## 4 Simulation and Experiment  
Since the numerical analysis of the VPP EM propulsion system is based on the design and numerical analysis of the LS-secondary DLIM, we now describe our validation of the equivalent circuit model. The intent of this experiment is to overcome the limited conditions in our laboratory, especially the lack of room to realize translational motion. Both the FEM simulation with Ansoft and the DLIM on the platform were designed according to DLIM parameters shown in Table 2, which are the same as those referenced in Section 1, namely, \(V_{\mathrm{s}}=4.5\) m/s, in the VPP EM propulsion. The distribution of the flux density and secondary eddy current, calculated in two-dimensional (2D) FEM, are shown in Figure 5, indicating that the LS-secondary DLIM operates in unsaturated condition. Figure 5b shows the distribution of secondary eddy current induced by three-phase space vector synthesis of primary excitations, which gradually decreases in each ladder along the motion \begin{table}
\begin{tabular}{c c c c c c c c c c} \hline \hline
**Supply** & **Category** & **Section** & \(q\) & \(V_{\mathrm{s}}\) **(m/s)** & \(f\) **(Hz)** & \(k_{a}\) & \begin{tabular}{c} **Displacement** \\ **(m)** \\ \end{tabular} & \
\begin{tabular}{c} **Performance Period** \\ **(s)** \\ \end{tabular} &
\begin{tabular}{c} **\(T_{e,max}\)** \\ **(k/m/m\({}^{2}\))** \\ \end{tabular} \\ \hline \multirow{4}{*}{10 kV} & Sections with & 1 & 1 & 340 & 300 & 1.44 & 172.81 & 6.18 & 33.2 \\  & a constant \(V_{\mathrm{s}}\) & 2 & 2 & 340 & 150 & 0.72 & 2254.41 & 17.59 & 17.4 \\  & a constant \(V_{\mathrm{s}}\) & 3 & 3 & 340 & 100 & 0.48 & 2979.75 & 11.5.1 & 29.4 \\  & Sum & - & - & - & - & 5405.97 & 35.28 & - \\ \cline{2-11}  & Sections with & 1 & 1 & 56.7 & 50 & 1.44 & 3.55 & 0.79 & 90.1 \\  & variable \(V_{\mathrm{s}}\) & 2 & 2 & 204 & 90 & 0.72 & 577.38 & 9.86 & 57.8 \\  & variable \(V_{\mathrm{s}}\) & 3 & 3 & 340 & 100 & 0.48 & 5052.85 & 24.65 & 29.4 \\  & Sum & - & - & - & - & 5633.78 & 35.30 & - \\ \hline \multirow{4}{*}{220 V} & Sections with & 1 & 18.9 & 210 & 1.44 & 4.89 & 2.17 & 6.57 \\  & a constant \(V_{\mathrm{s}}\) & 2 & 2 & 18.9 & 105 & 0.72 & 11.81 & 1.56 & 7.15 \\  & a constant \(V_{\mathrm{s}}\) & 3 & 3 & 18.9 & 70 & 0.48 & 54.72 & 3.37 & 6.27 \\  & Sum & - & - & - & - & 71.42 & 7.10 & - \\ \cline{1-1}  & & 1 & 4.5 & 50 & 1.44 & 56.02 & 17.38 & 1.76 \\ \cline{1-1}  & Sections with & 2 & 2 & 10.8 & 60 & 0.72 & 54.01 & 6.15 & 3.11 \\ \cline{1-1}  & variable \(V_{\mathrm{s}}\) & 3 & 3 & 18.9 & 70 & 0.48 & 54.72 & 3.37 & 6.27 \\ \cline{1-1}  & Sum & - & - & - & - & 164.76 & 26.89 & - \\ \hline \hline \end{tabular}
\end{table} 
Table 1: The variable pole pitch (VPP) electromagnetic (EM) propulsions analyzed in this paper. direction, in accordance with the distribution of eddy current amplitude referred to as [PERSON]'s model in Figure 2b. The structure of the platform is shown in Figure 6. Due to the space limitations, the LS-secondary was configured as an aluminum plate with a diameter of 0.74 m. The secondary motion can be considered to be a translational motion because it has a relatively larger diameter than the primary pole pitch. The characteristics of the LS-secondary DLIM are plotted in Figure 7, in which the theoretical, simulated and measured data are compared via fitting curves related to the slip of secondary speed. The relative error between the theoretical and the simulated results was less than 3.7%, which indicates that the results of the numerical analysis based on the equivalent circuit are consistent with the FEM results. For the most part, the relative error between the theoretical and measured ones was less than 10%, except for the power factor when the secondary slip approached 0.9. The measured power factor and measured thrust were relatively smaller than the theoretical data in general, which is much more clearly revealed via linear regression analysis in Figure 8, with 95% confidence intervals.