Multi-layer quasi-zero-stiffness meta-structure for high-efficiency vibration isolation at low frequency

An easily stackable multi-layer quasi-zero-stiffness(ML-QZS)meta-structure is proposed to achieve highly efficient vibration isolation performance at low frequency.First,the distributed shape optimization method is used to design the unit cel,i.e.,the single-layer QZS(SL-QZS)meta-structure.Second,the stiffness feature of the unit cell is investigated and verified through static experiments.Third,the unit cells are stacked one by one along the direction of vibration isolation,and thus the ML-QZS meta-structure is constructed.Fourth,the dynamic modeling of the ML-QZS vibration isolation metastructure is conducted,and the dynamic responses are obtained from the equations of motion,and verified by finite element(FE)simulations.Finally,a prototype of the ML-QZS vibration isolation meta-structure is fabricated by additive manufacturing,and the vibration isolation performance is evaluated experimentally.The results show that the vibration isolation performance substantially enhances when the number of unit cells increases.More importantly,the ML-QZS meta-structure can be easily extended in the direction of vibration isolation when the unit cells are properly stacked.Hence,the ML-FQZS vibration isolation meta-structure should be a fascinating solution for highly efficient vibration isolation performance at low frequency.

Nonlinear Characteristic Analysis of Gas-Interconnected Quasi-Zero Stiffness Pneumatic Suspension System:A Theoretical and Experimental Study

Because of significantly changed load and complex and variable driving road conditions of commercial vehicles,pneumatic suspension with lower natural frequencies is widely used in commercial vehicle suspension system.How ever,traditional pneumatic suspension system is hardly to respond the greatly changed load of commercial vehicles To address this issue,a new Gas-Interconnected Quasi-Zero Stiffness Pneumatic Suspension(GIQZSPS)is presented in this paper to improve the vibration isolation performance of commercial vehicle suspension systems under frequent load changes.This new structure adds negative stiffness air chambers on traditional pneumatic suspension to reduce the natural frequency of the suspension.It can adapt to different loads and road conditions by adjusting the solenoid valves between the negative stiffness air chambers.Firstly,a nonlinear mechanical model including the dimensionless stiffness characteristic and interconnected pipeline model is derived for GIQZSPS system.By the nonlinear mechanical model of GIQZSPS system,the force transmissibility rate is chosen as the evaluation index to analyze characteristics.Furthermore,a testing bench simulating 1/4 GIQZSPS system is designed,and the testing analysis of the model validation and isolating performance is carried out.The results show that compared to traditional pneumatic suspension,the GIQZSPS designed in the article has a lower natural frequency.And the system can achieve better vibration isolation performance under different load states by switching the solenoid valves between air chambers.

A vibration isolator with a controllable quasi-zero stiffness region based on nonlinear force design

To achieve stability optimization in low-frequency vibration control for precision instruments,this paper presents a quasi-zero stiffness(QZS)vibration isolator with adjustable nonlinear stiffness.Additionally,the stress-magnetism coupling model is established through meticulous theoretical derivation.The controllable QZS interval is constructed via parameter design and magnetic control,effectively segregating the high static stiffness bearing section from the QZS vibration isolation section.Furthermore,a displacement control scheme utilizing a magnetic force is proposed to regulate entry into the QZS working range for the vibration isolation platform.Experimental results demonstrate that the operation within this QZS region reduces the peak-to-peak acceleration signal by approximately 66.7%compared with the operation outside this region,thereby significantly improving the low frequency performance of the QZS vibration isolator.

