基于磁偶极子模型的材料缺陷漏磁检测正演问题的单元积分计算方法

摘要

In the magnetic flux leakage probing problem,the hypothesis that the magnetic charge is evenly distributed on the defective wall is not true,which is based on the magnetic dipole analysis model.The defective material is equivalent to the magnetic medium after magnetized.Considering the non-linearity of the material,the magnetic charge is non-uniformly distributed throughout the defective material and the defective wall.Therefore,considered the distribution of the magnetization strength in the area of the entire defective material,the vector sum of the magnetic dipole moments in the unit volume is equivalent to a magnetic dipole moment,as the source of the magnetic field.Based on the magnetic dipole model,the integral formula of the magnetic field generated by the magnetic medium of any unit is deduced,and the integral problem of the whole defective material is transformed into the superposition of several units.In this paper,the numerical integration method is used to solve the integral problem of any unit.Furthermore,this method is extended to the whole source region unit,and finally the calculation equation of the magnetic field at any field is obtained.The leakage magnetic field simulation model of the defective material was constructed by COMSOL multiphysics simulation software,and finally the simulation results were compared with the calculated results to verify the correctness of the method proposed in this paper.%在基于磁偶极子解析模型的漏磁检测正演问题中,已有文献关于磁荷在缺陷壁上均匀分布的假设不成立.磁化后的缺陷材料相当于磁媒质,考虑到材料的非线性,磁荷在整个缺陷材料内及缺陷壁上非均匀分布.所以,该文从磁化后整个缺陷材料区域中磁化强度的分布出发,将单位体积内的磁偶极矩的矢量和等效为一个磁偶极矩,并作为磁场源点.从磁偶极子模型出发,推导出任意单元的磁媒质在场点处产生的磁场的积分公式,将整个缺陷材料的积分问题转换为对若干单元进行积分后的叠加.对于任一单元的积分问题,采用数值积分方法求解,并将该方法扩展到整个源区单元,最终整理得到任一场点处磁场的计算方程.通过COMSOL多物理场仿真软件搭建缺陷材料的漏磁场仿真模型,将仿真结果与计算结果进行对比分析,验证该方法的有效性.