## 2 Research Method
### Numerical Analysis Modeling
#### 2.2.3 Magnetic Circuit Model  
A magnetic circuit that generates the damping force \(F_{MR}\) generated by the yield stress of the fluid consists of a solenoid coil, core, and flux ring. The MR fluid inside the flow path acts as a magnetic path of the magnetic field generated by the solenoid coil. However, when magnetic saturation occurs in the magnetic path, the magnetic flux does not increase, and the remaining current is converted into Joule heat, which reduces the performance of the MR fluid. Therefore, an action point must be selected in the linear interval of the B-H diagram where self-saturation does not occur.  
For these calculations, dampers containing MR fluids were modeled using ANSYS Maxwell 2D. In the electromagnetic analysis setting, the shape mode was cylindrical based on the \(Z\)-axis, the analysis mode was magneto-static, and the damper was located at the center of a vacuum sphere with a diameter of 1 m. The electromagnetic force generated by the solenoid core was modeled as the product of the number of coil windings and the current. The modeled MR damper was designed as a two-road type to eliminate deviations based on the accumulator and operating direction. The cylinder and piston rod used a non-magnetic material, AL6061, to prevent magnetic flux from flowing out of the magnetic circuit and to secure mechanical rigidity. In contrast, AISI 1008, a ferromagnetic material, was used as the core and flux ring corresponding to the magnetic circuit, and copper was used as the solenoid coil. The empty space inside the flow path and damper was input by extracting several action points from the B-H graph of the fluid provided by the manufacturer of MRF-132 DG. The designed magnetic circuit and numerical values are shown in Table 3 and Figure 13, and the physical properties and B-H diagrams of the materials constituting the magnetic circuit are shown in Tables 4 and 5 and Figures 14 and 15, respectively.  
\begin{table}
\begin{tabular}{c c c} \hline
**Parameter** & **Value** & **Units** \\ \hline CG to front wheel & 1.02 & m \\ \hline CG to rear wheel & 1.9 & m \\ \hline Vehicle tread & 1.7 & m \\ \hline \end{tabular}
\end{table}
Table 2: _Cont._  
\begin{table}
\begin{tabular}{c c} \hline
**Parameters** & **Values** \\ \hline \(D_{coil}\) & 0.42 mm \\ \hline \(A_{\text{\it piston}}\) & 388.09 mm\({}^{2}\) \\ \hline \(A_{\text{\it red}}\) & 36 mm\({}^{2}\) \\ \hline \(D_{\text{\it gap}}\) & 1.1 mm\({}^{2}\) \\ \hline \(L_{\text{\it gap}}\) & 26.1 mm \\ \hline \(L_{\text{\it cylinder}}\) & 80 mm \\ \hline \(D_{\text{\it orifice}}\) & 1.1 mm \\ \hline \(A_{\text{\it core}}\) & 84.8 mm\({}^{2}\) \\ \hline \(L_{\text{\it orifice}}\) & 26.1 mm \\ \hline No. turns per coil & 162 turns \\ \hline current & 0.2–1.0 A \\ \hline \end{tabular}
\end{table}
Table 3: Design parameters for the proposed MR damper.  
\begin{table}
\begin{tabular}{c c} \hline \hline Core and Flux Ring & AISI 1008 \\ \hline MR fluid & LOAD Cooperation MRF-132 DG \\ \hline Cylinders and piston rod & AL6061 \\ \hline \hline \end{tabular}
\end{table}
Table 4: Magnetic circuit materials.  
Figure 14: B-H curve of MRF-132 DG.  
Figure 13: Magnetic circuit model of the MR damper designed by ANSYS Maxwell.  
Figure 15: B-H curve of AISI 1008.  
\begin{table}
\begin{tabular}{c c} \hline \hline
**Properties** & **Values** \\ \hline \hline \(P\) & 2950 kg/m\({}^{3}\) \\ \hline \(C\) & 2.5 \\ \hline \(\mu\) & 0.03 \\ \hline \hline \end{tabular}
\end{table}
Table 5: Properties of the MR fluids (MRF-132 DG) used in this study.