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针对飞机多层金属结构中各类隐藏腐蚀导致的金属层减薄、层离间隙变化等问题,建立任意n层层叠导体结构脉冲涡流检测的电磁场理论模型,应用矢量磁势A推导得到了导体结构对线圈探头的反射系数,将之归纳为n个矩阵相乘的形式。进一步导出了同轴双线圈探头频域响应的积分表达式,并根据低频电磁场传播特性和偏微分方程理论,将二重广义积分转化为级数求和,采用快速傅里叶变换计算探头的瞬态响应,并与有限元时步法进行对比,验证理论推导的正确性,结果表明级数展开结合快速傅里叶变换是一种更快速有效的求解方法。
Aiming at the problems such as the thinning of the metal layer and the change of the layer-to-layer clearance caused by various hidden corrosion in the multi-layer metal structure of the aircraft, a theoretical electromagnetic field model of arbitrary eddy current detection of the n-layer laminated conductor structure is established. The vector structure A The reflection coefficient of the coil probe is summarized in the form of multiplication of n matrices. Based on the propagation characteristics of low-frequency electromagnetic field and the theory of partial differential equations, the double generalized integral is transformed into the summation of stages, and the fast Fourier transform is used to calculate the integral expression of the frequency domain response of the coaxial dual coil probe. Transient response, and compared with the finite element time-step method to verify the correctness of the theoretical derivation. The results show that the series expansion combined with Fast Fourier Transform is a faster and more efficient solution.