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Millimeter wave components, such as circulators and isolators, frequently use magnetic fields to break symmetry of the signal propagation and provide unidirectional signal transmission. While effective, these components have not seen the level of miniaturization of other millimeter wave components, primarily due to the discrete nature of the magnets used in the components. Using circulators in the 40-50 GHz range as a motivating application, requirements arise for the deposited films, namely immunity to eddy currents, sufficient magnetization to act as self-biasing magnets, and out-of-plane orientation of the self-biasing field. Based on these required properties, hexaferrite materials are selected for their strong magnetocrystalline anisotropy (MCA) and low conductance. The difficulty of integrating these components monolithically with monolithic microwave integrated circuits (MMIC) originates from the incompatibility of crystal structure with standard semiconductor materials and process conditions. Additive manufacturing using a composite of strontium hexaferrite (SrFe12O19) particles and photoresist has been chosen as a method to overcome the difficulties of integrating hexaferrite material to semiconductor substrates. Due to their large internal anisotropy field, the particles of strontium hexaferrite tend to rotate to the field direction instead of changing magnetization direction under application of an external magnetic field (less than the anisotropy field). We have developed a method for 3D printing composites of high strontium hexaferrite concentration (up to 20% by volume) in a liquid photoresist, SU8. Rotation of hexaferrite particles in polymer matrix and thus magnetic anisotropy has been demonstrated in the composite, which is subsequently cured to hold the physical position and orientation of the particles. The anisotropy of the self-biasing field provided by the films has been experimentally characterized, and a ferromagnetic resonance (FMR) frequency ~43 GHz has been observed. We have also characterized the viscosity of the particle-laden polymer at different particle concentrations. 3D printing of this composite with poling will make it possible to directly print magnetic components that require out-of-plane anisotropic magnetization.

In this article, an approach combining semi-empirical equations and the method of images is proposed for round conductor layer windings with un-gapped core. The new equation for proximity effect can convert the constant field strength from the magneto-motive force (MMF) across the core window into a frequency-dependent uniform background magnetic field strength, which can take partly the interaction between conductors into account. Geometric factors are introduced by fitting the finite element method (FEM) results to improve the accuracy. The method of images is used to calculate the field strength in order to counteract the impact of the 2-D edge effect. The new method is compared with the 2-D FEM, analytical methods, and is also validated by measurements with EE core transformers. The proposed method shows good accuracy (< 10% error) compared with 2-D FEM for both high and low porosity factor windings. Therefore, it can handle more winding configurations than other 1-D analytical methods.

Although permanent magnet couplings (PMCs) have been under research for many years and have found successful industrial applications, this is still a technology under development. Accurate parameter determination is of significance for performance analysis and critical decisions on PMC design. However, the determination can often lead to an unacceptable increase in computation, especially when the finite element (FE) method is used. The study aims to develop an FE model that is used for the structural design of a standard-disc type PMC for optimal torque. For the quick and accurate design, an integration optimal solution of the response surface methodology (RSM) and the Taguchi’s method was proposed. To verify the simulation, a series of experimental investigations were conducted on a self-developed testing platform. Furthermore, for a minimum set of FE analyses (FEA), a quantitative indicator called contribution rate, which can reflect effect level of structure parameters on the torque, was given based on the Taguchi method. Apart from this, the orthogonal matrix was used for the reduction of the FE calculation. Based on the contribution rate, the response surface methodology was adopted for the optimal torque determination with no increase in the PM volume. According to the optimization results, a fitting formula, which considers the contribution rates of the optimization variables, was presented. The results suggest that the FE simulations agree very well with the experiments, and the fitting formula can be used in the PMC design.

A material model for ferrite is presented, enabling an accurate calculation of the core losses from 100 kHz to 1000 kHz with a single set of scalar parameters over a decade of excitation current. It is based on the modelling of different material effects such as quantum tunnelling conduction between ferrite grains and atomic level magnetisation. The implications of the satisfying results of this approach on core loss modelling techniques at high frequencies are discussed., IEEE Transactions on Magnetics, ISSN:0018-9464, ISSN:1941-0069

Detecting defects in high-permeability steel components can be challenging when using the eddy current technique. This is due to the strong magnetization signal that is simultaneously generated along with the eddy current signal. To minimize the regions of the induced eddy current and its detection, an eddy current probe based on an array of miniature fluxgate sensors (DRV425, Texas Instrument, USA) and axial inductors was proposed and fabricated in the study. The fluxgate sensors were arranged in two layers, and the sensors were sandwiched between two layers of inductors. The output signals from the fluxgate array were sampled to obtain a differential signal of the eddy current intensity and direction. A phase-sensitive detection technique was implemented to isolate the strong magnetization signal from the detected eddy current signal and utilized to characterize artificial slits with varying depths. The developed probe successfully characterized both the vertically and horizontally oriented slits with depths from 2 to 10 mm on a 12 mm thick mild steel plate. A better sensitivity was notable in the evaluation of the vertical slits where the vertical slits would increase the eddy current intensity in contrast to the horizontal slits around the slits. It was shown that the eddy current’s distribution map obtained from the developed probe could be used to reveal the physical dimension of the slit.

