The theory and applications of eddy currents induced in conducting materials by time-varying magnetic fields are reviewed. The mathematical methods employed in solving the relevant problems are presented. Both analytical and numerical methods are described. Applications based on effects arising from eddy currents are discussed in detail. These applications are to magnetic levitation, electromagnetic launching, hyperthermia treatment of cancer, and nondestructive testing. >

Eddy currents: theory and applications

A method based on coupling the Bubnov-Galerkin method and the separation of variables method is described for the solution of alternating field problems in which the region of prime interest is embedded in an infinitely extending region where Laplace's equation holds. The proposed method can also be used when the stored energy associated with the exterior region and the boundary conditions at infinity are infinite. As an example illustrating the use of the method, the inner impedance of an elliptic conductor is calculated. By means of iterative numerical processes, the method enables the exact values of impedance to be obtained.

Use of the Bubnov-Galerkin method to skin effect problems for the case of unknown boundary conditions

It is demonstrated that the Bubnov-Galerkin method coupled with the separation of variables method can be applied for solving exterior alternating field problems. As an example illustrating the use of the method, the inner impedance of a rectangular conductor is calculated. Though the method is approximate, exact values of the impedance have been obtained by iterative numerical processes. The method can be used when the field or the vector potential do not vanish at infinity, and when the energy associated with the whole space is infinite.

http://iopscience.iop.org/article/10.1088/0022-3727/15/12/010/pdf

Bubnov-Galerkin method for solving exterior alternating field problems

In this paper the inner impedance and the electrodynamic force acting on a cylindrical conductor partly filling a semi-closed slot are calculated. The investigations are made by using the separation of variables method.

Impedance and elektrodynamic force acting on a cylindrical conductor partly filling a semi-closed slot

The impedance of a rectangular conductor of the starting cage of a double-cage motor is calculated by using the Babnow-Galerkin method. The working cage is assumed to consist of cylindrical conductors. Graphs of the resistance and inner reactance are given.

Impedance of a rectangular conductor of the starting cage of a double-cage motor

It is shown that the Ritz and Bubnow-Galerkin methods can be applied for the calculation of the inductance and the impedance, respectively. Moreover it is shown that the calculation of the impedance by the Bubnow-Galerkin method is a generalization of the calculation of the inductance by the Ritz method in the case of a nonhomogeneous Neumann boundary problem. For the illustration of these methods the inductance of a rectangular ferromagnetic conductor and the inner impedance of a rectangular conductor placed in a semi-closed slot are calculated.

R. Sikora

Papers

Use of Ritz and Bubnow-Galerkin methods for calculation of inductance and impedance of conductors