Analytical model of a shielded U-core sensor

Abstract

In this paper, a simple analytical model of an eddy current sensor having an U-shaped magnetic core and a conductive shielding is presented. Results obtained with the developed model are then compared with data issued from measurements and show a fair agreement. The main advantage of this analytical model lies in its simplicity of implementation and in its high execution speed comparatively to numerical models. In this section, the broad outlines of the modeling are presented. The geometry of the considered sensor with the plate under evaluation is shown in Fig. 1. The plate has a conductivity σ, a permeability µ and a thickness t. The lift-off of the sensor is noted l. In order to simplify the modeling, the magnetic core is assumed perfect (infinite permeability) as well as the conductive shielding (infinite conductivity). For axisymmetry reasons, the sensor is constituted of two discoidal magnetic poles (numbered 1 and 2) having a radius r0. It is fed by a sinusoidal excitation current. The view of the bottom of the sensor in the z =0 plane is shown in Fig. 2. It consists of the two discoidal poles surrounded by the shielding. The pole 1 has an outcoming magnetic flux φ whereas the pole 2 has an outcoming flux −φ. In order to avoid a magnetic flux weakening, the shielding between the two poles presents a nonconductive cut (otherwise there would be the equivalent of a shorted-circuit transformer secondary). The solution of the model lies in the determination of the complex external reluctance (� ) viewed between the two poles of the sensor.