Evaluation of defect depth in ferromagnetic materials via magnetic flux leakage method with a double Hall sensor

•A double Hall sensor configuration with a fixed lift-off interval is proposed to eliminate the lift-off effect.•The evaluation method of the defect depth is established through the MFL signals measured by double Hall sensor.•The proposed evaluation method based on double Hall sensor is unaffected by the lift-off effect in practical testing. In the magnetic flux leakage (MFL) testing method, a linear mapping is used for the direct evaluation of defects by applying a single Hall sensor to measure the signal under a certain lift-off value. Inevitably, the uncertainty of the lift-off value in practical testing affects the accuracy of the estimated defect size. To overcome this uncertainty in the lift-off value, this paper proposes a double Hall sensor configuration with a fixed lift-off interval, and establishes an evaluation method for the defect depth through the MFL signals measured by this sensor. The effectiveness of the proposed evaluation method is verified by theoretical analysis, with the double Hall sensor providing two different lift-off values above the surface of the specimen that characterize the tested defect. Based on the error between the measured signal characteristics induced by the tested defect and the predicted values from a fast calculation model, a particle swarm optimization algorithm is employed to realize accurate evaluation of the defect depth. Theoretical research shows that the characteristic values measured by the double Hall sensor enable the defect depth to be accurately estimated. The use of a double Hall sensor with a fixed lift-off interval allows the proposed evaluation method to compensate for the unknown lift-off value in practical testing.