Eddy Current Force Research Articles

Electromagnetic analyses and optimization for slit configuration of ITER blanket shield block

Electromagnetic (EM) load is one of the most concerned design issues for the in-vessel components in the Tokamak device. For shield block (SB), quite a few of slits cut on the SB are designed to mitigate the EM load. In this study, a solid model of blanket system with other main surrounding components, such as vacuum vessel, was developed, and FE analyses were performed to address the eddy current and Lorentz force during major disruption (MD) with ANSYS EMAG code package. In order to get a regular hexahedral mesh of the SB with complex interface, a brick-like meshing is used to get a more reliable result. Key factors which potentially have great impacts on the eddy current were studied individually by SB04 of the standard blanket module, such as the depth, location and number of the slits. To better understand the effects of cooling channels on the EM load, SB04 without cooling channel are calculated to make comparisons. Two important conclusions can be made from this study. The first one is that cooling channels have a little impact on the EM load. This is because the cooling channels cut into the eddy current locally, and the global current loop is not affected. The second is that slit configuration is important to control the EM load, and their depths, locations and numbers are also important.

A 3-D Analytic-Based Model of a Null-Flux Halbach Array Electrodynamic Suspension Device

The purpose of this paper is to present the derivation of a 3-D analytical solution of a null-flux electrodynamic suspension device for a conductive plate. The device consists of a linear Halbach magnet array placed above and below a conductive plate. The eddy current forces are derived using the second-order vector potential (SOVP). When the conductive plate is assumed to be large relative to the source field, the SOVP enables the equations to be derived in terms of reflection and transmission field components. A 3-D finite-element analysis model as well as the experimental results are used to validate the presented equations.

3-D Steady-State Eddy-Current Damping and Stiffness Terms for a Finite Thickness Conductive Plate

In this paper, the 3-D forces created by induced eddy currents in a conductive plate of finite thickness are derived using the concept of magnetic charge and energy. Using this approach the exact steady state based eddy-current damping and stiffness matrices for an arbitrary magnetic source moving above a conductive plate are derived. The damping and stiffness terms caused by both angular and spatial motion are accounted for. The presented equations can be utilized to create a linear state-space eddy-current force model.

Dynamic electromechanical eddy current force modeling

Purpose– The purpose of this paper is to validate dynamic analytic force modeling techniques with experimental results. The performance of previously presented 2-D and 3-D eddy current models will be assessed when the steady-state models are coupled to a dynamic mechanical model.Design/methodology/approach– The previously presented 2-D analytic model was formulated in terms of the magnetic vector potential in conductive region and magnetic scalar potential in non-conductive region whereas the 3-D model was formulated in terms of the magnetic vector potential in both the conductive and non-conductive regions.Findings– This paper experimentally confirms that incorporating the heave velocity term is important for accurately predicting the forces under dynamic mechanical motion while using a steady-state eddy current solution. A close agreement between the experimental and the dynamic analytic-based eddy current solution was achieved.Research limitations/implications– The force results presented from the previously developed 3-D analytic model assume that the width of the guideway is larger than that of the magnetic source and the magnetic source is placed at the center of the guideway along the z-axis.Practical implications– The rotational and translational motion of a permanent magnet rotor above a conductive plate create lift and thrust force that are suitable for magnetic levitated (maglev) transportation. The previously developed 2-D and 3-D analytic models are fundamental to such maglev research as the models can quickly compute the electromagnetic forces acting on the maglev vehicle. This paper is of immense importance as the paper experimentally validates the analytic models.Originality/value– The quasi-static analytic eddy current force models that are validated in this paper are different to analogous models developed by prior authors in that the heave velocity as well as the translational velocity of a magnetic source is incorporated into the eddy current force equation.

Fabrication and Test of a 40 T Long-Pulse Magnet Driven by Battery Bank

A 40 T long-pulse magnet has been constructed and tested to 32 T with total pulse width of 1.5 s at the Wuhan National High Magnetic Field Center (WHMFC). The magnet is energized by a battery bank power source consisting of 900 12 V/200 Ah lead-acid battery cells. The magnet consists of a polyhelix inner coil and an outer coil wound with copper foil. We made some improvements by adding axial slots on the helices due to the eddy current electromagnetic force, and each layer of helices is reinforced by Zylon-epoxy composite. The copper foil coil is insulated with polyimide film extending over the sides of the foil. The copper bar electrode is silver brazed on the ends of copper foil and has been proved to be quite feasible. In this paper, the calculated results of the electromagnetic force caused by eddy current will be presented. The magnet manufacture techniques will be described and the magnet test results will be listed and analyzed.

