Magnetic Vibration Isolator Research Articles

Multi-objective optimization design and experiment for a magnetic micro-vibration isolator considering stiffness trade-offs.

Vibration substantially degrades machining quality and measurement accuracy in ultra-precision processes, necessitating the implementation of vibration isolators to mitigate these effects. Magnetic vibration isolators represent a promising alternative due to their wide isolation frequency range, low energy consumption, and compatibility with vacuum environments. In designing the quasi-zero stiffness magnetic vibration isolator, the particle swarm optimization algorithm is employed to balance multiple performance indicators. To address the limitations of conventional optimization methods, which excessively prioritize stiffness and fail to encompass the entire performance spectrum of magnetic vibration isolators, this study presents an innovative optimization approach. This novel strategy directly enhances vibration isolation by integrating transmissibility and compliance considerations. Structural parameters for two types of magnetic vibration isolators were established through optimizations utilizing both conventional and innovative techniques. Simulations and experiments demonstrate that isolators developed using the proposed optimization method outperform those designed with conventional strategies, thereby validating the effectiveness of this advancement. The insights presented in this paper illuminate a novel and effective pathway for the conceptualization and refinement of magnetic vibration isolators.

Modeling and analysis of the magnetic force and stiffness of a low-frequency vibration isolator with axial magnetized magnetic rings.

The vibration isolator is a key part of many ultra-precision machines and measuring apparatus. Magnetic suspension vibration isolators (MSVIs) will have excellent application prospects in these instruments to restrain external oscillations. So this paper firstly proposes a new basic configuration of MSVI. Then, in order to study the mechanical characteristics of the MSVI, an analytical expression of the magnetic force is established. The effectiveness of which is demonstrated by the experiment and finite element analysis (FEA). The stiffness of the MSVI is obtained by the derivative of the established analytical magnetic force. Both the axial magnetic force and stiffness appear strong nonlinearity when the inner ring moves at both ends of the fixed outer ring. While the inner ring travels in the middle of the fixed outer one, the axial magnetic force and stiffness indicate approximate linearity with enough bearing capacity. Furthermore, parametric analysis, based on the created magnetic force and stiffness, is performed. The analytical results show that the axial magnetic stiffness may achieve a zero or even negative stiffness value in this range at some size dimensions. The MSVI appears to have a negative stiffness characteristic. More importantly, if a linear and nonlinear positive stiffness spring is combined with the MSVI, it can increase the load capacity of the MSVI. As an example study, the vibration isolation performance of the MSVI is analyzed. The vibration isolation calculation and experiment with the zero stiffness MSVI will be the further focus of the paper.

Magnetic Cooling and Vibration Isolation of a Sub-kHz Mechanical Resonator

We report recent progress toward the realization of a sub-mK, low-vibration environment at the bottom stage of a dry dilution refrigerator for use in mechanical tests of quantum mechanics. Using adiabatic nuclear demagnetization, we have cooled a silicon cantilever force sensor to Tapprox 1 mK. The temperature of the tip holder of the cantilever chip was determined via a primary magnetic flux noise thermometer. The quality factor of the cantilever continues to increase with decreasing temperature, reaching Qapprox 4cdot 10^4 at 2 mK. To demonstrate that the vibration isolation is not compromised, we report the detection of the thermal motion of the cantilever down to T approx 20 mK, only limited by the coupling to the SQUID readout circuit. We discuss feasible improvements that will allow us to probe unexplored regions of the parameter space of continuous spontaneous localization models.

Six degree of freedom quasi-zero stiffness magnetic spring with active control: Theoretical analysis of passive versus active stability for vibration isolation

This paper presents a comparison of passive and active stability analyses of a six degree of freedom (DOF) quasi-zero stiffness magnetic levitation vibration isolation system. The passive rotational stability of the system is varied by changing lever arms, and its effects on the vibration isolation performance and control cost are investigated via static and dynamic simulations. The practicality of the design is also discussed by simulating off-centred load scenarios. It is shown that the vibration isolation bandwidth reduces with increasing passive stiffness when such (passively) stable DOFs are close to being uncontrolled, and that the passively unstable rotational DOF benefits from an optimal control action. In practice, the effect of increasing the passive stability on the isolation performance is insignificant as the controller would typically be designed with a relatively large stability margin to account for uncertainties, thus dominating the closed-loop response. In contrast, the control does benefit from the improved passive stability. The robustness of the designed control system to probable time delay, sensor measurement noise, and actuation error is simulated and verified. Additionally, the importance of taking cross-coupling into consideration when designing a stabilising control through a decentralised control scheme is highlighted.

