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A magnet-rotating-type axial magnetic coupler (MAMC), namely, a novel axial magnetic coupler with rotatable monopole permanent magnets (PMs), is proposed. The speed of the MAMC can be adjusted by rotating the rotatable PMs mounted on the PM disk, or changing the axial air gap length between the PM disk and the conductor sheet (CS), or combining these methods. In order to analyze the torque performance, the magnetic circuit model of MAMC is established when the rotatable PMs are not parallel to the CS. Specifically, the influence of the induced eddy current is introduced into a new magnetic equivalent circuit (MEC) model. Combined with Kirchhoff’s law, the calculation formula of torque is derived. Moreover, according to Ampere’s law, the formula for calculating the induced eddy current is derived when the rotatable PMs after rotating are not parallel to the CS. Finally, the effectiveness of the proposed model is verified by the finite element method (FEM). The results obtained by the new MEC model proposed are consistent with those obtained by the FEM, and the formula derived is effective in the case of small rotational speed differences, small air gap lengths, and small thicknesses of the CS. [ABSTRACT FROM AUTHOR]

In this work, the solution to the eddy current problem for slowly moving conductors is investigated with the volume integral formulation of the electric field integral equation (EFIE). On the one hand, the formulation gives the possibility to mesh only the conductors; on the other hand, the inductance matrix is fully populated, thus limiting the size of the problem. Furthermore, the standard solution implies the reassembling of the stiffness matrix for each position assumed by the moving conductors. This results in a limit in the size of the problem to treat and a relevant cost in the computation time. To overcome this limit, in this work, the mutual coupling part of the system with two conductors is computed on the fly, thus giving the possibility to solve problems with a higher number of unknowns. Finally, to speed up the solution of the system, the Gauss–Seidel (GS) iterative techniques and the fast multipole method (FMM) are applied to take into account the mutual effects between the conductors. A comparison of the proposed method with a reference one shows the effectiveness of this technique. [ABSTRACT FROM AUTHOR]

A mesh-free semi-analytical Fourier-based method is presented to evaluate the frequency-dependent losses in the windings of solid-state transformers (SSTs) with foil-wound transformers. In the employed diffusion equation, which accounts for induced eddy currents, the imposed current density and conductivity in the transformer window area are represented using spatial Fourier series and method of images. As a result, induced current density distribution in foil conductors and ac loss in medium frequency transformers (MFTs) is calculated using the semi-analytical method. The proposed method is verified using the finite element method (FEM). It is observed that with the considered approach one can estimate the ac winding loss in the frequency range of 5–25 kHz, with 2.7% maximum absolute error and approximately 2.5 times less number of degrees-of-freedom compared to FEM computations. [ABSTRACT FROM AUTHOR]

This article proposes a novel numerical technique based on the combination of the kernel radial basis function (RBF) and traditional finite element methods (FEMs) for solving the integro-differential equation of 2-D time-harmonic eddy current problems. In this technique, the kernel RBF method is used to formulate the term of the differential operator, and the term of the integral operator is formulated by the FEM. In particular, these two methods use the same points generated by the finite element mesh in the entire computational domain. In addition, for increasing the accuracy of the proposed combination method, the algorithm of choosing shape parameters for our kernel RBFs is also used. To evaluate and demonstrate the advantages of the proposed approach, a benchmark integro-differential equation and the eddy currents in a three-phase busbar system in the 2-D domain are both investigated. The obtained numerical results demonstrate that the proposed numerical approach compares favorably with the traditional FEM. [ABSTRACT FROM AUTHOR]