Ultra-high-speed (UHS) surface-mounted permanent-magnet synchronous motors (SPMSMs) are widely used for driving air compressors. UHS SPMSMs can suffer from high stator iron loss and rotor eddy current loss due to their high rotational speed and changes in the magnetic flux density when loading. Since these losses do not have a linear trend but change according to the motor design parameters, mathematical models cannot always predict them. This study aims to design of UHS SPMSMs based on a kriging surrogate model that takes into account the stator iron loss and rotor eddy current loss. Since the kriging surrogate model is highly predictive for nonlinear inputs, it is the perfect candidate to take into account the stator iron loss and rotor eddy current loss. The design proposed in this study, allowed to minimize the size and losses of a motor that satisfied the power specification.

This paper presents an efficient multi-objective optimization model for linear induction motors (LIMs) with a novel approximation and prediction strategy. The proposed method can realize the optimization design with speediness and accuracy, while reducing the calculation complexity of eddy current analysis. The sample data in this model are obtained by 3D finite-element method (FEM) considering the skin effect and edge effect. Then, the Latin hypercube sampling (LHS) method is adopted to extract dimensional data including every structural parameter of the secondary. Based on these samples, a multiple analysis model is established using eXtreme Gradient Boosting (XGBoost) method. By employing this analysis model, several optimization structures are provided satisfying the limitation and rationality of designing structure and performance requirements. The precisions of the thrust force, vertical force, eddy current and copper loss of optimal structures are validated by FEM.

Aiming at the problem of excessive eddy current loss of permanent magnets in fractional slot concentrated winding permanent magnet synchronous motors (FSCW-PMSM) at high speed, a new PMSM with hybrid rotor structure for electric vehicles (EV) is proposed in the paper, the key is to introduce additional ferrite magnets in d and q axis magnetic flux paths, respectively. Furthermore, slotting on the rotor surface and genetic algorithm (GA) optimization are adopted to compensate for the side effects caused by the introduction of ferrite magnets and to obtain optimal parameters of the new motor. Compared with the traditional all-Nd-Fe-B structure, the proposed hybrid rotor structure can not only curb the magnet loss at high speed, but also present a cost-effective design approach for IPMSM for EV applications with less usage of expensive Nd-Fe-B magnets as well as enhanced reluctance torque capability.

As the vital equipment of UHVDC (ultra-high voltage direct current) transmission, the anodic saturable reactor is crucial to the safe operation of converter valve. Based on dynamic core loss model, the eddy current analysis and core loss calculation on saturable reactor are carried out by finite element method (FEM) simulation software Maxwell. Through the fast-mapping interpolation method between heterogeneous meshes, the core loss is mapped from electromagnetic field to the fluid field by Fluent UDF, which makes the distribution of heat source more realistic. The distributions of temperature and velocity of the anodic saturable reactor are obtained by computational fluid dynamics (CFD) simulation software Fluent. The temperature simulation results show that the hottest spots inside the core and on the reactor inner toroidal surface are 117 °C and 80.5 °C, respectively. The experimental results demonstrate the validity of the calculation methods of core loss and temperature distribution.

This paper proposes a new probe for suppressing the vibration component from the detection signal in eddy current testing. The work is motivated by the desire to develop a new inspection method that can suppress the effects of vibration generated in the manufacturing process of metal parts such as tubes, rods and wires in order to make the current manufacturing process faster. The novelty of the probe lies in its simultaneous use of self and mutual inductions. The proposed probe uses the different effects of the self and mutual inductions to suppress the vibration component. This paper simplifies the discussion by limiting the dynamic vibration of the test specimen to static displacement. The coil distance between the excitation and detection coils should be adjusted for each test specimen for the most effective suppression of the displacement signal. The simulation and measurement results show that the coil distance in the mutual induction probe can control the phase of the displacement signal. It was confirmed that the amplitude of displacement signals measured by the proposed probe was under 6 % of the amplitude measured by the self-induction probe when the optimal coil distance was used. The results obtained suggest that the proposed probe can suppress the vibration component.

