双对斜杆负刚度机制的恒值QZS隔振器研究

针对隔振质量偏离静态平衡位置导致准零刚度(quasi-zero stiffness,QZS)隔振器动态刚度增大而影响低频隔振性能的问题,基于双对斜杆负刚度机制,构造了恒值QZS隔振器,推导了隔振器的力和刚度表达式,通过静态平衡点处刚度及刚度二阶导数等于零的QZS条件,研究了参数影响下的力和刚度特性,获得了非线性刚度、恒值QZS和零刚度的参数条件。根据静态分析,设计了恒值QZS试验模型,通过万能试验机测得试验模型的力位移曲线,与理论值具有较好的一致性。进而采用激光测振仪和振动台开展谐波激励的动态试验,获得了恒值QZS和线性刚度隔振器的位移响应及传递率。动态试验结果表明,恒值QZS隔振器的起始隔振频率小于1.5 Hz,且传递率整体小于线性隔振器的位移传递率,而线性隔振器的起始隔振频率为4.5 Hz。综上,提出的恒值QZS隔振器不仅能实现任意恒值的QZS,并且可采用杆、弹簧方便地获得所需的恒值QZS,具有优越的低频隔振性能。

Modeling,analysis,and simulation of X-shape quasi-zero-stiffness-roller vibration isolators

Existing quasi-zero stiffness(QZS)isolators are reviewed.In terms of their advantages,a novel X-shape QZS isolator combined with the cam-roller-spring mechanism(CRSM)is proposed.Different from the existing X-shape isolators,oblique springs are used to enhance the negative stiffness of the system.Meanwhile,the CRSM is used to eliminate the gravity of the loading mass,while the X-shape structure leaves its static position.The existing QZS isolators are demonstrated and classified according to their nonlinearity mechanisms and classical shapes.It is shown that the oblique spring can realize negative stiffness based on the simplest mechanism.The X-shape has a strong capacity of loading mass,while the CRSM can achieve a designed restoring force at any position.The proposed isolator combines all these advantages together.Based on the harmonic balance method(HBM)and the simulation,the displacement transmissibilities of the proposed isolator,the X-shape isolators just with oblique springs,and the X-shape isolators in the traditional form are studied.The results show that the proposed isolator has the lowest beginning isolation frequency and the smallest maximum displacement transmissibility.However,it still has some disadvantages similar to the existing QZS isolators.This means that its parameters should be designed carefully so as to avoid becoming a bistable system,in which there are two potential wells in the potential energy curve and thus the isolation performance will be worsened.

Cascaded quasi-zero stiffness nonlinear low-frequency vibration isolator inspired by human spine

Human motion induced vibration has very low frequency,ranging from 2 Hz to 5 Hz.Traditional vibration isolators are not effective in low-frequency regions due to the trade-off between the low natural frequency and the high load capacity.In this paper,inspired by the human spine,we propose a novel bionic human spine inspired quasi-zero stiffness(QZS)vibration isolator which consists of a cascaded multi-stage negative stiffness structure.The force and stiffness characteristics are investigated first,the dynamic model is established by Newton’s second law,and the isolation performance is analyzed by the harmonic balance method(HBM).Numerical results show that the bionic isolator can obtain better low-frequency isolation performance by increasing the number of negative structure stages,and reducing the damping values and external force values can obtain better low-frequency isolation performance.In comparison with the linear structure and existing traditional QZS isolator,the bionic spine isolator has better vibration isolation performance in low-frequency regions.It paves the way for the design of bionic ultra-low-frequency isolators and shows potential in many engineering applications.

