Eddy Current Damping Research Articles

Performance Study of a Permanent-Magnet Eddy Current Damper for Guns Recoil Control

Eddy current damper (ECD) is a promising device for dissipating kinetic energy in dynamic systems, this study is conducted to analyze the dynamic characterization and structural optimization of linear ECD under guns launch load. The recoil resistance of ECD under guns launch load is highly nonlinear at high recoil velocity, and the recoil resistance curve shows an increase-decrease-increasing shape like a “saddle”, which is not conducive to the stability of ECD during operation. The effects of several structural parameters on the dynamic characterization of ECD were studied in details. Results show that the air-gap size, the thickness of the magnetic conduction tube and conductive tube all have a notable influence on the recoil resistance curve of ECD. Moreover, BP neural network and genetic algorithm were used for structural optimization and the optimal value was verified by FEM. The optimization results indicate that the “saddle” shape of optimized recoil resistance curve is basically invisible. The fullness of the recoil resistance curve is significantly improved from 84.93% to 92.1%, which guaranteeing a smooth recoil movement. Finally, an impact loading test system for eddy current damper was built and the experimental results were basically consistent with the simulation results.

Design and modeling of a novel triple-magnet magnetic dynamic vibration absorber

A novel Triple-magnet Magnetic Dynamic Vibration Absorber (TMDVA) with Eddy Current Damping (ECD) and Coulomb damping is proposed in this paper. A multi-storey structure is selected as the vibration reduction object. First, the equivalent dynamics model of the TMDVA multi-storey structure vibration reduction system is established. Then the nonlinear magnetic force model is built according to the magnetizing current theory. Next, an ECD accurate calculation model is developed and derived based on Faraday’s law of electromagnetic induction. Because of the model, the ECD coefficient can be designed and adjusted arbitrarily. The full text indicates that adjusting the ECD coefficient properly can not only improve the vibration reduction effect of the TMDVA, but also reduce the sensitivity of the vibration reduction effect to the excitation amplitude as well as enhance the broadband vibration reduction performance and the robustness of the TMDVA. With its simple structure, the TMDVA is easy to be implemented and miniaturized. And the low frequency vibration reduction effect of the TMDVA is better than other existing magnetic dynamic vibration absorbers. Taken together, the TMDVA has potential application value in passive vibration reduction of engineering structures.

Optimal design of tuned inerter eddy current damper

The tuned inerter eddy current damper (TIECD) is a vibration absorber for seismic protection of structures. This paper studies the dynamic characteristics of the TIECD and investigates its optimal design considering the nonlinear behavior of the eddy current damping (ECD). The relationship between the nonlinear parameters of the ECD and its equivalent damping coefficient is revealed by utilizing the energy equivalent linearization method. The optimal design formulae for a TIECD are derived. The comparisons indicate that the proposed solutions offer an ideal estimation for the TIECD optimal design parameters of a lightly damped structure. In contrast with the linear tuned viscous mass damper (TVMD), the nonlinear TIECD achieves better control performances. However, the fluctuation in dynamic loads for the TIECD-structure system could lead to some special nonstationary motions. For the natural ground motions, a practical iterative design procedure for the TIECD is proposed. The results show that the control performance of the TIECD can reach the level of the TVMD with lower maximum damper forces.

A novel tuned inerter eddy current damper: modeling, optimization, and evaluation

This study proposes a novel tuned inerter eddy current damper using a rack and gear mechanism (TIECD), in which the configuration and mechanical model are introduced in detail. The TIECD design procedure for the seismic control of primary structures is established based on the effective damping ratio enhancement (EDRE) effect. A closed-form solution for TIECD optimal design under white noise excitation is presented using stochastic linearization techniques (SLT) with force-based and energy-based equivalence criteria. The control performance of the TIECD obtained by the closed-form solution, including the EDRE effect and effective damping ratio, is in good agreement with the numerical results obtained from the Monte Carlo simulation when a suitable TIECD critical velocity is selected; a large critical velocity is conducive to improving the accuracy of the closed-form solution. Note that the effect of a low structural damping level on the optimal design of TIECD can be ignored, which is beneficial in practical engineering applications because structural damping cannot be precisely known in most cases. Furthermore, several numerical studies have been conducted to investigate the availability of TIECD under real seismic excitations. The results indicate that the effectiveness of TIECD in mitigating the seismic response of primary structures is approximately the same as that of a tuned viscous mass damper (TVMD) and much greater than that of the viscous and eddy current dampers with the same damping parameters. It can be considered that the maximum damping force and maximum deformation of TIECD and TVMD are the key design factors for short-period and long-period structures, respectively, and the advantages of TIECD over TVMD are owing to the damping force limiting characteristics and small deformation.

