Computation of Eigenvalues and Eigenfunctions in the Solution of Eddy Current Problems.

The solution of the eigenvalue problem in bounded domains with planar and cylindrical stratification is a necessary preliminary task for the construction of modal solutions to canonical problems with discontinuities. The computation of the complex eigenvalue spectrum must be very accurate since losing or misplacing one of the thereto linked modes will have an important impact on the field solution. The approach followed in a number of previous works is to construct the corresponding transcendental equation and locate its roots in the complex plane using the Newton-Raphson method or Cauchy-integral-based techniques. Nevertheless, this approach is cumbersome, and its numerical stability decreases dramatically with the number of layers. An alternative, approach consists in the numerical evaluation of the matrix eigenvalues for the weak formulation for the respective 1D Sturm-Liouville problem using linear algebra tools. An arbitrary number of layers can thus be easily and robustly treated, with continuous material gradients being a limiting case. Although this approach is often used in high frequency studies involving wave propagation, this is the first time that has been used for the induction problem arising in an eddy current inspection situation. The developed method is implemented in Matlab and is used to deal with the following problems: magnetic material with a hole, a magnetic cylinder, and a magnetic ring. In all the conducted tests, the results are obtained in a very short time, without missing a single eigenvalue.

Evaluation of the Properties of Eddy Current Sensors Based on Their Equivalent Parameters.

This paper presents a practical way of using the method of evaluating the metrological properties of eddy current sensors. The idea of the proposed approach consists of employing a mathematical model of an ideal filamentary coil to determine equivalent parameters of the sensor and sensitivity coefficients of tested physical quantities. These parameters were determined on the basis of the measured value of the real sensor's impedance. The measurements were carried out with an air-core sensor and an I-core sensor while they were positioned at different distances from the surface of tested copper and bronze plates. An analysis of the influence of the coil's position in relation to the I core on the equivalent parameters was also carried out, and the interpretation of the results obtained for various sensor configurations was presented in a graphical form. When equivalent parameters and sensitivity coefficients of examined physical quantities are known, it is possible to compare even very different sensors with the employment of one measure. The proposed approach makes it possible to make a significant simplification of the mechanisms of calibration of conductometers and defectoscopes, computer simulation of eddy current tests, creating the scale of a measuring device, and designing sensors.

Eddy Current Testing of Conductive Coatings Using a Pot-Core Sensor.

Conductors consisting of thin layers are commonly used in many industries as protective, insulating or thermal barrier coatings (TBC). Nondestructive testing of these types of structures allows one to determine their dimensions and technical condition, while also detecting defects, which significantly reduces the risk of failures and accidents. This work presents an eddy current system for testing thin layers and coatings, which has never been presented before. It consists of an analytical model and a pot-core sensor. The analytical model was derived through the employment of the truncated region eigenfunction expansion (TREE) method. The final formulas for the sensor impedance have been presented in a closed form and implemented in Matlab. The results of the calculations of the pot-core sensor impedance for thin layers with a thickness above 0.1 mm were compared with the measurement results. The calculations made for the TBC were verified with a numerical model created using the finite element method (FEM) in Comsol Multiphysics. In all the cases, the error in determining changes in the components of the pot-core sensor impedance was less than 4%. At the same time, it was shown that the sensitivity of the applied pot-core sensor in the case of thin-layer testing is much higher than the sensitivity of the air-core sensor and the I-core sensor.