This article presents an improved analytical spatial harmonics subdomain (SHSD) model for analyzing the influence of individual spatial harmonics, in stator magneto-motive forces (MMFs), on the performance of multiphase cage rotor induction motors (CRIMs). The proposed SHSD model is an extension of conventional techniques that consider each MMF spatial harmonic, caused by stator slots with tooth-tips, to be individual excitations when quantitatively analyzing the resulting physical effects. The solution domain was divided into four subdomains (SDs) in 2-D polar coordinates, including 1) rotor bars described by the Helmholtz equation; 2) air gaps; 3) slot openings described by Laplace’s equation; 4) stator slots represented by pure forced vibration equations. Current density in the stator structure was decomposed in a Fourier series of position angles to obtain MMF spatial harmonics. This produced a set of pure forced vibration equations in the stator slots, which were first solved in 2-D polar coordinates rather than the typical Poisson’s equation. This approach establishes a relationship between electromagnetic performance and stator parameters, for further optimization of IMs and analysis of electromagnetic vibrations. The proposed analytical model was validated using a series of finite element simulations, which exhibited high accuracy and computational efficiency. [ABSTRACT FROM AUTHOR]

Leakage flux penetrating laminated iron cores in power transformers and large generators induces eddy current and local loss. Due to the strong magnetic anisotropy of the lamination structure, the penetrating flux tends to saturate the lamination in its plane, even when the incident stray flux density is low. Therefore, the combined effect of anisotropy and nonlinearity has a great impact on the eddy current distribution and the associated power losses. Moreover, the incident normal flux often interacts with the main flux, where the phase angle between the two fluxes may play a significant role. A measurement device is developed to emulate the actual leakage flux in a steel lamination and the power losses are measured at the flux densities of various magnitudes and phases. The measurement results are compared and interpreted by the results obtained from a finite-element analysis, where the homogenization approach for material modeling is implemented, taking the combined effect of magnetic anisotropy and the saturation into account. [ABSTRACT FROM AUTHOR]

This article compares two methods for computing high-frequency harmonic currents (HFHCs) and losses in permanent magnet synchronous machines (PMSMs) driven by pulsewidth modulation (PWM) voltage-source inverters (VSIs). The first method uses the currents containing HFHCs, which are obtained from the SIMULINK-based inverter–motor simulation system, as input for time-stepping finite-element analysis (TSFEA) to compute the PWM effects, while the second method directly uses PWM voltage sources as input for conducting the coupled field-circuit TSFEA. It is pointed out that the HFHCs are underestimated with the first method due to neglecting the eddy current reaction effect. Hence, both the iron and permanent magnet losses will be underestimated with the first method. On the contrary, the second method is better for computing the PWM effects because high-frequency harmonic voltages are independent on the eddy current reaction effect under PWM VSI supply and are directly related to high-frequency flux density variations, which determine high-frequency losses. Experiment on an interior PMSM was conducted to validate the simulation in this article. [ABSTRACT FROM AUTHOR]

This article presents an eddy current probe with array tunnel magnetoresistance (TMR) sensors for inspection of the steam generator tube of the nuclear power plant. The TMR sensors are integrated on a circular printed circuit board (PCB) with the sensitive axis along the radius directions. The dimensions of each TMR sensor in the array are length (0.45 mm) $\times $ width (0.45 mm). Fine spatial resolution magnetic field imaging can be generated as the size of the sensor is small. The operating principle of the probe is based on Faraday’s law, where eddy current is induced in the tube wall by an excitation coil carrying ac current, and then, the disturbance of the eddy current is monitored in terms of the magnetic field measured by the TMR sensors. Thanks to the high sensitivity and fine spatial resolution of the TMR sensors, the probe is capable of detecting outer diameter (OD) defect with an effective size 0.127 mm $\times \,\, 0.436$ mm. Moreover, when the probe scans in a defect-free area, the variation of lift-off of the probe to the inner surface of the tube wall does not bring in noises, which is important for maintaining a high signal-to-noise ratio in the practical inspection. The operation principle of the probe was studied based on a finite-element method (FEM) model, and then, a prototype unit was developed and tested. The experimental results demonstrated the feasibility of the concept and validated that the probe has excellent ability to detect various defects. [ABSTRACT FROM AUTHOR]