Parametric optimization of the Eddy current dampers applied to a suspension bridge considering bi-directional earthquakes

The Eddy Current Damper (ECD) is a velocity-based passive energy dissipation device that can be used for structural vibration control. This study aims to reveal the damper behavior and determine the optimal parameters of the ECDs applied to a suspension bridge suffering from bi-directional earthquakes. The influence of the bi-directional vibration interaction on the damping force is theoretically investigated. An optimization method is proposed combining the Sobol Sequence sampling method, the Coefficient of Variation (COV) method, and the Backpropagation neural network (BPNN) algorithm. A numerical model of a long-span suspension bridge with bi-directional ECDs is established and taken as a case study to verify the feasibility of the proposed optimization method. The results indicate that the ECD system with bi-directional interaction will produce a larger maximum force and less energy dissipation than one without bi-directional interaction. The proposed optimization method possesses the characteristics of objectivity, accuracy, and effectiveness. The obtained optimal bi-directional ECDs can significantly reduce the longitudinal and transverse vibration. Failing to consider bi-directional effects will lead to an overestimation of longitudinal damper parameters and an underestimation to transverse ones, as well as ignoring the influence of damper length on its mechanical performance.

Seismic control of a smart structure with semiactive tuned mass damper and adaptive stiffness property

AbstractTo reduce structural responses under earthquake excitations effectively and improve their resilience, a smart structure with a semiactive tuned mass damper (STMD) on the top story and a semiactive adjustable stiffness device (SASD) on the first story which contributes to the structural adaptive stiffness property is developed in this study. The SASD consists of a diamond spring device composed of four linear springs and an electromagnetic actuator, which can change the angle of the diamond device and therefore retune the stiffness. Two typical STMDs developed previously are reviewed first, which are diamond device‐based STMD with variable stiffness and damping and pendulum‐type STMD with variable frequency and eddy current damping, respectively. Numerical results show that the proposed STMD has a better control performance than passive‐tuned mass damper and STMD with variable stiffness or damping acting independently. To enhance the seismic protection of the structure with an STMD on the top story further, based on the principle of base isolation, a diamond device‐based SASD is applied to the first story. The linear quadratic Gaussian‐based variable stiffness algorithm for SASD is proposed. A 10‐story building is presented as a case study. The variable stiffness range of SASD is discussed in detail, while it is found that a ±50% variable stiffness range achieves the best earthquake mitigation. Control effects of different numbers of SASD implemented along the height of the building are compared as well. Numerical results show that with the increase in the number of SASDs, the earthquake mitigation effect is better; however, the magnitude of the increase is decreasing. The smart structure with the combined SASD and STMD has an excellent seismic protection performance and is better than with SASD or STMD acting independently. Meanwhile, it is found that the proposed combination has a similar control effect to four SASDs installed from the first story to the fourth story, respectively, while it can reduce the number of additional electromechanical systems and the influence on the use function of the building.

Shock Vibration Control of SDOF Systems with Tubular Linear Eddy Current Dampers

The nonlinear dynamic characteristic of a tubular linear eddy current damper (TLECD) and the transient responses to shock excitations of a single-degree-of-freedom (SDOF) system with the TLECD are studied. First, the nonlinear force-velocity relationship of the TLECD is discussed using the finite element simulation and mathematical model fitting. Next, the influences of three forms of shock excitation and various mechanical parameters of the TLECD on shock vibration control of an SDOF system with the TLECD are investigated. Moreover, for the SDOF systems with the TLECD or the nonlinear fluid viscous dampers (FVD) at the same maximum displacement and maximum damper force, the time to reach the maximum displacement, the time to reach one-third of the maximum displacement, the energy input of the external loading, and the energy dissipation of dampers are analyzed and compared. Finally, the shock response spectrums (SRSs) of the SDOF system and the design flowchart for the TLECD are presented to provide a reference for shock vibration control of the SDOF system with the nonlinear TLECD and the design of TLECDs. The results show that there is an optimal dimensionless critical relative velocity that minimizes the dimensionless maximum damping force for reaching the target maximum displacement, and compared to the FVD, the TLECD greatly shortens the time to reach one-third of the maximum displacement.

