Akihisa Kameari

Calculation of transient 3D eddy current using edge-elements

The calculation of transient 3-D eddy current using edge elements in the modified A-method is presented. Quadratic 36-edge elements on the 20-node isoparametric elements are proposed. Specifically, the test problems of a square plate and a hollow sphere are solved with linear 12-edge and quadratic 36-edge elements, and the results are compared with the analytical solutions. The results using the two types of elements agree well with each other and with the analytical solution, demonstrating the applicability of these elements for eddy-current calculation. The spatial distributions of the current and magnetic field in elements interpolated by shape functions are approximated better by quadratic elements with fewer degrees of freedom than the linear elements. The accuracy of both types of elements is nearly the same in the test problem of a hollow sphere if the size of the quadratic elements is double that of the linear elements. >

Transient eddy current analysis on thin conductors with arbitrary connections and shapes

Abstract The numerical method for analyzing transient eddy currents on thin conductors with arbitrary connections and shapes is presented. The eddy currents are described by current functions and discretized in the usual manner of the finite element method. This method is successfully applied to the eddy currents on a sphere surface, a square plate and INTOR-J primary shield. It is shown that this method is accurate and efficient to analyze the eddy currents on complicated conductor structures.

FEM Computation of Magnetic Field and Iron Loss in Laminated Iron Core Using Homogenization Method

This paper presents a novel method for analyzing transient magnetic fields in laminated iron cores. It is based on the finite-element method and a newly developed homogenization method is applied to model the lamination effectively. The homogenized constitutive relations, of which the approximation is only applicable to low-frequency problems, are derived analytically, neglecting eddy currents induced by time-varying magnetic fluxes parallel to the lamination. The loss due to the neglected eddy currents is estimated in the postprocessing state utilizing the obtained magnetic field variation. The calculated magnetic field is in good agreement with the measurement for a benchmark problem. It is demonstrated that the homogenized relations can be applied to the low-frequency problems

Calculation of three dimensional eddy current by FEM-BEM coupling method

A coupled finite element-boundary element method is applied to three-dimensional eddy-current problems. The magnetic vector potential A and scalar potential phi are adopted for the formulation. The finite element method is used in the conducting region, while the boundary element method is used in the exterior vacant region. A symmetric linking method is chosen for the coupling procedure. The calculations show good agreement with analytical results and results obtained by other numerical methods. >

The Newton-Raphson method accelerated by using a line search - comparison between energy functional and residual minimization

A line search was combined with the Newton-Raphson method to accelerate the convergence of the iterative calculation in nonlinear magnetic field analysis. As a method for determining a step size for update, the minimization of an energy functional and a square of 2-norm of residual obtained from the finite-element discretization was investigated. It was demonstrated that the energy functional minimization is superior to the residual minimization from the viewpoint of computational cost. The line search is effective even in the magnetic vector potential formulation, which is said to be stable usually.

3-D analysis of induction motor with skewed slots using regular coupling mesh

A new method using a regular coupling mesh is proposed for problems involving movement in the FEM analysis of electric machines using edge elements. The fixed and moving regions are coupled through the mesh. The approach allows simple and independent generation of rotor and stator meshes. An induction motor with skewed slots is analyzed in 3-D by this method and the results are compared to measurements. The authors investigated the effects of the skewed slots and the end-rings on the characteristics of the induction motor, which are difficult to analyze in 2-D analysis. The good agreements between the numerical results and experimental data validate the applicability of the proposed method.

Convergence of ICCG method in FEM using edge elements without gauge condition

In the quasi-static magnetic field calculation, the equation is indefinite when we use edge elements without the gauge condition by the tree and co-tree decomposition. The convergence property of the incomplete Cholesky conjugate gradient (ICCG) method is investigated in the FEM of the A-/spl phi/ formulation using edge elements. Even when the continuity of the source current density is not satisfied strictly, we can obtain converged solutions including the error of the discontinuity by the ICCG. Also a method by two scalar potentials to impose divergence-free current density in the FEM mesh is proposed.

Symmetric second order edge elements for triangles and tetrahedra

A new type of second order edge elements for simplexes (triangles and tetrahedra) is proposed. The element is geometrically symmetric and the shape functions are orthogonal to each other in the integrals of the tangential components on edges. The number of nodes and edges are 14 and 24 in a tetrahedral element. The proposed elements are validated by eigenmode calculations in a cavity using newly developed method to solve eigenvalue problems with large matrices. Highly accurate eigenvalues are calculated using the elements.

Three-dimensional eddy current calculation using finite element method with A-V in conductor and Omega in vacuum

Three-dimensional eddy current equations are formulated in terms of a magnetic vector potential A and an electric scalar potential V in the conductive regions and a reduced magnetic scalar potential Omega in the nonconductive region. A finite-element computer code, EDDY3DT, has been developed using this A-V formulation. Application to test problems and comparison with the analytical solutions or results by other methods show that the A-V formulation is effective for problems involving anisotropic and discontinuous conductivities, cracks, and holes. >

Convergence Acceleration of Time-Periodic Electromagnetic Field Analysis by the Singularity Decomposition-Explicit Error Correction Method

This paper proposes a novel method for the improvement of the convergence to a steady state in time-periodic transient nonlinear eddy-current analyses. The proposed method, which is based on the time-periodic finite element method and the singularity decomposition-explicit error correction method, can extract poorly converged error components corresponding to the large time constants of an analyzed system. The correction of the extracted error components efficiently accelerates the convergence to a steady state. Numerical results verify the effectiveness of the proposed method.