Improved Concept and Model of Eddy Current Damper

2005 ◽  
Vol 128 (3) ◽  
pp. 294-302 ◽  
Author(s):  
Henry A. Sodano ◽  
Jae-Sung Bae ◽  
Daniel J. Inman ◽  
W. Keith Belvin
Keyword(s):  
Magnetic Field ◽  
Theoretical Model ◽  
Eddy Current ◽  
Eddy Currents ◽  
Opposite Polarity ◽  
Image Method ◽  
Time Varying ◽  
Transverse Beam ◽  
Eddy Current Damper ◽  
Improved Model

When a conductive material experiences a time-varying magnetic field, eddy currents are generated in the conductor. These eddy currents circulate such that they generate a magnetic field of their own, however the field generated is of opposite polarity, causing a repulsive force. The time-varying magnetic field needed to produce such currents can be induced either by movement of the conductor in the field or by changing the strength or position of the source of the magnetic field. In the case of a dynamic system the conductor is moving relative to the magnetic source, thus generating eddy currents that will dissipate into heat due to the resistivity of the conductor. This process of the generation and dissipation of eddy current causes the system to function as a viscous damper. In a previous study, the concept and theoretical model was developed for one eddy current damping system that was shown to be effective in the suppression of transverse beam vibrations. The mathematical model developed to predict the amount of damping induced on the structure was shown to be accurate when the magnet was far from the beam but was less accurate for the case that the gap between the magnet and beam was small. In the present study, an improved theoretical model of the previously developed system will be formulated using the image method, thus allowing the eddy current density to be more accurately computed. In addition to the development of an improved model, an improved concept of the eddy current damper configuration is developed, modeled, and tested. The new damper configuration adds significantly more damping to the structure than the previously implemented design and has the capability to critically damp the beam’s first bending mode. The eddy current damper is a noncontacting system, thus allowing it to be easily applied and able to add significant damping to the structure without changing dynamic response. Furthermore, the previous model and the improved model will be applied to the new damper design and the enhanced accuracy of this new theoretical model will be proven.

Modeling of Eddy Current Damper Composed of Spherical Magnet and Conducting Shell

2006 ◽  
Author(s):  
Yoshihisa Takayama ◽  
Atsuo Sueoka ◽  
Takahiro Kondou
Keyword(s):  
Magnetic Field ◽  
Eddy Current ◽  
Magnetic Force ◽  
Eddy Currents ◽  
Reaction Force ◽  
Damping Force ◽  
Magnetic Damping ◽  
Conducting Plate ◽  
Direction Of Movement ◽  
Eddy Current Damper

If a conducting plate moves through a nonuniform magnetic field, eddy currents are induced in the conducting plate. The eddy currents produce a magnetic force of drag, known as Fleming's left-hand rule. This rule means that a magnetic field perpendicular to the direction of movement generates a magnetic damping force. We have fabricated the eddy current damper composed of the spherical magnet and the conducting shell. The spherical magnet produces the axisymmetric magnetic field, and the shape of the conducting shell appears to combine a semispherical shell conductor and a cylinder conductor. When the eddy current damper works, the conducting shell is fixed in space, and the spherical magnet moves under the conducting shell. In this case, since there are magnetic flux densities perpendicular to the direction of movement, eddy currents flow inside the conducting shell, and then a magnetic force is produced. The reaction force of this magnetic force acts on the spherical magnet. In our study, eddy current dampers composed of a magnet and a conducting plate have been modeled using infinitesimal loop coils. As a result, magnetic damping forces are obtained. Our modeling has three merits as follows: the equation of a magnetic damping force is simple in the equation, we can use the static magnetic field obtained using FEM, the Biot-Savart law or experiments and the equation automatically satisfies boundary conditions using infinitesimal loop coils. In this study, we explain simply the principle of this method, and model an eddy current damper composed of a spherical magnet and a conducting shell. The analytical results of the modeling agree well with the experimental results.

