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Gives introductory remarks about chapter 1 of this group of 31 papers, from ISEF 1999 Proceedings, in the methodologies for field analysis, in the electromagnetic community. Observes that computer package implementation theory contributes to clarification. Discusses the areas covered by some of the papers ‐ such as artificial intelligence using fuzzy logic. Includes applications such as permanent magnets and looks at eddy current problems. States the finite element method is currently the most popular method used for field computation. Closes by pointing out the amalgam of topics.

The purpose of this paper is to validate dynamic analytic force modeling techniques with experimental results. The performance of previously presented 2-D and 3-D eddy current models will be assessed when the steady-state models are coupled to a dynamic mechanical model.

The previously presented 2-D analytic model was formulated in terms of the magnetic vector potential in conductive region and magnetic scalar potential in non-conductive region whereas the 3-D model was formulated in terms of the magnetic vector potential in both the conductive and non-conductive regions.

This paper experimentally confirms that incorporating the heave velocity term is important for accurately predicting the forces under dynamic mechanical motion while using a steady-state eddy current solution. A close agreement between the experimental and the dynamic analytic-based eddy current solution was achieved.

The force results presented from the previously developed 3-D analytic model assume that the width of the guideway is larger than that of the magnetic source and the magnetic source is placed at the center of the guideway along the z-axis.

The rotational and translational motion of a permanent magnet rotor above a conductive plate create lift and thrust force that are suitable for magnetic levitated (maglev) transportation. The previously developed 2-D and 3-D analytic models are fundamental to such maglev research as the models can quickly compute the electromagnetic forces acting on the maglev vehicle. This paper is of immense importance as the paper experimentally validates the analytic models.

The quasi-static analytic eddy current force models that are validated in this paper are different to analogous models developed by prior authors in that the heave velocity as well as the translational velocity of a magnetic source is incorporated into the eddy current force equation.

The purpose of this paper is to describe a semi-analytical modeling technique to predict eddy currents in three-dimensional (3D) conducting structures with finite dimensions. Using the developed method, power losses and parasitic forces that result from eddy current distributions can be computed.

In conducting regions, the Fourier-based solutions are developed to include a spatially dependent conductivity in the expressions of electromagnetic quantities. To validate the method, it is applied to an electromagnetic configuration and the results are compared to finite element results.

The method shows good agreement with the finite element method for a large range of frequencies. The convergence of the presented model is analyzed.

Because of the Fourier series basis of the solution, the results depend on the considered number of harmonics. When conducting structures are small with respect to the spatial period, the number of harmonics has to be relatively large.

Because of the general form of the solutions, the technique can be applied to a wide range of electromagnetic configurations to predict, e.g. eddy current losses in magnets or wireless energy transfer systems. By adaptation of the conductivity function in conducting regions, eddy current distributions in structures containing holes or slit patterns can be obtained.

With the presented technique, eddy currents in conducting structures of finite dimensions can be modeled. The semi-analytical model is for a relatively low number of harmonics computationally faster than 3D finite element methods. The method has been validated and shown to be computationally accurate.

The purpose of this paper is to show formulation of a dynamic E&S model, which enables analysis of the effects of eddy currents under vector magnetic behavior in numerical simulations and to demonstrate its usefulness.

When a magnetic flux waveform is distorted, effects of eddy currents increase due to harmonic flux components. In such a case, the result calculated by using the conventional E&S model does not agree with the measured one. The conventional E&S model is improved by considering magnetic flux waveform distortion. The harmonic components of the magnetic field strength waveform were estimated with the classical eddy current model.

In the verification of the dynamic E&S model, it was found that the magnetic field was suppressed by the effect of the eddy current. The conventional analysis overestimates the magnetic field, because the magnetic flux waveform cannot distort. In the magnetic characteristic analysis of a three‐phase transformer model core, the correlation between the eddy currents and the flux waveform distortion are clearly demonstrated.

Both magnetic flux and field strength waveform distortions can be represented in numerical simulations. The dynamic E&S model is very useful for magnetic core design, taking account of practical 2D vector magnetic properties.

The method presented in this paper enables effects of eddy currents in the magnetic characteristic analysis to be more accurately expressed, considering the 2D vector magnetic properties.

A 3-D analytic modeling technique for calculating the eddy current distribution, force and power loss in a conductive plate of finite width and thickness is presented. The derived equations are expressed in a general form so that any magnetic source can be utilized. The model assumes the length of the conductive plate is large and the thickness of the plate is thin but not negligible. The paper aims to discuss these issues.

