## 5 Analyses  
According to the above analysis, the main parameters are designed and given in Table 1.  
According to Table 1, the analysis model is established by MagNet 3D. The stator and rotor core is made of silicon steel, and the high-performance NdFeB is used to provide bias magnetic fluxes. To prove the bias magnetic circuit, only the magnets are excited, and the windings are not energized. The bias flux cloud diagram and the magnetic line diagram are obtained as shown in Figure 3a,b. It can be concluded that the bias fluxes pass through the internal and external air gaps respectively which proves the correctness of the bias magnetic circuit design. Furthermore, the flux density waveform of internal air gaps is obtained in Figure 3c. The air gap flux densities under magnetic poles X, Y, Z, a, b, and c are all equal to 0.6T, and the design meets the requirements. To verify the design of the control magnetic circuits, the control fluxes to generate the maximum suspension forces \(F_{-xmax}\) and \(F_{-ymax}\) in the \(-\)X and \(-\)Y directions are simulated. According to the suspension mechanism and design parameters, to generate the maximum levitation force \(F_{-xmax}\), the currents \(i_{W1,4}=-4\) A, \(i_{W2,5}=i_{W3,6}=2\) A are necessary. The control flux distribution is shown in Figure 4a. Then, the control currents \(i_{W1,4}=0\) A, \(i_{W2,5}=i_{W3,6}=-4\) A are electrified to obtain \(F_{-ymax}\) in the \(-\)Y direction. The control flux distribution is shown in Figure 4b. It can be seen from the two figures that the control fluxes are symmetrically distributed, which is the same as the suspension mechanism. \begin{table}
\begin{tabular}{c c} \hline \hline
**Parameter** & **Value** \\ \hline Radial inner air gap length & 0.5 mm \\ Radial outer air gap length & 2 mm \\ Outer diameter of rotor & 50 mm \\ Outer diameter of stator & 106 mm \\ Number of outer winding turns & 240 \\ Number of inner winding turns & 60 \\ Axial length of magnetic pole & 45 mm \\ Outer diameter of PM & 68 mm \\ Inner diameter of PM & 50.5 mm \\ Area of inner magnetic pole & 302 mm\({}^{2}\) \\ Air gap bias flux & 0.6 T \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Parameters Of Model. To further verify the suspension mechanism, the control currents under the conditions of Figure 4 are excited together with the magnets. That is, the bias fluxes are superimposed with the control fluxes. The resultant flux distributions under the conditions of generating the maximum suspension forces in the \(-\)X and \(-\)Y directions are shown in Figure 5, respectively. It can be seen that the control flux breaks the balance of the air gap bias flux, resulting in the increase of the internal air gap flux in the \(-\)X and \(-\)Y directions, while the internal air gap flux in the opposite direction decreases. Therefore, according to the generation mechanism of Maxwell force, it can be concluded that in these two cases, the suspension force pointing to the \(-\)X and \(-\)Y directions does occur on the rotor. Furthermore, it can be found that the air gap flux density in the \(-\)X and \(-\)Y directions basically reaches the maximum value of 1.2 T, while the air gap flux density in the opposite directions is about 0 T. It is further proved that in these two ways, the maximum suspension forces in the \(-\)X and \(-\)Y directions is indeed produced. Figure 4: The control flux distribution diagram. (**a**) The flux cloud diagram generating negative \(F_{-\text{xmax}}\): (**b**) The flux cloud diagram generating negative \(F_{-\text{ymax}}\). Figure 3: Bias flux. (**a**) The flux cloud diagram; (**b**) The magnetic lines diagram; (**c**) The air gap flux density waveform. In order to further analyze the air gap flux density in detail, the air gap control flux density and air gap resultant flux density waveforms are given, as shown in Figure 6. In Figure 6a, curve 1 represents the air gap control flux waveform corresponding to Figure 4a, and curve 2 represents the air gap resultant flux waveform corresponding to Figure 5a.