磁环型准零刚度隔振系统动态特性

doi:10.12382/bgxb.2022.0194

摘要/Abstract

摘要：

特种车辆由于其作战、行驶环境复杂多变,使乘员及车载大型精密设备常暴露于低频大幅振动环境中,直接影响作战功效,甚至危及生命安全、引发严重的设备故障。为有效隔离其低频振动,开发了一种磁环型准零刚度隔振系统,对其系统刚度特性和隔振特性进行了理论与实验研究。基于磁电理论和刚度耦合理论,建立正、负刚度理论模型,获得了系统等效刚度,对其刚度机理与参数特性进行分析;进一步建立准零刚度隔振系统的非线性动力学模型,采用谐波平衡法和牛顿-拉夫森迭代法对系统非线性动力学方程进行求解,分析与评估其隔振特性,并搭建实验台进行验证。研究结果表明:负刚度机构具有明显的负刚度效应,与正刚度系统配合,可产生较宽的准零刚度区间;与线性系统相比,该准零刚度隔振系统隔振频带向低频区拓宽71.9%,共振峰值降低65.7%,稳态区间下位移响应幅值下降75%,加速度响应幅值下降80%,具有更宽的隔振频带和更大的振动衰减率。

关键词: 特种车辆, 准零刚度, 磁环, 非线性动力学, 低频隔振

Abstract:

Due to the complexity and changeability of the operational and driving environment of special vehicles, personnel and large onboard precision equipment are often exposed to the low-frequency and large-amplitude vibration environment, which directly affects the operational efficiency, even endangers personnel safety and causes serious equipment failure. In order to effectively isolate its low-frequency vibrations, a quasi-zero-stiffness vibration isolation system with magnetic rings is developed, and its system stiffness characteristics and vibration isolation characteristics are studied theoretically and experimentally. Based on the magnetoelectric theory and stiffness coupling theory, the theoretical models of positive and negative stiffness are established and the equivalent stiffness of the system is obtained, and its stiffness mechanism and parameter characteristics are analyzed. The nonlinear dynamic model of the quasi-zero stiffness vibration isolation system is further developed, and the nonlinear dynamic equations of the system are solved by the harmonic balance method and the Newton-Raphson iterative method, its vibration isolation characteristics are analyzed and evaluated, and an experimental bench is built for verification. The results show that: the negative stiffness mechanism has obvious negative stiffness effect and can produce a wider quasi-zero stiffness interval with the positive stiffness system; compared with the linear system, the isolation frequency band of the quasi-zero stiffness vibration isolation system is widened to the low-frequency region by 71.9%, and the resonance peak reduced by 65.7%, the displacement response amplitude decreased by 75%, and the acceleration response amplitude decreased by 80% in the steady-state interval,meaning that the system has a wider vibration isolation frequency band and a larger vibration decay rate.

Key words: special vehicle, quasi-zero stiffness, magnetic rings, nonlinear dynamics, low-frequency vibration isolation

李占龙, 张正, 姜稳稳, 刘琪, 任志曌, 王瑶, 宋勇. 磁环型准零刚度隔振系统动态特性[J]. 兵工学报, 2023, 44(6): 1784-1794.

LI Zhanlong, ZHANG Zheng, JIANG Wenwen, LIU Qi, REN Zhizhao, WANG Yao, SONG Yong. Dynamic Characteristics of Quasi-Zero Stiffness Vibration Isolation System with Magnetic Rings[J]. Acta Armamentarii, 2023, 44(6): 1784-1794.

图/表 15

图1 磁环型准零刚度隔振系统

Fig.1 Quasi-zero-stiffness vibration isolation system with magnetic rings

图2 负刚度机构坐标系

Fig.2 Negative stiffness mechanism coordinate system

图3 正刚度机构坐标系

Fig.3 Positive stiffness mechanism coordinate system

图4 单个PAM隔振单元刚度与阻尼的三向分解

Fig.4 Three-direction stiffnessand damping decomposition of a PAM vibration isolation element

图5 单自由度非线性隔振系统动力学模型

Fig.5 Dynamic model of single-degree-of-freedom nonlinear vibration isolation system