The eddy current and the eddy current loss in permanent magnets (PMs) are important factors in high-speed machine design and performance prediction. The eddy current loss is related to the magnetic field, the shape of magnets, and rotating speed. In this article, the eddy current is analytically calculated with a 2-D method in a high-speed machine with the Halbach magnetization. This analytical method calculates the eddy current with two parts: one part is induced by the instantaneous radial flux density and the other part is induced by instantaneous tangential flux density. The instantaneous radial and tangential flux densities are varying in the PM when the rotor rotates. The flux density in the PM is calculated by the 2-D complex relative permeance method with the SC-Toolbox aid. When the slotted machine operated at no-load condition, the eddy current is analytically calculated in this article based on the instantaneous flux density, and the eddy current distribution in the magnet is compared with the finite-element method (FEM) solutions, the comparison shows that the 2-D analytical method is an effective method for the eddy current and eddy current loss calculation. In the slotted machine with the Halbach magnetization, the eddy current loss increases with the arc angle of the main segment magnet increases, the eddy current loss increases fast at high speeds and cannot be ignored, but Halbach magnetization can reduce it in the high-speed machine as long as the magnetization parameters are chosen properly. [ABSTRACT FROM AUTHOR]

Transmission line method (TLM) has been used in 2-D scalar finite-element (FE) analysis due to its parallelism and constant admittance matrix. In this paper, the TLM is extended for the 3-D nonlinear vector FE problem that is more widely used for electromagnetic apparatus in practice. TLM is specially adapted for tetrahedron edge elements to calculate quasi-static electromagnetic field distribution for eddy current problems, and a dummy scalar gauge is applied to make the reduced magnetic vector FE formulation full-ranked and uniquely solvable by TLM. For each element, the nonlinearity is separated by transmission lines and only local small-scale Newton–Rapson iteration is needed, which is suitable for massive parallelization due to the independence between different elements. The TLM is implemented on a many-core GPU for a nonlinear FE power inductor case study, and the comparison of the results with a commercial FE software shows over 50 times speedup with a relative error of less than 2%. [ABSTRACT FROM AUTHOR]

A novel eddy current speed sensor is developed to measure the rotational speed of conductive objects. The sensor consists of one excitation coil and two pick-up coils around a rotating cylinder or rod. The sensor does not use magnetic yoke. For the analysis and experimental verification, we used 30 mm diameter non-magnetic aluminum and also magnetic solid iron cylinders. The calculated and measured speed ranges are up to 1200 r/min. A 2-D analytical method is developed to calculate sensor performance. A 2-D finite element is also used for simulations to compare results with the 2-D analytical method. A 3-D finite-element analysis is required to take into account significant 3-D effects due to the air coil configuration. The experimental results are presented at different steady-state speeds. The calculation results are compared with measurements to validate theoretical models and sensor performance. The eddy current speed sensor shows high linearity even at low speeds. For ferromagnetic rods, we suggest a novel double-layer configuration: non-magnetic conductive ring or shell on top of the iron rod minimizes the influence of the permeability changes. The main advantage of the novel sensor is that it has neither mechanical nor electrical contact to the rotating rod. [ABSTRACT FROM AUTHOR]

Finite-element techniques are applied to the frequency response computation of the input impedance of antennas with the eddy current losses taken into account. Both time-domain and frequency-domain approaches are discussed. Comparison to results for a dipole patch antenna with T-match obtained by assuming infinite conductivity is presented. [ABSTRACT FROM AUTHOR]

Recently, as the use of the induction range has increased rapidly, many studies have been studied. However, most of them are research on inverters, and the effect of the ferrite cores is insufficient in the induction range. Therefore, in this paper, the effect of the ferrite core in the induction range was analyzed, and the ferrite structure for improving the efficiency was proposed by using 3-D finite-element method (FEM). In order to verify the simulation results, the efficiency improvement was verified through experiments with three inputs of 1.2, 1.8, and 3.0 kW. [ABSTRACT FROM AUTHOR]

