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.

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.

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.

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。

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.

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。

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。

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.

准零刚度隔振座椅的理论与实验研究

针对车辆座椅的低频隔振问题,基于经典三弹簧准零刚度(Quasi-zero Stiffness,QZS)模型,建立座椅隔振实验模型,采用仿真和实验方法评价座椅模型的隔振性能。首先,对于三弹簧QZS模型,讨论参数对QZS的影响,获得QZS条件。其次,采用ADAMS仿真分析三弹簧QZS座椅模型,仿真和理论位移传递率具有较好的一致性。然后,制作三弹簧QZS座椅实验模型,通过静态实验调整实验模型获得QZS特性。最后,采用振动台对QZS座椅在1~10 Hz频率范围内开展大幅谐波位移激励隔振实验,同时采用Polytec激光测振仪分别获得振动台和座椅的位移响应,通过实验位移传递率评价QZS座椅隔振性能并验证理论分析正确性;相比对应的线性刚度隔振座椅,三弹簧QZS座椅具有较宽隔振频带和较小传递率。研究三弹簧QZS座椅的隔振性能可为后续可供实际工程应用的QZS座椅研究提供参考,同时也指出QZS座椅研究中存在的困难。

竖向可调式准零刚度隔振系统设计与特性分析

将3对线性弹簧装置并联组合,建立一类准零刚度隔振系统的分段非线性动力学模型。对隔振系统模型进行一系列静态分析,确保了隔振系统模型产生准零刚度特性的条件,并考虑外界误差对隔振系统的影响,给定系统参数范围。利用谐波平衡法求解动力学方程,确定系统动态特性,从而分析出系统受阻尼与幅频响应等影响,对参数控制变量,并与传统线性隔振的力传递率对比。结果表明:该准零刚度隔振系统模型在低频隔振性能上优于线性系统。

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.

Height Variation in the Summer Quasi-Zero Wind Layer over Dunhuang, Northwest China: A Diagnostic Study

This study investigates the variation in the stratospheric quasi-zero wind layer(QZWL)over Dunhuang,Gansu Province,China,on 9 August 2020 using sounding observations from the Dunhuang national reference station and the fifth generation of ECMWF atmospheric reanalysis data(ERA5).The QZWL over Dunhuang was located between 18.6 and 20.4 km on 9 August 2020.The South Asian high(SAH)and subtropical westerly jet jointly affected the QZWL.As the SAH retreated westward,the upper-level westerly jet over Dunhuang strengthened,and the jet axis height increased.As a result,the zonal westerly wind was lifted to a higher altitude,and the wind speed of 100–70 hPa increased,raising the QZWL.In addition,the east–west oscillation of the SAH occurred earlier than the adjustment of the QZWL altitude,which can be used as a forecasting indicator for the QZWL.To further explore the mechanism responsible for the QZWL adjustment,the forcing terms in the equations for zonal wind,kinetic energy,and vertical wind shear were analyzed.The results showed that the upper-level geopotential gradient was the basic physical factor forcing the local change in zonal wind and kinetic energy.The change in zonal wind and kinetic energy led to the uplift of the QZWL.The results revealed that the vertical shear of horizontal wind could adequately indicate the stratospheric QZWL location.

一种新型准零刚度系统结构设计与特性分析

针对传统的线性隔振系统,提出一种由永磁铁与拉伸弹簧组合而成的新型准零刚度隔振系统,设计用于光栅刻划机等精密设备的低频或超低频隔振。首先,建立系统的静力学模型,求出该系统满足准零刚度所需条件,分析各结构参数对隔振性能的影响;其次,通过对准零刚度隔振系统模型的动力学分析,建立该系统在简谐力激励下的非线性动力学方程,通过谐波平衡法求出系统力传递率,分析了系统中阻尼比、立方非线性项、外部干扰幅值对系统力传递率的影响;最后,与传统的线性隔振系统进行对比,验证了该新型准零刚度系统的可行性。

液压弹簧式准零刚度隔振系统特性分析

针对车载精密仪器低频隔振,文章将两个液压弹簧作为负刚度元件,并与竖直弹簧并联构造了一种新型准零刚度隔振系统。通过对系统进行静力学分析,得到了实现准零刚度特性的参数条件;利用平均法求解了系统在简谐力激励下的幅频响应;采用马蒂厄方程判别法对系统的稳定性进行了分析;又分析了线性刚度参数和非线性刚度参数对力传递率的影响。研究结果表明,相较于线性系统,准零刚度系统的起始隔振频率降低了54%左右。该研究使得车载精密仪器在低频乃至超低频工况下也不会轻易损坏,具有广泛的应用前景。