A 3-D analytic eddy current model for a finite width conductive plate

Purpose – A 3-D analytic modeling technique for calculating the eddy current distribution, force and power loss in a conductive plate of finite width and thickness is presented. The derived equations are expressed in a general form so that any magnetic source can be utilized. The model assumes the length of the conductive plate is large and the thickness of the plate is thin but not negligible. The paper aims to discuss these issues. Design/methodology/approach – The conducting and non-conducting regions are formulated in terms of decoupled magnetic vector potential components. In order to accurately compute the eddy current fields and forces the source field only needs to be applied on the surface of the conducting plate. The primary focus is on reducing the eddy current computational time. Findings – The accuracy of the presented approach is verified by utilizing a magnetic rotor that has both a rotational and translational motion. The proposed method is computationally efficient and its accuracy is validated using the finite element method. Research limitations/implications – The conducting plate thickness is assumed to be thin (but not negligible), and this enables the field interaction through the edge of the plate to be neglected. The lateral force is not calculated in the proposed approach. Practical implications – The calculation procedure presented is computationally fast and therefore this can enable the 3-D eddy current forces to be computed in near real-time. Originality/value – This paper presents a fully 3-D analytic based eddy current formlation for computing the eddy current fields and forces in a conducting plate of finite thickness and finite width. The modeling approach is shown to be computationally accurate and relatively fast.

Electromagnetic and Stress Analyses of the ITER Equatorial Thermal Shield

The ITER equatorial thermal shield is located inside the cryostat and outside the vacuum vessel, and its purpose is to provide a thermal shield from hot components to the superconducting magnets. Electromagnetic analysis of the equatorial thermal shield was performed using the ANSYS code, because electromagnetic load was one of the main loads. The 40° sector finite element model was established including the vacuum vessel, equatorial thermal shield, and superconducting magnets. The main purpose of this analysis was to investigate the eddy current and electromagnetic force in the equatorial thermal shield during plasma disruption. Stress analysis was implemented under the electromagnetic load. The results show that the equatorial thermal shield can accommodate the calculated electromagnetic loads.

Dynamical Electromechanical Model for Magnetic Bearings Subject to Eddy Currents

Eddy-current forces may play a significant role in magnetic bearings. They generate losses and unpredicted forces, which may lead to a malfunction of the bearing. But eddy currents in magnetic bearings may also be used positively, to generate desired forces, like in electrodynamic bearings. This paper presents a model able to predict, analyze, or simulate the dynamical behavior of any rotating magnetic bearing in which classical eddy-current forces arise. This model integrates the mechanical aspects linked to the rotor dynamics and the electrical aspects linked to the electromagnetic nature of the forces. This paper explains how the parameters of the model can be identified on the basis of quasi-static finite element method (FEM) or experiments. The validation of the model is done by comparison with FEM results on an electrodynamic radial bearing.

Calculation of Eddy Current Loss and Short-circuit Force in SSZ11-50000/110 Power Transformer

The method is used in this paper to calculate the leakage magnetic field of SSZ11-50000/110 Power transformer, and by which the structures’ influences to the main leakage flux are analyzed. Through the combination of the product and TEAM Problem 21B, the surface impedance method shows its great advantage in the calculation of eddy current loss.

Vibration Transmission Analysis on a Superconducting Seismic Isolation Device With PM and Copper Plate Systems

We have devised a magnetic levitation type superconducting seismic isolation device using pinning effect of HTS bulk and investigated the characteristics of vibration transmission and damping in a model device with two types of permanent magnet (PM) systems with copper plates; the one was for stable stationary levitation named “PM-PM system” and the other was for improving damping effect named “vibration absorbing system (VAS)”. To clarify the electromagnetic behaviors of these systems, we calculated the distributions of eddy current and magnetic force within the copper plates during a horizontal vibration using a numerical simulation code based on the three-dimensional finite element method (3D-FEM) analysis. As the results, the vibration transmission was reduced due to the Lorenz force generated in the copper plate.

