## 2 Design of the Permanent Magnet TCV
### Design of the Permanent Magnet
Figure 11 shows the comparison of electromagnetic force and total electromagnetic force according to the stroke of the conventional TCV and the TCV to which the permanent magnet specification is applied. Figure 11a shows the results of the electromagnetic force and total electromagnetic force for each stroke when a current of 3.4 A is applied to the TCV. At 0.30 mm stroke, the total electromagnetic force was about 11.8% higher in permanent magnet TCV than conventional TCV and about 3.6% higher in 0 mm stroke. Because the total electromagnetic force of permanent magnet TCV is higher than that of conventional TCV, the initial use current can be lower than 3.4 A. However, the total electromagnetic force of TCV with permanent magnets of the N-35H, N-42H, N-48H, and N-50H specifications at 3.4 A were similar. As shown in Figure 11b, the conventional TCV does not generate any electromagnetic force at 0 A when the TCV is de-energized. Permanent magnet TCV exhibited a magnetic force of more than 5 N at 0 mm distance between plunger and sol-seat. TCV with N-50H specification permanent magnets showed the highest magnetic force of about 7.3 N. Therefore, the permanent magnet specification is designed as N-50H, which shows the highest magnetic force at 0 A when no current is supplied. \begin{table}
\begin{tabular}{c c c} \hline \hline  & **Parameter** & **Values** \\ \hline \multirow{2}{*}{N-35H} & Residual induction (T) & 1.16–1.22 \\  & Coercive force (KA/m) & 845 MIN \\ \hline \multirow{2}{*}{N-42H} & Residual induction (T) & 1.28–1.34 \\  & Coercive force (KA/m) & 938 MIN \\ \hline \multirow{2}{*}{N-48H} & Residual induction (T) & 1.36–1.43 \\  & Coercive force (KA/m) & 1000 MIN \\ \hline \multirow{2}{*}{N-50H} & Residual induction (T) & 1.39–1.46 \\  & Coercive force (KA/m) & 1035 MIN \\ \hline \multicolumn{2}{c}{Air gap (mm)} & 0.47 \\ \hline \multicolumn{2}{c}{Stroke (mm)} & 0.30 \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Design parameters of the permanent magnet. Figure 11: Total electromagnetic force for the permanent magnet specification: (**a**) total electromagnetic force for each stroke at 3.4 A; (**b**) total electromagnetic force for each stroke at 0 A. Figure 12 shows the electromagnetic force simulation results of the conventional TCV. Figure 12a,b shows the results of magnetic flux density and magnetic field strength when a current of 3.4 A is applied to the conventional TCV. This is the result at 0 mm of stroke where the plunger completely closes the sol-seat flow path. At 0 A, when no current is applied, the magnetic flux density and magnetic field strength are zero. Figure 13 shows the electromagnetic force for each stroke applying a current from \(-3.4\) A to 3.4 A. Conventional TCV showed the same value in left-right symmetry with respect to 0A. Figures 14 and 15 show the total electromagnetic force analysis results of TCV with N-50H permanent magnet applied. Figure 14 shows the magnetic flux density and magnetic flux strength at 3.4 A and 0 A. In the conventional TCV, the magnetic flux density and magnetic flux strength did not appear at 0 A, but in the permanent magnet TCV, the magnetic flux density and magnetic flux strength appeared even when no current was supplied. However, in the permanent magnet TCV, the magnetic flux density and magnetic flux strength were exhibited by the permanent magnet as shown in Figure 14c,d even when  
Figure 12: Conventional TCV: (**a**) magnetic flux density at 3.4 A; (**b**) magnetic field strength at 3.4 A.  
Figure 13: Electromagnetic force for each stroke in the conventional TCV. no current was supplied. Because the magnetism of permanent magnets is directional, a reverse current was supplied, as shown in Figure 15, to interrupt the flux flow between the magnetic material and the permanent magnet. Conventional TCV showed the same electromagnetic force at \(-3.4\) A and \(3.4\) A. However, for the permanent magnet TCV, the magnetic flux density and magnetic flux strength were greater when supplying a current of \(3.4\) A than \(-3.4\) A.