## 5 Analyses
It can be seen that the air gap control flux density at poles \(b\), \(Z\), \(c\), \(X\), \(a\), and \(Y\) is 0.6 T, 0.28 T, 0.28 T, 0.28 T, 0.6 T, 0.28 T, and 0.28 T, respectively. The flux, as shown in curve 1, is added with the bias flux shown in Figure 3c, which will produce a suspension force pointing in the \(-\)X direction. It can be seen from curve 2 that the air gap resultant flux densities of poles \(b\), \(Z\), \(c\), \(X\), \(a\), and \(Y\) are 1.2 T, 0.9 T, 0.32 T, 0 T, 0.32 T and 0.9 T, respectively. In this case, a suspension force pointing in the \(-\)X direction is indeed generated. Similarly, the air gap control flux and resultant flux to generate the suspension force in the \(-\)Y direction are calculated, and the waveforms are shown in curve 3 and curve 4 of Figure 6b. Figure 7 shows force-current relationships using the parametric analysis method. The currents \(i_{w1,4}=-2i_{w2,5}=-2i_{w3,6}=I\) are electrified to the three-phase windings, and \(I\) is changing from 0 A to 5 A. The calculation results are shown in Figure 7a. the force \(F_{\rm x}\) is generated, and the force-current relationships are basically linear. When the current is 4A, flux saturation occurs. In this case, the levitation force \(F_{\rm x}\) is 520 N, and the force \(F_{\rm y}\) is always 0 N. In Figure 7b, the currents \(i_{w1,4}=0\) A, \(i_{w2,5}=i_{w3,6}=I\) are electrified to the three-phase windings, and \(I\) is changing from 0 A to 5 A. It is clear that the force \(F_{\rm y}\) is generated, and when the current is 4 A, saturation has occurred. In this case, the suspension force \(F_{\rm y}\) is 297 N. However, the force \(F_{\rm x}\) is always 0 N. Under the unsaturated condition,  
Figure 5: The resultant flux distribution diagrams. (**a**) The resultant flux cloud diagram to generate \(F_{-\rm xmax}\) in the \(-\)X direction; (**b**) The resultant flux cloud diagram to generate \(F_{-\rm ymax}\) in the \(-\)Y direction. Figure 6: Waveform of the flux density. (**a**) The waveform of the air gap control flux density and resultant air gap flux density to generate \(F_{-\rm xmax}\) in the \(-\)X direction; (**b**) The waveform of the air gap control flux density and resultant air gap flux density to generate \(F_{-\rm xmax}\) in the \(-\)Y direction. the maximum suspension forces calculated by the finite element method basically coincide with the values calculated according to the Equation (8). The influences of rotor displacements on force-current relationships are calculated, and the results are shown in Figure 8. From Figure 8a, we calculate the curve of \(F_{y}/I_{y}\) when displacements X are \(-0.2\) mm, \(-0.1\) mm, \(0\) mm, \(0.2\) mm, and \(-0.2\) mm, respectively. It can be seen that the curve of \(F_{y}/I_{y}\) is linear when the rotor has the displacements in the X direction. In other words, the suspension force in the Y direction is not affected by the displacement in the X direction. A similar conclusion can be obtained by analyzing Figure 8b. The air gap length of the HMB designed in this paper is \(0.6\) mm. In fact, the allowable displacement of the magnetic suspension system is less than one-tenth of the air gap length. Therefore, when the rotor displacement is small, it can be considered that the suspension forces in X and Y directions are uncoupled. Finally, we build a prototype according to the design parameters. The STM 32H743 microcomputer and the PID control algorithm are used to realize the stable suspension of the rotor. The control system is shown in Figure 9. First, the current and displacement sensors detect the three-phase currents and radial displacements, respectively. The signals are input to the STM 32H743 microcontroller through the interface circuit for A/D sampling. In STM 32H743, the control algorithm is implemented, and the control signals are  
Figure 8: Influence of rotor displacement on force-current relationship.