On the design of a high-static-low-dynamic stiffness isolator using linear mechanical springs and magnets

The frequency range over which a linear passive vibration isolator is effective is often limited by the mount stiffness required to support a static load. This can be improved upon by incorporating a negative stiffness element in the mount such that the dynamic stiffness is much less than the static stiffness. In this case, it can be referred to as a high-static-low-dynamic stiffness (HSLDS) mount. This paper is concerned with a theoretical and experimental study of one such mount. It comprises two vertical mechanical springs between which an isolated mass is mounted. At the outer edge of each spring, there is a permanent magnet. In the experimental work reported here, the isolated mass is also a magnet arranged so that it is attracted by the other magnets. Thus, the combination of magnets acts as a negative stiffness counteracting the positive stiffness provided by the mechanical springs. Although the HSLDS suspension system will inevitably be nonlinear, it is shown that for small oscillations the mount considered here is linear. The measured transmissibility is compared with a comparable linear mass-spring-damper system to show the advantages offered by the HSLDS mount.     

一种光电载荷非线性隔振装置的研究

针对光电载荷对隔振性能的需求,提出一种采用菱形连杆机构作为负刚度组件,具有高静、低动刚度特点的非线性隔振器（简称菱形HSLDS隔振器）。采用静力学分析方法,建立了隔振器数学模型,研究了刚度参数设定以及非线性调节方法;利用谐波平衡法（HBM）求解动力学方程,分析了各参数对隔振性能的影响关系;采用动力学仿真软件ADAMS及实物样机对理论模型与结论进行了验证。测试结果表明:菱形HSLDS隔振器具有较方便的参数调整能力,零位刚度及刚度非线性可通过拉簧参数与连杆参数进行设定、优化,隔振的刚度非线性优化程度受主隔振器阻尼以及零位刚度参数影响。相比于传统线性隔振器,菱形HSLDS具有显著的非线性隔振优势,可较好地满足光电载荷隔振需求。     

Analysis and experiment of a vibration isolator using a novel magnetic spring with negative stiffness

The vibration isolator using a novel magnetic spring with negative stiffness (MS-NS) is proposed in this paper. The proposed isolator which combines a positive stiffness spring with the MS-NS in parallel possesses the characteristic of high-static–low-dynamic stiffness. The MS-NS is composed of three cuboidal magnets configured in repulsive interaction. An analytical expression of the stiffness of the MS-NS is derived by using the magnetic charge model, and the approximation to the exact analytical expression is sought. Then, the nonlinearity of the stiffness is analyzed, and it is shown that the MS-NS is approximately linear for small oscillations. In order to validate the correctness and effectiveness of the MS-NS, the vibration transmissibility of the proposed isolator with and without the MS-NS is measured. The experimental results demonstrate that combining a vibration isolator with the MS-NS in parallel can lower the natural frequency of the isolator; and the analytical calculations and experimental results show a good consistency.     

菱形HSLDS隔振器负刚度机构质量及摩擦力影响分析

以菱形负刚度机构HSLDS(high static low dynamic stiffness)隔振器(简称菱形HSLDS隔振器)为研究目标,采用虚功法建立负刚度机构等效摩擦力模型,并以拉格朗日方法建立包含负刚度机构质量及摩擦力因素的动力学方程;利用谐波平衡法(HBM)求解动力学方程,分析了负刚度机构质量及摩擦力对隔振...     

Experimental Investigation of Nonlinear Vibration Isolator with Fluidic Actuators (NLVIFA)

This paper elaborates a nonlinear fluidic low frequency vibration isolator designed with the characteristics of quasi-zero stiffness (QZS). The existing model of QZS vibration isolator enhances amplitude of vibration and attenuating vibration frequencies. This concern with displacement plays a vital role in the performance and instability of oblique spring setup reduces the isolator performance in horizontal non-nominal loads, in this accordance; this paper associates double acting hydraulic cylinder (fluidic actuators in short) in oblique and helical coil spring. An approximate expression of unique analytical relationship between the stiffness of vertical spring and bulk modulus of the fluid is derived for Quasi – Zero Stiffness Non-Linear Vibration Isolator with Fluidic Actuators (NLVIFA in short) system and the force transmissibility is formulated and damping ratio are discussed for characteristic analysis. Modal analysis carried out and compared with analytical results and an experimental prototype is developed and investigated. The performance of the NLVIFA reduces the external embarrassment more at low frequencies and the series of experimental studies showing that the soft nonlinearity causes limitation in the resonant frequency thereupon the isolation will be enhanced and NLVIFA greatly outperform some other type of nonlinear isolators.     

