## 2 Design of the Permanent Magnet TCV
### Design of the Permanent Magnet  
In order to set the polarity direction of the permanent magnet, it was designed with four conditions, as shown in Figure 8. The polarity design condition of the permanent magnet is that even if the magnetic coil power is cut off, the magnetic force between the armature and the magnet core must be maintained over a certain level. Total electromagnetic force analysis was performed using a Maxwell V14 for the four polarities of a permanent magnet. A two-dimensional (2D) axisymmetric model was used for TCV. Figure 9 shows the total electromagnetic force according to the polarity of the permanent magnet by applying the N-35H standard of Nd-Fe-B material to the permanent magnet. In Figure 8a,b, when the polarity of the permanent magnet is located at the top and bottom, the total electromagnetic force is 0 N at the current 0 A, as shown in Figure 9. In the TCV with a permanent magnet in Figure 8a or Figure 8b, when power is applied, the armature moves to the magnet core, and when the power is cut off, the armature returns to its original position. Therefore, if the polarity of the permanent magnet is located at the top and bottom, the function of the conventional TCV is similar. As shown in Figure 8c,d, when the polarity \begin{table}
\begin{tabular}{c c} \hline
**Parameter** & **Values** \\ \hline Voltage (V) & 12 \\ \hline Resistance (Ohm) & 3.5 \\ \hline Conduct diameter (C\({}_{d}\):\(\Phi\)) & 0.3 \\ \hline Overall diameter (N\({}_{d}\):\(\Phi\)) & 0.345 \\ \hline Bobbin inner diameter (B\({}_{i}\):\(\Phi\)) & 8.5 \\ \hline Bobbin outer diameter (B\({}_{o}\):\(\Phi\)) & 16.1 \\ \hline Bobbin height (h:mm) & 12.8 \\ \hline Bobbin width (w:mm) & 3.3 \\ \hline Specific resistance (Ohm-mm) & 1.7E\(-\)0.5 \\ \hline Resistance per unit length (Ohm-mm) & 2.44E\(-\)0.4 \\ \hline Layer (turns) & 36.5 \\ \hline Step & 10 \\ \hline Magnetic coil turns & 360 \\ \hline Ampere turn & 1234 \\ \hline \end{tabular}
\end{table} 
Table 1: Design parameters of the magnetic coil winding. Figure 7: Schematic of the magnetic coil winding. of the permanent magnet is located at the inner diameter and outer diameter, the total electromagnetic force becomes more than 6 N at 0 A, as shown in Figure 9. In a TCV with a permanent magnet in Figure 8c,d, the armature moves to the magnet core when power is applied. However, even if the power is cut off, the magnetic force of the permanent magnet will not return the armature to its original position. Therefore, the polarity direction of the permanent magnet can be set to (c) or (d) in Figure 8.  
The permanent magnet design is shown in Figure 10. According to the polarity direction results in Figures 8 and 9, the inner diameter was set to N pole and the outer diameter to S pole. In addition, the small size of the permanent magnet facilitates magnetization and is designed with four sections in the axial direction to minimize material loss. To design the specifications of permanent magnets, total electromagnetic force analysis was performed for each permanent magnet specification. The material of the permanent magnet was selected as Nd-Fe-B. The designs were reviewed by applying N-35H, N-42H, N-48H, and N-50H according to the residual magnetic flux density and coercive force that affect the total electromagnetic force. Table 2 shows the residual magnetic flux density and coercive force values for each permanent magnet. Figure 8: Polarity direction of the permanent magnet. Figure 10: Design of the permanent magnet. Figure 9: Total electromagnetic force according to the polarity direction of the permanent magnet. Total electromagnetic force analysis was performed from an initial air gap of 0.47 mm between the armature and the magnet core to a stroke of 0.30 mm with the plunger moving. In the conventional TCV, the lower case material was applied as S10C and the electromagnetic force analysis was performed. Permanent magnet TCV has applied permanent magnets of N-35H, N-42H, N-48H, N-50H specifications to the lower case.