Suppressing mechanical dissipation of diamagnetically levitated oscillator via engineering conductive geometry

Diamagnetically levitated oscillators of millimeter and submillimeter size are emerging ultrasensitive sensors for gravitylike force and acceleration measurements. However, improving the levitation capability while keeping mechanical dissipation low remains an open challenge. Here, we propose and experimentally demonstrate an engineering conductive geometry scheme to efficiently reduce the mechanical dissipation of a diamagnetically levitated oscillator made of pyrolytic graphite. We show that with a specially designed conductive geometry, the eddy current damping is reduced, and the reduction factor increases as the engraving pattern being denser. Under high vacuum and room temperature, eddy current damping is the dominant contribution to mechanical dissipation, and we reduce it by a factor of 50 in the experiment. Our work opens up a new way to achieve diamagnetically levitated oscillator with ultralow mechanical dissipation and strong levitation capability, a candidate platform for studying a broad range of fundamental physics.

Experimental investigation on the vortex-induced vibration of an arch steel bridge tower

This paper reports the wind tunnel study of the vortex-induced vibration (VIV) of a free-standing steel arch bridge tower with pentagon cross-section. The tests were carried out at different yaw angles β (0°–90°) of wind flow by employing a 1:50 scaled aeroelastic model. A series of aerodynamic measures were studied to mitigate the VIV of the tower at the most unfavorable yaw angle. Effects of turbulence intensity and structural damping on the VIV performance of the tower were evaluated. A sleeve-type eddy current damper (ECD) for increasing the structural damping of aeroelastic model was designed for reserved emergency measures. Experimental results indicate that the VIV occurs for a few yaw angles at wind velocity of 15–18 m/s and the maximum VIV amplitude happens for β = 35°. The aerodynamic measures are effective for some yaw angles but become invalid for other yaw angles. Compared to those in smooth flow, the VIV amplitude drops by 65% for a turbulence intensity of 8.5%. The VIV of the tower can be effectively suppressed by the eddy current damper which provides additional damping to the aeroelastic model. The sleeve-type eddy current damper is shown to be a convenient device to adjust the damping for aeroelastic models.

Novel Method for the Characterization of the Electrical Conductivity and Eddy Current Damping of Aluminum Foams

In this paper, we present a novel method for indirect characterization of eddy currents damping and loss coefficients, as well as the equivalent electrical conductivity of metal foams. The proposed method is based in the measurement of the braking torque when the metal foams are exposed to an alternating magnetic field generated by a set of rotating permanent magnets. Measurements are carried out in a low-frequency range (< 50 Hz) and for high amplitude magnetic fields (up to 0.4 T), both typical values observed in electromechanical devices. This method was used for accurate characterization of a set of open-cell aluminum foams with different compositions and porosities. Experimental results, in good agreement with the theoretical models, confirm the viscous damping behavior of aluminum foams in the tested frequency range. The quadratic dependency of the damping coefficient on the magnetic flux density is also confirmed in the measurement range.

Effects of Vibration Frequency on the Nonlinear Behavior of the Eddy Current Damping

Effects of Vibration Frequency on the Nonlinear Behavior of the Eddy Current Damping

진동감소 및 감쇠력 확보를 위한 와전류형 EM댐퍼 구조 설계

In this paper, we propose an eddy current type EM damper that can have the simple structure of an existing mechanical damper and the effective damping force of a magnetic fluid fluid damper at the same time. The proposed eddy current type EM damper has a structure similar to that of a mechanical damper, in which a permanent magnet is attached to a plunger and a conductor (copper) is provided on the outer wall of the cylinder to generate and generate an eddy current cutoff. Damping force. When the permanent magnet attached to the plunger vibrates up and down, an eddy current is generated, and a magnetic field having the opposite polarity to the magnetic field acting by the circulation of the eddy current is generated. In order to verify the reliability of the damping force of the eddy current type EM damper, analysis is performed using a finite element analysis method that applies axial symmetry analysis technology, and the direction in which the damping force is generated acts in the opposite direction to the vibration characteristics to generate external vibration. The damping ability to suppress was verified.

