中文摘要：

基于准静磁场条件下的Maxwell方程组,建立半无限大任意多层导电结构上方圆柱形线圈模型,推导线圈阻抗变化量的解析表达式。该表达式是含有Bessel函数积分的积分区域从零到无穷大的非常复杂的二重广义积分,并且被积函数在零点处有奇点。为选择合适的数值计算方法,证明线圈阻抗增量解析表达式的被积函数在零点处极限的存在性和极限值以及被积函数从零到无穷积分区域上的收敛性。在线圈阻抗增量的数值计算中分块化计算被积函数以提高计算效率,并采用自适应辛普森算法计算Bessel函数积分以提高计算精度。针对厚度检测问题进行仿真与试验验证。计算结果与试验结果吻合良好,表明研究结果是有效的,不仅有助于电涡流检测探头阻抗仿真器的建立,也可用于试验系统的参数优化。

英文摘要：

The cylindrical coil above arbitrary number of conductive plates is modeled and analytical closed-form solution to the impedance change of the coil is presented based on the Maxwell＇s equations under the quasi-static. The presented egpression is a very complicated double generalized integral, because it has a singularity at zero and an integral of Bessel function. To choose an appropriate numerical method, the limit for the integrand in the impedance change expression at zero is examined and the convergence over the interval from zero to plus infinity is also investigated. Then partition-based integrand precomputation method is used to calculate the integrand for higher efficiency and adaptive Simpson algorithm is employed to calculate the integral of Bessel function for better accuracy. Simulations and experiments are carried out for thickness measurement. Good agreement between the results demonstrates that the developed model and numerical calculation method are verified, which not only contribute s to the development of an analytical solver for probe impedance, but also can be used to optimize the parameters of experimental setup in eddy current testing.