A half-analytical formulation for the impedance variation in axisymmetrical modelling of eddy current non destructive testing

We present the calculation of the impedance variation using a half-analytical formulation based on coupled electromagnetic variables. Such a formulation concerns an axisymmetrical device constituted with a voltage supplied solenoidal inductor and a conducting workpiece. In this field of modelling, authors have already developed a method [Maouche and Feliachi, J. Phys. III France 10, 1967 (1997)] that determines the current distribution inside inductor coil loops in the case of weak skin depth and a low number of these coil loops. In the proposed development, the number of loops is relatively large and the skin effect in these loops is negligible. This formulation uses a voltage excitation, which makes the source field depending on induced currents and permits to consider the real geometry of the inductor. The model is applied to study an eddy current non destructive testing (ECNDT) device. The variation of the system impedance is calculated in the case of an axisymmetrical device. The obtained modelling results are validated by comparison to measurements and finite element computations [Remy, Ph.D. thesis, University of Compiegne, France, 1997; La et al., Rev. Prog. Quant. Non-Destructive Eval. 16A, 295 (1997)]. Once validated, the proposed model is applied to determine geometrical and physical characteristics of an ECNDT device. To assemble this interest, we visualise the evolution of the impedance variation according respectively to the air-gap, to the thickness of the workpiece and its electric conductivity. The model is implemented within a software tool (CECM: Coupling Electromagnetic Circuits Method) developed in Matlab environment.