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从准静磁场条件下的Maxwell方程组出发,采用矢量磁位法,推导了位于任意多层导电结构上方圆柱型电涡流探头的阻抗解析模型。在阻抗计算中引入符号运算法求解矢量磁位表达式系数,大大减小了程序计算量,提高了程序效率。将阻抗解析模型应用于单层和两层导电结构厚度检测,分别研究和分析了单层厚度、铝基体上铜涂镀层厚度及铜基体上铝涂镀层厚度变化对探头阻抗变化的影响规律。仿真及实验结果表明,所推导的理论模型正确,可应用于导电结构厚度和材料属性检测的反演以及电涡流检测系统的参数优化。
Starting from the Maxwell equations under quasi-static magnetic field, the impedance analytical model of a cylindrical eddy current probe located above an arbitrary multilayer conductive structure is deduced by the vector magnetic potential method. The symbolic algorithm is introduced into the impedance calculation to solve the coefficient expression of vector magnetic bit, which greatly reduces the computational complexity and improves the program efficiency. The impedance analytical model was applied to the thickness measurement of single and two conductive structures. The influence of single layer thickness, the thickness of copper coating on aluminum substrate and the thickness of aluminum coating on copper substrate on the impedance change of probe were studied and analyzed respectively. The simulation and experimental results show that the theoretical model is correct and can be applied to the inversion of the thickness of the conductive structure and the testing of the material properties and the parameter optimization of the eddy current testing system.