# One-Coil Long-Stroke Permanent Magnetic Actuator Design Applied to Load Breaker Switch for Railway
## 2 Permanent Magnet Actuator for Long-Stroke
### Holding Force  
Table 2 provides the specifications of the load breaker switch with double insulation applied in this study. This specification refers to the VI specification datasheet. The most important factor in the design of this load breaker switch was selecting the holding force. The holding force was obtained by adding the contact force + open spring force-VI vacuum hold force + margin. A margin of at least 300 N is recommended. If the margin is too high, it requires a higher increase in the electric current to offset the holding force during the opening operation, which prolongs the opening time. A long opening time is problematic if a circuit breaker is applied. A long opening time poses no problem if a load breaker switch is used.  
\begin{table}
\begin{tabular}{c c} \hline
**Specification** & **Values** \\ \hline Rated voltage (kV) & 29 \\ Short-time withstand current (kA) & 20 \\ Duration of short-circuit (s) & 1 \\ Rated normal current (A) & 2000 \\ Number of poles & 1 \\ VI Stroke (mm) & 21 \\ PMA stroke (mm) & 120 \\ Add contact force (N) & 1800 \\ VI vacuum hold force (N) & 315 \\ DS Contact spring force (N) & 500 \\ Open spring force (N) & Variable \\ VI Average closing speed (m/s) & 0.9\(\rightarrow\)1.3 \\ (1/2 of full stroke) & 1.1\(\rightarrow\)1.5 \\ VI Average opening speed (m/s) & 1.1\(\rightarrow\)1.5 \\ (1/2 of full stroke) & \\ \hline \end{tabular}
\end{table}
Table 2: Specifications of designed product.  
Figure 7: Flowchart for the development of one-coil long-stroke PMA.  
As the required holding force of a double-insulation load breaker switch needs to be adjusted according to the specifications while checking the characteristics of the open spring force, an overall holding force of 3500 to 4000 N was selected with the open spring force + margin as 1500 to 2000 N.  
Figure 8 shows the PMA holding force of the double-insulation load breaker switch and expresses magnetic flux density and magnetic flux vector with axisymmetric model analysis data from the finite element method. The empty space between plungers is intended for the open spring. The little space at the bottom core, which is in contact with the plunger, was designed to allow the air to leave during closing and opening operations and poses no problem to the operation due to the increased pressure. The results of FEM analysis showed the holding force is 3996 N and meets the required specifications for a load breaker switch.  
To confirm whether the FEM analysis value was suitable, a simplified prototype test-jig was produced and then the holding force was measured, as shown in Figure 9a. By connecting the pulling jig, the load cell, and the PMA plunger, the holding force as the load cell was pulled was measured, and this value was checked on the indicator. As shown in Table 3, The value measured by the load cell was about 3800 N, which was 5.2% different from the analysis value and confirmed that it achieved the holding force required for the load breaker switch. A flowchart of the holding force measurement with the prototype test-jig is illustrated in Figure 9b.  
\begin{table}
\begin{tabular}{c c c} \hline \hline
**Analysis Value (N)** & **Measurement Value (N)** & **Error (\%)** \\ \hline
3996 & 3800 & 5.2 \\ \hline \hline \end{tabular}
\end{table}
Table 3: Analysis value and measurement value error.  
Figure 8: Magnetic flux density and magnetic flux vector of PMA in (**a**) closed and (**b**) open states.