There are many space harmonics in the stator magnetomotive force (MMF) of fractional-slot concentrated winding (FSCW). These harmonics will produce high eddy current losses in the permanent magnet (PM), which will reduce motor efficiency and affect motor performance. Aiming at the above problems, the harmonic components of traditional stator MMF are firstly analyzed in this paper, and then a novel space-shifted unequal-turn winding structure is proposed for dual three-phase fractional-slot permanent magnet synchronous motors (PMSM). Meanwhile, the sub- and super-harmonics in the stator MMF can be simultaneously eliminated using the proposed winding structure. To verify the effectiveness of the proposed structure, an 18-slot/8-pole motor and a 30-slot/14-pole dual three-phase fractional-slot PMSM with low space harmonic are designed by using the proposed space-shifted unequal-turn winding structure based on the analysis of 9-slot/8-pole and 15-slot/14-pole motors. Finally, by compairing the finite element analysis (FEA) results, it is verified that the dual three-phase PMSM motor with the proposed structure has smaller eddy current losses in PM and better motor performance.

AC homopolar motors, with high-temperature superconductors (HTS) are considered to be a promising technology for high-power applications. With superconducting components being placed exclusively in non-rotating parts, a motor can reach high rotational speeds. However, the dynamic behaviour of the system creates a non-negligible magnetic ripple field which generates heat and makes thermal management of the cryogenic system more challenging. In this paper we present a case study for the thermal behaviour of a conduction-cooled, high-temperature superconducting field coil assembly in a 500 kW asynchronous homopolar motor. The analysis focusses on the investigation of the magnetic ripple field and its impact on heat generation due to AC loss in the HTS field coil and eddy current loss in copper parts present in the assembly. Using electromagnetic and thermal finite-element models, we construct a detailed description of the thermal bus design which considers different cooling scenarios and sizing of the conductive elements. Depending on the geometry of the thermal bus, we observe heat loads from AC losses of up to 0.4 W, and eddy current losses in the copper elements of up to 1 W. These heat loads translate to temperature increases as high as 10 K. Techniques to reduce the temperature rise based on thermal bus redesign are presented, along with recommendations for the most promising cooling scenarios and optimal thermal bus geometry.

Crack orientation is a vital factor in the behavioral study of fractures, especially the study of crack propagation in structures that are under dynamic or fatigue loading. Indeed, many non-destructive testing (NDT) techniques have been developed recently for the detection of cracks such as the eddy current testing (ECT). However, the crack orientation has not been undertaken into consideration. In this paper, a NDT based on eddy current using 3D finite element modeling, is proposed for the determination of the crack orientation. The idea of this proposed technique benefits from the influences of crack orientation, which can be observed on the components of eddy current and the related magnetic flux density following the x, y axes, for the estimation of the crack angle orientation based on an interpolation criteria. The obtained results through the presented simulation prove the validity of the proposed technique for the detection of crack angle orientation.

Nondestructive testing (NDT) methods are widely used in the rail industry to detect and characterize rolling contact fatigue (RCF) defects in railroads, which is very important for railway inspection and maintenance to prevent catastrophic accidents. Existing NDT methods, e.g., ultrasonic testing (UT), magnetic flux leakage (MFL), and eddy current testing (ECT) have been successfully applied in the rail industry, and the state-of-the-art UT method reported recently achieved a high speed of 40 mi/h with a probability of detection (POD) over 80% under 30% false alarms. However, NDT methods still suffer from a bottleneck in that a higher inspection speed causes lower detection sensitivity due to their physical limits, such as negative velocity effect and long sensing time. One of the leading challenges to the rail NDT community is to develop a high-speed high-sensitivity (HSHS) capability that can provide an improved POD of rail defects in high-speed inspection scenarios over 60 mi/h. This article proposes a horizontal U-shaped magnets-based motion-induced eddy current array (MIECA) method to detect rail surface defects with the HSHS capability. The MIECA method deploys a three-axis magnetic sensor array along the rail transverse direction at the middle of the magnets to measure the MIECA signals, which utilizes the wake effect of the diffused motion-induced eddy current (MIEC) caused by the relative high-speed motion between the magnets and the rail track. Finite-element method (FEM) simulations with a wide speed range from 0 to 62.5 mi/h are carried out to investigate the relationships between the MIEC generation, diffusion and magnitude, and the three-axis MIECA signals. The simulation results show that the higher the speed, the greater the magnitude of diffused MIEC, and the greater the peak-to-peak values of three-axis MIECA signals caused by rail surface defects, which shows a great promise for detecting rail surface defects in high-speed scenarios and is superior inspection relative to existing NDT methods in terms of inspection speed, detection sensitivity, and defect characterization capability.

