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The 3-D polycrystal magnetic field analysis method by means of coordinate transformation is proposed. The local coordinates are fixed in each crystal grain and the global coordinates are defined in the polycrystal steel. Though it is assumed that each crystal grain has the same magnetized characteristics as those of a single crystal grain, the crystal grain shape and its orientations of [alpha], [beta] and [gamma] angles are taken into account. When the proposed model is applied to the real grain oriented (GO) steel with 56 crystal grains in 80-mm x 80-mm, and with 0.35.mm thickness, the calculation results are compared with the grain orientations measured by X-ray diffraction. The GO steel has a higher degree of (110)[001] texture with about 3% silicon. The calculated results of higher magnetic flux density part and lower magnetic flux density part in the real GO steel are explained by the a angle distribution. The calculated inclination angle distribution and the measured [alpha] angle distribution seem to be in good agreement. The calculated normal component of the magnetic flux density reflects the [beta] angle distribution of the real GO steel. It is concluded that the proposed 3-D polycrystal magnetic field analysis is appropriate. Index Terms--Crystal grain shape, finite-element method, GO material, grain orientation, magnetic field analysis, polycrystal.

The authors investigate the effects of double-axis electromagnetic stirring (DAEMS) in continuous casting process, which is composed of a rotational electromagnetic stirrer and a vertical electromagnetic stirrer, using unsteady 3-D hydrodynamic calculation of the molten gallium model. To evaluate the free-surface stability, averaged standard deviation of the free surface is calculated. From the calculation results, it is found that there is an optimum intensity balance between a vertical magnetic stirrer and a rotational magnetic in order to stabilize the free surface. Index Terms--Continuous casting, electromagnetic stirring, free surface, 3-D magnetohydrodynamic calculation.

We propose a new type of magnetic shield structure, in which some closed magnetic paths surround a defined space. Because there are some openings between paths, the freedom in designing and the ease of constructing a shield room are attained. This structure shows better magnetic shield performance than conventional shield structures when openings between magnetic paths, widths of magnetic paths, and weight distribution of magnetic materials are designed appropriately. Index Terms--Electrical steels, magnetic noise, permeability, saturation magnetization, shield coefficient, shield efficiency, soft magnetic materials.

Basic characteristic of electromagnetic force in induction heating application of single-sided linear induction motor (SLIM) which uses electromagnetic AC field is investigated by means of 2-D and 3-D numerical electromagnetic FEM calculation. The electromagnetic force in the normal direction consists of the attractive force caused by magnetization and the repelling force caused by Lorentz force. Although the normal force is canceled by them and becomes zero at crossover frequency, the value is different, which is 2 kHz in 2-D model and is 5 kHz in 3-D one respectively. Since 2-D model expresses only center section of 3-D model and can not express the complex behavior of the eddy current in the whole model, the repelling force caused by Lorentz force is considered to be overestimated when the electromagnetic force value of 2-D model is converted into 3-D one. As a result, the crossover frequency of 3-D model becomes large in comparison with 2-D one. This means that an evaluation by using 3-D model is demanded in order to correctly evaluate the crossover frequency. On the other hand, at low frequency in which the attractive force caused by magnetization becomes dominant, the normal forces of the 2-D and 31D model are in good agreement. This means that the evaluation by using 2-D model is effective at low frequency. Index Terms--Crossover frequency, electromagnetic force, finite element method (FEM), induction heating, linear induction motor, thin steel plate.

The numerical model following the equivalent magnetic domain method is proposed to calculate the anisotropy of the magnetic properties of electrical steel. The angle difference between magnetic flux density vector and magnetic field vector, which is observed in the measurement data, is clearly expressed by the proposed model. The angles characteristics of stepwise or lamped shape are shown to be consequences of the strong magnetic anisotropic property. Index Terms--Angle difference, anisotropic steel, finite-element method, magnetic field vector, magnetic flux density vector, rotational magnetic field.

We describe a method to analyze the effects of shrink fitting and stamping on the mechanical stress distribution and iron loss in motor cores. Shrink fitting and stamping are important processes in manufacture of motor cores from electrical steel. The mechanical stress distribution is evaluated by a structural finite-element method, and the iron loss is evaluated by combined analysis of the electromagnetic field (by a finite-element method) and mechanical stress. The method dearly shows that the iron loss becomes larger as the width of the shrink fit increases, an effect borne out by experiment. In regard to the effect of stamping, calculation results again agree well with experimental data. Index Terms--Finite-element method, iron loss, mechanical stress, motor core, shrink fit, stamping effect.