Design and Analysis of a Horizontal Quasi-Zero Stiffness Vibration Isolator by Combining Rolling-Ball and Disk Springs in Parallel

Combining disk springs having negative stiffness with a rolling-ball in parallel is proposed in this paper. It is used to reduce the system stiffness and the positioning error in a non-ideal environment.The characteristics of a disk spring are analyzed. The dynamic equation of its motion has been obtained based on Newton＇s second law. After definition of a error margin,the dynamic equation of the motion can be treated as a Duffing oscillator,and the influences of non-dimensional parameters on the stiffness and transmissibility are studied. The natural frequency and transmissibility are achieved in a linearization range,where the ratio of linear to nonlinear items is small enough.The influence of mass ratio and non-dimensional parameters on natural frequency are analyzed. Finally,a comparison of numerical example demonstrates that the QZS system can realize a lower stiffness within an increased range.

Novel modular quasi-zero stiffness vibration isolator with high linearity and integrated fluid damping

Passive vibration isolation systems have been widely applied due to their low power consumption and high reliability.Nevertheless,the design of vibration isolators is usually limited by the narrow space of installation,and the requirement of heavy loads needs the high supporting stiffness that leads to the narrow isolation frequency band.To improve the vibration isolation performance of passive isolation systems for dynamic loaded equipment,a novel modular quasi-zero stiffness vibration isolator(MQZS-VI)with high linearity and integrated fluid damping is proposed.The MQZS-VI can achieve high-performance vibration isolation under a constraint mounted space,which is realized by highly integrating a novel combined magnetic negative stiffness mechanism into a damping structure:The stator magnets are integrated into the cylinder block,and the moving magnets providing negative-stiffness force also function as the piston supplying damping force simultaneously.An analytical model of the novel MQZS-VI is established and verified first.The effects of geometric parameters on the characteristics of negative stiffness and damping are then elucidated in detail based on the analytical model,and the design procedure is proposed to provide guidelines for the performance optimization of the MQZS-VI.Finally,static and dynamic experiments are conducted on the prototype.The experimental results demonstrate the proposed analytical model can be effectively utilized in the optimal design of the MQZS-VI,and the optimized MQZS-VI broadened greatly the isolation frequency band and suppressed the resonance peak simultaneously,which presented a substantial potential for application in vibration isolation for dynamic loaded equipment.

一种双连杆-弹簧-曲面机构的QZS隔振器设计和研究

基于正负刚度并联原理,运用双连杆-弹簧-曲面作为负刚度机构、竖直弹簧作为正刚度机构,提出了一种准零刚度(quasi-zero stiffness,QZS)隔振器的新构型。针对上述构型,通过静力分析,研究了系统的位移-刚度特性和位移-回复力特性,得到了系统静平衡下的QZS条件。此外,建立QZS系统的非线性动力学方程,应用谐波平衡法和龙格库塔法求解。针对不同的激励幅值、阻尼系数和QZS参数等因素,研究了系统动力学响应和传递率特性。理论研究表明,该QZS构型可以有效降低模型的共振频率与最大传递率幅值。基于隔振器的三维模型进行数值仿真和实验研究,发现提出的QZS构型拥有较好的低频隔振性能,并具备与线性系统相当的高频隔振性能。

Dynamic frequency response characteristics of a compound regulative quasi-zero stiffness air spring system

Quasi-zero stiffness(QZS) device is widely studied for their better performance in low-frequency and micro-vibration isolation due to the high-static and low-dynamic(HSLD) stiffness characteristics.The previous QZS isolator with determined parameters is not suitable for variable isolated mass.In this study,a novel compound regulative quasi-zero stiffness air spring(CRQSAS)has been proposed and designed by introducing a bidirectional regulator for the horizontal air springs.The CRQSAS could change the quasi-zero region depending on the payload.To identify the parameters of the convoluted air spring(CAS) and novel rubber air spring(NRAS),the air spring testing system is established.The stiffness functions of air springs are obtained by the multi-parameter fitting method.According to the structure of the CRQSAS,the dynamic model of the system is analyzed and simplified by Taylor Expansion.The harmonic balance method(HBM) is applied to calculate the frequency response and absolute displacement transmissibility.An experimental prototype has been set up to verify the theoretical model and simulation.Compared with the single NRAS,CRQSAS performs better in low-frequency and micro-amplitude vibration.The research proves that CRQSAS is a passive device widely applied for improving isolation precision under low-frequency vibration.

