Modeling of magnetic fields and signals of a ferromagnetic pipe flaw detector induced by a through hole defect

A numerical model has been developed for interaction of the magnetizing field of a short solenoid with a ferromagnetic pipe exhibiting a through hole in the wall, which takes into account nonlinear magnetic properties of the test object. This model was used to calculate spatial distribution of magnetic induction in the pipe wall and spatial distribution of the components of the magnetic induction vector near the pipe surface with a through hole. The validity of the numerical model was confirmed by physical modeling results. The results of theoretical and experimental studies were used to develop a simplified analytical model that describes behavior of the magnetic field of the defect and the electrical signal of the induction transducer of a magnetic flaw detector that implements the method of magnetic flux leakage. It is shown that the dependence of the signal of the induction transducer induced by the through hole on the gap is close to a linear one, and its dependence on the hole diameter is close to a quadratic one. The results obtained in the study can be used for creation, numerical modeling and measurement of magnetic fields.