A detailed analysis is presented for the inductance calculations of rectangular coils with parallel end faces, with the coils of parallel sides as the special case. Integral solutions are given by the theory of second-order scalar potential. The authors further provide the series solutions for the inductance, which are based on the truncated region eigenfunction expansion method. These series are quite concise and accurate, and with higher computational efficiency by comparison with the integrals. The integral and series solutions are also obtained for the planar rectangular coils. The numerical results of both methods are compared with those of the experimental data, and the proposed methods prove to be accurate and efficient enough for practical applications.
Boundary‐element method (BEM) is applied to the analysis of AC resistance of single‐layer coils. For simplification of the analysis, the coil windings are replaced by a system of parallel straight conductors. Applying the method of images and closed‐form solutions of off‐diagonal matrix elements, and exploiting the symmetry of submatrices, high computational efficiency can be achieved by the proposed approach. As a numerical method, it is suitable for solenoids or pancake coils evenly wound by round or rectangular wires, or other wire shapes with proper symmetry. The proposed method is verified by the numerical results compared with those of finite‐element method (FEM) and measurements, from which it is confirmed that the proposed approach has the same accuracy as the FEM, and the former is much faster and more memory efficient.
Truncated region eigenfunction expansion (TREE) method is applied to the analysis of impedance change of a coil in the vicinity of the edge of a metal plate. The analysis is carried out with the second order vector potentials (SOVPs) and provided for both cylindrical and rectangular coils. By full discretisation of the eigenvalues, double series solutions are obtained for the field and coil impedance variations. To simplify the solving procedure further, a novel approach for the determination of eigenvalues is proposed by means of the 1D finite element method (FEM), which is easy to implement and works well for the plate of non-magnetic material. Numerical results for the impedance variations of cylindrical and rectangular coils are compared with those of 3D FEM simulation, by which the efficiency and accuracy of the authors' method are confirmed, and the former is much faster and more memory efficient.
In this paper we present a modification of an existing analytical model for a long surface crack on a conductive plate. This is actually a thin skin model and the challenge for its successful implementation is the accurate calculation of the magnetic field on the defect-free surface on a conductor. We can now combine analytical expressions with numerical results to calculate the coil impedance changes, due to the defect existence. Using the numerical results by FEM for the coil’s magnetic field into the final impedance change analytical expression we can simulate eddy current probes with complex shape that are difficult to be described analytically.
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