Performance improvement of NES based on eddy current damping

This paper investigates the application of an eddy current damping (ECD) to improve the performance of a nonlinear energy sink (NES). The effect of the damping on the vibration suppression performance of the NES is presented. Next, the principle of the ECD is introduced and combined with the NES, namely ECD enhanced NES (ECD-NES). On this basis, the effect of the ECD-NES parameters on its vibration reduction performance is analyzed. Then, the proposed ECD-NES is applied to a cantilever beam system, and the vibration suppression performance of the ECD-NES is compared with that of the NES without ECD. An optimization strategy for the ECD-NES is proposed under the condition of comprehensive consideration of displacement control and energy dissipation. Lastly, the effectiveness of the ECD-NES is verified experimentally on the cantilever beam system. The results show that adding the ECD is effective in improving the performance of the NES. After ECD enhanced NES is installed, the amplitude decay speed is increased by 24.18% in simulations and 18.85% in experiments; the energy dissipation rate is increased by 7.3% compared with the NES without ECD.

Vibration Suppression for Flexible Plate with Tunable Magnetically Controlled Joint Stiffness/Damping

Large flexible solar panels have the properties of light weight, low stiffness, and weak damping, which leads to low-frequency and large-amplitude vibrations. The existing vibration control methods of solar panels mainly adopt intelligent piezoelectric structures. However, the disadvantage is that the large stroke drive and control are limited. In the present study, a semi-active vibration control approach is proposed for flexible space solar panels based on magnetically controlled joints. The magnetic stiffness comes from the linear relationship between the joint output torque and rotation angle. The magnetic damping stems from the eddy current damping resulting from the relative motion between the permanent magnet rotor and the stator core of the joint. Firstly, the coupling dynamic modeling of a flexible plate and magnetic joints is established by adopting the Lagrange equation and the assumed mode approach. Secondly, semi-active vibration control simulations of the coupled system are performed. Meanwhile, the influence of the variable joint stiffness on the system frequency-shift effect is studied. Finally, the experimental platform is built, and simultaneously, non-contact permanent magnets and airflow are used to simulate single- and multi- frequency excitations, respectively. The experimental results indicate that, in the range of 0.06–0.343 Hz, magnetic damping is the leading factor with magnetic stiffness being the auxiliary. Additionally, it is also experimentally verified that the dual joint actuation has good synchronization. This study provides a new solution for the low-frequency vibration control of large flexible space structures.

Structural dynamic vibration absorber using a tuned inerter eddy current damper

The advantages of eddy current dampers over conventional fluid dampers include the ability to produce resistive forces with no contact between the components wherein damping forces are generated, resulting in a less degradable mechanism. Thus far, the apparent mass effect, referred to as inertance, in an eddy current damper employing rotational motion has not been intentionally applied for vibration control. Therefore, this paper proposes utilizing the inertance effect in an inerter eddy current damper (IECD) to construct a dynamic vibration absorber for the seismic protection of civil structures, termed as the tuned inerter eddy current damper (TIECD). The IECD consists of a ball screw, a conductor, permanent magnets, and a back iron. The gravitational mass of the back iron disk is converted into inertance via the ball-screw mechanism, which amplifies the mass and damping effects of the rotational disk and eddy current, respectively, by converting low-speed translational motion into high-speed rotational motion. An analytical method based on the separation of variables is applied to estimate the eddy current damping force of the IECD at different velocities. Concurrently, a succinct damping model is developed to capture the mechanical behavior of the nonlinear eddy current damping. A series of dynamic tests using a small-scale prototype IECD is then conducted to confirm the feasibility and accuracy of the proposed numerical damping model. Next, an equivalent damping coefficient for eddy current damping is derived under harmonic excitation. Based on a combination of the fixed-point method, the equivalent damping coefficient of the IECD, and complex eigen analysis, an optimal design method for the TIECD is developed. Finally, the effectiveness of the proposed TIECD is validated through a shake table test and a numerical simulation.

