ET04.pdf

A a j 1 2 ωµ µ σ r a u v 2 2 z j i du dv b u v b

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a a j 1 2 0 = + ωµ µ σ r a u v = + 2 2 Z j I du dv B u v B u v a a a a a z z = ( ) × ( ) + ( ) −∞ −∞ 2 0 2 1 1 ω µ µ µ ˆ , ˆ , s s r r Z I dS = × ′ × × ( ) 1 2 E H E H n 72 Electromagnetic Testing
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Conclusions Analytical solutions in eddy current testing, although restricted to certain geometries as compared to the more general numerical solutions, have an explicit and closed form. The models are not computationally intensive and offer accurate solutions. They have limited scope but not limited value. Whenever plausible, analytical solutions are preferable to numerical ones because they are easier to apply, are less expensive to compute, are more accurate and finally allow for easy parametric studies of the test geometry. 73 Modeling of Electromagnetic Testing F IGURE 8. Eddy current testing with rectangular coil perpendicular to test object: (a) setup; (b) eddy current pattern. (a) Z X Y (b) Y axis coordinates, mm (in.) 10 (0.40) 8 (0.32) 6 (0.24) 4 (0.16) 2 (0.08) 0 –2 (–0.08) –4 (–0.16) –6 (–0.24) –8 (–0.32) –10 (–0.40) X axis coordinates, mm (in.) 10 6 2 0 –2 –6 –10 (0.40) (0.24) (0.08) (–0.08) (–0.24) (–0.40)
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Introduction Eddy current nondestructive testing uses inductive probes to excite currents in electrical conductors. The simple fact that the coil carrying an alternating current can sense a discontinuity in a metal is intuitively easy to understand but evaluating the signal for a given configuration of coil and discontinuity is not always easy. The present discussion describes calculations of probe signals from cracks, starting with a review of the basic theoretical concepts and moving on to a number of related techniques for evaluating probe response. Early investigators applied concepts from other fields of electromagnetism to problems in eddy current testing. The researcher in relatively unexplored areas of electromagnetic theory inevitably brings concepts from the parent discipline and adapts them for the new field of investigation. As advances in the new area begin to mature, the new discipline adopts distinct themes and approaches that are successful and rewarding. At the end of the twentieth century, eddy current nondestructive testing was at a point of early maturity. Basic problems had been solved satisfactorily yet many problems remained open and relatively underdeveloped. This discussion of crack theory briefly reviews a few significant early developments relevant to the treatment of crack problems in eddy current testing, including the analysis of the spherical inclusion and the penny shaped crack. Recent advanced developments in the evaluation of crack signals are then briefly outlined. Two approaches are described: (1) integral techniques that represent the effect of a discontinuity in terms of dipole distribution and (2) approaches valid at high frequencies that use small approximations of standard depth of penetration.
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  • Fall '19
  • Wind, The Land, Magnetic Field, Dodd, Modeling of Electromagnetic Testing

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