## 4 Parameter Design  
In order to avoid magnetic saturation, the inner air gap bias flux is half of the saturation flux, that is \(\phi_{PRj}=\phi_{PCj}=\phi_{P0}=\phi_{s}/2\) (\(j=1\), \(2\), \(3\), \(4\), \(5\), \(6\)). Thus, the saturation flux density \(B_{\text{s}}=1.2\) T, and inner air gap bias flux density \(B_{\text{i}}=0.6\) T. According to (1)-(5), the relationship between the inner and outer air gap parameters is obtained as follows.  
\[\frac{g_{i}}{S_{i}}\cdot\frac{S_{o}}{g_{o}}=\frac{1}{4} \tag{9}\]  
According to equivalent control magnetic circuit, the relationships of the turn numbers of \(N_{o}\) and \(N_{i}\) can be described by  
\[N_{i}=N_{o}(\frac{S_{o}}{S_{o}+\frac{g_{o}S_{i}}{g_{i}}}) \tag{10}\]  
Substituting Equation (9) into Equation (10), it is assumed that the \(S_{o}=S_{i}\), the relationships between \(N_{i}\) and \(N_{o}\) is given by  
\[N_{o}:N_{i}=5:1 \tag{11}\]  
The turn numbers of suspension winding can be calculated by the following formula.  
\[N_{i}i=\frac{B_{\text{s}}g_{i}}{4\mu_{0}} \tag{12}\]  
As it is known that the demagnetization curve of NdFeB magnets is almost linear, the magnetomotive force \(F_{m}\) and flux \(\phi_{m}\) for operating point can be expressed as  
\[\left\{\begin{array}{l}F_{m}=F_{c}/2\\ \phi_{m}=\frac{\phi_{r}}{F_{c}}\cdot(F_{c}-F_{m})\end{array}\right. \tag{13}\]  
where \(F_{c}\) and \(\phi_{r}\) are the coercive magnetomotive force and residual magnetic flux of PM, respectively. \(\phi_{m}\) is the external magnetic circuit flux of PM.  
When the rotor is in the no-load state, the following equations can be obtained.  
\[\left\{\begin{array}{l}B_{0}=\frac{\mu_{0}F_{m}}{2\phi_{0}}\\ \phi_{m}=B_{0}S_{i}\end{array}\right. \tag{14}\]  
Combining (7), (13), and (14), the height and area of PM can be obtained as  
\[\left\{\begin{array}{l}H_{pm}=\frac{F_{c}}{H_{c}}=\frac{4B_{0}S_{i}}{\mu_{0} \Omega_{c}}\\ A_{pm}=\frac{\phi_{r}}{B_{m}}=\frac{2B_{0}S_{i}}{B_{m}}\end{array}\right. \tag{15}\]where \(H_{pm}\) is the length of the permanent magnet, \(H_{c}\) is the coercivity of the permanent magnet, \(A_{pm}\) is the sectional area of the permanent magnet, and \(B_{r}\) is the residual magnetic flux density of the permanent magnet.  
Therefore, as long as the required maximum suspension force is given, the main parameters of the proposed HMB can be designed according to the above design scheme. In this paper, an HMB with a suspension force of no less than 300 N is designed. Firstly, considering the processing accuracy, suspension winding current, and power consumption, the inner air gap length \(g_{\rm i}=0.5\) mm is selected. Thus, from Equation (10), the outer air gap length \(g_{o}=2\) mm. In order to make full use of the iron cores, improve the suspension force density, and then reduce the volume of HMB, the air gap saturation flux density \(B_{\rm s}=1.2\) T is selected. Therefore, the inner air gap flux density \(B_{0}\) generated by magnets is 0.6 T, and the inner air gap flux density generated by the suspension currents to obtain the maximum suspension force is also 0.6 T. Thus, from Equation (13), the ampere turns of inner control winding is 238.8 AT. Therefore, the ampere turns 240 AT are required, and the ampere turns of outer control winding is 1200 AT. From Equation (8), the pole area \(S_{\rm i}=302\) mm\({}^{2}\).