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To reduce the iron loss and noise of a three-phase reactor composed of grain-oriented (GO) steel plates, two types of core structures are proposed in this article. In the first type, the ordinary brick core model is improved to a hybrid one composed of GO and nonoriented steel plates, and in the second type, the T-joint part of the ordinary oblique-joint core model is improved to a straight joint. To show the effectiveness of the improved models, the iron loss and displacement distributions in the four core structures are evaluated using the 2-D magnetic field and mechanical analyses. In these analyses, the magnetic characteristics of the anisotropic cores are considered in detail. Namely, in the magnetic field analysis, the ${B}$ – ${H}$ curves in the arbitrary directions are considered. In the iron loss calculation, the rotational iron loss is calculated using the iron loss curves in the arbitrary directions. Moreover, the methods of calculating the displacements due to electromagnetism and magnetostriction considering the anisotropic ${B}$ – ${H}$ curves and magnetostriction in the arbitrary directions are proposed. It is shown that the iron losses and displacements of the two proposed core structures can be reduced compared with the ordinary ones. Moreover, the second proposed model is the most attractive one because both the iron loss and displacement are smaller than the other models.

A fault current limiter is an effective mean of limiting fault currents. The simultaneous use of three single-phase current limiters requires significant amounts of ferromagnetic material and space. This article proposes a three-phase saturated-core fault current limiter (T-SCFCL) that employs a common yoke and a permanent magnet to mitigate the restrictions of material and space. T-SCFCL delivers good performance for single-phase, two-phase, and three-phase faults. In this configuration, flux flowing through the permanent magnets is generated by a three-phase unbalanced current, thereby reducing the loss in eddy current and improving stability while significantly reducing the volume of the core. An algorithm is provided for use in the design of the FCL structure. A simulation was conducted based on the finite element method and a prototype manufactured and tested to verify effectiveness. The results prove that the proposed method is efficient.

Large fault direct current with fast rising speed has always been a significant threat to high voltage direct current systems. Fault current limiters (FCLs) are one of the most promising solutions. However, the biased permanent magnets (PM)s in traditional FCLs have large magnetic reluctance that causes FCLs to have small inductance changing ratios when a fault occurs. In this study, a novel three-limb topology of a saturated iron core-type fault current limiter (TSFCL) is proposed and a central PM bias limb is inserted to force flux flow through this limb. Therefore, the inductance changing ratio is greatly enhanced and the steep rising trend of fault current will be restrained effectively. The operating principles and characteristics of the TSFCL are analyzed to verify the deductions. Moreover, different lengths and cross-sectional areas of the inserted PM are tested and optimization study is carried out. The results show that the clipping inductance has a 55% increase compared with a traditional two-limb model. Moreover, compared with the existing smoothing reactor and traditional two-limb model, proposed topology can decrease the fault current by 45% and 16% within 5 ms, respectively. Finally, a typical HVDC system was built and the effectiveness of proposed TSFCL was verified.

Soft magnetic composites (SMCs) are composed of ferromagnetic particles surrounded by electrical insulation. To establish a homogenization technique for the magnetic field analysis of an electrical machine with an SMC core, we have already proposed a method to evaluate the effective permeability and iron loss of the SMC core using a cell model of one particle taking into account the nonlinear magnetic characteristics and eddy currents. However, the measured eddy current loss cannot be represented by using the proposed method. In this article, a 3-D eddy current analysis method modeling the anomalous eddy current loss due to the movement of domain walls in the cell model is developed based on the Pry and Bean magnetic domain model. The effect of the non-uniformity of the domain structure on the anomalous eddy current loss is investigated. It is shown that the measured eddy current loss can be almost represented by adding the anomalous eddy current loss to the classical one.

To reduce the iron loss of a three-phase reactor composed of grain-oriented (GO) silicon steel plates, we proposed two reactor models. One applies oblique joints between the legs and the yokes, and the other applies butt joints composed of non-oriented (NO) silicon steel plates at the L and T joint parts. The proposed models are aimed to relax the flux concentration inside the iron cores that occurs due to the anisotropic magnetic characteristics of GO silicon steel plates. The effectiveness of the proposed models are investigated through magnetic field and iron loss analyses considering the anisotropic magnetic characteristics of the iron cores. It is found that the flux concentration in the yoke can be relaxed in both proposed models. And iron loss of the proposed model with NO steel plates at the L- and T-shaped joints can be reduced about 12% compared with the ordinary one.

