## 3 Structural Optimization and Characteristic Analysis of the Three-Phase AC Magnetic Separator
### Impacts of Mounting Tilt Angle  
In the alternating moving magnetic field, when the electromagnetic force of the magnetic particles is greater than the competitiveness of gravity and fluid resistance, the purpose of magnetic desulfurization can be achieved [18]. The tangential force (parallel to the surface of the three-phase AC magnetic separator) and radial force (perpendicular to the surface of the three-phase AC magnetic separator) generated by the gravity of magnetic particles gravity along the surface of the three-phase alternating current magnetic separator are closely related to the installation tilt angle of the device. Next, the influence of the installation angle of the device on the resultant force of the magnetic particles is analyzed. When the installation angles \(\theta\) of the three-phase AC magnetic separator are \(10^{\circ}\), \(30^{\circ}\), and \(60^{\circ}\), the tangential force and radial force caused by the gravity of magnetic particles of different particle sizes are shown in Tables 6 and 7, respectively. Figure 12: Electromagnetic force generated at different particle diameters. \begin{table}
\begin{tabular}{c c c c c c} \hline \hline
**The Size of** & **Electromagnetic** & **Electromagnetic** & **Friction/N** & **Resistance** & **Joint Force** & **Acceleration** \\
**Particle** & **Thrust/N** & **Pull/N** & **F\({}_{D}\)/N** & **/N** & **/m-s\({}^{-2}\)** \\ \hline
0.074 mm & \(0.6024\times 10^{-3}\) & \(4.6528\times 10^{-5}\) & \(1.2167\) & \(4.9914\) & \(4.8068\times 10^{-4}\) & 8.5561 \\  & & & \(\times 10^{-4}\) & \(\times 10^{-8}\) & \(10^{-4}\) & 6.5049 \\
0.10 mm & \(1.2075\times 10^{-3}\) & \(1.4152\times 10^{-4}\) & \(3.0558\) & \(6.7481\) & \(9.0185\times 10^{-4}\) & 6.5049 \\  & & & \(\times 10^{-4}\) & \(\times 10^{-8}\) & \(10^{-4}\) & 4.4555 \\ \hline \hline \end{tabular}
\end{table} 
Table 5: Various forces acting on magnetic particles. When the current is 5A, the force analysis of the magnetic particles on the three-phase AC magnetic separator is shown in Figure 13. The friction coefficient of the wear-resistant ceramic on the surface of the three-phase AC magnetic separator is 0.2, and the fluid resistance on the magnetic particles is obtained by the formula (3) \(F_{\mathrm{D}}=3\pi\eta\lambda\
u\), wherein \(\eta=17.6\times 10^{-6}\) pa-s. When the installation angle of the device is \(10^{\circ}\), \(30^{\circ}\), and \(60^{\circ}\), the specific values of the various forces applied to the magnetic particles are shown in Table 8.  
It can be known from Table 8 that, due to the large electromagnetic force received by the magnetic particles, the effect of gravity is small, so when the installation tilt angle of the three-phase AC magnetic separator increases, the acceleration change of the magnetic particles is not obvious. The diamagnetic particles are not affected by electromagnetic forces, so their gravity will affect the speed of their fall. \begin{table}
\begin{tabular}{c c c c} \hline \hline \multirow{2}{*}{**Installation Angle**} & \multicolumn{3}{c}{**The Size of Particle**} \\ \cline{2-4}  & **0.074 mm** & **0.10 mm** & **0.15 mm** \\ \hline \(10^{\circ}\) & \(1.71134\times 10^{-6}\) & \(4.2232\times 10^{-6}\) & \(1.4253\times 10^{-5}\) \\ \(30^{\circ}\) & \(5.13396\times 10^{-6}\) & \(1.2669\times 10^{-5}\) & \(4.2759\times 10^{-5}\) \\ \(60^{\circ}\) & \(1.02675\times 10^{-5}\) & \(2.5338\times 10^{-5}\) & \(8.5515\times 10^{-5}\) \\ \hline \hline \end{tabular}
\end{table} 
Table 6: Tangential forces(N) at different installation angles and different particle sizes.