## 3 Results and Discussion
### Flow Analysis Results  
The \(V_{piston}\) of the proposed MR damper was set to the range of \(-0.4\) m/s \(\leq V_{piston}\leq 0.4\) m/s to calculate the damping force in the main flow path, which is shown in Table 8 and Figures 24 and 25. \begin{table}
\begin{tabular}{c c c c} \hline \hline \multirow{2}{*}{**Ampere [A]**} & \multicolumn{3}{c}{**Magnetic Flux Density [T]**} & \multirow{2}{*}{**Error [\%]**} \\ \cline{2-3} \cline{5-5}  & **ANSYS Maxwell Model** & & **Permeance Model** \\ \hline
0.6 & 1.408 & 1.532 & 8.08\% \\ \hline
0.8 & 1.598 & 1.642 & 2.67\% \\ \hline
1.0 & 1.713 & 1.702 & \(-0.646\%\) \\ \hline \hline \end{tabular}
\end{table} 
Table 7: Comparison of ANSYS Maxwell and the permeance model. Figure 23: Yield stress according to the current. Figures 24 and 25 demonstrate the effect of the non-magnetic orifice on the damping force of the MR damper. In the case of a conventional MR damper without flow through a non-magnetic orifice, where only viscous damping in the gap and the MR fluid's damping effect due to the applied current are present, a significant variation in the total damping force is observed within the very low piston velocity range of \(-0.1\) m/s \(\leq V_{piston}\leq 0.1\) m/s, spanning approximately \(-479.39\) N \(\leq F_{damper}\leq 479.39\) N. Conversely, as seen in Figure 25, an MR damper with an auxiliary flow path containing a non-magnetic orifice exhibits a much smoother variation in total damping force within the same low piston velocity range, maintaining a range of approximately \(-270.22\) N \(\leq F_{damper}\leq 270.22\) N. This indicates that the damping force variation is reduced by about 56% compared to the conventional MR damper. Figure 24: Damping force in the gap according to the current. Figure 25: Total damping force in the proposed model. \begin{table}
\begin{tabular}{c c} \hline \hline
**Current [A]** & **Damping Force [N]** \\ \hline
0 & 0 \\ \hline
0.2 & 66.83 \\ \hline
0.6 & 258.98 \\ \hline
1 & 374.06 \\ \hline \hline \end{tabular}
\end{table} 
Table 8: Damping force according to the MR.  
damper. Therefore, in cases where vertical vibrations occur at low piston velocities, the \"block-up phenomenon\", characterized by abrupt shifts in damping force from positive to negative damping that degrade ride comfort, can be mitigated by incorporating a non-magnetic orifice. From Figures 24 and 25, it is possible to confirm the effect of the presence or absence of an orifice that is not affected by the magnetic field on the increase or decrease in the damping force of the damper. When only the viscous damping force in the gap and the damping force of the MR fluid according to the applied current are shown in Figure 24, the damping force of the damper changes rapidly at very low piston speeds. However, as shown in Figure 25, which shows the total damping force of the damper proposed in this study, the damping force changed slightly at low piston speeds with or without the additional flow path. In this study, to observe the damping force characteristics according to the shape of the additional flow path, the shape of the additional flow path was modified in the proposed MR damper, and the total damping force characteristics of the MR damper were confirmed accordingly. If the length of the additional flow path, \(L_{\mathit{office}}\), changed, then there was an overall change in the shape of the proposed MR damper. To prevent this, we checked the change in the damping force characteristics through changes in the diameter \(D_{\mathit{office}}\) of the additional flow path. The \(D_{\mathit{office}}\) of the proposed MR damper with an additional flow path was 1.1 mm. Observe the change when \(D_{\mathit{office}}\) increases or decreases, and calculate the total damping when \(D_{\mathit{office}}=1.2\) mm and \(D_{\mathit{office}}=1.0\) mm, which are values in an appropriate range that are not significantly affected by the magnetic field.