Determining the Impedance of an Eddy Current Probe Placed over a Defect-Free Conductive Cylinder with a Centred Circular Hole

The measurement of a probe impedance performed during eddy current inspections enables detection of flaws in electrically conductive materials. A correct interpretation of the measured impedance values constitutes a key aspect that determines the effectiveness of the inspections, and for this purpose, mathematical models are employed. Such models, which are becoming more and more frequently an integral part of eddy current measurement systems, enable carrying out the calculation of the probe impedance, through depicting the measurements being performed. What offer the shortest calculation time while maintaining high accuracy are analytical solutions. In this paper, to the best of the authors’ knowledge, this is the first time an analytical model of an eddy current probe placed over a small diameter cylinder containing a hole has been presented. The final formulas were obtained using the truncated region eigenfunction expansion (TREE) method, and then implemented in Matlab. The calculated values of the probe resistance and reactance were compared with the measurement results obtained for cylinders with a through defect. The tests were conducted on components made of several conductive materials with different geometric dimensions. The measurement error in all of the tests was small, i.e., it did not exceed 3% across the entire frequency range. The proposed solution can be used in defectoscopy for eddy current testing of tubes, pucks, washers, and any cylindrical elements.