):1110-1117
	( Shen Yongjun, Tian Jiayu, Zhao Yongxiang, et al. Analytical study on semi-active skyhook suspension with time delay, Journal of Vibration, Measurement & Diagnosis, 2014,34(6):1110-1117 (in Chinese))
[25]	Yu H, Sun X, Xu J, et al. The time-delay coupling nonlinear effect in sky-hook control of vibration isolation systems using Magneto-Rheological Fluid dampers. Journal of Mechanical Science and Technology, 2016,30(9):4157-4166 DOI URL
[26]	Fischer D, Isermann R. Mechatronic semi-active and active vehicle suspensions. Control Engineering Practice, 2004,12(11):1353-1367 DOI URL
[27]	王昊, 胡海岩. 基于磁流变阻尼器整车半主动悬架的开关控制. 动力学与控制学报, 2004,2(4):71-76
	( Wang Hao, Hu Haiyan. The on-off control of a semi-active suspension of the full-vehicle model based on MR dampers, Journal of Dynamics and Control, 2004,2(4):71-76 (in Chinese))
[28]	Kim HS, Chang C, Kang JW. Control performance evaluation of semi-active tmd subjected to various types of loads. International Journal of Steel Structures, 2015,15(3):581-594
[29]	Dong X, Yu M, Liao C, et al. Comparative research on semi-active control strategies for~magneto-rheological suspension. Nonlinear Dynamics, 2010,59(3):433-453
[30]	Sun X, Xu J, Fu J. The effect and design of time delay in feedback control for a nonlinear isolation system. Mechanical Systems and Signal Processing, 2017,87:206-217
[31]	胡海岩. 应用非线性动力学. 北京: 航空工业出版社, 2000: 48-51
	( Hu Haiyan. Applied Nonlinear Dynamics. Beijing: Aviation Industry Press, 2000: 48-51(in Chinese))
[32]	Li S, Yang S, Guo W. Investigation on chaotic motion in hysteretic non-linear suspension system with multi-frequency excitations. Mechanics Research Communications, 2004,31(2):229-236
[33]	张洪欣. 汽车系统动力学. 上海: 同济大学出版社, 1996: 126-140
	( Zhang Hongxin. Automobile System Dynamics. Shanghai: Tongji University Publishing House, 1996: 126-140(in Chinese))
[34]	Wang W, Song Y. Analytical computation method for steady-state stochastic response of a time-delay nonlinear automotive suspension system. Mechanical Systems and Signal Processing, 2019,131:434-445
[35]	Xu Y, Liu Q, Guo G, et al. Dynamical responses of airfoil models with harmonic excitation under uncertain disturbance. Nonlinear Dynamics, 2017,89:1579-1590
[36]	Liu Q, Xu Y, Kurths J. Bistability and stochastic jumps in an airfoil system with viscoelastic material property and random fluctuations. Commun Nonlinear Sci Numer Simulat, 2020,84:105184
[37]	刘俊, 陈林聪, 孙建桥. 随机激励下滞迟系统的稳态响应闭合解. 力学学报, 2017,49(3):685-692
	( Liu Jun, Chen Lincong, Sun Jianqiao. The closed-form solution of steady state response of hysteretic system under stochastic excitation. Chinese Journal of Theoretical and Applied Mechanics, 2017,49(3):685-692 (in Chinese))
[38]	公徐路, 许鹏飞. 含时滞反馈与涨落质量的记忆阻尼系统的随机共振. 力学学报, 2018,50(4):880-889
	( Gong Xulu, Xu Pengfei. Stochastic resonance of a memorial-damped system with time delay feedback and fluctuating mass. Chinese Journal of Theoretical and Applied Mechanics, 2018,50(4):880-889 (in Chinese))
[39]	邢昭阳, 申永军, 邢海军等. 一种含放大机构的负刚度动力吸振器的参数优化. 力学学报, 2019,51(3):894-903
	( Xing Zhaoyang, Shen Yongjun, Xing Haijun, et al. Parameters optimization of a dynamic vibration absorber with amplifying mechanism and negative stiffness. Chinese Journal of Theoretical and Applied Mechanics, 2019,51(3):894-903 (in Chinese))
[40]	刘献栋, 邓志党, 高峰. 公路路面不平度的数值模拟方法研究. 北京航空航天大学学报, 2003,29(9):843-846
	( Liu Xiandong, Deng Zhidang, Gao Feng. Research on the method of simulating road roughness numerically. Journal of Beijing University of Aeronautics and Astronautics, 2003,29(9):843-846 (in Chinese))
[41]	ISO 2631-1: 1997 (E). Mechanical vibration and shock-evaluation of human exposure to whole-body vibration. 1997

