IEEE TRANSACTIONS ON MAGNETICS, VOL. 38, NO. 2, MARCH 2002 1161 3-D Finite-Element Analysis of Eddy-Current Evaluation of Curved Plates Yann Le Bihan Abstract—The eddy current method allows thickness evaluation of conductive plates. However, EC measurements are sensitive to multiple parameters such as the sensor liftoff and the plate cur- vature. In this paper, the plate curvature effect is studied using a three-dimensional finite-element method, and it is shown that the curvature effect cannot be corrected by a conventional liftoff ef- fect correction. Consequently the curvature effect has to be specifi- cally corrected in the measurement inversion. A correction method using bifrequency measurements is implemented. Index Terms—Eddy-currents testing, finite-element methods, neural networks, thickness measurement. I. INTRODUCTION T HE EDDY-CURRENT (EC) method is widely used within the field of nondestructive evaluation (NDE) of the prop- erties of conductive materials. It notably allows high speed, low cost, and reliable evaluation of material properties [1], [2]. How- ever, an EC measurement is sensitive to multiple parameters and it is necessary to take them into account in the evaluation pro- cedure. One of the major applications of the EC method is the thickness evaluation of nonmagnetic conductive plates. In this case, besides the plate thickness value, EC measurements no- tably depend of the curvature of the plate. This paper deals with the effect of the plate curvature on the thickness evaluation. This effect occurs notably in the wall thickness evaluation of hollow turbine blades which show an external wall of variable curva- ture [3]. II. EC SENSOR MODELING A. EC Sensor Structure The EC sensor involved in this study was developed for the wall thickness evaluation of hollow turbine blades [3]. It con- sists of a pair of identical square coils wound around each end of an U-shaped ferrite core (Fig. 1). The two coils are connected in opposition and driven by an harmonic current. The EC mea- surement consists in the coil complex impedance (see Table I). According to the turbine blade features, the considered con- ductive material is a nickel-based superalloy which is nonmag- netic and shows an electrical conductivity of 6.5 10 ( m) [3]. Manuscript received July 5, 2001; revised October 25, 2001. This work was supported by Snecma Moteurs, France. The author was with the Laboratoire d’Electricité Signaux et Robotique, Ecole Normale Supérieure de Cachan, Cachan, France. He is now with the Laboratoire de Génie Electrique de Paris, Ecole Supérieure d’Electricité, Gif sur Yvette, France (e-mail: le-bihan@lgep.supelec.fr). Publisher Item Identifier S 0018-9464(02)02420-2. Fig. 1. View of the EC sensor. TABLE I SENSOR DIMENSIONS Fig. 2. FE meshing (convex curvature case). B. Finite-Element (FE) Modeling The effect of the curvature of the evaluated plate was studied using a low-frequency three-dimensional (FE) formulation. The chosen FE formulation combines the magnetic vector and the electric scalar potentials as degrees of freedom of hexahedral or tetrahedral mixed elements [4]. Thanks to the symmetry planes of the sensor-plate configuration, the curvature effect study re- quired to mesh only a quarter of the analyzed geometry. The im- plemented mesh is shown in Fig. 2 in the case of a plate showing a convex curvature. Since the coils of the actual sensor show a large amount of regularly distributed turns, both coils are approximated by uni- 0018-9464/02$17.00 © 2002 IEEE