Octo-strut vibration isolation platform and its application to whole spacecraft vibration isolation

Stewart platform is widely used for vibration isolation and precise pointing. As it is a statically determinate structure, if any strut has fault, a disaster could be unavoidable. In the present paper, an octo-strut passive vibration isolation platform with redundancy is introduced and applied to whole-spacecraft vibration isolation. This platform is modeled with the Newton–Euler method. To avoid such possibility that the spacecraft may interact with the fairing, an approach of stiffness design is proposed to reinforce the rotation stiffness of the platform. With the mathematical model, design parameters of the isolator that will affect the nature frequencies of the isolator-spacecraft system are studied. The transmissibility of the isolator topped with rigid and flexible spacecraft is also studied. Results of analytical and numerical studies show that the octo-strut platform is a reliable and effective approach to improving the dynamic environment of a spacecraft.     

Design and experiment of a compact quasi-zero-stiffness isolator capable of a wide range of loads

This paper proposes the design and experiment of a vibration isolator capable of isolating a wide range of loads. The isolator consists of two oblique springs and one vertical spring to achieve quasi-zero stiffness at the equilibrium position. The quasi-zero-stiffness characteristic makes the isolator attenuate external disturbance more at low frequencies, when compared with linear isolators. Unlike previous studies, this paper focuses on the analysis of the effect of different loads and the implementation of an adjustment mechanism to handle a wide range of loads. To ensure zero stiffness under imperfect stiffness matching, a lateral adjustment mechanism is also proposed. Instead of using coil springs, special planar springs are designed to realize the isolator in a compact space. Static and dynamic models are developed to evaluate the effect of key design parameters so that the isolator can have a wide isolation range without sacrificing its size. A prototype and its associated experiments are presented to validate the transmissibility curves under three different loads. The results clearly show the advantage of quasi-zero-stiffness isolators against linear isolators.     

A study of a nonlinear vibration isolator with a quasi-zero stiffness characteristic

A vibration isolator consisting of a vertical linear spring and two nonlinear pre-stressed oblique springs is considered in this paper. The system has both geometrical and physical nonlinearity. Firstly, a static analysis is carried out. The softening parameter leading to quasi-zero dynamic stiffness at the equilibrium position is obtained as a function of the initial geometry, pre-stress and the stiffness of the springs. The optimal combination of the system parameters is found that maximises the displacement from the equilibrium position when the prescribed stiffness is equal to that of the vertical spring alone. It also satisfies the condition that the dynamic stiffness only changes slightly in the neighbourhood of the static equilibrium position. For these values, a dynamical analysis of the isolator under asymmetric excitation is performed to quantify the undesirable effects of the nonlinearities. It includes considering the possibilities of the appearance of period-doubling bifurcation and its development into chaotic motion. For this purpose, approximate analytical methods and numerical simulations accompanied with qualitative methods including phase plane plots, Poincaré maps and Lyapunov exponents are used. Finally, the frequency at which the first period-doubling bifurcation appears is found and the effect of damping on this frequency determined.     

Vibration control for an overhung roller in textile machine considering the stiffness of control device stand

This paper treats a vibration control method that can be used in textile machinery to reduce the unbalanced vibration of an overhung roller–motor system. To control the vibration of the overhung roller, a drive motor with a hybrid type vibration control device consisted with rubber springs and electromagnets is used. When the vibration control system is set up in the textile machinery for industrial use, the stand supporting the control system to the base may be assumed not too rigid but elastic. For a certain value of the elastic stand stiffness, the vibration control performance of the overhung roller becomes very low. In order to prevent this deterioration, a stiffness control achieved by a positive feedback of the displacement signal of the rubber spring is proposed and the effectiveness of the stiffness control is confirmed by simulations and experiments.     

Vibration isolation characteristics of a nonlinear isolator using Euler buckled beam as negative stiffness corrector: A theoretical and experimental study

This paper concerns the vibration isolation characteristics of a nonlinear isolator using Euler buckled beams as negative stiffness corrector. Both analytical and experimental studies are carried out. The Harmonic Balance Method (HBM) is used to determine the primary resonance response for the single degree of freedom (SDOF) nonlinear system composed by a loaded mass and the nonlinear isolator. The distuning of the loaded mass is taken into consideration, resulting in a Helmoholtz–Duffing equation. The performance of the nonlinear isolator is evaluated by the defined two kinds of transmissibility and compared with that of the linear isolator without the stiffness corrector. The study shows that the asymmetric SDOF nonlinear system can behave like a purely softening, a softening–hardening or a purely hardening system, depending on the magnitude of the excitation level. An experimental apparatus is set up to validate the analytical results. The transmissibility results of the SDOF nonlinear system under base excitation with both discrete sinusoidal frequencies and slowly forward and backward sweeps are given and discussed. The complex jump phenomena under different excitation levels are identified. By introducing the stiffness corrector, the starting frequency of isolation of the nonlinear isolator is found to be lower than that of the linear one with the same support capacity. The proposed nonlinear isolator performs well in applications where the excitation amplitude is not too large.     