A novel squirrel cage eddy current coupling with adjustable radial air gap was presented, which can change the output speed by changing the air gap thickness in radial direction between the copper strips and the permanent magnet. It has the advantages of no axial force in speed regulation and less eccentric force in axisymmetric structure. The 2-D electromagnetic torque model of the rotor was established, and the influence of the air gap thickness on the electromagnetic torque was also studied by finite element method. Further, a novel method to solve the dynamic equation of the eddy current coupling was proposed based on the effect of air gap thickness and relative speed on torque characteristics, and was applied to the speed regulation performance analysis. In addition, the influence of the relative magnetic permeability of the permanent magnet back yoke and the internal rotor on the speed regulation performance was studied.

In order to accurately analyze the effect of combined magnetic shielding on stray load losses of converter transformer, a three-dimensional (3D) finite-element analysis (FEA) model is established. The total losses can be gotten by summing the simulated losses of each harmonic. The effectiveness of the presented simulation method is verified by comparing the simulated and tested stray load losses of the converter transformer in the case of rated operation without lobe-type magnetic shielding structure. Afterwards, the installation position of lobe-type magnetic shielding is optimized by considering its effect on stray load losses. Finally, the stray load losses under different DC bias currents are simulated and analyzed.

Conductor on round core (CORC) cables wound by high-temperature superconducting (HTS) tapes have received much attention due to the advantages in power capacity and mechanical flexibility. This paper first developed a 3D model for a CORC cable through the finite-element method (FEM). Next, the total AC loss caused by transported current only was investigated, revealing the eddy current loss in the tube former contributes to the cable loss. The numerical CORC model was validated by published measurements. Moreover, the AC loss that resulted from a simultaneous presence of transport current and magnetic field was explored. With the induced current, the magnetisation loss generated in superconductors can increase the total loss. It is concluded that the addition of a magnetic field can result in a surge in the total loss of a current-carrying cable.

The eddy-current loss of switched reluctance motor (SRM) is studied and analyzed in this paper. As a significant part of core loss, eddy-current loss has a great influence on motor performance. First, the average magnetic flux waveforms in every distributed region are derived from the magnetic equivalent circuit (MEC) model. Based on this, each harmonic of magnetic density is obtained by adopting the fast Fourier transform (FFT) method for further calculation. Then, each harmonic eddy-current loss is computed by sinusoidal magnetic density and the total eddy-current loss in different region of motor is derived by superposing of them. Therefore, the calculated results at different speed and conduction angles of each region are analyzed. Finally, the 3D finite element (FE) model is established in software FLUX and the experimental platform of the SRM prototype is built.

Effective medium theory replaces a given fine-scale heterostructure with a homogeneous one in such a way that the physically measurable quantities, e.g., reaction fields and losses, remain approximately the same. This article presents a peculiar case where the physical nature of the problem and the type of governing mathematical equations change upon homogenization. We consider a stratified nonlinear magnetic and conducting medium, where a low-frequency excitation induces eddy currents. It is shown that this eddy current problem becomes, upon homogenization, mathematically equivalent to a magnetostatic one and takes eddy currents into account via a complex-valued nonlinear $B$ – $H$ -curve. The homogenization procedure is demonstrated for a cylindrical laminated iron core. High accuracy of homogenization, even for the local loss distribution, is demonstrated.

Thermoplastic composites has attracted extensive attention in industrial process with excellent properties. As one of the most important parameters, electric conductivity is difficult to detect due to its inhomogeneity and anisotropy. In this paper, a novel method for measuring volume electric conductivity of composites based on eddy current loss has been introduced by using both experimental and numerical approaches. Initially, the eddy current loss and equivalent volume conductivity under different magnetic flux density are presented by analyzing voltage and current acquired in a designed air-gapless reactor under 500 Hz sinusoidal excitation with variety amplitudes. Then, to verify the measurement method and determine the influence of different materials on the eddy current loss, a 3-D electromagnetic model of the experimental devices is built and three cases with different materials are calculated. The parameters including eddy current loss and magnetic flux density are presented. The mechanism underlying the influence of different conductivity on the measuring model is analyzed according to the confidents and eddy current loss. Results show that the ratio of eddy current loss to the square of magnetic flux density is linear. The formula of equivalent volume conductivity needs to be revised by multiplying certain coefficients for high conductivity due to the eddy current effect on the detection coil. It is reasonable that magnetic flux density rang is set in 0.2∼0.8T during measurement.

