K.V. Namjoshi

Low-frequency eddy-current loss estimation in long conductors by using the moment of inertia of cross sections

A simple method is presented to estimate low-frequency eddy-current losses in long nonmagnetic conductors of uniform cross section when subjected to axial or transverse magnetic field. The method involves calculation of the moment of inertia of the conductor cross section. In the case of transverse fields, the relationship obtained agrees with analytical results for cross sections which have a symmetry axis parallel to the incident field. For axial fields the proposed relationship agrees with the analytical expressions for circular and elliptical cross sections and gives results with reasonable accuracy for rectangular cross sections. >

Efficiency of eddy current shielding of structural steel surrounding large currents: a circuit approach

The eddy current shielding of steel structures which surround power cables carrying large currents is considered. An important criterion for the effectiveness of the shield is the ratio of the power loss with the shield and the power loss without the shield. A method is suggested for the estimation of the effectiveness of the shield, provided the power loss without the shield and the resistance of the shield are known. A relation is developed between the effectiveness of the shield and the losses in the shield and in the steel structure. Short-circuited copper rings closely wound around the structure are considered as an eddy current shield. A transformer circuit model is used. The method is demonstrated for a circular geometry. >

Cross field heating of long plates by periodically placed magnets

A quasi-three dimensional model is used to calculate the current density distribution in a cross field heating system having a long work piece. Air gap field, both with and without the leakage field is considered. Results are shown for the current density and the average current density square, which determines the heat distribution, to demonstrate the influence of some of the system parameters.

Current distribution in exciting coil conductors in cross-field heating systems

The current distribution in the exciting coils of double-sided iron-backed cross-field heating systems is analyzed. The finite-difference method is used to calculate the internal resistance of the winding. The internal resistance is used as a criterion in studying the effect of the load on the winding current distribution. The concept of equivalent surface current density shows the influence of such parameters as the winding cross section and the skin depth. Equivalent surface current density is obtained by placing virtual current sources at the interface of the winding conductor and the air gap. Impedance values calculated using the two methods are in agreement. >

Multiple conductors in transverse magnetic field and their application in magnetic shielding

The problem of eddy currents induced in long conductors when placed in a transverse magnetic field is discussed. The induced currents are grouped into two types. The first type arises due to the flux incident over the region of the conductors. The second type arises due to the flux in the space between the conductors. The second type of current is possible only if the conductors are connected at the ends to form closed loops. To illustrate the two current types, a planar arrangement of perfect conductors is used. The possible use of multiple conductors as a magnetic shield is demonstrated. >

Cross field heating systems: influence of system parameters

A two-dimensional analysis of cross field heating systems is presented. An analytical method is used to obtain the impressed field in the air gap of the system without resorting to extensive calculations. The air-gap field in its turn makes it possible to calculate the power induced in the workpiece and provides some design guidelines. Expressions derived for the power induced in the workpiece are used to study the performance of the cross field systems as a function of parameters such as pole width, air-gap length, workpiece thickness, and supply frequency. The influence of the core permeability is also shown. The results indicate that the optimum value of the induced power in a system of given dimensions is almost independent of the workpiece thickness. The calculated value of the induced power shows good agreement with the measured value for a test system. >

Influence of the leakage field in cross field heating systems

The basic principles and expected current density distributions are presented for cross field heating. Two distinctly different cases are considered, one dealing with leakage free field and the other one which includes leakage. The induced current density distribution is shown both for symmetrical and asymmetrical placement of the load.

General properties of cross field heating systems

Field distribution is calculated in a cross field heating system with a symmetrically placed work piece. A two dimensional model is used. With the help of these results, the reflected impedance of the stator winding is obtained. The normalized form of the results provides one with suitable guide lines to select system parameters for optimum results. Both nonmagnetic and magnetic materials are considered for the work piece.

Surface power distribution in cross field heating of thin nonmagnetic plates

The problem of nonuniformity of the induced surface power density in the workpieces of cross-field heating systems is analyzed. Assuming the workpiece to be very thin, the induced current density and the induced power density are obtained using a method based on circuit theory. Calculation of the total power agrees with the measured value. The results suggest that, to obtain uniform current density, one may have to try different shapes for the exciting coils. Varying the distance between the coils or their lengths does not produce the desired effect. >

Electromagnetic coupling between heater coils of axial induction heaters

The problem of the electromagnetic coupling between the heater coils of longitudinal field heating systems is considered. An analytical model is used to show that the coupling between the coils can be reduced by placing a short-circuited dummy coil between the heater coils. Experimental results are included to show the validity of the model. >