Analysis and Simulation of the Stratospheric Quasi-zero Wind Layer over Korla, Xinjiang Province, China

The stratospheric quasi-zero wind layer (QZWL) is a transition region with low zonal wind speeds in the lower stratosphere at an altitude of ~20 km. The zonal wind direction above the QZWL layer is opposite to that below the QZWL layer and the north –south wind component is small. The atmospheric wind field near the stratospheric QZWL is an important factor affecting the flight altitude and dynamic control of stratospheric airships. It is therefore necessary to study the stratospheric QZWL to provide better environmental information for these aircraft. High-resolution radiosonde data were used to analyze the characteristics of the stratospheric QZWL over Korla, Xinjiang Province, China. A weak wind layer in which the wind direction suddenly reversed from westerly to easterly was observed at ~20 km in the lower stratosphere, characteristic of the stratospheric QZWL. The Weather Research and Forecasting model was used to simulate the profiles of the horizontal wind speed and direction over Korla. The forcing effect of each diagnostic term in the equation on the zonal wind speed was analyzed. The results showed that the advection term was the dominant factor forcing the zonal wind speed. The wave term had a secondary forcing role, although the forcing effect of the wave term on the zonal wind speed was significant in some regions.

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.

Uncertainty Analysis and Optimization of Quasi-Zero Stifness Air Suspension Based on Polynomial Chaos Method

To improve the vibration isolation performance of suspensions,various new structural forms of suspensions have been proposed.However,there is uncertainty in these new structure suspensions,so the deterministic research cannot refect the performance of the suspension under actual operating conditions.In this paper,a quasi-zero stifness isolator is used in automotive suspensions to form a new suspension−quasi-zero stifness air suspension(QZSAS).Due to the strong nonlinearity and structural complexity of quasi-zero stifness suspensions,changes in structural parameters may cause dramatic changes in suspension performance,so it is of practical importance to study the efect of structural parameter uncertainty on the suspension performance.In order to solve this problem,three suspension structural parameters d_(0),L_(0) and Pc_(0) are selected as random variables,and the polynomial chaos expansion(PCE)theory is used to solve the suspension performance parameters.The sensitivity of the performance parameters to diferent structural parameters was discussed and analyzed in the frequency domain.Furthermore,a multi-objective optimization of the structural parameters d_(0),L_(0) and Pc_(0) of QZSAS was performed with the mean and variance of the root-mean-square(RMS)acceleration values as the optimization objectives.The optimization results show that there is an improvement of about 8%−1_(0)%in the mean value and about 4_(0)%−55%in the standard deviation of acceleration(RMS)values.This paper verifes the feasibility of the PCE method for solving the uncertainty problem of complex nonlinear systems,which provide a reference for the future structural design and optimization of such suspension systems.

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.

Isolation performances and optimization of triple quasi-zero stiffness isolators

In this paper,triple quasi-zero stiffness(QZS)passive vibration isolators whose restoring force curve has a three-stage softening effect are proposed.Multi-coupled SD oscillators with three independent geometrical parameters are used as negative stiffness mechanisms to achieve QZS characteristics at the origin and symmetrical positions on both sides of the origin.Isolation performances of different triple QZS isolators are analyzed to show influences of the selection of QZS regions away from the origin on the range of isolation regions.Pareto optimizations of system parameters are carried out to get a larger range of small restoring force regions and small stiffness regions.Isolation performances of two triple QZS isolators are discussed to show the influence of different Pareto optimization solutions through the comparisons with single and double QZS isolators.Results showed that triple QZS isolators have both the advantages of single and double QZS isolators which results in better isolation performances under both small and large excitation amplitudes.An improvement in isolation performances for triple QZS isolators is found with the decrease in average stiffness due to the appearance of two symmetrical QZS regions away from the origin.Larger displacements of QZS regions away from the origin result in better isolation performances when excitation amplitude is large,and triple QZS characteristics are similar to double QZS isolators at this time.Smaller restoring forces of QZS regions away from the origin lead to better isolation performances when excitation amplitude is small,and triple QZS characteristics are similar to single QZS isolators at this moment.Compared with the decrease in average stiffness,the improvement of isolation performances shows a hysteresis phenomenon due to the difference between static and dynamic characteristics.

