康复机器人准零刚度隔振特性分析与实验
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摘要
为了解决康复机器人低频振动对人体的影响问题,提出并设计一种具有准零刚度特性的新型被动隔振机构,它由两个对称的具有负刚度特性的拉伸弹簧并联一个线性正刚度弹簧实现。首先,通过静力学特性,建立此隔振机构的力-位移和刚度-位移关系式,得出机构在静态平衡位置处具有准零刚度特性的参数条件;其次,通过动力学特性,建立其分别在简谐力和简谐位移激励下的非线性微分动力学方程,采用谐波平衡法分析机构参数与激励对系统力传递率、位移传递率的影响;最后,通过实验验证在有、无负刚度情况下,输入与输出的曲线。结果表明,在有负刚度机构的情况下,隔振系统具有一定范围的准零刚度特性,且低频隔振性能较好,达到了高静态、低动态刚度的效果。本研究对机器人低频隔振具有创新性和指导意义。
In this paper,a novel type of passive vibration isolation mechanism with quasi-zero-stiffness is proposed and designed,in order to solve the problem of low frequency vibration of rehabilitation robot.It is achieved by two symmetrical tension springs with a negative stiffness characteristic in parallel with a linear positive stiffness spring.Through the study of static characteristics,the relationship between the force displacement and the stiffness displacement of the vibration isolation mechanism is established,it is concluded that the parameters of the mechanism have quasi-zero-stiffness characteristics at the equilibrium position.The dynamic characteristics,nonlinear dynamic equations in harmonic power and the harmonic displacement excitation are studied,respectively.The influence of mechanism parameters and the excitation on the system force transfer rate and the displacement transfer rate are analyzed using a harmonic balance method.Finally,the curves of the input and output are compared with or without the negative stiffness through experiments.The results show that in the case of negative stiffness mechanism,the vibration isolation system has a certain range of quasi-zero-stiffness characteristics and the low frequency vibration isolation performance is better,which can achieve the effect of high static and low dynamic stiffness.It is innovative and instructive for the low frequency vibration isolation of robot.
In this paper,a novel type of passive vibration isolation mechanism with quasi-zero-stiffness is proposed and designed,in order to solve the problem of low frequency vibration of rehabilitation robot.It is achieved by two symmetrical tension springs with a negative stiffness characteristic in parallel with a linear positive stiffness spring.Through the study of static characteristics,the relationship between the force displacement and the stiffness displacement of the vibration isolation mechanism is established,it is concluded that the parameters of the mechanism have quasi-zero-stiffness characteristics at the equilibrium position.The dynamic characteristics,nonlinear dynamic equations in harmonic power and the harmonic displacement excitation are studied,respectively.The influence of mechanism parameters and the excitation on the system force transfer rate and the displacement transfer rate are analyzed using a harmonic balance method.Finally,the curves of the input and output are compared with or without the negative stiffness through experiments.The results show that in the case of negative stiffness mechanism,the vibration isolation system has a certain range of quasi-zero-stiffness characteristics and the low frequency vibration isolation performance is better,which can achieve the effect of high static and low dynamic stiffness.It is innovative and instructive for the low frequency vibration isolation of robot.
引文
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[11]Fulcher B A,Shahan D W,Haberman M R,et al.Analytical and experimental investigation of buckled Beams as negative stiffness elements for passivive vibration and shock isolation systems[J].Journal of Vibration&Acoustics,2014,136(3):1257-1268.
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[14]刘兴天,张志谊,华宏星.新型低频隔振器的特性研究[J].振动与冲击,2012,31(5):161-164.Liu Xingtian,Zhang Zhiyi,Hua Hongxing.Characteristics of a novel low-frequency isolator[J].Journal of Vibration and Shock,2012,31(5):161-164.(in Chinese)
[15]Huang Xiuchang,Liu Xingtian.Vibration isolation characteristics of a nonlinear isolator using Euler buckled beam as negative stiffness corrector:a theoretical and experimental study[J].Journal of Sound and Vibration,2014,333(4):1132-1148.
[16]Liu Xingtian,Huang Xiuchang,Hua Hongxing.On the characteristics of a quasi-zero stiffness isolator using Euler buckled beam as negative stiffness corrector[J].Journal of Sound and Vibration,2013,332(14):3359-3376.
