# New On-Line MFL Testing Method and Apparatus for Winding Mine Hoist Wire Rope
## 3 Analysis of the Novel Probe
### Open-Loop Permanent Magnetizer
The magnetically sensitive elements can be enclosed in ring probe shoes of varying diameters to detect wire ropes of varying diameters. A core is added between the two magnets for strength and mounting of the probe, but the two parts, the magnets and core, can still create a magnetic field for defect detection. The invention provides a device with integrated monetization and signal output, which has the advantages of small size, light weight and compatibility. It can adapt to some specimens with significant shake amplitudes and fast speeds. According to [PERSON]'s law in the magnetic circuit, the magnetic potential \(F\) of a ring-shaped permanent magnet can be expressed as the product of the reluctance and magnetic flux, and when the magnetic flux line passes through the air, the following equation can be obtained:  
\[F=\Phi_{1}\ R_{air}, \tag{1}\]  
where \(\Phi_{1}\) is magnetic flux outside of the permanent magnet, and \(R_{air}\) is the reluctance within the air. When the magnetic flux line passes through the magnetic core and the specimen of the wire rope, we can obtain  
\[F=\Phi_{2}\ (R_{left}+R_{specimen}+R_{right}), \tag{2}\]  
where \(\Phi_{2}\) is magnetic flux within the permanent magnet and the specimen, and \(R_{left}\) and \(R_{right}\) are the reluctance within the permanent magnet's left and right-side regions, respectively. By dividing Equation (1) by Equation (2), we can obtain the following relationships:  
\[\frac{\Phi_{1}}{\Phi_{2}}=\frac{R_{left}+R_{specimen}+R_{right}}{R_{air}}, \tag{3}\]  
\[\frac{\Phi_{1}}{\Phi_{1}+\Phi_{2}}=\frac{R_{left}+R_{specimen}+R_{right}}{R_ {left}+R_{specimen}+R_{right}+R_{air}}, \tag{4}\]  
The total magnetic flux produced by the ring-shaped permanent magnet of \(\Phi_{total}\) can be described as,  
\[\Phi_{total}=\Phi_{1}+\Phi_{2}, \tag{5}\]  
Thus, the magnetic dissipation rate \(\lambda\) of the permanent magnet in the new probe could be calculated as,  
\[\lambda=\frac{\Phi_{1}}{\Phi_{total}}=\frac{R_{left}+R_{specimen}+R_{right}} {R_{left}+R_{specimen}+R_{right}+R_{air}}, \tag{6}\]  
As Equation (6) shows the ratio of the flux leakage in the air by the excitation source to the total flux provided by the excitation source, in order to reduce the flux leakage in the air, it is necessary to reduce the magnetic dissipation rate \(\lambda\), i.e., to increase the flux inside the specimen and increase the magnetic saturation rate. The reluctance of \(R_{air}\) should be increased, or the parameters of \(R_{left}\), \(R_{right}\), and \(R_{specimen}\) should be decreased. As a result, the magnetic energy of the permanent magnet can be fully used. For the design of the open-loop permanent magnet detection sensor, the finite element method (FEM) simulation is used to analyze the effect of the magnetizer size on  
Figure 5: Detection principle of open-loop permanent magnetizers. the magnetic excitation performance of the defect, as shown in Figure 6. A finite element model is established for a steel bar with a diameter of 30 mm and a length of 1000 mm; the dimensions of the length \(\times\) width \(\times\) depth of the defect on its surface are 1 mm \(\times\) 1 mm \(\times\) 1 mm; and X52 steel is used as the material property. The MFL detector employs an open-magnetization method with a ring magnet and an intermediate magnetic core to form a magnetization loop, and a gap between the upper and lower magnetizers of the probe is 4 mm to allow for machining and assembly. The material of the magnet is NdFeB N52, which has a coercivity of 955,000 A/m, relative permeability of 1.21, and remanent magnetization of 1.45 T. The material property of the magnetic core is Q235 steel. The ring magnet and magnetic core have the same inner and outer diameters. Considering the magnetizing effect of the permanent ring magnet, the key dimensions of the magnetizer are the inner diameter (ID), the outer diameter (OD), the axial height of the magnet (H), and the axial length of the middle armature (L).