Approximate analytical solutions to eddy current field of a metal cylinder with a surface shallow defect

Analytical solutions to eddy current field of a pipe or cylinder with a surface defect is very important for eddy current NDT, but it is difficult to be deduced. In this paper, the perturbation method is used to get approximate analytical solutions. According to perturbation method, a surface shallow defect of a metal cylinder could be regarded as a perturbation of the boundary and then the eddy current field, boundary conditions and the normal to the surface could be expanded into a Taylor series. Thus, the eddy current field is divided into two parts: the eddy current field of an intact cylinder without any defects and the perturbance field caused by the defect. For the eddy current field of an intact cylinder is readily available, only the defect caused perturbance field is need to be solved and the problem of eddy current field of a cylinder with the surface defect is simplified. In this paper, we calculate coil impedance change which is caused by the perturbance field. Experiments with different defects are carried out and the calculated and experimental results have a good agreement which verifies the approximate analytical solutions.