## 4 Conclusions  
This study optimally designed an MR damper with an additional flow path for vehicle and road surface model excitation with sinusoidal frequency excitation. Using ANSYS and AMESim software, the movement of the upper part of a vehicle equipped with an MR damper with an additional flow path was observed to examine its damping performance. The following conclusions were obtained in this study:  
1. The MR damper with a non-magnetic orifice significantly reduces abrupt variations in damping force at very low piston velocities, decreasing force variation by approximately 56% compared to a conventional MR damper. This design modification effectively resolves the \"block-up phenomenon,\" resulting in smoother damping transitions and improved ride comfort during low-speed vertical vibrations;
2. The MR damper exhibits excellent performance in controlling the acceleration of the upper part of the vehicle by adjusting the applied current when the vehicle is driven at low and medium speeds. At 30 km/h, it could be adjusted by up to 37.9% from 0.0451 m/s\({}^{2}\) to 0.0622 m/s\({}^{2}\), and at 60 km/h it could be adjusted by up to 18.7% from 1.66 m/s\({}^{2}\) to 1.97 m/s\({}^{2}\);
3. The MR damper can significantly reduce the displacement, speed, and acceleration of the upper part of the vehicle owing to road excitation when the vehicle is driven at a high speed. The displacement decreased by up to 14.1% from 0.00708 m to 0.00608 m, the velocity decreased by up to 7.09% from 0.127 m/s to 0.118 m/s, and the acceleration decreased by up to 7.73% from 1.94 m/s\({}^{2}\) to 1.79 m/s\({}^{2}\). The MR damper has resolved the block-up phenomenon through the application of the additional flow path. Additionally, it was confirmed that the proposed MR damper has excellent performance in controlling the range of displacement, speed, and acceleration of the upper part of the vehicle at various vehicle speeds and sinusoidal road surface excitations. Future research will focus on validating the design method proposed in this study through the fabrication and testing of actual dampers, thereby enabling a more thorough evaluation of their performance in real-world applications. Additionally, further \begin{table}
\begin{tabular}{c c c} \hline \hline  & **Max Amplitude [m]** & **Period [s]** \\ \hline AMESim & 0.0143 & 1.20000 \\ \hline Theoretical Model & 0.013589 & 1.20012 \\ \hline Error [\%] & 5.23 & 0.01 \\ \hline \hline \end{tabular}
\end{table} 
Table 14: Comparison of AMESim and theoretical model. Figure 37: Result of AMESim and theoretical value when the vehicle velocity was 30 km/h. studies will be conducted on bump characteristics to analyze the response behavior under various driving conditions. Building upon these findings, the application of MR dampers to vehicle suspension systems is expected to enhance system performance and increase stability, leading to synergistic effects. These future research endeavors and their potential applications are anticipated to make a significant contribution to accelerating the practical implementation of MR damper technology. Methodology, M.K., S.Y., D.Y., C.J. and J.L. ; software, M.K., S.Y., D.Y. and C.J. ; validation, M.K., S.Y., D.Y. and C.J. ; formal analysis, M.K., S.Y., D.Y. and C.J. ; investigation, M.K., S.Y., D.Y. and C.J. ; data curation, M.K., S.Y., D.Y. and C.J. ; writing--original draft preparation, C.J. and S.W. ; writing--review and editing, J.L. ; supervision, J.L. ; project administration, J.L. ; funding acquisition, J.L. All authors have read and agreed to the published version of the manuscript. This research was funded by the Korea Institute of Energy Technology Evaluation and Planning (KETEP) and the Ministry of Trade, Industry & Energy (MOTIE) of the Republic of Korea (No. RS-2024-00398166). Not applicable. The data presented in this study are available on request from the corresponding author.