Analysis and Experiment of Vibration Isolation Performance of a Magnetic Levitation Vibration Isolator with Rectangular Permanent Magnets

Magnetic levitation vibration isolator (MLVI) is an efficient method to suppress the external oscillations transmitted to some small instruments in the laboratories. This paper first presents a basic configuration of a kind of MLVI with four sets of the repulsive rectangular permanent magnets. Then, the parametric studies are carried out to discuss how the structure and air gap parameters influence the magnetic force, stiffness, and natural frequency of the MLVI. Moreover, as an MLVI case study, an operating point is set and the size dimensions of the MLVI are determined based on the parametric studies. The transmissibility of the MLVI is calculated by the dynamic equation at the operating point. An experimental table is constructed for the analytical validation. The experimental results proved the validity of the theoretical analysis and showed that there are good consistencies between the experiment results and the theoretical calculation, which obtains that the natural frequency of the MLVI is 4.75 Hz and the initial cut-off frequency of the MLVI is approximately 6 Hz at the operating point. When the frequency of the external oscillations reaches 16 Hz, the attenuation amplitude becomes − 20 dB. All of these show ability of the proposed MLVI to attain low-frequency vibration isolation, and provide a new type of basic passive MLVI to exploit an active MLVI for practical applications.

Analysis and Design of Magnetic Levitation and Mechanical Spring Compound Vibration Isolation Control System

In this paper, the magnetic levitation and mechanical spring compound vibration isolation control system is designed by applying maglev active control on the basis of mechanical vibration isolator. The system can effectively solve the problems of fixed structure parameters and poor environmental adaptability of passive vibration isolators, and can be applied to the anti-vibration protection of precision instruments in complex environments. This paper analyses the mechanism and characteristics of maglev vibration isolation, deduces the dynamic model of the system, discusses the design of the active vibration isolation control strategies, and carries out several simulation experiments of vibration isolation in different environments. The results show that the design scheme of the system is reasonable and feasible.

Considering Operating Point Variation in 3-D Analytical Charge Model Used for Design of Low-Stiffness Permanent Magnet Vibration Isolator

Vibration isolators are a key technology in ultraprecision machining and ultraprecision measurements. The increasing performance requirements of magnetic vibration isolation systems (MVISs) continue to demand improvements in the accuracy on which these devices are modeled. However, a serious constraint exists in designing MVISs, as high stiffnesses will be introduced by nonlinear force–displacement characteristics. The traditional analytic magnetic charge model assumes that the relative magnetic permeability $\mu _{r} = 1$ , which causes the accuracy of the magnetic analytic model of the MVIS to decrease. To solve this defect, in this article, low-stiffness MVISs are designed by using the three-dimensional analytic magnetic charge model while considering the variations of the operating point. The optimized parameters of the MVIS are then obtained by combining the genetic algorithm. The feasibility of the proposed analytical charge method is verified from the results of experimental measurements and finite-element methods. The results of this article provide a powerful tool for the design of a high-performance MVIS and provide important support for the ultimate goal of ultraprecision machining and measurements.

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

A novel quasi-zero stiffness nonlinear magnetic isolator is designed by using magnetic springs in parallel with linear positive stiffness spring. Through the static analysis, the mathematical expressions of force-displacement-current and stiffness-displacement-current of the system are established, and the necessary conditions for the normal function and geometric parameters of the system are obtained. The nonlinear dynamic equations of the system under external excitation force are established. The amplitude and frequency characteristics of the system are deduced by harmonic balance method. The influence of system parameters and external excitation amplitude on the dynamic characteristics of the system is analyzed. Results showed that the vibration of the system can be controlled by controlling the electromagnet current or increasing the damping coefficient while the external excitation amplitude is kept in a certain of range. The researches provided a theoretical guidance for the design and application of the new quasi-zero stiffness nonlinear magnetic isolation system.