The high-temperature superconducting (HTS) maglev system has great potential to become a new type of rail transit due to its unique self-stabilizing levitation, low noise pollution, and environment-friendly operation. However, previous studies have shown that the damping properties of HTS system are low, and hence, its large-amplitude nonlinear vibration is prone to occur under external interference, which will affect the stability, safety, and comfort of the long-term operation of the maglev vehicle. Therefore, it is necessary to improve the damping performance of HTS maglev system, minimize the impact of vibration on the maglev system, improve the anti-interference ability of the system, and ensure the smoothness and stability of the system. In this work, an eddy current damper (ECD) is designed to suppress the vibration that may occur during the operation of the HTS maglev vehicle; the ECD is placed at the same height as the HTS bulks. And by collecting the displacement and acceleration signals of the HTS levitator, the efficiency of dampers in suppressing vibration with different copper thicknesses under different field cooling heights (FCHs) is analyzed. The experimental results show that the additional ECD can effectively reduce the vibration of the HTS levitator, especially among the resonance frequency range. And when the FCH is set to the commonly used engineering height of 30 mm, the ECD has the highest damping efficiency. The relevant research results in this work provide a possible solution to the problems encountered in the operation of the maglev train in the real scene.

The high-temperature superconducting (HTS) null-flux electrodynamic suspension (EDS) system is one of the most promising solutions for high-speed transportation. In this article, a 3-D model based on the finite-element method (FEM) is established to solve the electromagnetic forces in the HTS null-flux EDS system with the commercial software COMSOL Multiphysics. The current induced in the null-flux coils and the forces on the HTS magnets were studied and compared with the results from our dynamic circuit model. The two models agree with each other with a difference of less than 6%. The FEM model can deal with 3-D geometries, allowing the analysis of complex situations, such as the eddy current in the cryostat walls. Furthermore, the model can be readily extended to solve coupled problems, including the heat and mechanical behaviors of the HTS magnets and/or the null-flux coils, which are engineering concerns in real applications.

The performance of three-dimensional integrated circuits primarily depends on the filler material used in the through-silicon vias (TSVs). The most widely used filler material is Cu, but it faces severe reliability issues due to the skin effect and problems related to electromigration at high frequencies. Therefore, single- and multiwalled carbon nanotube (SWCNT and MWCNT) bundles have recently emerged as suitable filler materials for TSVs. Additionally, at high frequencies, electromagnetic forces induce eddy currents that adversely affect the overall performance of TSVs. This paper demonstrates for the first time the impact of eddy currents on TSVs based on Cu as well as SWCNT and MWCNT bundles. An accurate RLGC circuit model is proposed by considering the eddy effect at the depletion layer, neighboring TSVs and in the silicon substrate region. The resulting closed-form expressions for the TSV parasitic parameters are verified against previous experimental data obtained at an operating frequency of 2 GHz. Good agreement between the experimental and analytical data for the resistance and inductance is observed, revealing a difference of approximately 8.02% and 4.95%, respectively. The equivalent circuit parameters are modeled at the 7-nm technology node using a three-line driver-via-load setup. For the proposed setup, the crosstalk-induced delay, the peak noise voltage, and the power dissipation are analyzed with and without consideration of the eddy effect. Irrespective of the TSV height, the MWCNT bundle design demonstrates substantially lower crosstalk delay, peak noise, and power dissipation in comparison with the TSVs based on Cu or SWCNT bundles. The overall difference when including the eddy effect is approximately 16.55%, 2.45%, and 0.27% for the crosstalk delay, noise voltage, and power dissipation, respectively. Furthermore, to demonstrate the complexity of the model at smaller technology nodes, a comprehensive study is performed at the 5-nm and 7-nm technology nodes. It is observed that the delay without the eddy effect at the 5-nm technology node is higher on average by 3.4-fold for Cu, whereas for the TSVs based on MWCNT bundles it is only 2.6-fold higher.

