# A Method for Detecting Surface Defects in Railhead by Magnetic Flux Leakage
## 4 Experimental Results and Analysis  
### Finite Element Simulation Results and Analysis  
The finite element analysis software used in this paper is ANSYS Maxwell. A two-dimensional model is built as shown in Figure 4. The yoke is made of ferromagnetic material. The excitation coil adopts 4000 turns copper wire. The DC excitation voltage is 60 V, and the lift-off between the yoke and the rail is 20 mm. Three detection points with a lift-off of 1 mm are set up above the rail, represented by the black dots in Figure 4, the middle detection point represents the main sensor, and the other two represent the auxiliary sensors. In MFL detection, a defect with a different depth or width has different magnetic leakage field. Therefore, it is necessary to simulate the effect of the defect depth and width on the MFL signal. Keep the defect width at 2 mm and change the defect depth to 1, 1.5, 2, 2.5, and 3 mm, respectively. The lift-off is 1 mm. The simulation results of the main sensor are shown in Figure 5. As the depth increases, the maximum and minimum of the signal gradually increases. When the sensors are arranged according to the minimum defect depth, the main and auxiliary sensor signal difference of a deeper defect is greater than that of the minimum depth defect. Figure 4: Simulation Model. Figure 5: _Cont._  
Then keep the defect depth at 1 mm and change the defect width to 1, 1.5, 2, 2.5, and 3 mm, respectively. The simulation results of the main sensor are shown in Figure 6. In the \(x\)-direction, the maximum and minimum of the signal gradually increase while the defect width increased from 1 mm to 2.5 mm and the maximum value of the 3 mm wide defect decreases slightly. In the \(z\)-direction, the increase in width makes the maximum and minimum of the signal gradually increase. When the sensors are arranged according to the minimum defect width, the main and auxiliary sensor signal difference of a wider defect is greater than that of the minimum width defect. Figure 5: Results with different depths. Figure 6: _Cont_. According to Figures 5 and 6, the larger the defect, the easier it is to detect the defect. Then combined with the calculation formula, the spacing of the sensors is set according to the defect size of 2 mm in width and 1 mm in depth. The lift-off is 1 mm. The magnetic leakage field distribution of the defect is shown by the blue curve in Figures 5 and 6. The optimal distance between auxiliary sensors 1 and 2 to the main sensor theory is \(a+\sqrt{bz_{0}+z_{0}{}^{2}}\) mm, which is 3.449 mm. The optimal distance between auxiliary sensors 3 and 4 to the main sensor is \(\sqrt{a^{2}+z_{0}{}^{2}}\) mm, which is 2.236 mm. That is to say, when the main sensor is directly above the defect, the auxiliary sensors 1 and 2 are at the minimum of the blue curve in Figures 5a and 6a. The auxiliary sensor 3 is at the maximum of the blue curve in Figures 5a and 6a. The auxiliary sensor 4 is at the minimum of the blue curve in Figures 5b and 6b. Such arrangement of the sensors can maximize the difference of the signals among the main and auxiliary sensors when detecting a defect that is 2 mm in width and 1 mm in depth. When the depth or width of the defect increases, if the position of the sensors remains unchanged, the signal difference among the main and auxiliary sensors will also increase according to Figures 5 and 6. As discussed in Section 3, the more significant the difference, the better the defect detection. Therefore, the sensors set according to small defects are also suitable for detecting large defects. The \(x\)-component of the three detection points at different distances is analyzed. The distance of the sensors is set to 3.000 mm, 3.449 mm, 4.000 mm, respectively, and the simulation results in the \(x\)-direction are shown in Figure 7a-c. According to the simulation results from Figure 7, with the increase of the distance between the auxiliary sensors and the main sensor, the phase difference of their signals is getting more and more significant.