Modelling and dynamic properties of a novel solid and liquid mixture vibration isolator

Solid and Liquid Mixture (SALiM) vibration isolator is a new isolator which is designed for vibration isolation of heavy equipment with low frequency. The isolator contains liquid and elastic solid elements as working media. To get the stiffness property of the isolator, this paper establishes the mechanics model of elastic solid elements by introducing plate-shell model. Considering geometry nonlinearity, the stiffness of the element under outer liquid pressure and inner air pressure was obtained by perturbation method. Then the stiffness of isolator is derived. As a result, the stiffness is piecewise linear-nonlinear and determined by parameters of the elastic elements and elastic container. In addition, the equation of motion (EOM) of a single degree of freedom system supported by a SALiM isolator is given. The properties of the frequency response function (FRF) of the system are analysed using averaging method which is a classical approximation approach for estimating nonlinear system FRF. And it is found that the system with SALiM isolator shows softening stiffness behaviour. The jumping phenomenon clearly occurs under certain condition. Finally, the vibration isolation property is predicted based on energy transmissibility (ET) in different cases.     

Modelling of tuning of an ultra low frequency Roberts Linkage vibration isolator

We present an analytical model for a Roberts Linkage used as an ultra low frequency vibration isolator. The Roberts Linkage is a structure that simulates a very long radius conical pendulum, at a relatively small height. We show through an analytical solution that it is possible to independently tune the centre of percussion and the resonant frequency for arbitrary geometrical configurations. The result is shown to provide a practical tuning solution, which achieves near ideal vibration isolation.     

Surface effect on free transverse vibrations and dynamic instability of current-carrying nanowires in the presence of a longitudinal magnetic field

Free transverse vibration and instability of current-carrying nanowires immersed in a longitudinal magnetic field are of concern. On the basis of the surface elasticity theory, a model is developed to investigate the problem. The analytical expressions of dynamic transverse displacements as well as natural frequencies of the magnetically affected nanowire for carrying electric current are obtained. The influences of the surface effect, initial tensile force within the nanowire, strength of the longitudinal magnetic field, and electric current on the natural frequencies as well as dynamic displacements are examined. The obtained results reveal that the transverse stiffness of the nanostructure is enhanced by the surface effect and the initial tensile force, while electric current or longitudinal magnetic field reduces the nanowire's stiffness. The condition which leads to the dynamic instability of the nanostructure is obtained. Further, the roles of the influential parameters on its stability are inclusively discussed.     

Nonlinear vibration isolator with adjustable restoring force

This paper presents a vertical quasi-zero stiffness (QZS) vibration isolator with a mechanism for adjusting restoring force. QZS vibration isolators have high initial stiffness and QZS around the static equilibrium position. This way, excessive deformation due to self-weight can be avoided while having enough vibration reduction capability to dynamic excitations. One of the main issues left for QZS vibration isolators is the difficulty in keeping the vibration reduction capability when the vibration isolated object is replaced. In such a case, adjustment of its restoring force becomes necessary in accordance with the self-weight of the newly placed vibration isolated object. This paper attempts to address this issue by proposing a mechanism that enables quick and easy adjustment of the restoring force of a QZS vibration isolator. The proposed mechanism consists of cranks and a screw jack. With the present mechanism, the restoring force provided by horizontally placed springs can be converted into the vertical restoring force of the vibration isolator. In the conversion, the vertical resisting force can be adjusted simply by applying and removing torque to the screw jack to change and hold the angle of inclined bars placed in the cranks. In this study, a prototype of a class of QZS vibration isolator having the proposed mechanism is produced. Shaking table tests are performed to demonstrate the efficacy of the present mechanism, where the produced prototype is subjected to various sinusoidal and earthquake ground motions. It is demonstrated through the shaking table tests that the produced prototype can reduce the response acceleration within the same tolerance even when the mass of the vibration isolated object is changed.     

Performance analysis of nonlinear vibration isolator with magneto-rheological damper

A nonlinear vibration isolator is considered to study effectiveness of isolation against harmonic force and displacement excitations. Nonlinearity in the magneto-rheological (MR) fluid based damper as well as in the elastic member is taken into account. The MR-damper has been modeled including Bouc–Wen hysteretic element and the spring is taken to have cubic nonlinearity. Analytical expression for the energy dissipation characteristics of the damper has been derived. Near resonant response of the isolated mass is obtained by a modified averaging technique suitable for hysteretic type nonlinearity present in the system. The performance of the isolators is estimated for various nonlinear stiffness values, both hardening and softening types. Different performance measures are also proposed to judge the performance of the nonlinear isolator.     