When using magnetic vector potential (MVP)-based formulations for magnetostatic or eddy-current problems, either gauge conditions specifying the divergence of the MVP or tree gauging by eliminating redundant degrees of freedom of the MVP is usually imposed to ensure uniqueness of solutions. Explicit gauging of the MVP is not always necessary since classical iterative solvers can automatically and implicitly fix the gauge as long as the right-hand side vectors are consistent. Besides iterative solvers, implicit gauging is also observed when using state-of-the-art parallel sparse direct solvers (PSDSs), thanks to the built-in functions of handling null-spaces of either real symmetric positive semi-definite matrix systems or those complex symmetric systems from eddy-current problems. Both static and eddy-current examples are solved by PSDS to demonstrate results of local physical quantities or global quantities such as magnetic energy or joule losses. High-order edge/nodal elements are also considered in our numerical examples and it is observed that PSDS can also easily and correctly handle the delicate discrete null spaces. [ABSTRACT FROM AUTHOR]

An efficient method is proposed for the numerical simulation of the bundle-level skin effect and its consequences arising in certain types of litz wires. The method is based on a probabilistic approach. The theory presented allows characterization of the repartition of currents between bundles and predicts some unexpected unique features. The method is tested on a coil unit that is used for inductive wireless power transfer. Simulations are verified by experimental data. [ABSTRACT FROM AUTHOR]

This paper presents a method for the treatment of multiply connected regions within the semi-explicit time-domain discontinuous Galerkin (DG) eddy current solver based on the ${H}$ – $\Phi $ field formulation. The suggested method utilizes a multivalued magnetic scalar potential over a cutting surface that divides a multiply connected domain into two simply connected regions. The multivalued magnetic scalar potential in the nonconductive domain ($\Phi $ -domain) is regularly updated after a sequence of time steps of the explicit vector DG-finite element method solver in the electrically conductive domain (${H}$ -domain) yielding an accurate time-domain solution of the magnetic field in the multiply connected space surrounding the eddy current region. The efficiency and accuracy of the method are demonstrated by a 3-D example and the obtained results are verified by comparison against the corresponding frequency-domain solution. [ABSTRACT FROM AUTHOR]

A novel 3-D hybrid formulation for time-harmonic eddy current problems in multiply connected domains is presented. The interior problem (in conductive regions) is discretized by the cell method (CM) in terms of magnetic vector potentials a, whereas the exterior problem (in the unbounded air domain) is discretized by the boundary element method (BEM) in terms of reduced scalar potentials ${\varphi }_{r}$. Novel topological constraints are derived from magnetostatic energy conservation by using a decomposition of the magnetic field which minimizes the support and the number of cohomology generators. A fast algebraic procedure to pre-compute source fields to handle efficiently current-driven coils is also proposed. The final matrix system can be solved in a limited number of iterations by transpose-free quasi-minimal residual method with symmetric successive over-relaxation preconditioning. Convergence tests show that numerical results are in a very good agreement with third-order finite element method (FEM) on a 2-D axisymmetric model. The CM-BEM with piecewise uniform approximation shows also to be very effective when analyzing fully 3-D test cases, since second-order FEM accuracy is attained even with coarse mesh refinements, by using, however, a much lower number of degrees of freedom compared to FEM. [ABSTRACT FROM AUTHOR]

This paper investigates the action of eddy current on tank vibration. Sound pressure level (SPL) is measured in situations where the winding is covered with an empty tank and exposed to air to verify the action of eddy current on tank vibration. The results show that tank vibration increases the average SPL by about 23 dB. Through experimental modal analysis, natural frequencies of the winding are away from the 100 Hz excitation but the natural frequency 99.787 Hz of tank is quite close to 100 Hz, which also explains the increase in the SPL. To make simulations on tank vibration caused by eddy current, a 3-D finite-element model is used for analyzing eddy current, electromagnetic (EM) force, as well as tank response in frequency domain. The computation shows a good agreement with the theoretical analysis that the phase angle of the EM force on tank shows a 90° shift compared with that of the winding. Also, the computation simulates the tank vibration caused by eddy current successfully. [ABSTRACT FROM AUTHOR]