We present a finite-element method for numerical calculation of electromagnetic fields in silicon steel that takes into account the effect of mechanical stress on the steel's mechanical properties. The effect of the mechanical stress is considered in terms of the magnetic permeability in each element. To evaluate the usefulness of the calculation method, we have applied it to an electric motor under uniform and nonuniform mechanical stress distribution. In case of uniform stress distribution, the iron loss distribution is uniform too. The area of increased iron loss corresponds to the area where the mechanical compressive stress is applied. In case of nonuniform mechanical stress distribution, the magnetic flux flows so as to avoid the mechanical compression stress area. The iron loss has a tendency to increase further under mechanical compressive stress because of the increase of the magnetic flux density in the zone of no mechanical stress and the poorer characteristics of the iron loss as a function of magnetic flux density under mechanical compressive stress. Index Terms--Electrical motor, electromagnetic field calculation, finite-element method, magnetic characteristics, mechanical stress, silicon steel.

The free surface velocity strongly influences steel quality in the casting process, so an accurate calculation method is required. The velocity at the free surface is imparted through the wall of the continuous casting mold in an electromagnetic stirring operation. The wall friction in the solidification calculation model is modeled by the Darcy flow coefficient, which was found to be 0.7 from the operation data, according to the oscillation mark made by the free surface deformation. The calculated velocity is in good agreement with the operational velocity. Index Terms--Continuous casting, Darcy flow, electromagnetic stirring, magnetohydrodynamics, solidification, steel making.

A high-response inductive electromagnetic sensor can be made by arranging a conductive and/or magnetic material between the primary coil and the secondary coil. Compared with the conventional inductive electromagnetic sensor, the new sensor has a larger responsivity index (used here to evaluate its characteristics), though it also has a smaller induced voltage at the secondary coil. Index Terms--Electromagnetic sensor, high responsiveness, level sensor, linkage magnetic flux, magnetic flux density.

It is made clear why the pulse electromagnetic casting (EMC) makes the surface steel quality good from the point of view of fluid dynamics by means of magnetohydrodynamic calculation with shadow method. In order to obtain good surface quality, the free surface profile should follow the pulse electromagnetic force and fluid dynamics are stable and uniform for the rectangular axis. By means of the pulse mode in EMC operation, the fluid dynamics make stable and uniform the unstable flow in continuous EMC operation and the free surface profile is maintained as convex. Index Terms--Continuous casting, electromagnetic application, free surface, magnetohydrodynamic, magnetohydrodynamic calculation, pulse electromagnetic casting (EMC), shadow method, stability.

To get the optimal operation of in-mold electromagnetic stirring through the fundamental characteristics, we did the magnetohydrodynamic calculation. The electromagnetic force has the eddy distribution through the electromagnetic analysis in case of the rotating stirring mode which is thought to give the uniform velocity at surface. However, it does not much influence on the fluid dynamics, because the inertial effect and the continuity are large enough.

We evaluate the verification of combined system ac and dc electromagnetic field using magneto hydrodynamic calculation. For the effect of level magnetic flow (LMF) that gives the molten steel the breaking force in proportion to the velocity using dc magnetic field, we confirm that the velocity at meniscus becomes stabilized in the time domain and the space domain, though the conventional dual electromagnetic stirring is difficult to realize the stabilization of the meniscus flow dynamics. In the proposed process, it is also confirmed that the velocity at the inner mold is constant in spite of dc magnetic field. Index Terms--Continuous casting, electromagnetic analysis, electromagnetic stirring, magneto hydrodynamics calculation.

In order to improve steel quality in the continuous casting process, it is necessary to make the dynamic behavior of the free surface flows in a mold clear. The estimation of influences of in-mold electromagnetic stirring (M-EMS) electromagnetic force is especially important. We examined the difference of free surface flows by the different M-EMS exciting frequencies, using numerical experiment (magnetohydrodynamic calculation). We introduce a new index, the responsive ratio, to evaluate it. As a result, the free surface flow has different behavior according to exciting frequency and its responsive ratio is higher in low-frequency zone. The free surface flow has also high resonate-ability with natural frequency of the mold. Index Terms--Continuous casting, electromagnetic analysis, electromagnetic stirring, magneto hydrodynamics calculation.

To decrease the cost of low-frequency linear motor such as M-EMS (in-mold electromagnetic stirring) system and to obtain the process characteristics, it is necessary to estimate the maximum current and voltage as well as the distribution of magnetic flux density precisely. According to the measurement result of the M-EMS unbalanced three-phased electrical circuit, we find out that the standard deviation of the voltages is much smaller than that of currents. Then, it makes clear that the voltage source electromagnetic calculation is useful for the M-EMS design to obtain the maximum current and the magnetic flux density, through the comparison data of the experiment and the calculation. Index Terms--Electromagnetic analysis, electromagnetic stirring, end effect, linear motor, phase unbalance.

