## 3 Simulation Results and Analysis
### Obtaining the Optimal Exit Velocity  
Figure 6 displays the variation curves of the armature velocity with \(P\) and \(T\) for the PP and PN configuration launching devices with an inter-stage distance of \(D\) = 5 mm. Figure 7 displays the variation curves of the armature velocity with \(P\) and \(T\) for the PP and PN configuration launching devices with an inter-stage distance of \(D\) = 15 mm. Firstly, in the simulation of PP and PN configurations, the stationary armature is triggered from different initial positions, giving a certain increment to the first-stage triggering position \(P_{1}\) of the armature. The optimal \(P_{1}\) is obtained through successive experiments. In this process, although no pulse excitation current is applied to the subsequent three driving coils, the acceleration of the armature is still influenced by the induced currents in the subsequent three driving coils, which are induced by the excitation current in the first-stage coil. Figures 6a and 7a display the variation of armature velocity with the first-stage coil \(P_{1}\) for the PP and PN configurations of the launching device, respectively. It can be observed that these two configurations have the same optimal \(P_{1}\), and the armature velocity through the first-stage coil is slightly higher for the PP configuration compared to the PN configuration, which is due to the influence of the induced currents in the subsequent coils. Figure 6: The variation curves of the armature velocity with an inter-stage distance of \(D\) = 5 mm: (**a**) in the first-stage coil; (**b**) in the second-stage coil; (**c**) in the third-stage coil; and (**d**) in the fourth-stage coil. Based on the analysis above, the optimal triggering position \(P_{1}\) for the armature to reach the highest velocity in the first-stage drive coil of both configurations is determined. Then, the armature is accelerated with a certain initial velocity into the second-stage drive coil. In this article, the optimal triggering time \(T_{2}\) for the second-stage coil is obtained through successive experiments by incrementally varying the triggering time. Figures 6b and 7b display the variation of armature velocity with the triggering time \(T_{2}\) of the second-stage coil for the PP and PN configurations of the launching device, respectively. After obtaining the optimal triggering position \(P_{1}\) for the first-stage coil and the optimal triggering time \(T_{2}\) for the second-stage coil, the optimal triggering time \(T_{3}\) for the third-stage coil is obtained by incrementally changing the triggering time and conducting successive experiments. Figures 6c and 7c display the variation of armature velocity with the triggering time \(T_{3}\) of the third-stage coil for the PP and PN configurations of the launching device, respectively. Finally, the armature is accelerated using the optimal triggering positions and times for the first three stages. The optimal triggering time \(T_{4}\) for the fourth-stage coil is obtained by incrementally changing the triggering time and conducting successive experiments. Figures 6d and 7d display the variation of armature velocity with the triggering time \(T_{4}\) of the fourth-stage coil for the PP and PN configurations of the launching device, respectively. This article uses the optimal trigger timing obtained from simulations as the trigger sequence for the device. The trigger sequence is listed in Table 3. As can be seen from Figure 6, the optimal armature velocities after the second, third, and fourth stages of the PP configuration are higher than those of the PN configuration, and the triggering times of the PN configuration are delayed at each stage. However, in Figure 7, it is the PN configuration that achieves higher optimal armature velocities after the second, third, and fourth stages, while the triggering times of the PN configuration are also delayed at each stage.