[17]张建卓,董申,李旦.基于正负刚度并联的新型隔振系统研究[J].纳米技术与精密工程,2004,2(4):314-318.Zhang Jianzhuo,Dong Shen,Li Dan.Study on new type v ibration isolation system based on combined positive and negative stiffness[J].Nanotechnology and Precision Engineering,2004,2(4):314-318.(in Chinese)
[18]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 Jianzhuo,Li Dan,Dong Shen,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)
[19]Carrella A,Brennan M J,Waters T P.Static analysis of a passive vibration isolator with quasi-zero-stiffness characteristic[J].Journal of Sound and Vibration,2007,301(3-5):678-689.
[20]Carrella A,Brennan M J,Kovacic I,et al.On the force transmissibility of a vibration isolator with quasizero-stiffness[J].Journal of Sound and Vibration,2009,322(4/5):707-717.
[21]Carrella A,Brennan M J,Waters T P,et al.Force and displacement transmissibility of a nonlinear isolator with high-static-low-dynamic-stiffness[J].International Journal of Mechanical Sciences,2012,55(1):22-29.
[22]Thanh D L,Kyoung K A.A vibration isolation system in low frequency excitation region using negative stiffness structure for vehicle seat[J].Journal of Sound and Vibration,2011,330(26):6311-6335.
[23]Lan C C,Yang S A,Wu Y S.Design and experiment of a compact quasi-zero-stiffness isolator capable of a wide range of loads[J].Journal of Sound and Vibration,2014,333(20):4843-4858.
[24]彭献,张施详.一种准零刚度被动隔振系统的非线性共振响应分析[J].湖南大学学报:自然科学版,2011,38(8):34-39.Peng Xian,Zhang Shixiang.Nonlinear resonance response analysis of a kind of passive isolation system with quasi-zero stiffness[J].Journal of Hunan University:Natural Sciences,2011,38(8):34-39.(in Chinese)
[25]彭献,张施详.一种准零刚度隔振系统的静力与线性动力特性分析[J.力学季刊,2012,33(3):492-498.Peng Xian,Zhang Shixiang.Static and linear dynamic characteristics analysis for a kind of vibration isolation system with quasi-zero-stiffness[J].Chinese Quarterly of Mechanics,2012,33(3):492-498.(in Chinese)
[26]彭献,陈树年,宋福磐.负刚度的工作原理及应用初探[J].湖南大学学报,:自然科学版,1992,19(4):89-94.Peng Xian,Chen Shunian,Song Fupan.Research on theory of negative stiffness and its application[J].Journal of Hunan University:Natural Science,1992,19(4):89-94.(in Chinese)
[27]孟令帅.新型准零刚度隔振器的设计和特性研究[D].北京:中国人民解放军军事医学科学院,2015.
[28]周加喜,王心龙,徐道临,等.含凸轮-滚轮机构的准零刚度系统隔振特性实验研究[J].振动工程学报,2015,28(3):449-455.Zhou Jiaxi,Wang Xinlong,Xu Daolin,et al..Experimental study on vibration isolation characteristics of quasi zero stiffness system with cam-roller mechanism[J].Journal of Vibration Engineering,2015,28(3):449-455.(in Chinese)
[29]申正宇.被动隔振技术在超精密领域内应用的初探[J].民营科技,2009(3):3-3.Shen Zhengyu.A preliminary study on the application of passive vibration isolation technology in the field of ultra precision[J].Private Science and Technology,2009(3):3-3.(in Chinese)
[30]李星.车用发动机隔振的仿真研究[D].沈阳:沈阳理工大学,2012.
