基于二阶矢量位的矩形截面回折线圈阻抗和脉冲磁场的解析建模与计算

Analytical modelling and calculation of impedance and pulsed magnetic field for rectangular meander coil based on second order potential

本文基于二阶矢量位建立了回折线圈的阻抗和磁场计算的解析模型,并提出了计算磁场脉冲响应的方法.根据回折线圈用于涡流检测和电磁超声检测时的通用模型,将回折线圈的阻抗和磁场计算问题转化为多个单匝矩形线圈阻抗和磁场的叠加问题.基于二阶矢量位和时谐电磁场方程,推导了回折线圈的频域标势表达式;利用标势与矢量磁位和磁通密度间的关系,推导了计算区域的磁通密度和式样表面涡流的频域解析计算公式;通过计算线圈的感应电势和阻抗变化表达式,得到了线圈阻抗的频域解析表达式;采用FFT-IFFT方法计算了脉冲磁场的时域响应.以一双层双分裂线圈和铝板试样为例进行计算,计算结果与实验结果以及时步有限元法计算结果相一致,验证了解析模型和计算方法的有效性和准确性,与时步有限元法相比,基于解析模型的计算很大程度上缩短了计算时间.

Meander coil is an important kind of coil configuration used in eddy current testing and electromagnetic acoustic testing. Owing to lack of analytical calculation formulas of impedance and magnetic field for meander coil, the analytical modeling is performed and a method of calculating pulsed response is presented. In terms of the general model for eddy current testing and electromagnetic acoustic testing, the calculation of impedance and pulsed magnetic field is transformed into the superposition of impedance and pulsed magnetic field of single rectangular coils. Based on the second order vector potential and the time harmonic magnetic field equations, the scalar potential analytical expressions of the meander coil are derived. Then the analytical expressions of magnetic flux in all solution area and eddy current in the specimen are obtained. By calculating the induction electric potential and the impedance change, the impedance analytical expression of the rectangular meander coil is derived. An FFT-IFFT method is used to calculate the time domain response to pulsed magnetic field. A model with an 8-meander double-layer double-bundle coil above an aluminium plate is used in calculation, and the results are in good agreement with the experimental result and the TSFEM calculation result, which verifies the analytical model and the accuracy of the calculation method. The analytical calculation largely shortens the calculation time compared with that by TSFEM method.