Time‐varying magnetic fields of 60 Hz at 7 mT induce DNA double‐strand breaks and activate DNA damage checkpoints without apoptosis

The potential genotoxic effect of a time-varying magnetic field (MF) on human cells was investigated. Upon continuous exposure of human primary fibroblast and cervical cancer cells to a 60 Hz MF at 7 mT for 10-60 min, no significant change in cell viability was observed. However, deoxyribonucleic acid (DNA) double-strand breaks (DSBs) were detected, and the DNA damage checkpoint pathway was activated in these cells without programmed cell death (called apoptosis). The exposure of human cells to a 60 Hz MF did not induce intracellular reactive oxygen species (ROS) production, suggesting that the observed DNA DSBs are not directly caused by ROS. We also compared the position and time dependency of DNA DSBs with numerical simulation of MFs. The Lorentz force and eddy currents in these experiments were numerically calculated to investigate the influence of each factor on DNA DSBs. The DNA DSBs mainly occurred at the central region, where the MF was strongest, after a 30-min exposure. After 90 min, however, the amount of DNA DSBs increased rapidly in the outer regions, where the eddy current and Lorentz force were strong.

Transient Simulation of Electromagnetic Field during EMCC Process

A transient analysis mathematic model was established via ANSYS. The variation laws of magnetic induction density, induced eddy current and electromagnetic force in molten steel changing with the high frequency sine exciting current were investigated. The results indicate that the magnetic induction density and induced eddy current in molten steel vary at the same frequency as exciting current. Moreover, the variations of magnetic induction density and induced eddy current are not in step with exciting current. This proves that the high frequency electromagnetic field in mold and steel is not a time-harmonic wave. The electromagnetic force varies at the double frequency of the exciting current. When the exciting current reaches the amplitude value, the electromagnetic force is close to the max value, whereas when the exciting current returns to zero, the electromagnetic force is not zero. At the same time, there is partial electromagnetic force reversing its direction. If the reversed electromagnetic force is expanded seriously, the fluctuation of liquid level is induced, so it must be controlled.

Eddy-Current Analysis of Cold Mass and Thermal Shield for Series-Connected Hybrid Magnet

The National High Magnetic Field Laboratory currently has three series-connected hybrid (SCH) magnet projects, where resistive coils are connected in series with superconducting coils using cable-in-conduit-conductor (CICC) underway: first for the magnet laboratory in Tallahassee, FL; second for the Helmholtz Zentrum Berlin for Materials and Energy (HZB), Germany; and the third for the Spallation Neutron Source at the Oak Ridge National Laboratory, TN. The one for HZB has a horizontal conical bore with a 30^ opening angle for neutron scattering experiments. During power supply trip, superconducting magnet quench, resistive insert short, and insert fault, transient electromagnetic effects as a result of fast decay of the coil current introduce a significant amount of eddy current and Lorentz force on the conductive components of the cryostat such as the metallic cold-mass magnet frame and the 50-K thermal radiation shield. Although the eddy-current heating is not a concern during quench and fault operations, the eddy-current-induced Lorentz forces need to be taken into account in the structural design of the SCH cryostat. In this paper, a detailed eddy-current analysis for the HZB magnet during abnormal operations has been performed for its cryostat based on the dry magnet design concept. The nonuniform eddy-current distribution from the finite-element analysis implies that local hot spots may develop under abnormal operations. The eddy-current-induced Lorentz forces are quantified to ensure the strength and stability of the cryostat structure and, most importantly, safety of the SCH magnet during abnormal conditions.

Analytical modelling and calculation of pulsed magnetic field and input impedance for EMATs with planar spiral coils

The analytical expressions of magnetic flux density, pulsed eddy current and input impedance for EMATs with single-layer and double-layer planar spiral coils in frequency-domain were derived in terms of separation of variables and superposition theorem. The Truncated Domain Eigen-function Expansion method (TREE) was used to solving the infinite integral problem by series summation. The time-domain magnetic flux density, pulsed eddy current and Lorentz force were calculated through FFT-IFFT method. The calculated results of the proposed method were compared with those of time step FEM method and measurement. Their good agreement verifies the accuracy and validity of the proposed model and method.

Analysis of The Harmonic Order Affecting The Eddy Current Braking Force in Electrical Machines

This paper presents a computer analysis of the eddy current brake in electric machines. It presents a formula for the braking force when the actual width of the pole is considered. This formula is suitable for both thin and thick discs and may be employed for a wide range of working speed. For this purpose, a mathematical analysis of the problem is presented together with the formula achieved for the braking force. The brake is first represented by a mathematical model based on certain assumptions and then the braking force is obtained as a result of solving a field problem. The problem is simplified to a one-dimensional problem, where a solution for the magnetic vector potential is obtained, and by employing Lorentz force equation, a formula for the braking force of the nth harmonic order is obtained.