A quasi-zero stiffness energy harvesting isolator with triple negative stiffness

Vibration isolation for low frequency excitation and the power supply for low power monitoring sensors are important issues in bridge engineering.The main problem is how to effectively combine the vibration isolator with the energy harvester to form a multi-functional structure.In this paper,a system called quasi-zero stiffness energy harvesting isolator(QZS-EHI)with triple negative stiffness(TNS)is proposed.The TNS structure consists of linear springs,rigid links,sliders,and ring permanent magnets.Newton’s second law and Kirchhoff’s law construct dynamic equations of the QZS-EHI,and a comparison is made to contrast it with other QZS and linear isolators.The comparison field includes the QZS range,amplitude-frequency relationship,force transmissibility,and energy harvested power.The isolator can be applied to many engineering fields such as bridges,automobiles,and railway transportation.This paper selects bridge engineering as the main field for the dynamic analysis of this system.Considering the multi-span beam bridge,this paper compares different situations including the bridge with QZS-EHI support,with linear stiffness isolator support,and with single beam support.All results show that the QZS-EHI is not only better than the traditional isolator with linear stiffness under both harmonic and stochastic excitation,but also better than some QZS isolators with double or single negative stiffness in bridge vibration isolation and energy harvesting.Theoretical analysis is verified to correspond to the simulation analysis,which means the proposed QZS-EHI has practical application value.

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.

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.

仿猫类落地姿态的准零刚度隔振器

对设备加装隔振装置是保证其高效工作的重要方法之一.本文从仿生学的角度,根据猫科动物落地时优秀的抗冲击能力,通过观察其落地动作姿态,利用非线性补偿原理,以空气弹簧作为正刚度结构,设计出一种具有非对称刚度特性的高静低动刚度隔振器.以其为研究对象,建立了动力学模型,利用特定的方法对非对称刚度系统进行分析求解,并与数值结果和有限元仿真结果进行对比.结果表明,在较低阻尼以及较高激励幅值下,还会出现倍周期响应甚至混沌响应.同时,通过将本文设计的隔振结构和单一空气弹簧的隔振性能对比,可以得到隔振效果明显优于单一空气弹簧的结论,从而验证了所设计隔振结构的有效性和可行性.

基于准零刚度支撑结构的低频主动隔振平台研究

针对量子科学试验、精密制造等先进应用对亚赫兹微振动的抑制需求,研究基于准零刚度支撑结构和分离式音圈作动器的低频主动隔振技术。首先,给出一种低频主动隔振平台设计方法,考虑准零刚度结构的等效动力学特性,采用牛顿-欧拉方法建立平台的动力学模型;然后,基于所建立动力学模型分析多自由度耦合下平台的扰动传递特性并设计主动隔振算法;最后,研制低频主动隔振平台进行试验验证。试验结果表明,所开发主动隔振平台能够在三个线自由度上实现优于98.3%的微振动抑制效果,在0.1~10.0 Hz内载荷z方向微振动小于1.3×10^(-8) g。

基于准零刚度机构与间接力控制的恒拉力系统设计与分析

现有的悬吊式微低重力模拟恒拉力系统常采用力传感器数值作为反馈直接控制系统,但实际情况下力作为反馈信号常会产生突变,影响系统控制精度。为了改进刚性控制策略下系统稳定性差与大冲击条件下力误差大的状况,文中设计了包含准零刚度机构的恒拉力系统,通过控制准零刚度机构长度间接对恒拉力系统输出拉力进行控制。对准零刚度机构进行受力分析,明确影响准零刚度机构性能的关键指标和准零刚度机构的工作行程区间,建立恒拉力系统动力学模型,设计控制系统。为了验证系统控制精度与系统抗干扰性能,进行了动力学联合仿真对设计进行验证,仿真结果表明:该恒拉力系统拉力的控制误差可控制在2%以内,且具有较好的鲁棒性。