We evaluate an effect of the dual in-mold electromagnetic stirring (M-EMS) which is arranged in series to control the molten steel velocity distribution using magnetohydrodynamic calculation. A stirring force ratio (SFR) defined as [F.sub.u]/[F.sub.1] where [F.sub.u] is an electromagnetic force of upper M-EMS and [F.sub.i] is the one of the lower M-EMS is introduced as an index of input. The value of SFR at the optimal condition that meniscus velocity is almost zero, but some velocity is realized at lower M-EMS position. Especially, the SFR condition to have no velocity at free surface is extremely rigorous. This means that it is very difficult to be stable at meniscus by the dual M-EMS system. The lower velocity hardly changes when the SFR changes. Index Terms--Continuous casting, electromagnetic analysis, electromagnetic stirring, magneto hydrodynamics calculation.

To get the fundamental characteristics of magnetohydrodynamics is extremely important, because in-mold electromagnetic stirring is required to get high quality steel. We have researched magnetohydrodynamic calculations to estimate the experimental data. At first, we compared the calculation velocity and measurement velocity in a pot mold. There is good agreement, though the calculation data depend upon the procedure after flow dynamic calculation. Next, we compared molten metals such as molten steel, mercury and fused metal. Since molten steel provides difficulties for measurements, we often estimate the magnetohydrodynamic characteristics through measurement data from mercury or fused metal. The calculation data show that molten steel has the highest speed, though the fused metal has the lowest speed. Lastly, we compare the fluid dynamic characteristics between a pot mold and an endless mold. Though an endless mold is already used in practice, the experimental mold is a pot one. After we get measurement data from the pot mold, we must estimate the characteristics of the endless mold. The calculated data show that the velocity of the pot mold near the meniscus level is larger than that of the endless mold, because the endless mold has the turned over flow from the fixed bottom in the pot mold.

Electromagnetic stirring is used at billet molds as well as at slab mold, to get high quality steel at continuous casting in steel making plant. In order to get the same electromagnetic force in each billet mold and thus the same quality, phase characteristics of electromagnetic stirring is investigated. From the calculation result, it is found that the relative phase at which the difference of the electromagnetic torque in each mold becomes the smallest is 0 or 240 deg. To apply the phase characteristics of the EMS to the quality control, we propose the dynamic phase control system by two inverters to get the high quality in the surface crack.

To depress the vibration and meandering of a thin steel plate in a steel making plant, electromagnets are applied to the plate. According to the results of numerical calculation, the different pole arrangement is superior to the same pole arrangement for the vertical position control, though the same pole arrangement is superior to the different pole arrangement for the lateral position control. There is no significant difference in the electromagnetic forces obtained at room temperature as compared to 700 [degrees] C. However, the investigation shows that the smallest electromagnetic forces are obtained at the 765 [degrees] C.

Molten metal flow control using linear induction motor is expected much to be a new revolutionary basic technology to realize high quality and low cost processes. We report an experiment with fused metal (melting point : 45 [degrees] C) and 100kg molten steel. According to the fused metal experiment, the linear induction motor has a good ability for stopping and acceleration as well as braking of metal flow. However, the electromagnetic force to be able to stop the metal flow in vertical arrangement is several times larger than the one in horizontal arrangement because of the liquid metal effect. A resonance condenser is useful to reduce the required power source capacity. Therefore, to control the molten metal flow, voltage(current) regulation is superior to frequency regulation. Though the large air gap also makes the electromagnetic force reduced, a conductive shorting bar([Z.sub.r][B.sup.2]), installed inside the non-conductive firebrick, increases the electromagnetic force.

The electromagnetic application system to improve the running characteristics at the runout table of the hot strip mill in a steel-making plant by means of electromagnetic force is proposed. According to the fundamental analysis, such as electromagnetic calculation and experimental data, this system is frequently used in online operation, even in consideration of magnetic saturation and electromagnetic braking. Index Terms--Electromagnetic braking, electromagnetic force, hot strip mill, magnetic saturation, runout table, thin strip.

To get the optimal operation of in-mold electromagnetic stirring through the fundamental characteristics, a three-dimensional magnetohydrodynamic calculation model was used, taking into consideration heat transfer and solidification as well as free surface. Comparison between measured velocity and calculated velocity is in agreement. A shadow method that calculates electromagnetic force in consideration of free surface transition is proposed to reduce computing time and maintain sufficient accuracy. A calculated free surface of mercury under 200-Hz magnetic field shows an adequate agreement with the experimental one. Calculation results applied to the continuous casting process taking into consideration heat transfer and solidification are in good agreement with operation data. This model shows that electromagnetic stirring makes the solidified shell uniform and dynamic deviation of temperature stable. Index Terms--Continuous casting, electromagnetic stirring, free surface, heat transfer, magnetohydrodynamic, numerical calculation, solidification.