The conductor on round core (CORC) cable wound with second-generation high-temperature superconducting (HTS) tapes is a promising cable candidate with superiority in current capacity and mechanical strength. The composing superconductors and the former are tightly assembled, resulting in a strong electro-magnetic interaction between them. Correspondingly, the AC loss is influenced by the cable structure. In this paper, a 3D finite-element model of the CORC cable is first built, and it includes the complex geometry, the angular dependence of critical current and the periodic settings. The modelling is verified by the measurements conducted for the transport loss of a two-layer CORC cable. Subsequently, the simulated results show that the primary transport loss shifts from the former to the superconductors as the current increases. Meanwhile, the loss exhibited in the outer layer is larger than that of the inner layer, which is caused by the shielding effect among layers and the former. This also leads to the current inhomogeneity in CORC cables. In contrast with the two-layer case, the simulated single-layer structure indicates stronger frequency dependence because the eddy current loss in the copper former is always dominant without the cancellation of the opposite-wound layers. The core eddy current of the single structure is denser on the outer surface. Finally, the AC transport losses among a straight HTS tape, a two-layer cable and a single-layer cable are compared. The two-layer structure is confirmed to minimise the loss, meaning an even-numbered arrangement makes better use of the cable space and superconducting materials. Having illustrated the electro-magnetic behaviour inside the CORC cable, this work is an essential reference for the structure design of CORC cables.

It is still a big challenge to calculate the probability of defect detection for inspecting pits on austenitic stainless steel welding using traditional POD models. Because we determine the decision threshold, the POD curve has a lot of changes as the decision threshold changes, there is no clear reason to insist which threshold is reasonable. This study proposes a new probability of detection (POD) model to quantitatively assess the detection capability of eddy current probes for inspecting pits on austenitic stainless steel welding. The experimental results show that the proposed model is more reasonable than traditional ones. The novel POD model was employed to analyze three eddy current probes, uniform, TR, plus-point probes on austenitic stainless steel welding. The results reveal that the uniform eddy current probe has the best detection capability for inspecting pits on among the three probes.

In this study, we explore the vector magnetic properties of the electrical steel sheet under dc-biased flux and rotating magnetic field of different frequencies. The corresponding iron loss and the rotational eddy current loss are discussed. An enhanced vector magnetic hysteresis model is proposed to describe the $B$ – $H$ behavior under these conditions. The accuracy of the proposed model is verified by the close agreement between the hysteresis loops calculated with the proposed model and those measured experimentally, as well as by the neglectable calculation error of the total iron loss.

The conductive magnetic film will produce eddy current loss when it works in a high-frequency band, which will reduce the performance of bulk acoustic wave magnetoelectric (BAW ME) devices. If the eddy current loss is not taken into account in the devices modeling, the models will be seriously distorted. Therefore, combining the Maxwell’s equations with constitutive relations of ME material, we define the eddy current loss angle as a figure of merit to evaluate the eddy current loss. Then the models of eddy current loss rate of the potential energy and average radiated power are constructed, respectively. The finite element analysis is used to further validate the analytic model. In addition, the effect of isolation layers on eddy current suppression is studied by using the analytical model. The results show that the analytical solutions match with the numerical simulation results perfectly.

An eddy current damper comprising a magnet and a conducting plate moving perpendicularly to it is called a perpendicular-motion-type eddy current damper, whereas one with a magnet and a conducting plate moving parallel to it is called a parallel-motion-type eddy current damper. In this article, a method of using magnetic vector potentials in a stationary-conductor coordinate system to obtain easily the damping coefficient (the A method) is proposed and applied to a perpendicular-motion-type eddy current damper comprising a ring magnet and conducting disk. The previously proposed coil method is also applied. Because both methods utilize the magnetic flux densities and magnetic vector potentials obtained using a circular current loop, they cannot be considered to be the effect of the magnetic field generated by eddy currents on the damping coefficients. However, the damping coefficients were in good agreement with those obtained using a 3-D finite element method (3-D-FEM). Hence, the effect of the secondary magnetic field can be ignored. Moreover, the A method is as precise as the 3-D-FEM, is less complicated, and does not require an air region and boundary conditions for computation. In addition, although the errors of the damping ratios calculated from measured data and the A method were 17%, the error of the modified damping ratios obtained by applying the equivalent mass of the disk to the A method decreased to 6%.

Iron (Fe) nano-polycrystalline metal obtained by sintering reduced iron nanoparticles from iron oxide was applied to an axial flux generator. When the thickness of the core material is 1/10, it has the same ability of the power generation as when Fe bulk is used as the core. We can also reduce the iron loss (hysteresis loss and eddy current loss), which enables the construction of thin and axial flux generators with light weight. We investigated the magnetization property of the core inductor at the direct current and found that Fe nanoparticles were produced from iron oxide particles by high voltage pulse or laser ablation in liquids. Core inductors with these materials were fabricated. It has been clarified from measurements of the core inductor magnetization that the relative permeability of the sintered Fe nanopolycrystalline was one million.