图6 负刚度机构计算模型

Fig.6 Computation model of negative stiffness mechanism

表1 环形永磁体的参数

Table 1 Parameters of permanent magnet rings

磁环参数	内径/ mm	外径/ mm	厚度/ mm	剩磁/ T	磁导率/ (H·m^-1)
内磁环	20	35	15	1.25	1.05
上磁环	55	80	15	1.25	1.05
下磁环	55	80	15	1.25	1.05

图7 负刚度实验台

Fig.7 Negative stiffness experimental bench

图8 负刚度计算模型与实验数据曲线

Fig.8 Curves of negative stiffness computation model and experimental data

图9 负刚度模型在不同kk下的力-位移曲线

Fig.9 Force-displacement curves of negative stiffness model under different kk

图10 负刚度力-位移拟合曲线

Fig.10 Fitted force-displacement curves of negative stiffness

图11 准零刚度隔振系统与负刚度机构力-位移特性曲线

Fig.11 Force-displacement characteristic curves of quasi-zero-stiffness vibration isolation system and negative stiffness mechanism

图12 不同参数下准零刚度隔振系统的位移传递率

Fig.12 Displacement transmissibility of quasi-zero-stiffness vibration isolation system under different parameters

图13 实验方案示意图

Fig.13 Schematic diagram of experimental scheme

图14 准零刚度隔振系统与线性隔振系统对比

Fig.14 Comparison between quasi-zero stiffness vibration isolation system and linear vibration isolation system