[31]张晓平,何琳,周炜.一种新型磁致负刚度机构的研究[J].噪声与振动控制,2015,35(4):159-162.Zhang Xiaoping,He Lin,Zhou Wei.Study on a new negative-stiffness mechanism using tri-magnets[J].Noise and Vibration Control,2015,35(4):159-162.(in Chinese)
[32]何琳,徐伟.舰船隔振装置技术及其进展[J].声学学报,2013(2):129-136.He Lin,Xu Wei.Naval vessel machinery mounting technology and its recent advances[J].Acata Acustica,2013(2):129-136.(in Chinese)
[2]李军,钟华,毛伟伟,等.足式机器人主被动联合减振抗冲研究[J].电子技术,2015(9):9-12.Li Jun,Zhong Hua,Mao Weiwei,et al.Active and passive composite vibration damping and impact resistance research for biped robots[J].Electronic technique,2015(9):9-12.(in Chinese)
[3]毛伟伟,周烽,李军,等.双足机器人小腿减振研究[J].计算机仿真,2016,33(2):355-360.Mao Weiwei,Zhou Feng,Li Jun,et al.Study of active-passive vibration attenuation system for crus of biped robots[J].Computer Simulation,2016,33(2):355-360.((in Chinese)
[4]毛伟伟,周烽,梁青,等.基于自抗扰控制的机器人小腿减振研究[J].计算机工程,2016,42(7):293-298.Mao Weiwei,Zhou Feng,Liang Qing,et al.Study on vibration attenuation for robot crus based on active disturbance rejection control[J].Computer Engineering,2016,42(7):293-298.(in Chinese)
[5]路纯红,白鸿柏.新型超低频非线性被动隔振系统的设计[J].振动与冲击,2011,30(1):234-236.Lu Chunhong,Bai Hongbai.A new type nonlinear ultra-low frequency passive vibration isolation system[J],Journal of Vibration and Shock,2011,30(1):234-236.(in Chinese)
[6]徐道临,余奇平,周加喜,等.准零刚度隔振系统跳跃频率区间隔振研究[J].中国机械工程,2014,25(2):230-235.Xu Daolin,Yu Qipin,Zhou Jiaxi,et al.Study on vibration attenuation in jumping frequency interval of quasi-zero-stiffness vibration isolator[J].China Mechanical Engineering,2014,25(2):230-235.(in Chinese)
[7]李欣业,张明路.机械振动[M].北京:清华大学出版社,2009:19-26.
[8]聂高法,张军.新型准零刚度隔振系统设计与特性研究[J].荆楚理工学院学报,2016,31(2):26-32.Nie Gaofa,Zhang Jun.Design and characterization of a new quasi zero stiffness vibration isolation system[J].Journal of Jingchu University of Technology,2016,31(2):26-32.(in Chinese)
[9]孟令帅,孙景工.新型准零刚度隔振系统的设计与研究[J].振动与冲击,2014,33(11):195-199.Meng Lingshuai,Sun Jinggong.Design and analysis of a novel quasi-zero stiffness vibration isolation system[J].Journal of Vibration and Shock,2014,33(11):195-199.(in Chinese)
[10]Alabuzhev P,Gritchin A,Kim L,et al,Vibration protecting and measuring systems with quasi-zero stiffness[M].New York,USA:Hemisphere Publishing Corporation,1989:55-78.
[11]Fulcher B A,Shahan D W,Haberman M R,et al.Analytical and experimental investigation of buckled Beams as negative stiffness elements for passivive vibration and shock isolation systems[J].Journal of Vibration&Acoustics,2014,136(3):1257-1268.
[12]Benjamin A.Fulcher,evaluation of systems containing negative stiffness elements for vibration and shock isolation[D].Texas:The University of Texas at Austin,2012.
[13]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 Xingtian,Sun Jingya,Xiao Feng,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)
[14]刘兴天,张志谊,华宏星.新型低频隔振器的特性研究[J].振动与冲击,2012,31(5):161-164.Liu Xingtian,Zhang Zhiyi,Hua Hongxing.Characteristics of a novel low-frequency isolator[J].Journal of Vibration and Shock,2012,31(5):161-164.(in Chinese)
[15]Huang Xiuchang,Liu Xingtian.Vibration isolation characteristics of a nonlinear isolator using Euler buckled beam as negative stiffness corrector:a theoretical and experimental study[J].Journal of Sound and Vibration,2014,333(4):1132-1148.
[16]Liu Xingtian,Huang Xiuchang,Hua Hongxing.On the characteristics of a quasi-zero stiffness isolator using Euler buckled beam as negative stiffness corrector[J].Journal of Sound and Vibration,2013,332(14):3359-3376.