Study on the dynamics of two-degree-of-freedom system with variable stiffness magnetic isolator

This paper presents a novel variable stiffness isolator designed by magnetic springs in parallel with linear positive stiffness spring. Firstly, the two-degree-of-freedom vibration system model with variable stiffness magnetic isolator is established. The amplitude frequency characteristic equation of the system is derived based on the multi-harmonic method, and the corresponding curve of the relationship between the amplitude and frequency is given. The influence of the current on the curve is researched. Results showed that there are two pseudo-resonant peaks in the amplitude–frequency curve, and one is in the low frequency band, the other exists in higher frequency band. The first peak does not exhibit the frequency shift, but the second one bends to the natural frequency obviously. With the increasing of the current, the peaks decrease and the backbone curve changes greatly for the second resonant crest. The Lyapunov exponent curve around the resonant frequency is calculated. It is shown that there is chaotic parameter region for the system, and chaos can be controlled with the variable stiffness magnetic vibration isolator according to this research, which is beneficial to the design of nonlinear vibration isolation system.

Research on typical topologies of a tubular horizontal-gap passive magnetic levitation vibration isolator

Magnetic levitation vibration isolators have attracted more and more attention in the field of high-precision measuring and machining equipment. In this paper, we describe a tubular horizontal-gap passive magnetic levitation vibration isolator. Four typical topologies of the tubular horizontal-gap passive magnetic levitation vibration isolator are proposed. The analytical expression of magnetic force is derived. The relationship between levitation force, force density, force ripple and major structural parameters are analysed by finite element method, which is conductive to the design and optimization of the tubular horizontal-gap passive magnetic levitation vibration isolator. The force characteristics of different topologies of the tubular horizontal-gap passive magnetic levitation vibration isolator are compared and evaluated from the aspect of force density, force ripple and manufacturability. In comparison with conventional passive magnetic levitation vibration isolators, the proposed tubular horizontal-gap passive magnetic levitation vibration isolator shows advantage in higher force density.

Investigation on the design of magnetic spring-beam vibration isolator with negative stiffness characteristic

Investigation on the design of magnetic spring-beam vibration isolator with negative stiffness characteristic

Simulated and experimental studies on a high-static-low-dynamic stiffness isolator using magnetic negative stiffness spring

For the purpose of isolating the low frequency vibration, a magnetic vibration isolator with the feature of high-static-low-dynamic stiffness (HSLDS) is developed in this paper, which is constructed by combining a magnetic negative stiffness spring (MNSS) with a spiral flexure spring (SFS) in parallel. The MNSS comprises three magnetic rings configured in attraction and is utilized to reduce the resonant frequency of the isolator. Then an analytical expression of magnetic negative stiffness (MNS) of the MNSS is deduced in terms of the current model, and an approximation to the MNS is further sought. To support the object, the axial positive stiffness of SFSs, which can behave with a smaller static deformation if a specified weight is applied, is analyzed with finite element method (FEM). After that, the governing equation of the isolator is established and solved via harmonic balance method (HBM). Finally, an experimental prototype is developed and tested. The experimental results demonstrate that the MNSS can reduce the resonant frequency of the isolator to expand the isolation frequency band to low frequency range; and the theoretical calculations and experimental results shows a good agreement.

Electromagnetic and Mechanical Characteristics Analysis of a Flat-Type Vertical-Gap Passive Magnetic Levitation Vibration Isolator

In this paper, we describe a flat-type vertical-gap passive magnetic levitation vibration isolator (FVPMLVI) for active vibration isolation system (AVIS). A dual-stator scheme and a special stator magnet array are adopted in the proposed FVPMLVI, which has the effect of decreasing its natural frequency, and this enhances the vibration isolation capability of the FVPMLVI. The structure, operating principle, analytical model, and electromagnetic and mechanical characteristics of the FVPMLVI are investigated. The relationship between the force characteristics (levitation force, horizontal force, force ripple, and force density) and major structural parameters (width and thickness of stator and mover magnets) is analyzed by finite element method. The experiment result is in good agreement with the theoretical analysis.

A comparison between cylindrical and cross-shaped magnetic vibration isolators: ideal and practical

Abstract In this paper a cross-shaped isolator consisting of cuboidal magnets and a cylindrical isolator are compared by resonance frequency to volume ratio and shape. Both isolators are capable of obtaining a low resonance frequency, i.e. 0.15 Hz and 0.01 Hz for the cross and cylinder, respectively. The volume of both isolators is comparable, only the shape is different, resulting in a tall structure with a small footprint for the cross and a flat with a large diameter cylindrical structure. A sensitivity analysis shows that due to the large amount of magnets, the cross-shaped isolator is less sensitive to manufacturing tolerances

Analytical Force, Stiffness, and Resonance Frequency Calculations of a Magnetic Vibration Isolator for a Microbalance

The accuracy of a microbalance is highly dependent on the level of floor vibrations. One strategy to reduce floor vibrations is a magnetic vibration isolator. Magnetic vibration isolators have the possibility to obtain a zero-stiffness region, which is beneficial for attenuating vibrations. In this paper, a 3-D analytical magnetic surface charge model is used to calculate the spring characteristics of a cone-shaped magnetic vibration isolator for different angles.