参考文献 29

[1]	赵雷雷, 于曰伟, 周长城, 等. 特种车辆驾驶室减振器节流阀片开度及阻尼特性研究[J]. 兵工学报, 2018, 39(4): 645-654. doi: 10.3969/j.issn.1000-1093.2018.04.003
	ZHAO L L, YU Y W, ZHOU C C, et al. Throttle slice opening size and damping characteristics of cab damper for special vehicles[J]. Acta Armanentarii, 2018, 39(4): 645-654. (in Chinese)
[2]	房凌晖, 郑翔玉, 蔡宏图, 等. 坦克装甲车辆防护技术发展研究[J]. 四川兵工学报, 2014, 35(3): 23-26.
	FANG L H, ZHENG X Y, CAI H T, et al. Development of tank and armored vehicle protection technology[J]. Si Chuan Ordnance Journal, 2014, 35(3): 23-26. (in Chinese)
[3]	HARRIS C M, PIERSOL A G. Harris’ shock and vibration handbook[M]. 6th ed. New York, NY, US: McGraw Hill, 2010.
[4]	PLATUS D L. Negative-stiffness-mechanism vibration isolation systems[J]. Physica A: Statistical Mechanics and its Applications, 1992, 161: 44-54.
[5]	ROBERTSON W S, KIDNER M R F, CAZZOLATO B S, et al. Theoretical design parameters for a quasi-zero stiffness magnetic spring for vibration isolation[J]. Journal of Sound and Vibration, 2009, 326(1/2): 88-103. doi: 10.1016/j.jsv.2009.04.015 URL
[6]	刘兴天, 孙靖雅, 肖锋, 等. 准零刚度微振动隔振器的原理和性能研究[J]. 振动与冲击, 2013, 32(21): 69-73.
	LIU X T, SUN J Y, XIAO F, et al. Principle and performance of a quasi-zero stiffness isolator for micro-vibration isolation[J]. Journal of Vibration and Shock, 2013, 32(21): 69-73. (in Chinese)
[7]	刘琪, 李占龙, 王建梅, 等. 准零刚度低频隔振技术的研究进展[J]. 机械强度, 2020, 42(4): 13-22.
	LIU Q, LI Z L, WANG J M, et al. Research progress on quasi-zero stiffness low-frequency vibration isolation technology[J]. Journal of Mechanical Strength, 2020, 42(4): 13-22. (in Chinese)
[8]	张建卓, 李旦, 董申, 等. 精密仪器用超低频非线性并联隔振系统研究[J]. 中国机械工程, 2004, 15(1):69-71.
	ZHANG J Z, LI D, DONG S, et al. Study on ultra-low frequency parallel connection isolator used for precision instruments[J]. China Mechanical Engineering, 2004, 15(1):69-71. (in Chinese)
[9]	胡光军, 周生通, 李鸿光. 一种非线性隔振器的静力分析与实验研究[J]. 噪声与振动控制, 2011, 31(6): 69-71. doi: 10.3969/j.issn.1006-1355-2011.06.015
	HU G J, ZHOU S T, LI H G. Static analysis and experiment of a nonlinear vibration isolator[J]. Noise and Vibration Control, 2011, 31(6): 69-71. (in Chinese)
[10]	路纯红, 白鸿柏, 杨建春, 等. 超低频非线性隔振系统的研究[J]. 噪声与振动控制, 2010, 30(4): 10-12. doi: 10.3969/j.issn.1006-1355.2010.04.003
	LU C H, BAI H B, YANG J C, et al. Research on ultra-low frequency nonlinear vibration isolation system[J]. Noise and Vibration Control, 2010, 30(4): 10-12. (in Chinese)
[11]	王晓杰, 刘辉, 郦文平, 等. 准零刚度扭转隔振器振动传递特性研究[J]. 机械工程学报, 2018, 54(21): 49-56. doi: 10.3901/JME.2018.21.049
	WANG X J, LIU H, LI W P, et al. Vibration transmission characteristics of a quasi-zero stiffness torsional isolator[J]. Journal of Mechanical Engineering, 2018, 54(21): 49-56. (in Chinese) doi: 10.3901/JME.2018.21.049
[12]	KOVACIC I, M. BRENNA J, WATERS T P. A study of a nonlinear vibration isolator with a qusia-zero stiffness characteristic[J]. Journal of Sound and Vibration, 2008, 315(3): 700-711. doi: 10.1016/j.jsv.2007.12.019 URL
[13]	CARRELLA A, BRENNA M J, KOVACIC I, et al. On the force transmissibility of a vibration isolator with quasi-zero-stiffness[J]. Journal of Sound and Vibration, 2009, 322(4/5): 707-717. doi: 10.1016/j.jsv.2008.11.034 URL
[14]	VALEEV A, ZOTOV A, KHARISOV S. Designing of compact low frequency vibration isolator with quasi-zero stiffness[J]. Journal of low frequency noise vibration and active control, 2015, 34(4): 459-473. doi: 10.1260/0263-0923.34.4.459 URL
[15]	任旭东. 空气弹簧准零刚度隔振器的特性分析及应用研究[D]. 北京: 军事医学科学院, 2017.
	REN X D. Characteristics analysis and application study of the quasi-zero stiffness isolator using air spring[D]. Beijing: Academy of Military Medical Sciences, 2017. (in Chinese)
[16]	徐道临, 张月英, 周加喜, 等. 一种准零刚度隔振器的特性分析与实验研究[J]. 振动与冲击, 2014, 33(11): 208-213.
	XU D L, ZHANG Y Y, ZHOU J X, et al. Characteristic analysis and experimental investigation for a vibration isolator with quasi-zero stiffness[J]. Journal of Vibration and Shock, 2014, 33(11): 208-213. (in Chinese)