This article proposes a novel analysis method for the losses in a litz wire considering the circulating and eddy currents. In the proposed method, the macroscopic complex permeability is introduced to evaluate the eddy current loss owing to the proximity effect. Homogenization-based finite element analysis using the macroscopic complex permeability can effectively compute the proximity effect loss. The loss owing to the circulating currents is evaluated by solving the corresponding circuit equation. It is shown that the eddy current loss is dominant for the solenoidal and spiral coils without magnetic cores because of the uniform magnetic field distribution along the wire. Moreover, the magnetic reactors in which the circulating current loss cannot be ignored are analyzed using the proposed method. It is shown that the losses computed by the proposed method agree well with the measured results.

This article proposes a new, computationally inexpensive calculation approach for eddy current losses in nonmagnetic pressure fingers for open-circuit operation. The field calculation was presented in a previous article (Fricke et al. , 2019) and is based on a Schwarz–Christoffel mapping. An alternative 2-D FEA field calculation is presented. The loss model discretizes the pressure fingers similar to 2-D FEA and solves an electric network, while allowing for geometric different alterations, such as slits, to be considered. The proposed approach takes only around one second to compute, with the loss model itself taking only around 60 ms. Comparisons to a time-step 3-D FEA model are used to validate the new method.

This article presents a boundary element method (BEM) formulation coupled with high-order surface impedance boundary conditions (SIBCs) for axisymmetric eddy current problems. The formulation is based on the perturbation theory (PT) and the reduced magnetic scalar potential. A big advantage of the proposed approach is that if the solution is sought at different frequencies, the boundary integral equations can be solved only once and, then, the fields are easily computed at any frequency using a series expansion according to PT. Three test problems are solved, for which the reference solution is given by the standard finite-element method (FEM). The convergence of BEM-SIBC results toward FEM solution with respect to frequency is verified. The proposed approach requires reduced memory and computational times compared to the standard FEM and can be applied with linear, isotropic, and homogeneous materials.

The soft magnetic performances including frequency-dependent permeability, core loss, and DC-bias properties of the Fe-6.5 wt.%Si (FeSi) soft magnetic composites (SMCs) coated with different contents of NiZn-ferrite and compacted with different forming pressures were compared and analyzed. The retained permeability at an applied field of 7960 A/m has a proportional relationship to the real part of complex permeability, which is observed to be closely related to cores’ bulk density. A three-dimensional loss separation model and its related fitting analysis on the domain walls and magnetic objects were established to investigate the relative loss mechanism for the FeSi SMCs fabricated under different parameters. The variation of total core loss (Pcv) is mainly induced by the changes of hysteresis loss (Ph) and excess loss (Pexc) with different fabrication parameters, wherein both the Ph and Pexc are sensitive of the number of pinning site that inhibits the motion of domain wall. The inter-part eddy current loss is only 1/600–1/250 of total core loss for all the ferrite-coated SMCs owing to the relatively high electrical resistivity of 1.22–2.8 Ω m. These results offer an in-depth observation into regulating the comprehensive soft magnetic properties of the SMCs coated with magnetic insulating layer for high-frequency and high-power applications in electromagnetic components.

Soft magnetic composites (SMC) with a bionic shell structure and a delicate, regular layered arrangement were prepared via a casting process. The permeability of composite samples was 140 at 5 MHz for plane anisotropy, while that of the spherical-particle-constructed material is only 14. According to classical loss separation results, the layered bulk material without an SiO2 coating exhibited lower hysteresis loss. In contrast, the layered bulk material coated with SiO2 showed lower eddy current loss, attributed to the increase in resistivity resulting from the SiO2 coating. The magnetic loss of the layered bulk materials was 588 kW/m3 at 50 mT and 100 kHz. SMC materials with this structure are anticipated to have strong potential for magnetic cores used in high-efficiency power supplies.

This article develops a multi-scale model order reduction (MOR) method including both material and machine scale MOR. The material-scale MOR homogenizes the eddy-current (EC) field in laminated cores using the Legendre expansion of magnetic induction along the stacking direction within each steel sheet. The machine-scale MOR represents the EC field in electromagnetic devices with their equivalent Cauer ladder network (CLN). The former MOR is built into the latter by applying the CLN procedure to the homogenized EC field equation.

