A fundamental problem in eddy-current nondestructive evaluation is one of finding the quasi-static electromagnetic field of a cylindrical coil in the vicinity of the edge of a metal block. Although the field can be calculated numerically, an effective analytical approach can potentially provide a better understanding of the edge fields and form the basis of a procedure for solving a whole class of related edge problems including edge structures that contain corner cracks. One can represent the metal block as a conductive quarter space in an unbounded region. However, it has been found that the analysis is more straightforward if the problem domain is truncated in two dimensions. With the domain boundaries far from both the coil and the corner, the truncation has a negligible effect on the solution near the edge but the field calculation becomes much easier. A double Fourier series representation of the field is used, as in the case of a rectangular waveguide problem. The field in the conductor is then matched at the interfaces with that in air to determine the expansion coefficients that are used to represent the field in different parts of the domain. In this way we have derived expressions for the magnetic field, the induced eddy-current density and the coil impedance at arbitrary position and orientation of the coil.

This work investigates the problem of efficiency optimization in capacitor-run single-phase induction motors. The double-revolving-field concept is employed in the theoretical analysis and a relation between the main and auxiliary stator currents is derived that accomplishes optimal efficiency under constant torque operation. A triac-based drive with an optimal efficiency voltage controller is proposed. The controller is easily implemented since an experimental procedure is used for adjusting its parameters. Moreover, the proposed control scheme satisfies all of the prerequisites of simplicity, reliability, and cost-effectiveness that are imposed by the utilization of a single-phase motor. Several experimental results are presented to validate the effectiveness of the proposed efficiency optimization control method.

A model of an axisymmetric probe coil with a cylindrical ferrite core in the presence of a layered conducting half space is developed. The boundary value problem is formulated in terms of the magnetic vector potential, which is expanded in a series of appropriate eigenfunctions. The corresponding eigenvalues are the real roots of a function with the radius and the magnetic permeability of the core as parameters. The unknown coefficients of the series are computed by solving a matrix system, which is formed by applying the usual interface conditions. Expressions are derived for the induced eddy current density and the impedance of the coil. Numerical results for the latter are in good agreement with experimental data.

The electromagnetic field and impedance of a cylindrical eddy-current probe coil are calculated analytically for arbitrary coil orientation above a conductive half-space. The remarkably simple closed-form expressions are provided as a function of coil tilt angle. The effect of tilt on the impedance change produced by a long crack is also investigated by combining the analytical model with an existing thin-skin theory for surface crack inspections. Results for both cracked and uncracked conductors are expected to be useful for evaluation of movement-generated noise in eddy-current inspections.