Model of Eddy Current Damping Mechanism for the Suppression of Beam Vibrations

Aerospace ◽  
2004 ◽  
Author(s):  
Henry A. Sodano ◽  
Jae-Sung Bae ◽  
Daniel J. Inman ◽  
W. Keith Belvin
Keyword(s):  
Magnetic Field ◽  
Theoretical Model ◽  
Eddy Current ◽  
Damping Ratio ◽  
Power Supplies ◽  
Damping Force ◽  
Electromagnetic Damping ◽  
Eddy Current Damping ◽  
Eddy Current Damper ◽  
External Power

The movement of a conductor through a stationary magnetic field or a time varying magnetic field through a stationary conductor generates electromagnetic forces that can be used to suppress the vibrations of a flexible structure. In the present study, a new electromagnetic damping mechanism is introduced. This mechanism differs from previously developed electromagnetic braking systems and eddy current dampers because the system investigated in the following manuscript uses the radial magnetic flux of a permanent magnet to generate the electromagnetic damping force rather than the flux perpendicular to the magnet’s face as done in other studies. One important advantage of the proposed mechanism is that it is simple and easy to be applied. Additionally, a single magnet can be used to damp the transverse vibrations that are present in many structures. Furthermore, it doesn’t require any electronic devices or external power supplies, therefore functioning as a non-contacting passive damper. A theoretical model of the system is derived using electromagnetic theory, enabling us to estimate the electromagnetic damping force induced on the structure. The proposed eddy current damper was constructed and experiments were performed to verify the precision of the theoretical model. It is found that the proposed eddy current damping mechanism increases the damping ratio by up to 150 times and provides sufficient damping force to quickly suppress the beam’s vibration.

Analysis and Experiments of Eddy Current Brakes with Moving Magnets

2008 ◽  
Vol 575-578 ◽  
pp. 1299-1304 ◽  
Author(s):  
Jaw Kuen Shiau ◽  
Der Ming Ma ◽  
Min Jou
Keyword(s):  
Drag Force ◽  
Relative Motion ◽  
Eddy Current ◽  
Eddy Currents ◽  
Test System ◽  
Image Method ◽  
Electromagnetic Interactions ◽  
Finite Dimensional ◽  
Conducting Plate ◽  
Lorentz Force Law

This paper discusses the magnetic drag force resulting from the relative motion of a permanent magnet moving along a finite dimensional conducting plate. The image method with imaginary eddy currents is investigated. Boundary conditions are established to ensure that the eddy currents vanished at the boundaries of the conducting plate. Magnetic drag force is computed based on the eddy current distributions using Lorentz force law. A test system is built to demonstrate the magnetic brakes arose from the electromagnetic interactions.

Modeling of a New Active Eddy Current Vibration Control System

2008 ◽  
Vol 130 (2) ◽  
Author(s):  
Henry A. Sodano ◽  
Daniel J. Inman
Keyword(s):  
Magnetic Field ◽  
Vibration Control ◽  
Electric Fields ◽  
Eddy Current ◽  
Eddy Currents ◽  
Vibration Suppression ◽  
Frequency Doubling ◽  
Damping Force ◽  
Theoretical Derivation ◽  
Eddy Current Damping

There exist many methods of adding damping to a vibrating structure; however, eddy current damping is one of few that can function without ever coming into contact with that structure. This magnetic damping scheme functions due to the eddy currents that are generated in a conductive material when it is subjected to a time changing magnetic field. Due to the circulation of these currents, a magnetic field is generated, which interacts with the applied field resulting in a force. In this manuscript, an active damper will be theoretically developed that functions by dynamically modifying the current flowing through a coil, thus generating a time-varying magnetic field. By actively controlling the strength of the field around the conductor, the induced eddy currents and the resulting damping force can be controlled. This actuation method is easy to apply and allows significant magnitudes of forces to be applied without ever coming into contact with the structure. Therefore, vibration control can be applied without inducing mass loading or added stiffness, which are downfalls of other methods. This manuscript will provide a theoretical derivation of the equations defining the electric fields generated and the dynamic forces induced in the structure. This derivation will show that when eddy currents are generated due to a variation in the strength of the magnetic source, the resulting force occurs at twice the frequency of the applied current. This frequency doubling effect will be experimentally verified. Furthermore, a feedback controller will be designed to account for the frequency doubling effect and a simulation performed to show that significant vibration suppression can be achieved with this technique.