FeSiAl/SrFe12O19 composites with different SrFe12O19 contents were prepared, and their microstructure magnetic properties were studied. It can be seen from the SEM morphology picture that the SrFe12O19 powder is relatively fine, filling the gaps between the FeSiAl spherical particles. The SrFe12O19 ferrite has a higher resistivity than FeSiAl alloy and can be used as an insulating agent. Hysteresis loop results show that the saturation magnetization of all composites is relatively high (up to 163 emu/g). Magnetic loss analysis shows that the hysteresis loss increases with the increase in the SrFe12O19 content, which may be caused by the high anisotropy of SrFe12O19 powder. The eddy current loss is the smallest when the SrFe12O19 content is 10.7 wt%. Our research illustrates that proper addition of SrFe12O19 content can reduce eddy current loss and SrFe12O19 can be used as an insulating agent for soft magnetic composites.

This article describes the characteristic calculation of induction motors with the same shaped rotor bars in equal spaces by considering hysteresis loops in stator and rotor cores. A fast calculation method based on the symmetrical bar shape is proposed to realize this calculation. The validity of the calculation is confirmed by experimental results. It is clarified that the accuracies of the calculated motor characteristics are improved by considering the reaction field caused by the hysteresis phenomenon and eddy currents in the core.

The multiscale finite element method (MSFEM) is a valuable tool to solve the eddy current problem in laminated materials consisting of many iron sheets, which would be prohibitively expensive to resolve in a finite element mesh. It allows using a coarse mesh that does not resolve each sheet and constructs the local fields using predefined micro-shape functions. This article presents for the first time an a posteriori error estimator for the MSFEM, which considers the error with respect to the exact solution. It is based on flux equilibration and a modification of the theorem of Prager and Synge and provides an upper bound for the error that does not include generic constants. Numerical examples show a good performance in both linear and nonlinear cases.

Metaconductors with near-zero permeability is an incentive for the development of high-frequency passive components due to effective suppression of skin effect. In this work, an asymmetric multilayered structure is proposed to broaden the bandwidth of skin effect suppression while preserving a sufficient lower frequency limit of permeability compensation. Coplanar waveguide (CPW) transmission lines consisting of two ferromagnetic layers alternatively stacking with Cu layers were designed and fabricated. Near-zero permeability is obtained at two separated frequencies, which enables broadband eddy current canceling and resistance reduction. The measured results manifest a resistance reduction up to 46% at 11.1 GHz, compared to a Cu transmission line with the same dimensions, and a broad skin effect suppression band between 7.5 and 30.0 GHz, which is sufficient to cover the important 5G applications.

This article presents a numerical model dedicated to the computation of a quasi-static field induced by a 3-D eddy current probe in unidirectional composite material presenting delamination. The specimen is homogeneously anisotropic and the flaw is represented by a local deformation in the planar geometry. The curvilinear coordinate method (CCM) is used to solve Maxwell’s equations in covariant form. Based on the Fourier modal method, the semi-analytical approach consists of presenting the electromagnetic field components as eigenmode expansion in a new non-orthogonal coordinate system fitting the geometrical perturbation. Then, interface conditions can be analytically included in order to evaluate the unknown amplitude of eigenmodes. To take into account the contribution of lower interfaces, a recursive and stable scattering matrix algorithm is implemented. The numerical validation shows a good agreement between simulation results and finite element (FE) data.

In order to calculate the iron loss in motors with high accuracy, it is necessary to consider skin effect of the eddy current in laminated electrical steel sheets. To solve this problem, the post 1-D analysis is used. It divides every element along the thickness and calculates the distribution of the eddy current and magnetic flux density. In this article, we propose improved post 1-D analysis using the distribution of the differential permeability. In this method, 1-D equation has second differential term using differential permeability coefficient. By using the differential permeability, it is possible to express the sensitivity of the magnetization correctly.

As coaxial magnetic gears use NdFeB permanent magnets with high-energy density, they have a torque density comparable to that of mechanical gears, and active research activities have been conducted since. However, NdFeB permanent magnets have conductivity and cause high permanent magnet eddy current losses due to the driving characteristics of coaxial magnetic gears. Ferrite has no conductivity, but because of its weak magnetic force, its competitiveness is poor. In this article, Nd-bonded permanent magnet which has high magnetic force and no conductivity is used. Finite element analysis (FEA) calculations and experimental results of coaxial magnetic gears using Nd-bonded permanent magnets were compared, and the direction of applying Nd-bonded to coaxial magnetic gears was presented by comparing the magnetization method of Nd-bonded.

An accurate control of the magnetic boundary ofa thermonuclear plasma is an important issue in magnetic confinement research. The development of methods for the active control of magnetohydrodynamic instabilities and correction oferror fields is mandatory. A substantial modification of the layoutof the RFX-mod device is in progress: the aim of this paper isto assess the potential advantages of the proposed solution with advanced numerical techniques based on integral formulations.

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.

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.