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.

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.

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.

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.

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.

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.

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.

Three-magnet-ring quasi-zero stiffness isolator for low-frequency vibration isolation

A three-magnet-ring quasi-zero stiffness(QZS-TMR)isolator is designed to solve the problem of low-frequency vibration isolation in the vertical direction of precision equipment.QZS-TMR has both positive and negative stiffness structures.The positive stiffness structure consists of two mutually repelling magnetic rings and the negative stiffness structure consists of two magnetic rings nested within each other.By modulating the relative distance between positive and negative stiffness structures,the isolator can have QZS characteristics.Compared with other QZS isolators,the QZS-TMR is compact and easy to manufacture.In addition,the working load of QZS-TMR can be flexibly adjusted by varying the radial widths of the inner magnetic ring.In this paper,the static analysis of QZS-TMR is carried out to guide the design,and the low-frequency vibration isolation performance is studied.In addition,the experimental prototype of QZS-TMR is designed and manufactured.The static and vibration isolation experiments are carried out on the prototype.The results show that the initial vibration isolation frequency of the experimental prototype is about 4 Hz.The results show an excellent low-frequency vibration isolation effect,which is consistent with the theoretical research.This paper introduces a new approach to the design of the QZS isolator.

十堰某体育馆106m跨内凹弦支穹顶结构设计关键问题研究

十堰某体育馆主体结构采用框架-剪力墙结构体系,上部106m大跨内凹形屋盖采用弦支穹顶结构体系。为了满足建筑简洁性及结构合理性需求,对屋盖进行了四角锥网架、弦支穹顶及网架-弦支穹顶组合的不同结构形式对比,最终选用结构轻巧、经济性好的弦支穹顶结构体系。结合弦支穹顶结构自身的受力特点以及其对下部结构的不利影响,对弦支穹顶结构上下弦布置、扭转刚度、支座约束条件、撑杆高度等进行了优化。对弦支穹顶断索情况下的响应、不同工况下的支座位移以及拉索低应力状态下的刚度退化进行了验算。结果表明,优化后的屋盖结构满足结构安全、适用性的要求,同时也有较高的冗余度。

基于滑动元法的连续拉索滑移分析

实际工程中,拉索在索撑节点处滑移十分普遍。考虑滑移的影响,索撑节点不能简单地用铰接模拟。现有的拉索滑移分析方法往往需要迭代,计算过程复杂且收敛性无法保证。本文提出一种拉索滑移分析新方法——滑动元法,以预应力鱼腹梁为例进行理论推导,介绍了滑动元法的基本原理和计算步骤。结合有限元软件,利用滑动元法对算例进行计算分析,结果表明,滑动元法计算快速无需迭代,可以较为准确地分析拉索滑移。

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.

地铁车站狭长基坑支撑异常轴力分析

【目的】研究地铁车站狭长型基坑施工过程中第一道支撑轴力过大的问题。【方法】通过土体小应变刚度硬化模型(HSS)有限元分析,对车站基坑土方的开挖方式、钢支撑安装质量差、钢支撑未及时受力等情况进行精细化模拟,分析其对第一道支撑轴力的影响。【结果】结果表明:采用盆式开挖对第一道支撑的轴力影响显著,相较分层开挖的情况增大45%,应及时安装对应位置的钢支撑;安装钢支撑的预应力未达到设计值时,会导致开挖到底时的顶层支撑轴力增大,增大幅度在10%以内,底层支撑轴力减小。【结论】在地铁车站狭长基坑开挖过程中应限制盆式超挖;温度变化对支撑轴力的影响不能忽视;安装下层钢支撑预应力达不到设计值时,会导致开挖到底时的顶部支撑轴力偏大。

A human-sensitive frequency band vibration isolator for heavy-duty truck seats

In this study,a human-sensitive frequency band vibration isolator(HFBVI)with quasi-zero stiffness(QZS)characteristics for heavy-duty truck seats is designed to improve the comfort of heavy-duty truck drivers on uneven roads.First,the analytical expressions for the force and displacement of the HFBVI are derived with the Lagrange equation and d'Alembert's principle,and are validated through the prototype restoring force testing.Second,the harmonic balance method(HBM)is used to obtain the dynamic responses under harmonic excitation,and further the influence of pre-stretching on the dynamic characteristics and transmissibility is discussed.Finally,the experimental prototype of the HFBVI is fabricated,and vibration experiments are conducted under harmonic excitation to verify the vibration isolation performance(VIP)of the proposed vibration isolator.The experimental results indicate that the HFBVI can effectively suppress the frequency band(4-8 Hz)to which the human body is sensitive to vertical vibration.In addition,under real random road spectrum excitation,the HFBVI can achieve low-frequency vibration isolation close to 2 Hz,providing new prospects for ensuring the health of heavy-duty truck drivers.

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.

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.

深基坑组合型钢支撑梁稳定性分析

深基坑组合型钢支撑由多根H型钢通过高强螺栓连接而成,支撑梁被横梁和立柱组成的门架近似等间距支承,实践表明支撑梁承载力常被高估。根据支撑体系实际受力情况简化问题,假定横梁和立柱组成的门架为弹性支座,将均布在横梁上的多根型钢简化为作用横梁跨中的单根型钢,利用位移连续条件,先推导出单根横梁时支撑梁在竖向平面内稳定性计算长度取相邻横梁间距所要求的最小横梁刚度,而后分析横梁数量和结构初始缺陷对横梁刚度要求的影响,并指出将支撑梁简化为单根型钢偏于安全,还探讨将弹性分析结果应用到弹塑性结构的方法。结合某深基坑工程实例,按横梁强度计算的支撑梁承载力和支撑梁轴力监测结果都小于按支撑梁截面计算的承载力,说明所用横梁刚度低于最小刚度要求,支撑梁承载力由横梁刚度控制;现有立柱抗侧刚度不及横梁刚度1/10,支撑梁在水平面内稳定计算长度应取支撑梁全长。

麦弗逊式螺旋弹簧悬架的刚度与阻尼特性分析

为提高麦弗逊式独立悬架分析与设计效率,建立悬架受力分析以及进行刚度与阻尼计算的数学模型,给出按选定的偏频和相对阻尼比确定螺旋弹簧刚度和减震器阻尼参数的设计步骤,并研制了方便实用的麦弗逊螺旋弹簧悬架系统刚度和阻尼参数分析与设计计算软件.虚拟样机试验结果验证了数学模型和计算软件的正确性.