Lorentz force evaluation: A new approximation method for defect reconstruction

We propose a new method for contactless, nondestructive evaluation of moving laminated conductors, the so-called Lorentz force evaluation (LFE). The Lorentz force (LF) exerting on a permanent magnet moving relative to the specimen is measured. We propose a novel fast forward calculation of the LF based on a three-dimensional finite volume discretization of the specimen and an approximation of defects using local current distributions in the defect region. The approximate solution is compared with solutions from detailed finite element models developed for parallelepipedic subsurface defects. We obtain differences in LF that range between 1.7% and 6.7%, indicating that our approximation method yields sufficient performance. Furthermore, a linear inverse solution based on the novel forward method is presented. We invert the experimental data measured from a subsurface flaw with the dimensions of 2 mm×2 mm×12 mm located within a laminated conductive bar. The reconstruction method yields the correct position of the flaw with an accuracy of 1 mm in each direction. The reconstruction results are compared with high-resolution finite element analysis of the same crack configuration. We obtain correct lateral positions of the cracks, although the depth estimation shows a slight bias.