A novel 2-D/1-D approach to simulate the eddy currents in a single thin iron sheet is presented. The introduced method utilizes ideas of the multiscale finite-element method by reducing the 3-D problem to a 2-D one. This is achieved via a decomposition of the solution with respect to its dependence on the coordinate directions. The decomposition is approximated using an expansion into polynomial shape functions. Integration over the respective coordinate gives an explicit 2-D problem. This eliminates the need to iteratively solve two coupled problems, as it is done in conventional 2-D/1-D methods. As another important advantage, the presented method allows for the incorporation of air gaps between the steel sheets. This can be done “for free,” i.e., without the introduction of additional unknowns and without changing the complexity of the resulting problem. The derivation is shown in detail for both the magnetic vector potential and the current vector potential formulation, giving explicit formulas for low polynomial orders of the used shape functions and illustrating how to proceed for shape functions of arbitrary degree. Finally, the developed method is tested in two numerical examples utilizing different geometries for the iron sheet and the computational efficiency is studied via comparison with a suitable standard finite-element model. [ABSTRACT FROM AUTHOR]

Novel eddy current speed sensor with axisymmetric coils and solid iron rod as moving part is presented. The analysis is performed for both dc and ac coil currents and for variable iron rod translational speed. The coil inductance and induced voltage results using the analytical method and finite-element method calculation are compared with the measured values. Two different coil configurations are used for simulations and measurement. [ABSTRACT FROM AUTHOR]

To control the quality of conductive materials such as copper, aluminum, or steel, various non-destructive testing techniques based on eddy current monitoring are routinely employed. Some marine alloys such as the Al-5000 series are the subject of interest notably in shipbuilding because of their good mechanical properties. However, this type of material is often subjected to intergranular corrosion and stress corrosion cracking when sensitized (i.e., after a regular increase in temperature). This paper deals with the evaluation of sensitization on an aluminum alloy by using an eddy current technique utilizing an improved giant magnetoresistance magnetometer as the head sensor. The magnetic field responses of different samples, which have been subjected to different heat treatments, are presented. The results are compared to an analytical model, which takes account of the setup and sample, in order to evaluate the material property evolution due to the sensitization. We show, clearly, that the given heat treatment (>175 °C) has induced a material conductivity variation. [ABSTRACT FROM AUTHOR]

In this paper, we investigated the magnetohydrodynamic effects of extremely low-frequency fields produced by a prototype diverted from an existing alternating magnetic therapy apparatus (AMTA). Diverting the use of a commercial AMTA, we prepared a prototype equipped with two additional coils for twisting the magnetic field of the apparatus. Five healthy male subjects ranging in age from 33 to 68 (two subjects each in their 30s and 40s, and one subject in his 60s) took part in this experiment. The heart beat fluctuation index [LF/HF: low frequency (LF) and high frequency (HF)] was measured with a prefrontal probe every 0.1 s during functional near-infrared spectroscopic (fNIRS) measurement sessions. Our experimental results showed the fact that the proper twisted magnetic fields induced from the prototyped machine were able to control the autonomic nervous system, judging from the LF/HF indexes on fNIRS measurements. [ABSTRACT FROM AUTHOR]

A matrix formulation of the Cauer ladder network (CLN) method is derived using the finite-element method to clarify the mathematical aspects of the CLN method. The CLN method directly yields orthogonal expansions of electric and magnetic fields that ensure the equivalence of the Cauer network to the eddy-current field. The CLN method is as exact as the Padé approximation via the Lanczos (PVL) process but more efficiently provides the circuit parameters and the orthogonal expansion than the PVL. [ABSTRACT FROM AUTHOR]