Local high iron loss may occur due to the deviation of magnetic flux from the rolling direction of electrical steel in the T-joint area of the transformer core. In this paper, to reduce the iron core loss in the T-joint region, a hybrid iron core model using nonoriented and grain-oriented magnetic materials is proposed. Three-dimensional magnetic field analysis considering the nonlinearity and laminated structure of the original and proposed iron core models is carried out by using the finite element analysis. The flux and iron loss distributions of the original and the hybrid cores are compared. The results show that approximately 2% iron loss reduction can be achieved by using the proposed hybrid structure.

To investigate the noise reduction of an electrical machine, the deformation and vibration of the cores are evaluated by using the coupled magnetic and mechanical analyses [1]. In these analyses, the local force calculated by using the flux distribution obtained from the magnetic field analysis is required in the mechanical analysis. In the local force calculation [2], the Maxwell stress tensor is usually used. The Maxwell stress tensors are often represented by the Minkowski and Chu models with linear and nonlinear energy expressions, respectively. In the nonlinear magnetic field analysis, the volume forces, which move the magnetic bodies, obtained from both models coincide with each other, whereas their local forces, which deform the magnetic bodies, are different. Therefore, more investigation is required to clarify the suitable expression of the Maxwell stress tensor. In this paper, to clarify the proper expression of the Maxwell stress tensor for the local force calculation of a nonlinear magnetic body, the Maxwell stress tensors are derived from the Fleming’s left hand rule because the volume current density can be used to determine the magnetization in the nonlinear magnetic body. As a result, a new Maxwell stress tensor is derived. The surface force obtained from the new Maxwell stress tensor is compared with those obtained from the ordinary Minkowski and Chu models, and the equivalent magnetizing current method [3] to show the effectiveness and validity of the proposed Maxwell stress tensor.

In this paper, an excess loss modeling method of the laminated iron core is proposed. The 1-D single sheet silicon steel plate analysis is combined with the 3-D solid-core analysis to model the laminated structure. The modeling is improved by including the domain wall bowing due to pinning effect, which is considered as the main cause of excess loss. The domain wall bowing due to pinning is considered in the 1-D steel plate analysis because the excess loss generated by the flux density in the parallel direction of the stack is dominant compared with that in the perpendicular direction. In the 1-D analysis, an initial bowing flux distribution along the thickness direction of one lamination is introduced. The results of iron losses show that the hysteresis and eddy current losses vary with the flux and eddy current distribution in the laminated iron cores. Finally, the 1-D–3-D combined method is applied to a single-phase reactor; the magnetic flux and eddy current distribution are analyzed in detail. The eddy currents generated by the parallel flux are increased, hence, the skin effect of flux in the parallel direction of laminations is enhanced; thus, the hysteresis and eddy current losses are increased and the iron loss is increased by 8%.

A novel direct current system fault current limiter (DCSFCL) based on the principle of nonlinear magnetization was proposed to limit fast rising fault current of the dc system. Different materials were also tested to find the iron core material. However, the existing material is not able to obtain both two necessary indexes, namely, a large saturation point and fast demagnetization speed. Hence, the performance is not satisfactory using a single material. In order to obtain the best performance for the DCSFCL, mixed materials were applied to combine the advantages of different soft magnetic materials. Furthermore, magnetic valves were also added to the original DCSFCL topology, which is an effective method to optimize the clipping performance and reduce the usage of materials. The 2-D models were built and finite-element analyses were carried out to verify these assumptions. Compared with a traditional smoothing reactor, the proposed new model not only limits the fault current by 55.4%, but also reduces the usage of both magnetic material and permanent magnets by over 20%.

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.

The saturated-core fault current limiter (SFCL) is an effective device for limiting fault current. This paper proposes and analyzes a novel bridge-type SFCL (BSFCL) that uses a permanent magnet (PM) to reduce dc bias while improving the stability of the PM. The bridge structure in the BSFCL consists of four coils and a fault-limiting reactor which is used to limit fault current. The ac and the dc share coils to help reduce energy loss. The iron core uses air-gap branches to offer paths for ac flux, which reduces eddy current in the PMs and enhances their stability. The operating principle and characteristics of the BSFCL were analyzed using the electromagnetic coupling method. To investigate the effects of parameters on the performance of the BSFCL, various finite-element analysis simulations were performed by Maxwell. Experimental results of a 220 V prototype verify the effectiveness of the BSFCL.