A bio-inspired spider-like structure isolator for low-frequency vibration

This paper proposes a quasi-zero stiffness(QZS)isolator composed of a curved beam(as spider foot)and a linear spring(as spider muscle)inspired by the precise capturing ability of spiders in vibrating environments.The curved beam is simplified as an inclined horizontal spring,and a static analysis is carried out to explore the effects of different structural parameters on the stiffness performance of the QZS isolator.The finite element simulation analysis verifies that the QZS isolator can significantly reduce the first-order natural frequency under the load in the QZS region.The harmonic balance method(HBM)is used to explore the effects of the excitation amplitude,damping ratio,and stiffness coefficient on the system’s amplitude-frequency response and transmissibility performance,and the accuracy of the analytical results is verified by the fourth-order Runge-Kutta integral method(RK-4).The experimental data of the QZS isolator prototype are fitted to a ninth-degree polynomial,and the RK-4 can theoretically predict the experimental results.The experimental results show that the QZS isolator has a lower initial isolation frequency and a wider isolation frequency bandwidth than the equivalent linear isolator.The frequency sweep test of prototypes with different harmonic excitation amplitudes shows that the initial isolation frequency of the QZS isolator is 3 Hz,and it can isolate 90%of the excitation signal at 7 Hz.The proposed biomimetic spider-like QZS isolator has high application prospects and can provide a reference for optimizing low-frequency or ultra-low-frequency isolators.

A two degree of freedom stable quasi-zero stiffness prototype and its applications in aseismic engineering

In this paper, an archetypal aseismic system is proposed with 2-degree of freedom based on a smooth and discontinuous(SD)oscillator to avoid the failure of electric power system under the complex excitation of seismic waves. This model comprises two vibration isolation units for the orthogonal horizontal directions, and each of them admits the stable quasi-zero stiffness(SQZS)with a pair of inclined linear elastic springs. The equation of motion is formulated by using Lagrange equation, and the SQZS condition is obtained by optimizing the parameters of the system. The analysis shows that the system behaves a remarkable vibration isolation performance with low resonant frequency and a large stroke of SQZS interval. The experimental investigations are carried out to show a high sonsistency with the theoretical results, which demonstrates the improvement of aseismic behavior of the proposed model under the seismic wave.

A limb-inspired bionic quasi-zero stiffness vibration isolator

Vibration reduction has always been one of hot and important topics in mechanical engineering,especially for the special measurement instrument.In this paper,a novel limb-inspired bionic structure is proposed to generate negative stiffness and design a new quasi-zero stiffness isolator via torsion springs,distinguishing from the existing tension spring structures in the literature.The nonlinear mathematical model of the proposed structure is developed and the corresponding dynamic properties are further investigated by using the Harmonic Balance method and ADAMS verification.To evaluate the vibration isolation performance,typical three-springs quasi-zero stiffness(TS QZS)system is selected to compare with the proposed bionic structure.And the graphical processing unit(GPU)parallel technology is applied to perform necessary two-parameter analyses,providing more insights into the effects of parameters on the transmissibility.It is shown that the proposed structure can show advantages over the typical TS QZS system in a wider vibration isolation range for harmonic excitation case and shorter decay time for the impact excitation case.

Gravity compensation method via magnetic quasi-zero stiffness combined with a quasi-zero deformation control strategy

