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In this paper, we investigate losses, including magnet eddy-current loss of permanent-magnet synchronous motors with concentrated windings. A 3-D finite-element method that considers carrier harmonics of pulsewidth modulation inverters is utilized to calculate the losses in each part of the motor separately. A simple linear magnetic circuit model is also introduced in order to understand the mechanism of eddy-current loss generation in the magnet. First, the measured and calculated results are compared to verify the validity of the analysis. Next, the variation of the losses due to the stator and rotor shapes is investigated, for instance, concentrated and distributed stator windings and interior and surface-mounted permanent magnets. It is clarified that the eddy-current loss of the permanent magnet in the concentrated winding motor is much larger than that in the distributed winding motor. The difference of the loss generation mechanism due to the rotor shape is also clarified. Index Terms--Concentrated winding, eddy-current loss, finite-element method, iron loss, permanent-magnet motor.

In this paper, we investigate losses of interior permanent-magnet motors driven by pulsewidth-modulated inverters using 3-D finite-element analysis, which can estimate the eddy-current loss in the permanent magnet accurately. The calculated losses are compared with the measured results and the theoretical solution to verify the validity of the analysis. The variation of the magnet eddy-current loss due to the division of the magnet is also investigated. It is clarified that the eddy-current loss in the permanent magnet is mainly produced by the carrier harmonics of the inverter and that the axial length of the divided magnet should be smaller than the skin depth of the eddy currents produced by the major harmonics for the loss reduction. Index Terms--Carrier harmonics, finite-element analysis, interior permanent-magnet synchronous motor, iron loss, pulsewidth-modulated (PWM) inverter.

A novel method using combination of 2-D and 3-D finite element analyses is proposed for the rotor loss calculation of interior permanent magnet motors. First, the differential permeability at the average flux density of the rotor core is estimated by the 2-D nonlinear time-domain analysis. Then, the 3-D frequency-domain finite element analyses at each remarkable harmonic field are carried out with this permeability, in order to consider the magnetic saturation. Using this method, the calculation time is reduced to less than 1/100 compared with the full 3-D analysis, whereas the accuracy is nearly same. Index Terms--Differential permeability, eddy current loss, finite element method, interior permanent magnet motor.

In this paper, we investigate eddy current loss in divided Nd-Fe-B sintered magnets for synchronous motors, from both sides of measurement and finite element analysis. First, the basic experiments with an exciting coil and divided magnets are carried out. The results are compared with the 3-D finite element analysis to clarify the effects of insulation resistance between divided magnets, number of magnet divisions, and frequency. Next, a permanent magnet synchronous motor is analyzed to understand the eddy current generation in the magnets applied to the motors. It is clarified that the effect of the eddy current loss reduction by the magnet division is weakened in the case of high frequency harmonic magnetic fields. The critical insulation resistance between the divided magnets is also clarified. Index Terms--Eddy current, insulation, Nd-Fe-B magnet, synchronous motor.

In this paper, we introduce a calculation method for in-plane eddy currents produced by perpendicular flux at stator core-ends of turbine generators. In the method, the laminated core is subdivided into each electrical steel sheet by 3-D finite elements. The insulated layers of the sheets are modeled by the gap elements, which represent the magnetic resistance of the layers. The combination method of double nodes and anisotropic conductivity is proposed to consider the insulation between the steel sheets. It is especially required for the stator teeth with slits. The validity of the calculation method is verified by comparing the measured and calculated results in the ease of a simple model that simulates the end part of the turbine generator. The method is also applied to the real machine to clarify the eddy current distribution. Index Terms--Core-end, in-plane eddy current, lamination, perpendicular flux, 3-D finite element method, turbine generator.

In this paper, we propose a method of adaptive finite element meshing, which is effective for minor shape modifications in optimization of electric machines. In the method, the mesh for the new shape in the optimization process is generated from the mesh of the previous shape with minimum modification. The locations of the nodes for the new shape are decided by solving the Laplace's equation, whose unknowns are displacements of the nodes. The adaptive finite element meshing is started from the modified mesh. The method can reduce the calculation time and improve the quality of the optimized results. Index Terms--Adaptive finite element method, electric machine, Laplace's equation, optimization.

In this paper, we propose a method to predict the strict numerical solution, which will be given by the infinitely dense finite element mesh, from the solutions obtained by several different meshes generated by the adaptive meshing method. The proposed method is applied to characteristics calculation of several kinds of motors to verify the validity and usefulness. It is clarified that the proposed method gives accurate results with short calculation time. The method is also useful to understand the required mesh in each analyzed model. Index Terms--Adaptive finite element method, cogging torque, error estimator, iron loss.

The losses and efficiency of induction motors are analyzed considering the interbar currents, which flow from the rotor bars into the rotor core. The three-dimensional (3-D) finite-element method with the modeling of the laminated rotor core is applied in order to take the skin effect and the magnetic saturation of the core into account. The calculated losses and efficiency are compared with the measurement. The measured and calculated results agree well. It is clarified that both the rotor core and rotor cage losses increase due to the interbar currents and that the main components of these losses are caused by the stator slot harmonics. Index Terms--Combined three-dimensional (3-D)-two-dimensional (2-D) analysis, induction motor, interbar current, lamination.

In this paper, we propose a novel method to calculate harmonic losses of permanent-magnet motors driven by pulsewidth modulation inverters. First, two-dimensional (2-D) nonlinear time-domain finite-element analysis is applied to estimate the harmonic rotational magnetic field at the air gap of the motor. Next, the three-dimensional frequency domain finite-element analyses at each remarkable harmonic field are carried out with the results of the harmonic gap flux densities obtained by the 2-D analysis. Using this procedure, the magnet eddy-current loss caused by the carrier harmonics of the inverter can be calculated with practical computer resources. Index Terms--Carrier harmonics, combined 3-D/2-D analysis, core loss, eddy-current loss, inverter, permanent-magnet motor.

