Differential eddy current probes are commonly used to detect shallow surface cracks in conductive materials. In recent years, a growing number of research works on their numerical modelling was conducted since the development of analytical or semi-analytical models for such a sensor may be prone to intractable complications. In this paper finite element modelling (FEM) has been employed to simulate the interaction of a reflection differential split-D probe with surface electrical discharge machined (EDM) notches in 3-dimensional (3-D) half-space. In order to attain a better insight into the correct setup of the FEM parameters, a simple multi-turn cylindrical absolute coil has also been modelled. The outcome generated through the simulated scan of this absolute coil over a surface notch in aluminum is validated with existing experimental impedance data taken from the literature. Parameters contributing to reliable FEM simulation results, such as maximum mesh size, mesh distribution, the extent of the surrounding air domain and conductivity of the air are investigated for the 3-D modelling of both absolute and differential probes. This study shows that the simulation results on a commercial reflection differential split-D surface pencil probe closely estimate the experimental measurements of the probe’s impedance variations as it scans three EDM notches having different depths in aluminum. The simulation results, generated by Comsol Multiphysics FEM package (COMSOL I, COMSOL multiphysics reference manual, version 5.3, COMSOL AB, 2018, www.comsol.com), for the cases of absolute and differential probes are checked for their extent of validity.

中文翻译：

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反射差分分裂-D涡流探头扫描表面凹口的有限元建模

差分涡流探头通常用于检测导电材料中的浅表面裂纹。近年来，由于此类传感器的分析或半分析模型的开发可能容易出现难以处理的并发症，因此对其数值建模进行了越来越多的研究工作。在本文中，有限元建模 (FEM) 已被用于模拟反射差分分裂 D 探针与 3 维 (3-D) 半空间中的表面放电加工 (EDM) 凹口的相互作用。为了更好地了解 FEM 参数的正确设置，还对一个简单的多匝圆柱形绝对线圈进行了建模。通过该绝对线圈在铝表面凹口上的模拟扫描产生的结果通过文献中的现有实验阻抗数据进行了验证。为绝对和差分探头的 3D 建模研究了有助于可靠 FEM 模拟结果的参数，例如最大网格尺寸、网格分布、周围空气域的范围和空气的电导率。该研究表明，商用反射差分分裂 D 表面笔形探针的模拟结果在其扫描铝中具有不同深度的三个 EDM 凹口时，可以精确估计探针阻抗变化的实验测量值。仿真结果由 Comsol Multiphysics FEM 包生成（COMSOL I，COM​​SOL multiphysics 参考手册，5.3 版，COMSOL AB，2018，www.