# Modeling and Design of a Novel 5-DOF AC-DC Hybrid Magnetic Bearing
## 4 Magnetic Analysis
### Suspension Force Analysis  
For a better analysis of the relationship between current and force, three different situations were analyzed through FEM and the equivalent magnetic circuit method. First, only the radial control current was applied, and the resulting FEM simulation and equivalent magnetic circuit analysis were performed. Figure 6 shows the relationship between forces in the radial direction and the radial current at the central position of the rotor.  
From the FEM results, it was found that the radial suspension force changed from \(-523.4\) to \(523.4\) N with the control current changing from \(-5\) to \(5\) A, and the result of the equivalent magnetic circuit indicated that the radial suspension force changed from \(-561.2\) to \(561.2\) N. Thus, the results of FEM were in accordance with the results of the equivalent magnetic circuit method. It is clear that the relationship was linear between the radial force \(F_{x}\) and the radial current.  
In the second experiment, the excitation of the axial current was only used, and the radial current was zero. The characteristics of the axial forces versus axial current at the equilibrium position of the rotor were analyzed using the FEM and equivalent magnetic circuit; the results are shown in Figure 7. Furthermore, the FEM results showed that the axial suspension force changed from \(-1183.6\) to \(1183.6\) N with the axial current changing from \(-5\) to \(5\) A. The calculation result of the equivalent magnetic circuit revealed that the axial suspension force changed from \(-1195.5\) to \(1195.5\) N. We can see that when the axial  
Figure 5: Magnetic flux density diagram: (**a**) radial bias fluxes, (**b**) axial bias fluxes, (**c**) radial fluxes, (**d**) axial fluxes, and (**e**) resultant fluxes.  
current was small, the axial suspension force was linear with the axial current, and the FEM analysis result was consistent with the theoretical result. With the increase in the axial current, the axial force of the FEM was less than that of the equivalent magnetic circuit due to the magnetic saturation. Therefore, the linearity and consistency were ideal when working in a small current range, which can meet the actual operation requirements.  
In the third experiment, under the condition of a simultaneous application of radial and axial current, Figure 8 shows the variation between the force in the radial and axial directions and the current at the central position. There are six curves in Figure 8, three of which represent \(F_{x}\), \(F_{y}\), and \(F_{z}\) calculated using FEM, and the other three represent \(F_{x}\), \(F_{y}\), and \(F_{z}\) calculated using the equivalent magnetic circuit. The results of the analysis showed that the suspension forces of the combined action of axial and radial control currents were basically the same as those of the separate action of the two control currents, which means that the radial control fluxes and axial control fluxes were basically uncoupled.  
The difference between the two methods mainly results from the consideration of flux leakage, eddy current loss, and magnetic saturation. The flux leakage, eddy current loss, and magnetic saturation were considered in the FEM analysis but neglected in the equivalent magnetic circuit model. Nevertheless, the correctness of theoretical analysis was proved by a comparison of its results with those found using the FEM analysis.  
Figure 6: The curves show the correlation between radial suspension forces and radial current.  
Figure 7: The curves show the correlation between axial suspension forces and axial current.