## Materials and Methods
### Electromagnetic Analysis  
When designing and manufacturing a magnetic bearing, choosing the right number of poles is essential. The number of poles was chosen to be eight after the design was optimized to improve performance, as shown in Figure 1. All the dimensions are listed in detail in Table 1. The upper electromagnets in the y direction (vertical) obtained 5 A, while the electromagnets on the left and right sides obtained 3.3 A in the x direction (horizontal). This was carried out to determine the maximum holding force. The holding force is heavily dependent on three major factors. The first factor is the size of the air gap between the legs and the shaft; the bigger the gap, the more the force needs to be given. The depth of the apparatus in the z direction is the second factor; double the depth equals double the force. Finally, the thickness of the crowns affects how much force may be generated [41]. Finding the highest holding force in the y direction was the biggest issue. The radial AMB generates the x-axis force and the y-axis force, two perpendicular radial forces. The current in each of the four electromagnets is independently regulated as the four electromagnets operate in differential mode. Figure 1 depicts an eight-pole radial magnetic bearing. Figure 2 depicts an electromagnet used to suspend a C-shaped core using magnetic forces. The dotted line denotes the major flux path. Figure 2 shows how the C-core's flux route lengths are defined. The winding has N turns. When set to its default state, the air gap has a length g. The I-shaped core position's coordinate location x is established in order for the air gap length to be \((\mathrm{g}-\mathrm{x})\). The reluctance of the magnetic circuit is defined as  
\[R=\frac{1f\mathrm{p}}{\mu mt\;S} \tag{1}\]  
where \(\mathrm{J_{fp}}\) = flux path length = 2D\({}_{\mathrm{U}}\), \(\mu mt\) = permeability in the material, and S = cross-section area of flux path. Figure 3 depicts a comparable circuit for the electromagnet's magnetic circuit. A constant (dc) magnetic circuit may be thought of in terms of MMF (voltage), flux (current), and reluctance (resistance), much like an electric circuit. The primary distinction is that magnetic reluctance, the \"dc voltage\" produced by the winding current, is an energy storage component as opposed to a loss component. Rg stands for the magnetic reluctance at the air gap, while Rc is the magnetic reluctance [42]. These magnetic reluctances are written as  
\[\mathrm{R_{g}}=\frac{g-x}{\mu \begin{table}
\begin{tabular}{c c} \hline \hline
**Parameter** & **Value** \\ \hline Height of the stack & 20 mm \\ \hline Shaft diameter & 24 mm \\ \hline Operating air gap & 1 mm (radial) \\ \hline The outer diameter of the MB & 100 mm \\ \hline The inner diameter of the MB & 31 mm \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Different parameters used. Figure 1: Radial active magnetic bearing. Figure 2: C-shaped cores. \[\mathrm{R_{c}}=\frac{2D_{i}+l}{\mu 0\mu rW} \tag{3}\]  
where  
\(\mu_{0}\) is the permeability of free space (\(\mu_{0}=4\pi\times 10^{-7}\) H/m). \(\mu_{r}\) is the relative permeability (\(\mu_{\mathrm{mt}}=\mu r\mu 0\)). The relative permeability of air is approximately equal to 1.0. The value of \(\mu r\) for iron is typically in the range of 1000-10,000. The magnetic reluctance in the iron may be disregarded in the following calculation since, in the majority of situations, the air gap reluctance is substantially more important than the iron reluctance.