新型准零刚度空气悬架系统的设计与分析

为提高商用汽车在低频外部激励环境下的隔振性能以及行驶平顺性,基于准零刚度理论,采用正负刚度并联的方式,将负刚度碟形弹簧组与正刚度空气弹簧相结合,设计一种新型准零刚度悬架系统。通过静力学特性分析,建立力位移和刚度位移表达式,得到系统达到准零刚度的参数条件;通过动力学特性分析,建立系统的二自由度模型和简谐力作用下的非线性运动微分方程,得到力传递率特性曲线并对其进行分析。结果表明新结构的低频隔振性能显著提升。基于刚度位移表达式建立2自由度1/4悬架模型,分别对准零刚度系统与传统系统的垂向加速度、悬架动行程和轮胎动载荷等平顺性指标的差异性进行分析,仿真结果表明,该准零刚度系统的平顺性改善效果亦优于传统结构。

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.

折纸型准零刚度系统的隔振性能研究

准零刚度隔振系统因具备高静态低动态的刚度特性得到广泛研究,但是较短的准零刚度行程限制了其在低频隔振领域的应用推广。基于非线性正刚度和非线性负刚度并联的理念,由Kresling折纸构型启发设计一种新型的准零刚度隔振系统,采用有限元分析准零刚度隔振系统的可行性。建立了折纸型准零刚度系统的力学模型,研究了在正常工况下阻尼比、荷载幅值和回复力模型高阶项对幅频特性和力传递特性的影响,并扩展到过载工况下折纸型准零刚度系统隔振性能研究。开展折纸型准零刚度系统隔振试验并与有限元结果进行对比分析。分析结果表明,隔振系统随着阻尼增大和激振力幅值减小,响应幅值和传递率均会减小。具备高阶项的回复力模型使折纸型准零刚度系统在正常和过载工况下具有更低的起始隔振频率、共振频率以及振动传递率。试验验证折纸型准零刚度系统具备较为良好的隔振性能。

仿足弓准零刚度隔振器特性分析与实验

为满足光学精密仪器更高的精度及动态特性要求,解决其安装空间逼仄与宽频域隔振的矛盾,提出了一种由屈曲梁与黏弹性材料并联构成的仿生准零刚度隔振装置,并建立了该仿生隔振装置的非线性动力学模型,结合谐波平衡法对其振动传递特性进行了分析。仿真与实验结果表明:当频率比大于15时,振动幅值传递率小于0.2,系统共振区振动幅值传递率低于0.75,隔振效果良好。该结论验证了仿足弓准零刚度隔振器的有效性,为光学精密仪器复杂隔振系统设计提供了参考。

非线性准零刚度文物隔震系统动力特性分析

为实现地震时浮放文物的安全防护,对一种非线性准零刚度隔震系统进行动力分析。构建隔震系统的刚度模型与运动平衡方程,使用谐波平衡法与牛顿迭代联合法进行理论分析,并使用四阶龙格-库塔(Runge-Kutta,R-K)数值分析法对运动平衡方程在简谐激励和地震动激励作用下进行数值分析。结果表明:非线性准零刚度文物隔震系统在简谐激励作用下,在外激励频率为低频阶段时,系统的响应存在不稳定区域,提高系统的阻尼比和刚度都会降低系统的不稳定区域范围以及系统的振幅响应峰值,使其趋于线性隔震系统的特征;增加系统的阻尼比可以降低隔震系统的有效起始频率,但在隔震有效频带范围内增加系统的阻尼比会使系统的传递系数增大;增加弹簧刚度会增大隔震系统有效初始频率,但可以降低系统在低频阶段的振幅响应,但在隔震系统有效频带范围内会增大系统的传递系数。数值分析表明隔震系统在不稳定区域范围内只存在2个稳定解,系统的响应状态与系统初始状态相关;系统在实际地震动激励作用下能显著降低输入地震动的加速度响应;隔震系统的减震系数对于长周期成分较少的地震动输入峰值变化不敏感,但对于长周期成分较多的地震动输入峰值变化较为敏感,表明系统对于短周期地震动的隔震性能更好,与在简谐激励作用下的理论分析结果一致。