The permanent-magnet-biasing saturated core fault current limiter (PMFCL) is one of the most promising devices to limit the fault current. To improve the biasing ability of permanent-magnets (PMs) and reduce the cost of PMFCL, this paper proposes a novel compact permanent-magnet-biased fault current limiter (CPMFCL). The three-limb structure can reduce the size and cost; the optimal small-section structure can improve the biasing ability of PMs and reduce the usage amount of PMs. First, the principle, equivalent magnetic circuit, and small-section optimized structure are introduced. To validate the principle and performance of CPMFCL, various finite element analysis simulation and optimization study are performed in Maxwell-3D. A 220 V/10 A CPMFCL prototype is designed and tested. The simulation and experimental results demonstrate that, compared with traditional PMFCLs, the CPMFCL has the advantages of smaller size, better biasing capacity of PMs, lower possibility of demagnetization, and excellent fault clipping performance.

The application of fault current limiter is an effective method to limit fault current. The saturated-core fault current limiter (SFCL) is one of the promising devices. However, its commercialization is limited by the high demands for the ferromagnetic material and the dc source generating magneto motive force. This paper proposes a novel three-phase compact SFCL (CSFCL) in which a common core and a permanent magnet are used to solve the mentioned challenges. The common core can significantly reduce the amount of required ferromagnetic material. The basic operating principle of CSFCL is introduced based on the analysis of the CSFCL’s magnetic circuit and equivalent electrical circuit. Finite-element analysis (FEA) simulations were performed by ANSOFT to validate the effectiveness of the CSFCL’s fault clipping performance.

When a magnetically shielded room (MSR) to shield leakage fluxes of electric machines is designed by using magnetic field analysis, it is difficult to represent the leakage magnetic field of an electric machine accurately. In this paper, a method of modeling it using a simple solid model with multiple magnetization vectors is proposed. In this method, the magnetization vectors are determined by an inverse technique to represent a real leakage flux distribution. First, the proposed method is explained and verified using a simple 2-D linear magnetostatic one-phase transformer model. Then, the method is applied to a 3-D model and the effect of selected measured surface on representation of leakage flux is investigated. Finally, an experimental verification is carried out. It is shown that the proposed method can represent the leakage magnetic field with small number of magnetizations. The leakage flux only in the region behind the measured surface can be represented, and it is verified by experiment. Moreover, the shielding performance of MSR can be evaluated by using the proposed solid model with suitable permeability.

The saturated core fault current limiter (SFCL) is one of the most effective methods for limiting fault current. A permanent magnet (PM)-biased SFCL (PFCL) can reduce dc bias current and additional energy consumption. However, the thermal stability of NdFeB PMs in PFCL poses a major challenge. This paper proposes a novel hybrid-type SFCL (HSFCL) topology that can reduce this risk. In the HSFCL, a hybrid PM/dc coil is designed to saturate the core, and a fault-limiting reactor is used to guarantee fault-clipping performance. The new structure provides air-gap branches for the time-varying magnetic field produced by alternating current, which reduces the eddy current in the PMs and enhances their stability. Electromagnetic coupling is used to analyze the operating principles and characteristics of HSFCL. Finite-element analysis simulations were performed using Maxwell and compared with verification experiments, proving that HSFCL is efficient in fault clipping and PM reliability enhancement.

Eddy-current loss of NdFeB permanent magnets (PMs) is widely analyzed in PM motors. This paper proposes a coupled 2-D transient finite-element analysis (FEA) of the saturated core fault current limiter (SCFCL) and 3-D analytical model of PMs to evaluate eddy-current loss in SCFCL. The comparison between the result from coupled method and that from 3-D FEA verifies the applicability of the coupled method in analyzing eddy current loss of PMs in SCFCL. The 3-D analytical model of PM is applied to analyze the effect of segmentation on the reduction of PM's eddy-current loss. And the results show that segmentation along width has a better performance, which is also verified by 3-D FEA.