[17]张建卓,董申,李旦.基于正负刚度并联的新型隔振系统研究[J].纳米技术与精密工程,2004,2(4):314-318.Zhang Jianzhuo,Dong Shen,Li Dan.Study on new type v ibration isolation system based on combined positive and negative stiffness[J].Nanotechnology and Precision Engineering,2004,2(4):314-318.(in Chinese)
[18]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 Jianzhuo,Li Dan,Dong Shen,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)
[19]Carrella A,Brennan M J,Waters T P.Static analysis of a passive vibration isolator with quasi-zero-stiffness characteristic[J].Journal of Sound and Vibration,2007,301(3-5):678-689.
[20]Carrella A,Brennan M J,Kovacic I,et al.On the force transmissibility of a vibration isolator with quasizero-stiffness[J].Journal of Sound and Vibration,2009,322(4/5):707-717.
[21]Carrella A,Brennan M J,Waters T P,et al.Force and displacement transmissibility of a nonlinear isolator with high-static-low-dynamic-stiffness[J].International Journal of Mechanical Sciences,2012,55(1):22-29.
[22]Thanh D L,Kyoung K A.A vibration isolation system in low frequency excitation region using negative stiffness structure for vehicle seat[J].Journal of Sound and Vibration,2011,330(26):6311-6335.
[23]Lan C C,Yang S A,Wu Y S.Design and experiment of a compact quasi-zero-stiffness isolator capable of a wide range of loads[J].Journal of Sound and Vibration,2014,333(20):4843-4858.
[24]彭献,张施详.一种准零刚度被动隔振系统的非线性共振响应分析[J].湖南大学学报:自然科学版,2011,38(8):34-39.Peng Xian,Zhang Shixiang.Nonlinear resonance response analysis of a kind of passive isolation system with quasi-zero stiffness[J].Journal of Hunan University:Natural Sciences,2011,38(8):34-39.(in Chinese)
[25]彭献,张施详.一种准零刚度隔振系统的静力与线性动力特性分析[J.力学季刊,2012,33(3):492-498.Peng Xian,Zhang Shixiang.Static and linear dynamic characteristics analysis for a kind of vibration isolation system with quasi-zero-stiffness[J].Chinese Quarterly of Mechanics,2012,33(3):492-498.(in Chinese)
[26]彭献,陈树年,宋福磐.负刚度的工作原理及应用初探[J].湖南大学学报,:自然科学版,1992,19(4):89-94.Peng Xian,Chen Shunian,Song Fupan.Research on theory of negative stiffness and its application[J].Journal of Hunan University:Natural Science,1992,19(4):89-94.(in Chinese)
[27]孟令帅.新型准零刚度隔振器的设计和特性研究[D].北京:中国人民解放军军事医学科学院,2015.
[28]周加喜,王心龙,徐道临,等.含凸轮-滚轮机构的准零刚度系统隔振特性实验研究[J].振动工程学报,2015,28(3):449-455.Zhou Jiaxi,Wang Xinlong,Xu Daolin,et al..Experimental study on vibration isolation characteristics of quasi zero stiffness system with cam-roller mechanism[J].Journal of Vibration Engineering,2015,28(3):449-455.(in Chinese)
[29]申正宇.被动隔振技术在超精密领域内应用的初探[J].民营科技,2009(3):3-3.Shen Zhengyu.A preliminary study on the application of passive vibration isolation technology in the field of ultra precision[J].Private Science and Technology,2009(3):3-3.(in Chinese)
[30]李星.车用发动机隔振的仿真研究[D].沈阳:沈阳理工大学,2012.
[31]张晓平,何琳,周炜.一种新型磁致负刚度机构的研究[J].噪声与振动控制,2015,35(4):159-162.Zhang Xiaoping,He Lin,Zhou Wei.Study on a new negative-stiffness mechanism using tri-magnets[J].Noise and Vibration Control,2015,35(4):159-162.(in Chinese)
[32]何琳,徐伟.舰船隔振装置技术及其进展[J].声学学报,2013(2):129-136.He Lin,Xu Wei.Naval vessel machinery mounting technology and its recent advances[J].Acata Acustica,2013(2):129-136.(in Chinese)