and closed contour has been described; (d) probe leavessupport plate and trailing coil experiences large change;(e) probe is far from support plate and complete impedanceplane trajectory has been described and, because ofasymmetry in geometry, signal is asymmetric.(a)(b)(c)(d)(e)FIGURE29.Differential eddy current probe inside tube withoutside diameter axisymmetric slot: (a) geometry; (b) finiteelement mesh (half region).(a)zHeat resistantnickel chromiumalloy tubeAxisymmetric slotEddy current coilsVariable spacingdbc19.7 mm (0.775 in.)22.2 mm (0.875 in.)Legendr= radial coordinatesz= axial coordinates(b)zr
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discretized by using triangular finiteelements.171In this situation, both thespacing and the width of the coils can bevaried.The geometry in Fig. 29a is discretizedinto a large number of triangular elementsas shown in Fig. 29b. The finite elementtechnique is applied to solve for themagnetic vector potential at each node ofthe mesh in Fig. 29b. From these values,the impedance of the coil is calculated atdiscrete probe positions to form theimpedance plane trajectory caused by thediscontinuity.Symmetry exists about the Z axis andonly half of the geometry is analyzedusing the axisymmetric formulation. Also,because symmetry exists about the centerof the discontinuity, the probe is allowedto move up to the point where it iscentered with the discontinuity and thecalculated impedance values are reflectedto form a full impedance plane trajectory.Figure 30 compares the experimentalresults (Fig. 30a) and finite element results(Fig. 30b) from a differential probe withcoils 2 mm (0.08 in.) wide at spacingsfrom 1 to 8.5 mm (0.04 to 0.34 in.). Theindication is from a slot (shown inFig. 29a) measuring 1 mm (0.04 in.) wideand 0.4 mm (0.015 in.) deep on the outersurface of a 22 mm (0.87 in.) tube madeof heat resistant nickel chromium alloy(Unified Numbering System N06600).The experimental results were obtainedusing a specially designed eddy currentprobe with interchangeable coils andvariable spacing between the coils. Theseresults show clearly that as the spacing ofthe coils increases the resultingimpedance plane trajectory loses itsdifferential nature and the probe behavesincreasingly as two distinct absoluteprobes. On the other hand, decreasing thespacing widens the loops but also reducesthe amplitude of the trajectories.Figure 31 compares different sized coilsat a constant spacing for the samediscontinuity as in Fig. 30. The spacing is2.5 mm (0.1 in.) and the coil width variesfrom 0.5 to 7.5 mm (0.02 to 0.3 in.). In110Electromagnetic TestingFIGURE30.Impedance plane trajectories for outside diameteraxisymmetric slot and distance dbetween 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.)FIGURE31.Impedance plane trajectories for different coil sizesat 100 kHz and constant spacing between coils for slot inFig. 30: (a) experimental; (b) finite element.
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