Purpose

This paper aims to present a lightened 3D finite element model (FEM) for coupled electromagnetic thermal simulation of the induction thermography non-destructive testing (NDT) technique to reduce the computation time.

Design/methodology/approach

The time harmonic electromagnetic problem is expressed in A – ϕ formulation and lightened by using the surface impedance boundary condition (SIBC) applied to both the massive induction coil surface and the surface of conductor workpiece including open cracks. The external circuit is taken into account by using the impressed voltage or the impressed current formulation. The thermal diffusion in the workpiece is solved by using surface electromagnetic power density as thermal source.

Findings

The accuracy and the usefulness of the method for the design of the induction thermography NDT technique have been shown with acceptable deviation compared with a full FEM model. It is also observed that at high frequency, when the ratio between the local radius of the conductor and the skin depth is high, a very good accuracy can be obtained with the SIBC methods. At lower frequency, the effect of the curvature of the surface becomes significant. In this case, the use of the Mitzner’s impedance can help to correct the error.

Originality/value

The SIBC can be used for both massive coil and workpieces with open cracks to alleviate 3D FEMs of the coupled electrothermal model. The implementation in matrix form of the coupled electrothermal formulation is given in details. The comparisons with reference analytical solution and full 3D FEM show the accuracy and performance of the method. In the test case presented, the computation time is 6.6 times lower than the classical model.

中文翻译：

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利用SIBC模拟感应热成像NDT技术

目的

本文旨在提出一种简化的3D有限元模型（FEM），用于耦合感应热成像无损检测（NDT）技术的电磁热仿真，以减少计算时间。

设计/方法/方法

时间谐波电磁问题用A – ϕ公式表示，并通过使用适用于大型感应线圈表面和导体工件表面（包括开裂）的表面阻抗边界条件（SIBC）来减轻。通过使用外加电压或外加电流公式来考虑外部电路。通过使用表面电磁功率密度作为热源来解决工件中的热扩散。

发现

与完整的有限元模型相比，该方法在设计感应热成像无损检测技术上的准确性和实用性已经可以接受。还可以观察到，在高频下，当导体的局部半径与集肤深度之间的比率较高时，可以使用SIBC方法获得非常好的精度。在较低频率下，表面曲率的影响变得明显。在这种情况下，使用米兹纳阻抗可以帮助纠正误差。

创意/价值

SIBC可用于大型线圈和具有开裂裂纹的工件，以减轻耦合电热模型的3D FEM。给出了耦合电热制剂的矩阵形式的实施方案。与参考分析解决方案和完整的3D FEM的比较显示了该方法的准确性和性能。在给出的测试案例中，计算时间比经典模型少6.6倍。