Nowadays, with the development of computer technology, the limitations shown by analytical models are exceeded by numerical models, but there are actual configurations which can be satisfactorily described by analytical models. ft is the case of tube inspection with bobbin coil probes, which is a major application of eddy current technique in the nuclear and petrochemical industries. A model consisting in modules operated on portable computers has been developed and is applied to non ferromagnetic tubes examined with axial (bobbin-coil) probes, featuring no magnetic parts. ft simulates signals from absolute or differential measurements. The model also features the capability of simulating complex signals which cannot be analysed using classical methods. The model calculates the impedance of the probe in connection with the tube and the defect. Most applications in tube testing reduce significantly the field of validity of the model by actual test conditions (tube wall-thickness, eddy current flow, excitation frequencies ...). The model includes the physical and geometrical parameters describing the test and the defect and is fed with the knowledge from manual eddy current signal analysis. Defects with the same axial symmetry as the tube and the bobbin coil (axial) probe are considered The 3D space is represented by the addition of concentric tores with varying diameters and position but with equivalent rectangular sections. The defect is also simulated by a network; each cell is characterised by its position and its physical properties. The geometry of the system tube-defect-probe can thus be fully described by a 2D cellular network. The induction flux through any closed surface built on a torical element of the probe is modified by the presence of each torical element of the defect. The resulting Probe impedance variation is assumed to be the sum of all the interactions of the defect-probe cells in the 2D network. Each interaction is linked to the value of induction due to the element of sensor in the element of tube. This induction is analytically modelled using the planar wave model frequently used in eddy current theory. For each position of the probe, a large number of couples of cells must be included in the calculation of the total variation of impedance and this would imply a long time of computation. But the subdivision of space in cells makes a certain number of interactions identical. Moreover, if the probe is moved along the axis of the network, this again reduces the number of different interactions. Each distinct interaction is calculated once and then placed in a matrix of interactions. For repetitive examinations of tubes, the contributions of all the elements of the probe are summed and the probe is reduced to a single element A << matrix of examination >> is coupled to the reduced probe and can be stored for further use if needed. Each element of the matrix is the probe impedance variation due to the defect cell. The matrix size depends on the area of coverage of the probe; this processing allows fast computations even for long defects. The latest version of the model has allowed to describe, with an excellent correlation, the modification of a signal due to the variation of one parameter (frequency, distance between coils .. ) Since, ferromagnetic support plate signals cannot be simulated using the model as developed the actual signal given by a probe on a support plate is digitized during the probe movement at constant speed and is mixed with that of a simulated defect. The basic assumption of multifrequency eddy current technique which is additivity of signals is fully verified by the comparison of simulated signals with actual signals obtained in identical conditions The analytical model developed has immediate applications in educational courses for analysts, in training of automated signal analysis systems as well as in pre-feasibility studies.