Compared with grain-oriented SiFe sheets, the domain structure of nonoriented (NO) SiFe sheets is very different, and the magnetization processes of NO SiFe sheets are much less investigated. Thus, the excess loss of NO SiFe sheets is less well-known. In this paper, we propose a numerical method to estimate the excess loss in NO SiFe sheets, considering the pinning and skin effects. We apply an initial magnetic field distribution that reflects the pinning effect in our nonlinear eddy current finite element analysis model, which reflects the skin effect of the magnetic flux. Thus, the pinning effect can be coupled with the skin effect in the proposed numerical method. The hysteresis loss and eddy current loss calculated from the flux and eddy current distributions are directly obtained from the proposed analysis method. Thus, excess loss is included in both the hysteresis and the eddy current loss calculations. We first apply the proposed method to two different grades of NO SiFe sheets. The calculated iron losses in one sheet are compared at various frequencies with the measured losses from catalogue data, and less than 2% deviation can be achieved. Finally, we apply the proposed method to the loss calculation for the iron core of a reactor.

A method of 3-D finite element magnetomechanical analysis is developed to investigate the effect of magnetostriction (MS) and stress on the core loss and vibration of motors. Shrink-fit stress calculation is carried out using static structural analysis and equivalent thermal force calculated by a novel method using the thermal stress tensor. A method of core loss calculation is proposed to take account of the 3-D stress in the core loss calculation. The methods are applied to the core loss and the vibration analysis of a permanent magnet motor. Numerical results show that the stator core loss increases significantly due to the shrink-fit stress. However, the radial velocity of the housing surface slightly decreases due to the MS and further decreases due to the shrink-fit stress because the MS increases under compressive stress.

The standard of Japan Electronics and Information Technology Industries Association EM-4502, in which the shielding factor (SFo) of magnetically shielded rooms (MSRs) for the uniform magnetic field can be estimated using coils within 10% error for the extremely low-frequency region of

In this paper, a model for the coupled analysis of magneto-mechanical problems with isotropic materials is proposed in which the effect of stress in transverse direction with respect to the flux density is also considered. To take into account the Villari effect in this case, magnetization data under zero stress and magnetostriction (MS) data under various levels of stress are required. The model uses stress-free magnetization curve and a set of MS curves together with the stress tensor to calculate the permeability variation due to the stress, including the stress-induced anisotropy. Unlike available methods in which an equivalent scalar stress is defined and used for the evaluation of permeability, the proposed method uses the full stress tensor. The model is then applied to a simple 2-D problem and the flux distribution in three cases of uncoupled, coupled without, and coupled with considering the transverse stress are compared.

To reduce the iron loss of a reactor stacked with non-oriented steel plates, we have proposed the method of loss reduction improving the iron core configuration using the magnetic field analysis taking account of the laminated structure by the homogenization technique. In this paper, the iron loss reduction method is expanded to a reactor stacked with grain-oriented steel plates. The magnetic field analysis taking account of the laminated structure and steel plate anisotropy using homogenization technique is developed. The flux concentration due to the laminated structure, steel plate anisotropy, and joint between the leg and yoke of the reactor is analyzed and relaxed by the improvement of the core and joint configurations. It is shown that the iron loss can be about 36% reduced by the improvements.

A homogenization technique of a laminated core taking account of the eddy currents in the steel plates by combining a three-dimensional (3-D) solid core model with a one-dimensional (1-D) steel plate model has already been proposed. In this paper, to apply the proposed technique to a motor core, in which flux rotates, the 1-D eddy current analysis of the steel plate is expanded to a 3-D analysis. The proposed method is applied to a simple laminated core model under the rotational flux in the linear analysis. Then, the eddy current loss obtained from the developed method is compared with those obtained by the homogeneous solid core model with 1-D steel plate model and the real laminated core model. It is shown that error occurs by neglecting the edge of the model but the accuracy is much improved in the eddy current loss calculated by using the proposed method.

To develop further higher efficiency induction motors, the reduction of the stray load losses, which are the increase of loss in the load condition relative to that in no-load test condition, should be investigated by using the magnetic field analysis. However, the calculation of the stray load losses using the magnetic field analysis requires high computation cost due to consideration of the slot harmonics in the flux densities, and the large time constant. In this paper, to evaluate the stray load losses in the cores and the secondary conductors of induction motors using the two-dimensional (2-D) magnetic field analysis within practical computation cost, some useful techniques, to mention a few, the nonconforming technique and the simplified time-periodic explicit error correction method, are introduced. Then, the stray load loss of an actual induction motor without skew is evaluated by the developed 2-D magnetic field analysis. It is shown that the calculated no-load losses are almost the same with the measured one, and the stray load losses in the stator core and secondary conductors due to the harmonic components in the secondary current are large.