Dynamics of a Rotating System With a Nonlinear Eddy-Current Damper

1998 ◽  
Vol 120 (4) ◽  
pp. 848-853 ◽  
Author(s):  
Y. Kligerman ◽  
O. Gottlieb
Keyword(s):  
Nonlinear Dynamics ◽  
Eddy Current ◽  
Eddy Currents ◽  
Nonlinear Behavior ◽  
Forced Response ◽  
System Response ◽  
Rotating System ◽  
Restoring Force ◽  
Rotating Systems ◽  
Eddy Current Damper

We investigate the nonlinear dynamics and stability of a rotating system with an electromagnetic noncontact eddy-current damper. The damper is modeled by a thin nonmagnetic disk that is translating and rotating with a shaft in an air gap of a direct current electromagnet. The damper dissipates energy of the rotating system lateral vibration through induced eddy-currents. The dynamical system also includes a cubic restoring force representing nonlinear behavior of rubber o-rings supporting the shaft. The equilibrium state of the balanced rotating system with an eddy-current damper becomes unstable via a Hopf bifurcation and exact solutions for the limit cycle radius and frequency of the self-excited oscillation are obtained analytically. Forced vibration induced by the rotating system mass imbalance is also investigated analytically and numerically. System response includes periodic and quasiperiodic solutions. Stability of the periodic solutions obtained from the balanced self-excited motion and the imbalance forced response is analyzed by use of Floquet theory. This analysis enables an explanation of the nonlinear dynamics and stability phenomena documented for rotating systems controlled by electromagnetic eddy-current dampers.

scholarly journals A fast forward solution with a boundary element method for eddy current nondestructive testing

2002 ◽  
Vol 15 (2) ◽  
pp. 205-216
Author(s):  
Hermann Uhlmann ◽  
Olaf Michelsson
Keyword(s):  
Magnetic Field ◽  
Boundary Element Method ◽  
Boundary Element ◽  
Eddy Current ◽  
Eddy Currents ◽  
Order Approximation ◽  
Approximation Schemes ◽  
Constant Field ◽  
The Magnetic Field ◽  
Element Method

Eddy current non-destructive testing is used to determine position and size of cracks or other defects in conducting materials. The presence of a crack normal to the excited eddy currents distorts the magnetic field; so for the identification of defects a very accurate and fast 3D-computation of the magnetic field is necessary. A computation scheme for 3D quasistatic electromagnetic fields by means of the Boundary Element Method is presented. Although the use of constant field approximations on boundary elements is the easiest way, it often provides an insufficient accuracy. This can be overcome by higher order approximation schemes. The numerical results are compared against some analytically solvable arrangements.

scholarly journals General 3D Analytical Method for Eddy-Current Coupling with Halbach Magnet Arrays Based on Magnetic Scalar Potential and H-Functions

Energies ◽  
2021 ◽  
Vol 14 (24) ◽  
pp. 8458
Author(s):  
Xiaoquan Lu ◽  
Xinyi He ◽  
Ping Jin ◽  
Qifeng Huang ◽  
Shihai Yang ◽  
...  
Keyword(s):  
Magnetic Field ◽  
Eddy Current ◽  
Analytical Method ◽  
Eddy Currents ◽  
Scalar Potential ◽  
Fourier Decomposition ◽  
Field Distributions ◽  
Current Coupling ◽  
Current Calculation ◽  
Laplacian Equations

Rapid and accurate eddy-current calculation is necessary to analyze eddy-current couplings (ECCs). This paper presents a general 3D analytical method for calculating the magnetic field distributions, eddy currents, and torques of ECCs with different Halbach magnet arrays. By using Fourier decomposition, the magnetization components of Halbach magnet arrays are determined. Then, with a group of H-formulations in the conductor region and Laplacian equations with magnetic scalar potential in the others, analytical magnetic field distributions are predicted and verified by 3D finite element models. Based on Ohm’s law for moving conductors, eddy-current distributions and torques are obtained at different speeds. Finally, the Halbach magnet arrays with different segments are optimized to enhance the fundamental amplitude and reduce the harmonic contents of air-gap flux densities. The proposed method shows its correctness and validation in analyzing and optimizing ECCs with Halbach magnet arrays.

