T. Misaki

Eddy current and deflection analyses of a thin plate in time-changing magnetic field

Eddy current and deflection analysis of a thin-plate model in a time-changing magnetic field is described. The model is solved as a coupled problem in which the time-changing magnetic field induces eddy currents and the eddy currents cause deflection of the thin plate by the Lorentz force. The eddy current analysis and deflection analysis are performed by an integro-differential method using a current vector potential and a structural finite element method using beam elements, respectively. The formulations of the motional electromotive force and the Lorentz force for the thin-plate model are presented. In addition, the applicability of the proposed method is verified by using a cantilevered-beam model. >

Three-dimensional eddy current analysis of induction melting in cold crucibles

In order to reduce computer resources for the analysis of the eddy current distribution of cold crucible models, the authors used a current sheet approximation for the eddy current distribution because the penetration depth of the eddy current is relatively small in comparison with the dimension of the conducting bodies. The eddy current distributions approximated by current sheets are solved by an integrodifferential method using an electric vector potential. Furthermore, the magnetic flux density, power loss, Lorentz force, and lifting force of the molten metals are obtained from the solved eddy current distribution. The calculated results for the power loss and the Lorentz force gave good agreement with experimental results. >

Eddy current analysis on thin conducting plate by an integral equation method using edge elements

Eddy current distributions on a thin conducting plate are solved by an integral equation method using edge elements. The normal component of eddy current density across the edge of triangular element is chosen as the unknown variable. In this paper, the authors investigate how to define the set of unknowns. The tree and co-tree of surface eddy current paths are introduced. The unknown surface current densities are defined on the paths of the co-tree and the zero divergence condition is applied to those of the tree. The proposed method is applied to a simple computation model in order to verify the applicability of the method.

Adaptive triangular mesh generation for boundary element method in three-dimensional electrostatic problems

An adaptive triangular mesh generation method for BEM is proposed. In this method, an estimated error is used as the criterion for refinement of triangular mesh. The error estimation is performed by using a smoothness of unknown variable distribution, which is an approximate equation of the Laplacian of the discrete unknown variables at the node on the triangular element. In this paper, the procedure of the adaptive triangular mesh generation and some examples are described.

An edge element for boundary element method using vector variables

An edge element for a boundary element method using vector variables is proposed. The tangential component of the unknown variable on the boundary surface is approximated by a vector interpolation function on the edge element. The proposed edged element is introduced into a boundary element method using magnetic flux density and electric field as unknown vector variables. In the boundary element method, unknown variables are reduced to only the tangential components of magnetic flux density and electric field. The applicability of the proposed method was verified by computation results for the benchmark model of the IEE of Japan for three-dimensional eddy current problems. >

Three-dimensional analysis of eddy current and electromagnetic force in cold crucibles

Three-dimensional eddy current distributions in cold crucibles are analyzed by using an integro-differential method. The electromagnetic force is calculated from the obtained eddy current distributions. In this paper, computations of eddy current and levitation force of the molten metal in some cold crucible models are performed, and the influences of coil position, the number of segments of the crucible, frequency of the coil current and gap length between the segments on the levitation force are discussed. Furthermore, an experimental verification is presented. >

Computation of electric current distribution on thin conducting plate using edge element

An edge element is applied to the analysis of the electric current distribution on a thin conducting plate. The normal component of the surface current density across the edge of the triangular element is chosen as the unknown variable preserving the normal continuity. By using Galerkins weighted residual method, the formulation of the analysis is done for the electric field on the thin conductor surface taking account of the eddy current and the displacement current. In addition, the proposed method is applied to simple computation models in order to verify the applicability of the method.

Reduction of vector unknowns using geometric symmetry in a triangular-patch moment method for electromagnetic scattering and radiation analysis

A simplification method for the boundary element model developed by H. Tsuboi et al. (1990) is applied to the triangular-patch moment method in order to reduce the number of vector unknowns. The simplification of the computational model is performed by a variable transformation using the spatial eigenmodes, which is similar to transformation used in the boundary element case. However, the unknown vectors have to be arranged according to the geometry of the rotational symmetry because of the varying directions of the unknown vectors. The applicability of the simplification method was verified by a flat square plate model and a TEM (transverse electromagnetic) cell model. >

Efficient boundary element analysis superposing known solution for electrostatic problems

An efficient boundary element method for electrostatic problems is proposed. When a relatively small conductor or dielectric is added to the computation model where the solution is known, we can reduce the number of unknowns by superposing the known solution and the field induced by the unknown distributions on the boundary surfaces. In the proposed method, unknowns are the flux distributions and/or potential distributions induced by only the added small conductor or dielectric body on the boundary surfaces. Therefore, the area to be analyzed becomes small and the number of unknowns is reduced because the influence of the added body is small. >

Transient eddy current analysis by the boundary element method using Fourier transforms

Techniques of transient analysis by the boundary-element method (BEM) using the Fourier transform are presented. In the proposed method, the response of the frequency domain is obtained by boundary-element analysis in sinusoidal steady-state analysis. Transient analysis is examined by the inverse Fourier transform using the response of the frequency domain. Therefore, the volume integral with respect to the region to be analyzed is not necessary. The applicability of the method is shown by comparison of the computation results of the 2-D model and 3-D model with the theoretical values. The time integration of the proposed method is more stable than that of the time-differential method. >