A general model for the coupled analysis of magneto-mechanical systems is developed by minimizing the continuum energy functional of the system using the calculus of variation. This approach, which is in contrast with the traditional approach of minimizing after discretization, allows the use of strain and stress tensors, vector identities and the divergence theorem, and results in coupled governing equations of the system with three coupling terms; the magnetic stress tensor, the magnetostriction stress tensor, and the magnetostriction reluctivity. The model uses the information contained in the set of experimental magnetostriction curves dependent on stress to calculate the permeability variation due to stress. The governing equations are then discretized using the Galerkin method resulting in methods for the calculation of nodal magnetic and magnetostriction forces including the coupling effects. Finally the model is applied to a simple 2D problem and the flux density distributions using the proposed method and the traditional method of using experimental magnetization curves are compared.

To calculate the iron loss in an electric machine accurately, the anomalous eddy current loss generated by domain wall motion should be considered. A simple numeric modeling of anomalous eddy current loss by modifying the conductivity of steel plates is sometimes used. However, investigation on this method in detail has not been carried out. In this paper, this method is investigated in two iron-loss models neglecting and including the skin effect and then applied to the loss calculation of various kinds of nonoriented and oriented silicon steel plates. Then, the dependence of the modified conductivity on the amplitude and frequency of the induction magnetic field for each material is obtained and the appropriate iron-loss model and method for modifying the conductivity are proposed for the nonoriented and oriented silicon steel plates. The calculated iron losses using the appropriate iron-loss model with modified conductivity are compared with the measured data. It is clarified that for nonoriented materials, the iron-loss model including the skin effect with constant modified conductivity shows good agreement. And for oriented materials, the model neglecting the skin effect with the modified conductivity depending on frequency is better.

To establish a large scale magnetic field analysis, we have already proposed a magnetic field analysis using the first-order voxel modeling with nonconforming technique. The effectiveness of the nonconforming voxel modeling is shown using a simple 3-D eddy current model, a 2-D nonlinear IPM motor model, etc. In this paper, to make the proposed method more applicable for large scale analysis, the nested geometric multigrid method is introduced. First, to apply the multigrid method to the nonconforming finite element method, the treatments of the restriction and the prolongation are discussed. Then, the methods for nesting the fine mesh in the coarse mesh are discussed. Finally, the convergence characteristics of the multigrid method for the nonconforming voxel modeling are investigated using a simple 2-D magnetostatic model. It is shown that the essential convergence characteristic of the multigrid method can be obtained in the nonconforming voxel modeling when the restriction and the prolongation are treated appropriately and the geometries of models of the coarse and fine meshes are coincide with each other.

To reduce the noise of a reactor connected to an inverter power supply, we have already proposed an improved one-phase reactor, in which the hard materials are chosen as the insulators inserted in the gaps between the cores, and gaps are added in the yokes, using a three-dimensional (3-D) coupled magnetic field and vibration analyses taking account of both the electromagnetism and magnetostriction. The effectiveness was shown by experiment. In this paper, the design method is improved and applied to a three-phase reactor. First, the method of determining the optimal hardness of insulators inserted in gaps, so that both the displacements by electromagnetism and magnetostriction are canceled with each other, is proposed. In this method, the optimal hardness of gaps can be represented using a simple equation involving the lengths of the iron cores and the gaps, and a parameter concerned with magnetostriction. Moreover, the method of adding gaps in the yokes without changing the balance and reluctance of a three-phase reactor is also proposed. It is shown that the displacements of the reactor improved by using the proposed methods can be reduced to be 1/25 of the ordinary reactor in the 3-D coupled magnetic field and mechanical analyses taking account of both the electromagnetism and magnetostriction and laminated structure of the iron cores.

To shield the environmental magnetic noises, magnetically shielded rooms (MSRs) are used for biomagnetic measurements, etc. The sources of environmental noises are far away from the MSR, in such a way that almost uniform magnetic field is applied to the MSR. To evaluate the shielding factor SFo for the uniform magnetic field in a construction site, the magnetic noises are applied by coils. However, SFs depend on the size and position of the coils, so a standardization of the method for accurately evaluating SFo using coils is being discussed in the Japan Electronics and Information Technology Industries Association (JEITA). In JEITA, we have already proposed and verified the method of estimating SFo's by smaller coils placed near MSRs in the low frequency region without eddy current effect. In this paper, the suitable size and position of coils, such that the errors of the SFo's estimated and directly evaluated are within 10%, on various shapes of MSRs are obtained using 3-D linear magnetostatic field analysis. Moreover, to correct SFs when the magnetic noises are applied to MSRs through a reinforced concrete wall, etc., the effect of wall on the applied magnetic field is also obtained from the experiment. Finally, the suitable coil conditions and the correction method are verified by the experiment using an actual double-layered MSR.