Design of a Long Stroke Nanopositioning Stage With Self-Damping Actuator and Flexure Guide

Long stroke nanopositioning stages with high natural frequency and compact size are demanded in precision engineering. However, in previous researches, the natural frequency of the long stroke nanopositioning stage is normally below 50 Hz because the actuated force, moving mass, stiffness, motion range, and damping ratio are not considered simultaneously and optimized thereafter. To solve this problem, a long stroke nanopositioning stage driven by the self-damping moving magnet actuator (SMMA) and supported by the flexure guide is integrated and designed in this article. The SMMA consists of two identical tooth-slot structure stators and one moving magnet which is embedded inside the flexure guide. Copper plates that functioned as eddy-current dampers are attached on the tooth surfaces to suppress the resonance peak at the natural frequency. An integrated dynamics model that consists of force, damping coefficient, and stiffness is established. The dimensional parameters of the proposed positioning stage are optimized to improve the system performances based on the developed model. Experimental results show that the natural frequency of the positioning stage reaches up to 71 Hz. The stage can achieve 20 nm positioning resolution within a motion range of <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$\pm$</tex-math></inline-formula> 5 mm, and the root mean square tracking errors for 1 Hz sinusoidal and triangular commands are below 0.1% of the trajectory amplitudes.

Stochastic seismic analysis of structures with nonlinear eddy current dampers

Eddy current damper (ECD), a contactless energy-dissipating device, is applying to control the vibration induced by earthquake and strong wind in civil structures. Combining with motion magnification mechanisms improves the damping effect of the ECD while significantly strengthens its nonlinearity. The response of single degree of freedom and multi-degree of freedom system with ECDs under a stationary stochastic earthquake characterized by the power spectral density function is evaluated using the stochastic linearization technique and expressions of the equivalent linear damping coefficient based on force criterion and energy criterion have been found, respectively. Comparisons with results obtained by Monte Carlo simulations confirm that for the nonlinearity of eddy current dampers the force-based criterion stochastic linearization technique gives accurate estimation.

Design and Experimental Validation of a Micro-Newton Torsional Thrust Balance for Ionic Liquid Electrospray Thruster

This work describes the advances on a micro-newton torsional thrust balance for ionic liquid electrospray thruster (ILET) being developed in the National University of Defense Technology. The torsional thrust balance adopts an asymmetric pendulum arm about a flexural pivot, and an electrostatic comb device is used for calibration, which makes the balance compact and allows the measurement of the micro-newton level thrust with high accuracy. To minimize the influence of gravity on the measurement results, a two-dimensional adjustable counterweight mechanism is adapted to balance the entire arm and make its mass center close to the pivot axis. Mechanical oscillations are passively damped with an eddy current damper. A series of experimental studies are carried out in a vacuum chamber; the results provide validation that the balance has good linearity in the range of 2–30 μN, with the resolution better than 0.21 μN and the settling time to a step force is less than 7 s, which can meet the thrust measurement requirements of the ILET operating in the mode of alternating work voltage polarity. In addition, we find that the electrostatic force generated by the power supply wire has a non-negligible influence on thrust measurement results, which needs to be considered in the actual thrust measurement.

Damped Chatter Resistant Boring Bar Integrated with an Absorber Working in Conjunction with an Eddy Current Damper

Damped Chatter Resistant Boring Bar Integrated with an Absorber Working in Conjunction with an Eddy Current Damper

Dynamic behavior and damping enhancement of cable with negative stiffness inerter damper

To improve the control performance of stay cables, a novel negative stiffness inerter damper (NSID) that consists of a negative stiffness device in parallel with an eddy current inerter damper is proposed in this study. The novelty of the NSID is that the damper can utilize the damping enhancement of the negative stiffness and inerter for cable vibration control, simultaneously. A further novelty is to carefully explore the modal behavior of the cable based on optimum parameters of the NSID. On this basis, the damping enhancement principle and conditions of the NSID for cable vibration control are demonstrated. In addition, the closed-form equation of the cable modal damping ratio and the design equation of the NSID for multi-mode cable vibration control are derived. And the control efficacy of the NSID is evaluated through the damping enhancement of the design cable modes. The results show that the modal behavior in the nth cable mode can be divided into three distinct regimes according to the negative stiffness and the corresponding optimum inertance, which are underdamped mode, subcritical damped mode, and the (n − 1)th underdamped mode. In the first regime, the inerter and negative stiffness have similar effects on enhancing damping ratio of the cable and reducing the optimum damping coefficient of the NSID. In the second and third regimes, the mode crossover phenomenon is observed, and the actual damping ratio of the nth cable mode decreases as the negative stiffness or inertance increases. The NSID performs better than the VD, VID, and NSD in mitigating multi-mode cable vibrations. Increasing negative stiffness can further improve the control performance and reduce the optimum inertance and damping coefficient of the NSID.