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And closed contour has been described d probe leaves

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and closed contour has been described; (d) probe leaves support plate and trailing coil experiences large change; (e) probe is far from support plate and complete impedance plane trajectory has been described and, because of asymmetry in geometry, signal is asymmetric. (a) (b) (c) (d) (e) F IGURE 29. Differential eddy current probe inside tube with outside diameter axisymmetric slot: (a) geometry; (b) finite element mesh (half region). (a) z Heat resistant nickel chromium alloy tube Axisymmetric slot Eddy current coils Variable spacing d b c 19.7 mm (0.775 in.) 22.2 mm (0.875 in.) Legend r = radial coordinates z = axial coordinates (b) z r
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discretized by using triangular finite elements. 171 In this situation, both the spacing and the width of the coils can be varied. The geometry in Fig. 29a is discretized into a large number of triangular elements as shown in Fig. 29b. The finite element technique is applied to solve for the magnetic vector potential at each node of the mesh in Fig. 29b. From these values, the impedance of the coil is calculated at discrete probe positions to form the impedance plane trajectory caused by the discontinuity. Symmetry exists about the Z axis and only half of the geometry is analyzed using the axisymmetric formulation. Also, because symmetry exists about the center of the discontinuity, the probe is allowed to move up to the point where it is centered with the discontinuity and the calculated impedance values are reflected to form a full impedance plane trajectory. Figure 30 compares the experimental results (Fig. 30a) and finite element results (Fig. 30b) from a differential probe with coils 2 mm (0.08 in.) wide at spacings from 1 to 8.5 mm (0.04 to 0.34 in.). The indication is from a slot (shown in Fig. 29a) measuring 1 mm (0.04 in.) wide and 0.4 mm (0.015 in.) deep on the outer surface of a 22 mm (0.87 in.) tube made of heat resistant nickel chromium alloy (Unified Numbering System N06600). The experimental results were obtained using a specially designed eddy current probe with interchangeable coils and variable spacing between the coils. These results show clearly that as the spacing of the coils increases the resulting impedance plane trajectory loses its differential nature and the probe behaves increasingly as two distinct absolute probes. On the other hand, decreasing the spacing widens the loops but also reduces the amplitude of the trajectories. Figure 31 compares different sized coils at a constant spacing for the same discontinuity as in Fig. 30. The spacing is 2.5 mm (0.1 in.) and the coil width varies from 0.5 to 7.5 mm (0.02 to 0.3 in.). In 110 Electromagnetic Testing F IGURE 30. Impedance plane trajectories for outside diameter axisymmetric slot and distance d between two coils of probe: (a) experimental element; (b) finite element. (a) d = 1 mm (0.04 in.) d = 2.5 mm (0.1 in.) d = 4 mm (0.16 in.) d = 5.6 mm (0.22 in.) d = 7 mm (0.28 in.) d = 8.6 mm (0.34 in.) (b) d = 1 mm (0.04 in.) d = 2.5 mm (0.1 in.) d = 4 mm (0.16 in.) d = 5.6 mm (0.22 in.) d = 7 mm (0.28 in.) d = 8.5 mm (0.34 in.) F IGURE 31. Impedance plane trajectories for different coil sizes at 100 kHz and constant spacing between coils for slot in Fig. 30: (a) experimental; (b) finite element.
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  • Fall '19
  • Wind, The Land, Magnetic Field, Dodd, Modeling of Electromagnetic Testing

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