DYNAMICAL ANALYSIS ON A KIND OF SEMI-ACTIVE VIBRATION ISOLATION SYSTEMS WITH DAMPING CONTROL ¹⁾

RichHTML

PDF (PC)

Knowledge

Abstract

Cite this article

share this article

Figures/Tables 14

References 41

Related Articles 10

Recommended Articles

Metrics

Comments

[1]	Jiang Yuan, Shen Yongjun, Wen Shaofang, Yang Shaopu. SUPER-HARMONIC AND SUB-HARMONIC SIMULTANEOUS RESONANCES OF FRACTIONAL-ORDER DUFFING OSCILLATOR [J]. Chinese Journal of Theoretical and Applied Mechani, 2017, 49(5): 1008-1019.
[2]	Ren Yongsheng, Yao Donghui. PRIMARY RESONANCES OF AN INTERNALLY DAMPED ROTATING COMPOSITE SHAFT WITH NONLINEARITIES IN CURVATURE AND INERTIA [J]. Chinese Journal of Theoretical and Applied Mechani, 2017, 49(4): 907-919.
[3]	Niu Jiangchuan, Shen Yongjun, Yang Shaopu, Li Sujuan. PRIMARY RESONANCE OF DUFFING OSCILLATOR WITH FRACTIONAL-ORDER PID CONTROLLER BASED ON VELOCITY FEEDBACK [J]. Chinese Journal of Theoretical and Applied Mechani, 2016, 48(2): 422-429.
[4]	Wang Haoyu, Wu Yongjun. THE INFLUENCE OF ONE-TO-ONE INTERNAL RESONANCE ON RELIABILITY OF RANDOM VIBRATION SYSTEM [J]. Chinese Journal of Theoretical and Applied Mechani, 2015, 47(5): 807-813.
[5]	Shen Yongjun, Zhao Yongxiang, Tian Jiayu, Yang Shaopu. DYNAMICAL ANALYSIS ON A KIND OF SEMI-ACTIVE SUSPENSION WITH TIME DELAY [J]. Chinese Journal of Theoretical and Applied Mechani, 2013, 45(5): 755-762.
[6]	,. TRIPLE RESONANCES OF TORSIONAL VIBRATION OF A SHAFTING SYSTEM SIMULATING A GENERATOR SET ROTOR [J]. Chinese Journal of Theoretical and Applied Mechani, 1997, 29(6): 733-739.
[7]	,. ON THE HOPF BIFURCATION SYSTEM IN THE PRESENCE OF PARAMETRIC REAL NOISES [J]. Chinese Journal of Theoretical and Applied Mechani, 1997, 29(2): 158-166.
[8]	,. NONLINEAR VIBRATION OF THE HIGH DIMENSIONAL SYSTEMS WITH PARAMETERS [J]. Chinese Journal of Theoretical and Applied Mechani, 1996, 28(1): 109-113.
[9]	,,,. APPROXIMATE ANALYTICAL METHOD OF CURVILINEAR SEARCH FOR STRUCTURAL SYNTHESIS [J]. Chinese Journal of Theoretical and Applied Mechani, 1996, 28(1): 114-118.
[10]	,. ASYMPTOTIC METHOD FOR PRIMARY RESONANCE OF A STRONGLY NONLINEAR VIBRATION SYSTEM WITH MANY DEGREES OF FREEDOM [J]. Chinese Journal of Theoretical and Applied Mechani, 1995, 27(5): 577-586.