Transcranial magnetic stimulation (TMS) is one of the most widely used noninvasive brain stimulation methods. It has been utilized for both treatment and diagnosis of many neural diseases, such as neuropathic pain and loss of function caused by stroke. Existing TMS tools cannot deliver focused electric field to targeted penetration depth even though many important neurological disorders are originated from there. A breakthrough is needed to achieve noninvasive, focused brain stimulation. We demonstrated using magnetic shield to achieve magnetic focusing without sacrificing significant amount of throughput. The shield is composed of multiple layers of copper ring arrays, which utilize induced current to generate counter magnetic fields. We experimentally set up a two-pole stimulator system to verify device simulation. A transient magnetic field probe was used for field measurements. The focusing effect highly depends on the geometric design of shield. A tight focal spot with a diameter of smaller than 5 mm (plotted in MATLAB contour map) can be achieved by using copper ring arrays. With properly designed array structures and ring locations, the combined original and induced counter fields can produce a tightly focused field distribution with enhanced field strength at a depth of 7.5 mm beyond the shield plane, which is sufficient to reach many deep and critical parts of a mouse brain. [ABSTRACT FROM PUBLISHER]

Soft magnetic composite (SMC) is composed of ferromagnetic particles surrounded by electrical insulation. SMC has advantages such as isotropic magnetic characteristics, low eddy current loss, and easy to be manufactured into complex shapes compared with electrical steel sheets. In this paper, to establish the homogenization technique for the magnetic field analysis of an electrical machine using SMC, a method to evaluate the effective permeability and iron loss taking account of nonlinear magnetic characteristics and eddy currents is proposed by using a cell model composed of one particle of SMC. Then, the effects of the frequency and particle size on the effective permeability and iron loss are investigated numerically. Finally, the effective permeability and iron losses of an actual SMC are calculated, and they are compared with measured results to verify the proposed method. It is shown that theoretically proper results are obtained by using the proposed method. The calculated iron losses coincide well with the measured ones below 10 kHz, whereas the calculated effective permeability is smaller than the measured one due to different effective gap lengths. [ABSTRACT FROM AUTHOR]

In this paper, open boundary techniques are employed to represent the Cauer ladder network (CLN) for unbounded eddy-current problems. Recently, a novel and effective model order reduction method, called the CLN method, has been proposed in which linear eddy-current fields are represented by a CLN. The CLN method was initially formulated for closed domain eddy-current problems. This paper demonstrates that the CLN method can be extended to unbounded-domain problems when combined with conventional open boundary techniques. The CLN network parameter extractions of two parallel busbars are demonstrated as a numerical example. [ABSTRACT FROM AUTHOR]

Two different forward models for Lorentz force evaluation, the approximate forward solution (AFS) and the novel extended area approach (EAA), are evaluated using a goal function scan. A setup that contains a spherical permanent magnet and a specimen of stacked aluminum sheets with a cuboidal defect of size 12~\mathrm mm\times 2 ~\mathrm mm\times 2~ \mathrm mm at a depth of 2 mm is simulated by the finite-element method (FEM). Deviations between force perturbation of FEM and AFS or EAA are compared in terms of normalized root mean square errors (NRMSEs). The goal function scan yields minimal NRMSE for the correct depth with values of 6.1% for AFS and 1.7% for EAA, corresponding to the determined defect dimensions of 7 ~\mathrm mm\times 10~ \mathrm mm\times 2 ~\mathrm mm for AFS and 11 ~\mathrm mm\times 2~ \mathrm mm\times 2 ~\mathrm mm for EAA. [ABSTRACT FROM AUTHOR]

A rigorous stability analysis of the previously published semi-explicit time domain discontinuous Galerkin (DG) H– $\Phi $ approach for eddy current simulations is presented. The considered DG finite-element method (FEM) enables explicit time stepping in electrically conducting regions and eliminates the need for solving large sparse ill-conditioned equation systems. The considered method utilizes the magnetic scalar potential in electrically non-conducting regions computed by using the nodal finite elements. The theoretical stability limit of the considered semi-explicit time domain approach is obtained by applying the z-transform on the discrete time domain DG-FEM equations and by performing an eigenvalue analysis of the underlying elemental DG-FEM matrices. The obtained results are tested on simple 3-D examples, and an excellent agreement between the theoretical stability limit and the empirically obtained values was found. [ABSTRACT FROM AUTHOR]