Abstract
Distribution of eddy current density for three types of coils of excitation of moving surface eddy current probes, in particular circular, rectangular, orthogonal-rectangular shapes was calculated according to the formulas of exact electrodynamic mathematical models with allowance for the speed effect. Calculation time from 8 to 20 hours was established for a circular excitation coil with dimensions of testing zone 50´50 mm at speed u x =40 m/s. The calculation time was from 8 to 9 hours for a rectangular excitation coil at a speed of movement in direction of two components u x , u y =20 m/s with the testing zone dimensions of 80´48 mm. The calculation time was more than 7 hours for an excitation coil of orthogonal rectangular shape with dimensions of the testing zone of 15´35 mm at a speed of movement in direction of components u x , u y =40 m/s; and for the testing zone dimensions of 12´24 mm for u x , u y =40 m/s it was longer than 9 hours. It was found that the computational complexity of calculation of distribution of the eddy current density with the use of exact mathematical models was rather large when changing even two spatial coordinates in the testing zone. That is, the direct use of exact mathematical models when calculating the values of distribution of the eddy currents density in the points of the controlled zone is inappropriate taking into account the considerable resource intensity of the computational process. The necessity for using a mathematical apparatus of surrogate optimization was substantiated for designing eddy current probes with a uniform distribution of eddy current density in the testing zone. This study is useful for non-destructive testing specialists in the field of mechanical engineering. The study results can be used in designing eddy current probes with improved metrological characteristics, in particular homogeneous sensitivity, localization of the probing excitation field, improved noise immunity, possibility of eliminating the edge effect manifestations in testing
Highlights
Today, the eddy current testing method and devices based on it are widely used for nondestructive testing in industry, e. g. for material discontinuity detection in defectoscopy and defectometry; measuring dimensions of testing objects (TO) and vibration parameters in thickness metering and vibrometry; definition of physical and mechanical parameters and structural state of materials in structuroscopy; detection of electric conducting objects, etc.An important characteristic of the eddy current method is its sensitivity which depends on testing conditions, product material and positional relationship of the eddy current probe (ECP) and TO
‒ for a circular coil of ECP excitation with dimensions of the testing zone 50 ́50 mm, eddy current density (ECD) distribution calculation time with application of the “exact” mathematical model was 8 to 20 hours taking into account speed ux=40 m/s;
‒ for a rectangular coil of ECP excitation with dimensions of the testing zone 80 ́48 mm, the ECD distribution calculation time with application of the “exact” mathematical model was 8 to 9 hours taking into consideration speed in direction of two components ux, uy=20 m/s;
Summary
The eddy current testing method and devices based on it are widely used for nondestructive testing in industry, e. g. for material discontinuity detection in defectoscopy and defectometry; measuring dimensions of testing objects (TO) and vibration parameters in thickness metering and vibrometry; definition of physical and mechanical parameters and structural state of materials in structuroscopy; detection of electric conducting objects, etc. To reduce dependence of probe sensitivity to defects on ECP position relative to TO, it is necessary to ensure homogeneous distribution of the eddy current density (ECD) in the testing zone. In order to solve the optimal synthesis problem, it is necessary to solve the analysis problem over and over again for each excitation structure performing calculation of ECD for a set of points in the testing zone. Urgency of this task consists in a necessity of studying the possibility of using mathematical models of moving ECP. The metamodel approximates the “exact” mathematical model, that is, it is the model of model
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