## 2 Magnetorheological Suspension Structure Design
### Suspension Magnetic Circuit Design  
The purpose of magnetic circuit design is to select the appropriate magnetic circuit parameters and excitation coil. Due to the symmetry of the structure of the magnetorheological suspension magnetic circuit, only half of the magnetic circuit structure is selected as an example to facilitate the structural calculation. The structural diagram of each segment of the magnetic circuit is shown in Figure 5.  
In Figure 5, \(\mathrm{r_{2}-r_{1}}\) is the thickness depth of the excitation coil, \(\mathrm{L_{1}}\) is the height of the excitation coil from the bottom end of the magnetic core, \(\mathrm{L_{3}}\) is the thickness of the upper extruded plate, \(\mathrm{r_{3}}\) is the radius of the upper extruded plate, \(\mathrm{f}\) is the radius of the damping gap, and \(\mathrm{h_{0}}\) is the gap of the extrusion channel plate. The magnetic force line passes through the upper and lower magnetic cores of the magnetic circuit structure and the damping channel, in turn, to form a closed loop. According to the direction of the magnetic force line in different structures of the magnetic circuit, the suspended magnetic circuit is divided into 6 magnetoresitances, which are respectively used: \(\mathrm{R_{1}}\) is the upper plate magnetoresistive, \(\mathrm{R_{2}}\) is the outer ring area magnetoresistive of the plate gap, \(\mathrm{R_{3}}\) is the outer magnetic core magnetoresistive, \(\mathrm{R_{4}}\) is the bottom magnetic core magnetoresistive, \(\mathrm{R_{5}}\) is the extruded magnetic core magnetoresistive and \(\mathrm{R_{6}}\) is the inner ring magnetoresistive between the plates. The magnetic field line generated by the excitation coil passes successively through the area of the pair and then returns to the starting area to form a closed loop.  
Based on the calculation method of the magnetic circuit, the total reluctance calculated for the designed magnetic circuit is [13].  
\[R=R_{1}+R_{2}+R_{3}+R_{4}+R_{5}+R_{6} \tag{2}\]  
\[R_{1}=\frac{1}{\mu_{0}\mu_{1}\pi L_{3}} \tag{3}\]  
Figure 5: Structural diagram of each segment of the magnetic circuit.  
\[R_{2} = \frac{1}{\mu_{0}\mu_{2}\pi(r_{3}^{2}-r_{2}^{2})} \tag{4}\] \[R_{3} = \frac{L_{2}-h_{0}}{\mu_{0}\mu_{3}\pi(r_{3}^{2}-r_{2}^{2})}\] (5) \[R_{4} = \frac{1}{\mu_{0}\mu_{4}\pi L_{1}}\] (6) \[R_{5} = \frac{1}{\mu_{0}\mu_{5}\pi r_{1}^{2}}\] (7) \[R_{6} = \frac{1}{\mu_{0}\mu_{6}\pi r_{1}^{2}} \tag{8}\]  
where \(\mu_{0}\)--air permeability;  
The relative magnetic permeability of regions \(R_{2},\ R_{3},\ R_{4},\ R_{5},\ R_{6}\) are \(\mu_{2},\ \mu_{3},\ \mu_{4},\ \mu_{5}\), \(\mu_{6}\) respectively.  
According to the magnetic circuit theory, the magnetic induction intensity of the internal and external parts passing through the plate gap without considering magnetic leakage is expressed as [14]  
\[B_{2} = \frac{NI}{RS_{2}} \tag{9}\] \[B_{6} = \frac{NI}{RS_{6}} \tag{10}\]  
where \(S_{2}\)--the magnetic field line outside the plate gap intersects with the operational area of the magnetorheological; m\({}^{2}\).  
\(S_{6}\)--the magnetic field line inside the plate gap intersects with the operational area of the magnetorheological; m\({}^{2}\).  
N--number of turns of excitation coil.  
A--Current.  
At this juncture, it is imperative to uphold parity in the magnetic induction intensity both outside and inside the plate gap, as can be inferred from Equations (9) and (10). \(S_{2}\) and \(S_{6}\) ought to be equivalent. Given the orthogonal relationship between the magnetic field line and the upper extruded plate, we can derive:  
\[\pi\left(r_{4}^{2}-r_{2}^{2}\right)=\pi r_{1}^{2} \tag{11}\]  
Thus, according to Formula (11), it only needs to be true: \(r_{4}^{2}-r_{2}^{2}=r_{1}^{2}\).  
After consulting relevant literature and considering many factors, such as the space size of the designed magnetorheological suspension, the initial structural size design of the magnetic circuit is shown in Table 1[15].  
Table 1 shows the initial structure size of the magnetic circuit.