Control of a unique active vibration isolator with a phase compensation technique and automatic on/off switching

This work examines the characteristics of a unique active vibration isolator and develops a control strategy for it. The proposed active vibration isolator is introduced and its dynamic model is presented. A characterization study is conducted to identify system parameters. It is shown that with a simple proportional feedback the closed-loop system has a very narrow stability margin due to the inherent dynamics of the actuator. To improve the stability of the closed-loop system and enhance the performance of vibration isolation, a phase compensator is incorporated in the control scheme. An optimization problem is formulated to determine the optimum controller parameters by minimizing the 2nd norm of the displacement transmissibility. Both absolute position feedback and relative position feedback are considered. In real time implementation, an automatic on/off switching strategy is devised to take full advantage of both the active isolator and passive isolator. The experimental results show that with the proposed control scheme, the isolator is capable of suppressing base excitations effectively.     

Design optimization of a damped hybrid vibration absorber

In this article, the H_∞ optimization design of a hybrid vibration absorber (HVA), including both passive and active elements, for the minimization of the resonant vibration amplitude of a single degree-of-freedom (sdof) vibrating structure is derived by using the fixed-points theory. The optimum tuning parameters are the feedback gain, the tuning frequency, damping and mass ratios of the absorber. The effects of these parameters on the vibration reduction of the primary structure are revealed based on the analytical model. Design parameters of both passive and active elements of the HVA are optimized for the minimization of the resonant vibration amplitude of the primary system. One of the inherent limitations of the traditional passive vibration absorber is that its vibration absorption is low if the mass ratio between the absorber mass and the mass of the primary structure is low. The proposed HVA overcomes this limitation and provides very good vibration reduction performance even at a low mass ratio. The proposed optimized HVA is compared to a recently published HVA designed for similar propose and it shows that the present design requires less energy for the active element of the HVA than the compared design.     

Vibration isolation via a scissor-like structured platform

More and more attentions are attracted to the analysis and design of nonlinear vibration control/isolation systems for better isolation performance. In this study, an isolation platform with n-layer scissor-like truss structure is investigated to explore novel design of passive/semi-active/active vibration control/isolation systems and to exploit potential nonlinear benefits in vibration suppression. Due to the special scissor-like structure, the dynamic response of the platform has inherent nonlinearities both in equivalent damping and stiffness characteristics (although only linear components are applied), and demonstrates good loading capacity and excellent equilibrium stability. With the mathematical modeling and analysis of the equivalent stiffness and damping of the system, it is shown that: (a) the structural nonlinearity in the system is very helpful in vibration isolation, (b) both equivalent stiffness and damping characteristics are nonlinear and could be designed/adjusted to a desired nonlinearity by tuning structural parameters, and (c) superior vibration isolation performances (e.g., quasi-zero stiffness characteristics etc.) can be achieved with different structural parameters. This scissor-like truss structure can potentially be employed in different engineering practices for much better vibration isolation or control.     

机械转镜隔离器的光束位置复原特性研究

本文给出了运动光束位置复原的分析方法,对用于高功率激光核聚变实验装置的高速机械转镜隔离器的光束复原特性作了详细的讨论,并得到了光束复原应满足的条件.     

Vibration modelling of helical springs with non-uniform ends

Helical springs constitute an integral part of many mechanical systems. Usually, a helical spring is modelled as a massless, frequency independent stiffness element. For a typical suspension spring, these assumptions are only valid in the quasi-static case or at low frequencies. At higher frequencies, the influence of the internal resonances of the spring grows and thus a detailed model is required. In some cases, such as when the spring is uniform, analytical models can be developed. However, in typical springs, only the central turns are uniform; the ends are often not (for example, having a varying helix angle or cross-section). Thus, obtaining analytical models in this case can be very difficult if at all possible. In this paper, the modelling of such non-uniform springs are considered. The uniform (central) part of helical springs is modelled using the wave and finite element (WFE) method since a helical spring can be regarded as a curved waveguide. The WFE model is obtained by post-processing the finite element (FE) model of a single straight or curved beam element using periodic structure theory. This yields the wave characteristics which can be used to find the dynamic stiffness matrix of the central turns of the spring. As for the non-uniform ends, they are modelled using the standard finite element (FE) method. The dynamic stiffness matrices of the ends and the central turns can be assembled as in standard FE yielding a FE/WFE model whose size is much smaller than a full FE model of the spring. This can be used to predict the stiffness of the spring and the force transmissibility. Numerical examples are presented.