To establish a large-scale magnetic field analysis, the magnetic field analysis with the voxel modeling is investigated. To reduce the number of elements, the nonconforming technique is introduced. The accuracy of flux densities, eddy current densities, and forces obtained from the nonconforming voxel modeling is verified by comparing with those obtained from the ordinary voxel modeling in a simple 2-D model. Moreover, the proposed method is applied to a 3-D eddy current model as well as to a 2-D nonlinear IPM motor model. It is shown that the results obtained from the proposed method sometimes converge to true values slowly, whereas it provides acceptable results.

To investigate the noise reduction for an electrical machine, coupled magnetic field and mechanical analyses should be carried out. In this paper, the method of modeling the laminated core using a homogeneous core model with equivalent anisotropic parameters considering the laminated structure in the coupled magnetic field and mechanical analyses is proposed and the effect of the laminated structure on the coupled analysis is investigated. The distributions of the flux densities, nodal forces by electromagnetism and magnetostriction, and displacements corresponding to these forces of the real laminated iron core model, the solid core model neglecting the laminated structure and the homogeneous core model considering the laminated structure are obtained and compared. It is shown that the laminated structure cannot be neglected in both the magnetic field and mechanical analyses and the displacement distribution obtained from the homogeneous model is in good agreement with the real model.

In order to increase amenity for hospital patients, we introduce an open-type magnetically shielded room (MSR) in tight space composed of magnetic and conductive cylinders for a magnetic resonance imaging (MRI). This paper presents a design for the MSR opening part for an actual 3T MRI that combines magnetic cylinders with magnetic mullions to decrease the leakage flux density to less than 0.5 mT, taking magnetic saturation into account. The design utilizes the homogenization technique to model the opening part which reduces the number of elements. Moreover, a newly optimized design approach is proposed for the design of openings. First, the opening part is designed while treating the magnetic property in linear analysis to obtain an ideal flux distribution without magnetic saturation. Then, the thickness of the magnetic cylinders is determined for magnetic cylinders to stay unsaturated. Finally, the open-type MSR presented in this paper is built in a hospital, and the design method is verified.

When the magnetic field analyses of the architectural components, in which magnetic materials are distributed complicatedly, are carried out, great efforts toward the modellings and high computational costs are required. To overcome these problems, the homogenization technique seems to be attractive. In this paper, from the standpoint of a practical use, the effectiveness of the homogenization technique is investigated in the analyses of the magnetic disturbance due to a building and the shielding performance of an open-type magnetically shielded room with a wall made up of magnetic cylinders. First, the effect of the region, where the homogenization technique is applied, on the accuracy of the flux distribution is investigated. Then, to examine the possibility that the homogenization technique can be applied to a practical design, the accuracy of the homogenization technique to a real model is investigated. Moreover, the reproduction of the flux distribution of the real model using that obtained from the homogenization technique is also tried. It is shown that the homogenization technique should be applied to not only the region of the magnetic materials but also the air region surrounding them. Moreover, the accuracy of the flux distribution obtained from the homogenization technique is satisfactory for a practical design.

To shield the environmental magnetic noises, magnetically shielded rooms (MSRs) are used for biomagnetic measurements, etc. The sources of environmental noises are placed far away from the MSR, in such way that almost uniform magnetic fluxes are applied to the MSR. Therefore, to specify the shielding performance of MSR, the shielding factor SF? for the uniform magnetic flux density should be evaluated. To evaluate SF?, in a construction site, the magnetic noise is applied by coils. However, SF's depend on the size and position of the coil. Therefore, to accomplish a standardization of the method for evaluating SF?, accurately, by coils, the method for estimating SF?'s by smaller coil placed near MSR is being investigated in JEITA (Japan Electronics and Information Technology Industries Association). In JEITA, we have already proposed the method of estimating SF?'s by the extrapolation using simple numerical expressions representing the relations between the SF and the size, position of coil. The proposed method was verified by the actual single-layered MSR using coils placed on double sides. In this paper, the method of estimating SF? of the double-layered MSR, using coils placed only on one side of MSR and taking account of door effect, is investigated using 3D nonlinear magnetic field analysis and measurements. By using the analysis, it is shown that the single coil should be set in front of the door. Moreover, SF?'s estimated by using the measured data with the optimal coil setting can almost represent the tendencies of the true SF?.