In this paper, we propose a novel method for the transient eddy current analysis of moving conductors using the moving coordinate system and the adaptive finite element meshing. The error estimation and the automeshing are applied at each time step to obtain the appropriate finite element mesh at each position of the conductor automatically. The interpolate calculation is carried out to obtain the potential of the conductor at the previous time step for the calculation of eddy currents. The proposed method is applied to the solid and the cage induction motors, which include homogeneous and heterogeneous moving parts, to clarify the validity and the advantages. It is clarified that the proposed method gives accurate results with a small number of finite elements. Index Terms--Adaptive meshing, eddy current, induction motor, moving conductor.

In order to examine estimation methods of iron losses of rotating machines, a verification model of the surface permanent magnet (SPM) motor is manufactured and measured by the investigation committee of the IEE of Japan. The effect of stress due to the insertion to aluminum case on magnetic characteristics can also be investigated by using the model. In this paper, features of the benchmark model are discussed, and some results of calculation and measurement are shown. Various kinds of methods for estimating iron losses due to distorted elliptical rotating flux are discussed. It is illustrated that the difference between results estimated using those methods and measured iron loss is within 10%. Index Terms--Benchmark model, finite element method, iron loss, rotating machines.

A method to calculate the torque of induction motors considering the effects of harmonic core losses is proposed. The negative torque caused by the eddy current and the hysteresis phenomena in the stator and the rotor core is calculated from the time variation of the magnetic field distribution obtained by the nonlinear time-stepping finite element analysis. The calculated negative and total torques agree well with the experimental results. It is clarified that the negative torque is not negligible in the case of the motor with semiclosed slots and that the accuracy of the torque calculation is improved by the proposed method. Index Terms--Core loss, induction motor, negative torque, slot harmonics.

The purpose of this paper is to specify the main components of the stray load loss of induction motors from both results of measurement and analysis. The IEEE standard 112 Method B is applied to the cage induction motor for the measurement of the stray load loss. On the other hand, the losses generated at the stator core, the rotor core, and the rotor cage are calculated directly by the finite-element method considering the magnetic saturation and the harmonic fields, which vary due to the load condition. The measured and the calculated torque, losses, and efficiency agree well. It is clarified that the main parts of the stray load loss in the case of the analyzed motor are the increase of harmonic losses due to load, which are the harmonic Joule losses of the rotor cage and the harmonic core losses of the stator and the rotor. The relationships between the losses separated by the measurement and the losses calculated directly by the finite-element method are also clarified. Index Terms--Core loss, eddy-current loss, finite-element method, hysteresis loss, IEEE standard 112, induction motor, stray load loss.

This paper presents a procedure to obtain equivalent circuit parameters of induction motors considering skin effect, harmonics, magnetic saturation, movement of the rotor and the end effects of the motor using the three-dimensional (3-D) finite-element method. The 3-D frequency domain analysis is applied in advance to obtain the primary value of the magnetic vector potential. The 3-D nonlinear time-stepping finite-element analysis is carried out with this primary value. A method, which reduces the calculation term by utilizing the symmetry shape of the rotor, is also applied. As a result, we can obtain the whole time-variation of not only the stator, but also the rotor electromagnetic fields at steady rotation with small calculation time. Index Terms--3-D analysis, circuit parameter, induction motor, slip frequency, time-stepping analysis.

A general formulation for moving conductors using 3D edge finite elements is introduced. In the formulation, the velocity of the coordinate system can be selected arbitrarily. A proper gauge condition for this formulation is also indicated. The optimal velocities of the coordinate system are investigated by numerical experiments. It is clarified that the accuracy of the analysis depends on the time variation of electromagnetic fields, which are observed differently in each coordinate system. From this point of view, we introduce a novel method that uses several different coordinate systems in one conductive region. Index terms- Eddy currents, moving conductor, coordinate system, edge element

This paper presents an analyzing method for induction motors with skewed slots using combination of 2D and 3D finite element methods. 2D electromagnetic field equations at several cross sections of the motor are combined with consideration of currents continuity. A 3D analysis is applied to estimate the end effects of the motor and to modify the 2D equations. The method can estimate axial variation of the harmonic magnetic fields with small computer resources. The results of the method are compared with experimental data to examine the validity. The break points of the approximation used in the method are also shown. Index terms - Induction Motor, Skew, Harmonics, End Effect

An analyzing method for induction machines is proposed. Voltage drop of the end-rings is estimated by a 3D linear analysis using phasor and edge-elements. As a result, a 2D nonlinear time-stepping analysis is modified to estimate magnetic saturation and harmonics. The method takes the skin effect of the end-rings into account. It is based on the property that the voltage drop of the end-rings is related to the electric scalar potential in the 3D formulation with an appropriate gauge condition. The method can be applied to both linear and cage induction machines using limited computer resources.

The paper presents variation of 3D eddy current analysis for moving conductors with two parameters. One is the velocity of coordinate systems and the other is the gauge conditions which specify the electromagnetic potentials. The general formulation due to these parameters is obtained and the numerical experiments are carried out. The edge finite elements and the backward difference method are applied to the formulations. It is clarified that the potentials are determined by both of these parameters and that a proper relation between the parameters is required to analyze the conductors sliding in electrical contact.