Gravity compensation refers to the creation of a constant supporting force to fully or partly counteract the gravitational force for ground verification to simulate the spacecraft dynamics in outer space with zero-or micro-gravity. Gravity compensation is usually implemented via a very low stiffness suspension/supporting unit, and a servo system in series is adopted to extend the simulation range to hundreds of millimeters. The error of suspension force can be up to tens of Newton due to the contact/friction in the suspension/supporting unit and the error of the force/pressure sensor. It has become a bottleneck for the ground verification of spacecraft guidance, navigation, and control systems with extreme requirements, such as tons of payload and fine thrust in sub-Newtons. In this article, a novel gravity compensation method characterized by quasi-zero stiffness plus quasi-zero deformation(QZS-QZD) is proposed. A magnetic negative stiffness spring in parallel with positive springs and aerostatic bearing is adopted to form a QZS supporting unit, and disturbance forces, such as contact or friction, can be eliminated. The deformation of the QZS supporting unit is measured via a displacement sensor, and the QZD control strategy is applied to guarantee the force error of gravity compensation to be less than sub-newtons and irrelevant to the payload. The principle of gravity compensation with QZS-QZD is analyzed, and performance tests on a prototype are carried out. The results show that when the spacecraft moves smoothly, the absolute force error is less than 0.5 N, the relative error of gravity compensation is less than 0.1%, and when collisions with other objects occur, the relative errors are 0.32% and 0.65%. The proposed method can significantly improve the gravity compensation accuracy in comparison with conventional approaches.

准零刚度隔振系统跳跃频率区间隔振研究

基于跳跃频率区间内准零刚度隔振系统的隔振效果具有不确定性的问题,提出了一种阻尼扰动控制方法。当控制系统阻尼增大到一定程度时,向下跳跃频率将低于激振频率,在原共振支上的大幅振动响应便会失稳并跌落到低幅振动的非共振支上,在此过程中借助范德波尔平面来判断何时撤除阻尼控制,从而实现了跳跃频率区间内的有效隔振,拓宽了准零刚度隔振系统的有效隔振频率区间。

屈曲板型准零刚度隔振器的设计和特性分析

设计一款屈曲板型准零刚度隔振器,该隔振器由竖直的橡胶垫和屈曲的弹簧钢板组合而成.为便于分析该隔振器的刚度特性,基于Abaqus软件分析和Matlab拟合给出力与位移的近似表达式.通过理论分析,给出该系统出现准零刚度时,竖直橡胶垫需满足的刚度条件.依据谐波平衡法研究了阻尼对系统动力学特性的影响,得到了系统的力传递率,并对其隔振性能进行了评估.结果表明,屈曲板型准零刚度隔振器能够显著提高低频段的隔振效率;在适当的阻尼情况下,该准零刚度隔振系统没有共振问题.

准零刚度绝对位移传感器设计及运用

设计了一种准零刚度(QZS)绝对位移传感器。分析了QZS传感器的结构参数,得到了保证QZS传感器特性的参数要求。给定不同激励,对QZS传感器测量精度及响应速度进行了检测,并分析总结QZS传感器的一些不足及其使用范围。将QZS传感器运用于Stewart平台的速度反馈,通过谐波平衡法得到平台z轴、绕x轴、绕y轴方向的幅频特性曲线。仿真结果表明,QZS传感器能够有效地测量平台z轴、绕x轴、绕y轴方向的绝对位移。

准零刚度隔振器的时域仿真

为分析准零刚度隔振器的隔振性能,建立了准零刚度隔振器的Matlab/Simulink模型,进行了扫频力激励、扫频基础激励、基础位移冲击激励下的时域仿真,给出了准零刚度隔振器的隔振性能数据。仿真模型运行稳定,仿真结果揭示了准零刚度隔振器良好的隔振、隔冲击效果以及超范围使用时的振动放大特性。

含有时滞控制的准零刚度隔振器动力学分析

准零刚度隔振器可以通过正负刚度并联来实现。研究了一种由三弹簧系统并联而成的准零刚度隔振器在简谐力激励下的动力学特性,并引入线性位移时滞控制策略。通过平均法分析得到系统在简谐力激励下的响应特性,并利用一阶李亚普洛夫近似稳定理论和劳斯-赫尔维茨准则分析了受控系统的稳定性和跳跃现象以及Hopf分叉现象。研究结果表明,时滞控制可以有效地改善准零刚度系统的稳定性,并且能够抑制系统跳跃现象的发生;通过选择合适的控制参数,可以避免系统发生Hopf分叉现象。