To reduce the noise of a reactor under inverter power supply, the cause of noise should be investigated. For this purpose, we have already proposed a 3-D vibration analysis considering electromagnetism and magnetostriction, and the proposed method was applied to one phase of a reactor. It was found that the displacements in the yoke of the reactor are large and the hardness of insulators inserted in the gaps between cores affects the displacements. However, the optimal design to reduce the noise is not carried out. In this paper, first the better hardness of the gaps are determined by using the static structure analysis and a new design is proposed to reduce the noise. Moreover, the effectiveness of the improved hardness of gaps and the proposed new design of reactor is investigated by using the vibration analysis and the experiment.

In order to detect steel bars and power cables inside pliable plastic conduit tubes buried in concrete walls and slabs during the renovation of old buildings, we have developed a new nondestructive inspection (NDI) system. This system, which enables high precision detection and easy handling at low cost, works by measuring the impedance due to the inductance change of a solenoid coil which exposes the test material to a magnetic field. In this system, the solenoid coil is connected to a compensating capacitor with a series-resonant circuit to reduce the impedance and multiply the impedance change by increasing the quality factor, Q, i.e., the ratio of the inductive reactance, ?L, to the coil resistance, R, which contributes to improving the signal-to-noise ratio for detection. This paper describes the validity of the design method of this NDI system. Firstly, the fractional deviation of inductance, ?, the inductance changes between with and without a steel bar and power cables were analyzed. The deviations due to the eddy currents and magnetization induced in the steel bars and power cables were computed through 3-D magnetic field analysis taking eddy currents at 5, 40 and 800 kHz into account. Secondly, the rates of change of impedance (RCIs) and phase angles were measured with the impedance meter of the newly developed NDI system. This system was designed so that the value of became roughly 200 and the resonance frequencies became about 5, 40 and 800 kHz. For steel bars, the predicted RCIs, which were calculated from the computed s multiplied by the designed Q factor, roughly matched those measured. In case of power cables, the tendency of predicted RCIs were roughly in accord with those measured. The validity of the design method's detecting system was verified. In addition, the analysis and measurement proved that this NDI system can distinguish steel bars from power cables by the polarity of the phase angle.

Metallic implants composed of paramagnetic materials, such as stainless steel (SUS), Ti, Co-Cr-Mo alloy, etc., are widely used as artificial hip joints or aneurysm clips. When the metallic implant is placed in a uniform magnetic field of a magnetic resonance scanner, a magnetic disturbance is created due to its magnetization. This magnetic disturbance distorts the image of the metallic implant and body tissues in the magnetic resonance imaging (MRI). In order to overcome this problem, a method of coating the metallic implant with diamagnetic material has been proposed as the magnetic disturbance created by the metallic implant can be removed by the cancellation of the respective magnetizations of the paramagnetic and diamagnetic materials. But the optimal thickness of the diamagnetic coating has been obtained only for a sphere model by mathematical modeling. In this paper, the effects of a straight cylindrical hip joint model and an aneurysm clip model on the magnetic disturbance are investigated by using the magnetic field analysis of the finite element method (FEM). First, the magnetic disturbances generated by the two models made of paramagnetic material are calculated and compared with measured results. Moreover, the associations of susceptibilities chipar and chidia of the paramagnetic and diamagnetic materials and the optimal thicknesses of the diamagnetic coating when the magnetic disturbances can be reduced for the two models are shown.

To design a new model to reduce the noise of a reactor under inverter power supply, the cause of noise should be investigated. We carry out vibration analysis of a single phase of a reactor while considering electromagnetism and magnetostriction to clarify the mechanism of noise generation in the reactor. In this analysis, magnetostriction is modeled three-dimensionally with equivalent nodal forces. First, the nodal forces in the cores of reactor due to the electromagetism and magnetostriction are calculated using the flux distribution obtained from magnetic field analysis. To determine the dominant cause of noise, the spatial distributions of displacements generated by both nodal forces are then obtained by static structure analysis and they are compared in detail. Moreover, the actual movements of the cores are calculated by vibration analysis. Finally, the effect of the hardness of the cores on noise generation is calculated and measured. It is shown that the hardness of the insulator inserted in gaps between cores affects the vibration and it seems to have an optimal value. Moreover, the analyzed results are proved by measurement.