Analysis and Experimental Evaluation of Inherent Instability in Electromagnetic Eddy-Current Dampers Intended for Reducing Lateral Vibration of Rotating Machinery

1995 ◽  
Author(s):  
Yuri Kligerman ◽  
Asif Grushkevich ◽  
Mark S. Darlow ◽  
Adrian Zuckerberger
Keyword(s):  
Magnetic Field ◽  
Eddy Current ◽  
High Speed ◽  
Experimental Tests ◽  
Rotating Machinery ◽  
Lateral Vibration ◽  
Negative Effect ◽  
Eddy Current Damper ◽  
Analytical Approaches ◽  
The Magnetic Field

Abstract There have been a number of papers published that concern the design and operation of electromagnetic, eddy-current dampers for controlling lateral vibration of rotating machinery. Many of these papers have included analysis approaches and all have been generally effective for low-speed operations. There have been a few reports concerning high-speed (supercritical) operations and many of these have indicated instability problems, but none of these have provided a valid analysis to account for instability. That is, all of the analytical approaches have ignored the disk rotation, relative to the magnetic field, and no obvious sources of instability have been found. In this paper, we will present our work in which we have rederived the analyses of this system in which we have not made the common assumption of no rotation between the disk and the magnetic field. In this case, the potential of instability for supercritical speed operation is clear and, in fact, the equivalent negative damping contribution of the eddy-current damper, under these conditions, has a negative effect on the system even if not fully unstable. We have carefully performed a series of experimental tests which corroborate this analytical approach. Finally, we briefly discuss alternative eddy-current damper design approaches that could be considered to provide effective damping at all speeds and avoid these instability problems.

The Simulation Study on Temperature Field Distribution of 220 kV Gas Insulated Switchgear

2021 ◽  
Vol 16 (5) ◽  
pp. 797-805
Author(s):  
Bao-Ming Gao ◽  
Zheng-Yu Li ◽  
Jin-Wen Gao ◽  
Hao Liang ◽  
Zhi Yan ◽  
...  
Keyword(s):  
Magnetic Field ◽  
Field Distribution ◽  
Eddy Current ◽  
Temperature Rise ◽  
Heat Dissipation ◽  
Eddy Currents ◽  
Coupling Effect ◽  
Eddy Current Loss ◽  
Element Analysis ◽  
Current Loss

Under working conditions, the conductive rods in the GIS flow through the power frequency alternating current. Due to the coupling effect of the magnetic field and electric field between the metal aluminum shell and the conductive rod, induced eddy currents are generated in the metal shell of the GIS. The heat generated by the current heating effect of the GIS conductive rod and the eddy current loss of the metal casing will cause the temperature rise of GIS equipment. Due to the limited volume, the heat dissipation capacity of GIS is poor. Excessive temperature rise will accelerate the insulation aging of GIS equipment, and even damage its insulation, which will affect safe operation. In order to obtain the temperature change law of GIS, related influencing factors such as eddy current loss, skin effect, proximity effect, convective heat transfer of SF6 gas, and gravity of SF6 gas are comprehensively considered. The finite element analysis is used to research and discuss GIS magnetic field distribution, eddy current, temperature distribution and SF6 gas velocity. The initial value of the temperature of each part is set to 293.15 K (20 °C), and the temperature in the GIS is calculated to gradually decrease from the inside to the outside under the rated AC current of 3150 A. The temperature at the conductive rod position is the highest at 335.32 K, and the temperature at the housing position is the lowest at 294.65 K.

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