基于准零刚度隔振器的船舶推进轴系纵向减振研究

通过对准零刚度隔振器的静力学特性研究,比较分析了两种模型的结构参数对低动刚度位移范围的影响。利用有限元法,将隔振器的回复力作为一端边界条件,建立了基于准零刚度隔振器的推进轴系纵振动力学模型,应用谐波平衡法求解出系统的力传递率。结合船舶模拟工况参数,对比研究了基于不同隔振器模型的推进轴系,在叶频激励下的隔振效果。分析结果表明,准零刚度隔振器可以在等效线性系统的基础上实现推进轴系的纵向叶频隔振,选择适当的准零刚度隔振器模型和阻尼,可以避免主共振出现跳跃现象并保持低频隔振效果。

一种准零刚度车载隔振系统的设计与试验研究

针对车辆行驶工况环境以及振动频率,研制了一种空间占比小、安装方便的准零刚度(quasi-zero-stiffness,QZS)车载隔振系统。将垂向弹簧与两个对称的负刚度结构并联,负刚度机构用于刚度校正,通过静力学特性分析,初步确定了系统在平衡位置具有准零刚度的参数条件,在推导中引入了加工误差系数,分析了加工误差系数对系统准零刚度的影响机理。建立了系统非线性动力学方程,采用平均法求解了系统在车体简谐位移激励下的动力学响应,分析了系统参数和激励幅值对位移传递率的影响。在此基础上,设计制作了准零刚度隔振系统,进行了不同激励幅值、激励频率下的测试,得到了实测的位移传递率幅频响应曲线,并与理论计算结果进行了比较。另外,还通过TruckSim/Simulink联合仿真进行了车载随机激励工况仿真分析。研究表明,试验与理论结果吻合较好,验证了准零刚度隔振系统理论建模和分析方法的正确性。准零刚度的起始隔振频率在1.4 Hz左右,优于线性系统的起始隔振频率2.9 Hz。与车体相应相比,隔振后的位移响应均方根值降低80%以上,加速度均方根值降低90%左右,且稳态时准零刚度隔振系统的稳定性较好,具有良好的隔振性能。

一种准零刚度系统隔振性能的几何参数优化分析

提出了一种采用菱形连杆组件作为负刚度机构的准零刚度隔振器(下文简称菱形准零刚度隔振器)。通过静力学分析方法,建立了菱形准零刚度隔振器数学模型,并与其他调节变量较少的隔振器模型进行了对比;以被测量曲线在隔振器平衡位置处的曲率作为评价参数,研究了负刚度机构几何参数对系统刚度、阻尼非线性的影响,推导了利用几何参数进行隔振优化的条件;采用谐波平衡法求解系统动力学方程,对隔振器在不同几何参数下的隔振性能进行了分析。结果表明:菱形准零刚度隔振器具有体积相对较小且非线性调节能力较好的特点,可通过调节杆长,或满足相关临界值条件时调节杆长偏差量(下文简称杆长差)对刚度及阻尼非线性特征进行优化;刚度与阻尼的非线性优化方向不同,但通常情况下,刚度非线性因素对隔振优化起主导作用;归一化振动相对位移小于0.1时,由刚度曲线曲率得到的临界值可以较好地作为杆长差参数的隔振优化调节依据。本文提出的非线性评价方法与几何非线性优化临界值计算方法,对于类似隔振器研究和设计具有一定的指导意义。

等效非线性阻尼控制的准零刚度振动传感系统

为准确测量移动平台的绝对振动位移并进一步扩展测量频带,采用等效非线性阻尼控制方法设计了一种准零刚度(QZS)传感器。为使QZS传感器具有准零刚度特性,建立了传感器的动力学模型,并对其结构和静态特性进行分析;讨论了在不同预压缩量下传感器的幅频特性和相频特性,分析了不同等效非线性阻尼和激励对测量信号的精度影响。结果表明,等效非线性阻尼控制有效拓宽了准零刚度传感器系统的测量频带范围,该系统能够精确测量移动平台的绝对位移,满足工程实践要求。