[17]	蓝双, 杨晓翔. 新型准零刚度系统的设计、分析与仿真[J]. 机械强度, 2018, 40(3): 515-521. doi: 10.16579/j.issn.1001.9669.2018.03.002
	LAN S, YANG X X. Design, analysis and simulation of a novel quasi-zero stiffness vibration isolation system[J]. Journal of Mechanical Strength, 2018, 40(3): 515-521. (in Chinese) doi: 10.16579/j.issn.1001.9669.2018.03.002
[18]	杜宁, 胡明勇, 毕勇, 等. 一种车载设备的低频水平减振方法[J]. 振动与冲击, 2017, 36(7): 184-190.
	DU N, HU M Y, BI Y, et al. A low frequency horizontal vibration reduction method for a vehicle-borne photoelectric instrument[J]. Journal of Vibration and Shock, 2017, 36(7): 184-190. (in Chinese)
[19]	LIU Y Q, XU L L, SONG C F. Dynamic characteristics of a quasi-zero stiffness vibration isolator with nonlinear stiffness and damping[J]. Archive of Applied Mechanics, 2019, 89: 1743-1759. doi: 10.1007/s00419-019-01541-0
[20]	张春辉, 曾泽璀, 张磊, 等. 预紧式准零刚度隔冲器的隔冲性能研究[J]. 振动工程学报, 2019, 32(5): 767-777.
	ZHANG C H, ZENG Z C, ZHANG L, et al. Research on the shock isolation performance of preload quasi-zerostiffness isolator[J]. Journal of Vibration Engineering, 2019, 32(5): 767-777. (in Chinese)
[21]	DONG G X, ZHANG X N, LUO Y J, et al. Analytical study of the low frequency multi-direction isolator with high-static-low-dynamic stiffness struts and spatial pendulum[J]. Mechanical Systems and Signal Processing, 2018, 110: 521-539. doi: 10.1016/j.ymssp.2018.03.041 URL
[22]	柴凯, 杨庆超, 朱石坚, 等. 矩形永磁铁的磁力计算及其应用[J]. 噪声与振动控制, 2016, 36(6):51-55, 66. doi: 10.3969/j.issn.1006-1335.2016.06.010
	CHAI K, YANG Q C, ZHU S J, et al. Magnetic force calculation of rectangular permanent magnets and its application[J]. Noise and Vibration Control, 2016, 36(6):51-55, 66. (in Chinese) doi: 10.3969/j.issn.1006-1335.2016.06.010
[23]	王迎春, 柴凯, 刘树勇, 等. 永磁体型高静低动刚度隔振器试验研究[J]. 噪声与振动控制, 2019, 39(5): 223-230.
	WANG Y C, CHAI K, LIU S Y, et al. Experimental study on the permanent magnets vibration isolators with high-static and low-dynamic stiffness[J]. Noise and Vibration Control, 2019, 39(5): 223-230. (in Chinese)
[24]	柴凯, 杨庆超, 朱石坚, 等. 双环永磁铁型准零刚度隔振器的设计和分析[J/OL]. 解放军理工大学学报(自然科学版), 2017(2017-04-11). http://kns.cnki.net/kcms/detail/32.1430.N.20170411.1118.004.html.
	CHAI K, YANG Q C, ZHU S J, et al. Design and analysis of quasi-zero stiffness vibration isolator with bi-annular-shaped permanent magnet[J/OL]. Journal of PLA University of Science and Technology(Natural Science Edition), 2017(2017-04-11). http://kns.cnki.net/kcms/detail/32.1430.N.20170411.1118.004.html. in Chinese)
[25]	李爽, 楼京俊, 杨庆超, 等. 双环永磁体型高静低动刚度隔振器设计、建模与试验研究[J]. 振动工程学报, 2019, 32(4): 675-684.
	LI S, LOU J J, YANG Q C, et al. Design and experiment of a vibration isolator using double-ring permanent magnets springs with negative stiffness[J]. Journal of Vibration Engineering, 2019, 32(4): 675-684. (in Chinese)
[26]	KIM J, JEON Y, UM S, et al. A Novel passive quasi-zero stiffness isolator for ultra-precision measurement systems[J]. International Journal of Precision Engineering and Manufacturing, 2019, 20(9): 1573-1580. doi: 10.1007/s12541-019-00149-2
[27]	王瑶, 李占龙, 刘琪, 等. 非接触多磁环负刚度机构非线性刚度行为特性研究[J]. 振动与冲击, 2021, 40(15): 41-47.
	WANG Y, LI Z L, LIU Q, et al. Nonlinear stiffness behavior of non-contact multi-magnetic ring negative stiffness mechanism[J]. Journal of Vibration and Shock, 2021, 40(15): 41-47. (in Chinese)
[28]	彭远生, 代洪华, 张皓, 等. 仿生抗冲击Stewart隔振平台的动力学与控制[J]. 西北工业大学学报, 2021, 39(2): 258-266.
	PENG Y S, DAI H H, ZHANG H, et al. Dynamics and control of a bio-inspired Stewart platform[J]. Journal of Northwestern Polytechnical University, 2021, 39(2): 258-266. (in Chinese) doi: 10.1051/jnwpu/20213920258 URL
[29]	张春辉, 汪玉, 温肇东, 等. 被动式Stewart隔冲平台的刚度特性[J]. 振动、测试与诊断, 2015, 35(2): 289-294, 399.
	ZHANG C H, WANG Y, WEN Z D, et al. Research on stiffness characteristics of a passive stewart shock isolation platform[J]. Journal of Vibration, Measurement &Diagnosis, 2015, 35(2): 289-294, 399. (in Chinese)