Development of eddy current microscopy for high resolution electrical conductivity imaging using atomic force microscopy

We present a high resolution electrical conductivity imaging technique based on the principles of eddy current and atomic force microscopy (AFM). An electromagnetic coil is used to generate eddy currents in an electrically conducting material. The eddy currents generated in the conducting sample are detected and measured with a magnetic tip attached to a flexible cantilever of an AFM. The eddy current generation and its interaction with the magnetic tip cantilever are theoretically modeled using monopole approximation. The model is used to estimate the eddy current force between the magnetic tip and the electrically conducting sample. The theoretical model is also used to choose a magnetic tip-cantilever system with appropriate magnetic field and spring constant to facilitate the design of a high resolution electrical conductivity imaging system. The force between the tip and the sample due to eddy currents is measured as a function of the separation distance and compared to the model in a single crystal copper. Images of electrical conductivity variations in a polycrystalline dual phase titanium alloy (Ti-6Al-4V) sample are obtained by scanning the magnetic tip-cantilever held at a standoff distance from the sample surface. The contrast in the image is explained based on the electrical conductivity and eddy current force between the magnetic tip and the sample. The spatial resolution of the eddy current imaging system is determined by imaging carbon nanofibers in a polymer matrix. The advantages, limitations, and applications of the technique are discussed.

Non-contact vibration control system employing an active eddy current damper

When a conductive material is subjected to a time-changing magnetic field, eddy currents are formed in the conductor. These currents circulate inside the conductor such that a magnetic field is formed. This eddy current field then interacts with the applied field resulting in a dynamic force between the conductor and the magnetic source. The force can be considered dynamic because as the eddy currents circulate inside the conductor they are dissipated by the internal resistance of the conductor. Therefore, if a continuously changing field is not applied to the conductor the force will disappear. However, the eddy current forces can be utilized to form an actuator by applying a time-changing current to an electromagnet that is in close proximity to a conductive material. This actuation method is easy to incorporate into the system and allows significant forces to be applied without every coming into contact with the structure. In this manuscript, the authors develop the concept and show that it can be accurately modeled and effectively used to control the vibration of a structure. The active eddy current actuator has not been previously demonstrated and therefore this article will present the first use of the system for providing transverse vibration suppression. Furthermore, the constraints necessary to design an active control filter will be presented. This vibration control system will use a velocity feedback filter to actively modify the current applied to the coil. Using this system, experiments are performed on a cantilever beam showing the system can effectively suppress each of the first five modes of vibration by upwards of 20 dB, demonstrating the actuator has an increased bandwidth over previously used eddy current methods.

Current density and forces for a current loop moving parallel over a thin conducting sheet

An analytical expression for the eddy current forces on a circular current loop moving with constant velocity over a thin conducting sheet is derived in this paper. This calculation is based on using the boundary conditions across the conducting sheet to solve for the total magnetic vector potential. The eddy currents in the sheet and the forces on the sheet are first presented in the ‘quasi-static’ limit and the perfect conductor limit. Finally, an analytical expression for both the drag and lift force is derived.

AC magnetic field-induced rotation in levitating magnetostrictive wire

The rotation of magnetostrictive wires under excitation of an alternating axial magnetic field is a phenomenon discovered few years ago. Previous results and a recent mechanical experiment indicate that the appearance of these rotations is related to the sample vibrations associated to magnetoelastic resonance. This surprising behavior is here experimentally reported in polycrystalline FeNi levitating wires. An introductory analysis considering the balance of gravitational, magnetic gradient, and eddy-current forces is additionally carried out.

The effect of electric fields in a classic introductory physics treatment of eddy current forces

A simple model of eddy currents in which current is computed solely from magnetic forces acting on electrons proves accessible to introductory students and gives a good qualitative account of eddy current forces. However, this model cannot be complete; it ignores the electric fields that drive current outside regions of significant magnetic field. In this paper we show how to extend the model to obtain a boundary value problem for current density. Solution of this problem in polar coordinates shows that the electric field significantly affects the quantitative results and presents an exercise suitable for upper division students. We apply elliptic cylindrical coordinates to generalize the result and offer an exercise useful for teaching graduate students how to use nonstandard coordinate systems.