On the performance of a single degree-of-freedom high-static-low-dynamic stiffness magnetic vibration isolator

Recently, a mechanism for the High-Static-Low-Dynamic Stiffness (HSLDS) magnetic vibration isolator was introduced to overcome the fundamental limitation of a linear vibration isolator. The mechanism has a particularly useful property whereby the stiffness of the isolator is large enough to hold the weight of a load, but produces much softer stiffness when it responds to a dynamic motion. That is, the HSLDS magnetic vibration isolator shows highly nonlinear vibration isolation characteristic depending on the system parameters as well as the amplitude of base excitation. In this paper, the isolation performance of the HSLDS magnetic vibration isolator is examined both analytically and experimentally by considering both the key system parameter and the excitation amplitude of the base. The results show that the vibration isolation performance improves as the amplitude of base excitation increases. It was also found that the suggested key system parameter has an important role in the design of a practical system, and guarantees the minimum isolation performance regardless of the excitation amplitude.

Recent Study on the Passive and Active Vibration Isolators

The vibration isolators have witnessed significant developments due to pressing demands for high resolution metrology and manufacturing, optical, physical and chemical experiments. In the view of these requirements, the engineers and physicists have exploited different types of vibration isolators. This paper firstly presents the recent developments on the passive vibration isolators. It finds that the passive vibration isolators can constrain the high frequency oscillation. The active control is the efficient method to cancel the low frequency vibration. Then, the paper is concerned with the recent advances on the active vibration isolator. The appropriate actuator, sensor and advanced control method are the key component of the active vibration isolator to enhance their vibration isolation properties. Finally, the author proposes that the magnetic suspension vibration isolator is a future research direction in the field of the vibration isolation.

Design and Analysis of a Magnetic QZS Vibration Isolator

In this paper, a novel nonlinear magnetic vibration isolator is developed. The developed isolators possess the characteristic of quasi-zero stiffness (QZS). It is obtained by connecting a vertical coil spring with two permanent magnet springs in couple with three permanent magnets. Firstly, the permanent magnet spring is introduced, and approximate expression of repulsive force in the permanent magnet spring is proposed. Secondly, characteristic analysis of system is investigated. It is shown that there is a unique relationship between the stiffness of vertical spring and parameters of system that yields a QZS system. The approximate stiffness of QZS system can be used instead of the analytical stiffness in dynamic analysis.

Fuzzy control of a semi-active multiple degree-of-freedom vibration isolation system

Semi-active isolation systems fill the gap between passive and active systems, delivering the versatility and adaptability of fully active systems, by expending a small amount of energy to change system parameters such as stiffness and damping. Magnetic suspension vibration isolation provides an excellent active isolation technology, and has shown useful characteristics including noncontact isolation, fast response, high reliability and long lifespan. However, because it is highly nonlinear and time variant, the control of magnetic suspension vibration isolation is an area that still requires further exploration. This paper presents a fuzzy control algorithm for a semi-active multi-degree-of-freedom vibration system. The fuzzy control is based on the minimization of the weighted sum of squared output forces. The output force response of the fuzzy, PID control semi-active vibration isolation system and passive system under the same excitation are simulated. The simulation results show that the fuzzy control system has much better performance in vibration isolation. An experimental platform is developed to test the performance of the magnetic suspension vibration isolation system and the proposed fuzzy control algorithm. The experimental results are found to be in good agreement with simulation.

Theoretical and experimental analyses of a nonlinear magnetic vibration isolator with quasi-zero-stiffness characteristic

This paper presents a nonlinear magnetic low-frequency vibration isolator designed with the characteristic of quasi-zero stiffness (QZS). An approximate expression of the magnet repulsive force is proposed and a unique analytical relationship between the stiffness of vertical spring and initial gap settings of the magnet springs is derived for the QZS system. Based on the harmonic balance (HB) method, the force transmissibility is formulated and the jumping frequencies, effect of excitation force and damping ratio are discussed for characteristic analysis. An experimental prototype is developed and tested. The performance of the QZS system is verified through a series of experimental studies showing that the new model greatly outperforms standard linear isolation systems especially in low-frequency domain. The tuning techniques for adapting to the change of loading mass and adjusting the QZS property in practice are also addressed.