To evaluate eddy current losses of permanent magnets (PMs) in motors driven by inverter power supplies in less computation time, we propose the coupled 2-D analysis of the motor and 3-D eddy current analysis of only the PM. In the proposed method, we carry out 2-D nonlinear magnetostatic analysis of the PM motor by rotating the rotor. We then perform 3-D eddy current analysis of only the PM using the temporally varying flux distributions in the PM obtained from the 2-D analysis. For 3-D eddy current analysis, we investigate methods that do and do not consider the compensation field generated by eddy currents. Moreover, for the case in which the compensation field is considered, we demonstrate the method of considering the reluctance of the motor core by the equivalent gap. Finally, we verify the proposed method by comparing results obtained using the proposed method and results obtained by full 3-D analysis for an interior PM motor. We show that the eddy current loss can be estimated in 1/15 of the computation time required for full 3-D analysis when the proposed method takes both the compensation field and the reluctance of motor core into account.

A method of magnetic field analysis which takes eddy currents into account in laminated steel core is extended into loss calculation to investigate the loss reduction of reactor connected to inverter power supply. In the proposed method, the iron loss in the laminated core can be calculated considering the flux and eddy current distributions in steel plate affected by harmonic components. The proposed method is applied to a single-phase model of reactor connected to inverter power supply and the loss distributions are demonstrated in detail. Moreover, in order to reduce the loss, the shape configurations of core and plate are improved. Finally, the experiments using three-phase reactors are carried out to verify the calculation and investigate the effectiveness of the proposed shape configuration.

In order to calculate the eddy current losses in the thin surface layer of a laminated core, in which the insulation between steel sheets is broken by a process of a polish, the leaf element is expanded into the edge finite element method. Several treatments for the leaf element are illustrated and the effectiveness is investigated by using a simple model. Then, the effect of the surface layer on the iron losses is discussed in an actual magnetic bearing system

In order to investigate an effective method for removing the residual magnetization in the steel structure of a building by a demagnetizing coil, a method for estimating the distribution of residual magnetization by means of a three-dimensional nonlinear eddy-current analysis was proposed. The tendency of the result obtained from the proposed method was in good agreement with the experimental result. Moreover, it was found that the demagnetizing coil should be set perpendicular to the steel structure.

A method for analyzing three-dimensional (3-D) magnetic field in a model including moving parts, such as linear actuator, was developed by using a nonconforming mesh with edge elements. In this method, the meshes for moving and nonmoving parts are generated individually, and they are overlapped together at an arbitrary position. Then, the magnetic field analysis is carried out by using the nonconforming technique with interpolation. It is shown that the proposed method is useful for a dynamic analysis of a 3-D actuator model.

A highly practical method for evaluating magnetic disturbance due to adjacent buildings for the design of a magnetic testing site with nearly zero magnetic field was proposed. A modeling technique for complicatedly distributed magnetic materials in buildings was verified by the measurement using an actually constructed building. Moreover, a convenient formula was conceived, in which a building is replaced simply into a brick magnetic body and the flux distribution due to its magnetization is calculated analytically. It was shown that the proposed formula is useful for investigating the effect of the positions of buildings for additional construction on the magnetic disturbance.

In this paper, the method for modeling laminated core by a solid one is investigated. The method for taking into account eddy current in each steel plate used for laminating, which has already been developed in linear analysis, is expanded to nonlinear analysis by using one-dimensional finite-element analysis and the step-by-step method instead of the analytical solution and the phasor method, respectively. The effectiveness of the proposed method is shown by using a simple model.

Methods of analyzing three-dimensional magnetic fields using nonconforming mesh with edge elements are investigated. Two kinds of interpolation techniques at the nonconforming surface, of which the tangential components of the potential are discontinuous and continuous, are proposed. Both methods are compared with each other using a simple model from a viewpoint of the accuracy. It is shown that the tangential components of the potential should be continuous at the nonconforming surface.

A method for three-dimensional steady-state eddy-current analysis of moving conductor using nodal elements and moving-coordinate system is changed to the edge finite-element method (FEM). This method uses the interpolation of the unknown values on edges at any positions. The new method is verified using the iron cylinder rotating in the uniform magnetic field. Moreover, it is shown that more accurate results by using the new method can be obtained within shorter central processing unit time compared with the nodal FEM.