Analytical Modeling of Mirrored Coplanar Rectangular Coils in Probe Design for Non-Destructive Testing

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applied physics , non-destructive testing , non-destructive evaluation , electromagnetics , probe design , Barkhausen noise , eddy current , analytical modeling , modeling , finite element , finite element modeling , coils , rectangular coils
Currently, the non-destructive testing technique of Barkhausen noise is overwhelmingly studied using only experimental and finite element methods. While analytical methods are largely absent, they boast the advantages of reduced computation time, mesh-independent analysis, and enhanced mathematical insight. Additionally, Barkhausen noise results are notoriously dependant on numerous parameters, such as surface stress. This thesis examines analytical models of the electromagnetic fields generated by rectangular coplanar excitation coils, typically used in Barkhausen noise probes, as a first step towards fully analytically modeling the probe to better understand the conditions under which Barkhausen noise is generated. An analytical model of two mirrored coplanar rectangular coils was constructed using Maxwell’s equations with the aid of symmetric and anti-symmetric Fourier transforms, and the resulting fields from an AC current source were also modeled assuming samples with linear magnetic permeabilities. To validate the behaviour of the analytical model, two air coils were wound around plastic bobbin forms and connected in series. The coils were placed above conducting half-spaces as well as plates and a thin foil to study their impedance and eddy current responses. Their signal response was tested at multiple frequencies using a signal generator and oscilloscope. The static half-space model produced excellent agreement with experimental measurements of impedance, as well as real and imaginary components of complex self-inductance. From the analysis of the experimental results, the true relative permeability of steel likely differed from the value that was taken from literature. The harmonic half-space model produced realistic results showing induced eddy current amplitude and induced magnetic flux density. The plate model also showed excellent agreement with experimental impedance and complex self-inductance measurements. Larger disagreements between the model and experimental results for steel suggested that the literature permeability value used for steel was inaccurate. As a final step, the thin plate model was extended to a thin foil model, which was able to predict the thickness of aluminum foil at high frequencies. These results provide a necessary first step towards developing a fully analytical model to describe the electromagnetic behaviour of the Barkhausen noise probe independent from finite element methods.
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