The conducting and non-conducting regions are formulated in terms of decoupled magnetic vector potential components. In order to accurately compute the eddy current fields and forces the source field only needs to be applied on the surface of the conducting plate. The primary focus is on reducing the eddy current computational time.

The accuracy of the presented approach is verified by utilizing a magnetic rotor that has both a rotational and translational motion. The proposed method is computationally efficient and its accuracy is validated using the finite element method.

The conducting plate thickness is assumed to be thin (but not negligible), and this enables the field interaction through the edge of the plate to be neglected. The lateral force is not calculated in the proposed approach.

The calculation procedure presented is computationally fast and therefore this can enable the 3-D eddy current forces to be computed in near real-time.

This paper presents a fully 3-D analytic based eddy current formlation for computing the eddy current fields and forces in a conducting plate of finite thickness and finite width. The modeling approach is shown to be computationally accurate and relatively fast.

The purpose of this paper is to study the effects of inverter supply on the iron loss characteristics of slip-ring induction machines. Pulse width modulated (PWM) voltage supply on the stator side, as well as a doubly fed operation mode with rotor-sided inverter, are investigated.

An inverter fed machine model is coupled to previously developed eddy current and hysteresis loss models. The eddy current model is based on a finite element method and considers the three-dimensional (3D) eddy current distribution in the steel sheets. The hysteresis losses are computed by a static Preisach vector model.

It is found that under stator-sided inverter supply the eddy current losses do significantly increase when compared to sinusoidal feeding, contributing to a total loss increase of 10-15 percent. In doubly fed operation, the additional losses are generally lower owing to the winding topology of the studied machine.

The analyses presented are restricted to single PWM pattern only. The influences of different PWM parameters remain to be investigated in future.

Regarding practical applications, the reduced additional losses in doubly fed configurations can be considered as a further advantage when competing against other topologies available.

The 3D eddy current model is applied for the first time to quantify the effects of inverter supply. Furthermore, the presented studies on the iron losses in doubly fed operation are original and of practical value for designers and researches.

The purpose of this paper is an accurate computation of eddy currents in laminated media with minimal computer resources.

Modeling each laminate of the laminated core of electrical devices requires prohibitively many finite elements (FEs). To overcome this restriction a higher order multi-scale FE method with the magnetic vector potential

has been developed to cope with 3D problems considering edge effects.

The multi-scale FE approach facilitates an accurate simulation of the eddy current losses with minimal computer resources. Numerical simulations demonstrate a remarkable accuracy and low computational costs. The effect of regularization on the results is shown.

The eddy current losses are of great interest in the design of electrical devices with laminated cores.

The multi-scale FE approach takes also into account of the edge effects in 3D.

Discusses the 27 papers in ISEF 1999 Proceedings on the subject of electromagnetisms. States the groups of papers cover such subjects within the discipline as: induction machines; reluctance motors; PM motors; transformers and reactors; and special problems and applications. Debates all of these in great detail and itemizes each with greater in‐depth discussion of the various technical applications and areas. Concludes that the recommendations made should be adhered to.

Introduces papers from this area of expertise from the ISEF 1999 Proceedings. States the goal herein is one of identifying devices or systems able to provide prescribed performance. Notes that 18 papers from the Symposium are grouped in the area of automated optimal design. Describes the main challenges that condition computational electromagnetism’s future development. Concludes by itemizing the range of applications from small activators to optimization of induction heating systems in this third chapter.

Eddy currents are inevitable in magnetic resonance imaging (MRI) systems. These currents are mainly induced by gradient fields. This study aims to propose a fast analytical method to calculate eddy currents induced by frequently switching gradient fields in a traditional C-shape MRI system.

Fourier decomposition and magnetic vector potentials were used to calculate the eddy currents. Calculations with the proposed analytical method revealed the spatial distribution and temporal evolution of eddy currents.

Calculation and Maxwell simulation results were consistent. The agreement between calculation and simulation results indicates that increasingly sophisticated structures could be developed. The calculated results could guide the design of improved gradient coils.

Eddy currents induced by gradient current are decomposed into currents induced by each time-harmonic component, and then adding them together to obtain complete contribution of the eddy current. The analytical method was used to characterize the properties of symmetric and asymmetric eddy currents induced by gradient coils in MRI systems. The analytical method can be used to improve the gradient shield during the design of the gradient coil in the MRI system.