## 5 Conclusions  
This study presents a novel approach for determining the optimal gear ratio by considering the drive performance and fuel efficiency, as in traditional methods, as well as the relative damage to the drive shaft, wheel wear, and overall motor efficiency. By addressing durability factors like shaft wear and wheel maintenance alongside energy efficiency, this study offers a more holistic method for drivetrain optimization in electric trains. To achieve these insights, a performance model of the drivetrain and relative damage was developed, accompanied by a MATLAB-based simulator for quantitative performance analysis using real driving data.  
The performance simulator was used to evaluate the relative damage to the drive shaft and motor operating range and to calculate the average energy efficiency across various gear ratios. Since the actual driving data remains consistent regardless of gear ratio changes, it was assumed that the timing of wheel flange wear and profiling is determined solely by the travel distance, without influence from the gear ratio.  
The study results show that as the gear ratio increases, the relative damage on the input shaft decreases while it increases on the output shaft. Additionally, the average energy efficiency initially increases and then decreases.  
Figure 19: Pareto optimal points and utopia point for QD and efficiency.  
\begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Gear Ratio** & \(\mathbf{QD_{H}}\) & \(\mathbf{QD_{Out}}\) & **Efficiency (\%)** & **Euclidean Distance** \\ \hline \(r_{G}\): 5 & 0.091 & 3.86 & 89.21 & 1.003 \\ \(r_{G}\): 6 & 0.064 & 4.18 & 89.27 & 0.634 \\ \(r_{G}\): 7 & 0.048 & 4.44 & 88.92 & 0.869 \\ \(r_{G}\): 8 & 0.037 & 4.68 & 88.51 & 1.414 \\ \hline \hline \end{tabular}
\end{table}
Table 5: Euclidean distances for different gear ratios based on QD and efficiency. (Unit of QD: \(10^{20}\)_rev-Nm_[33; 33]).  
By considering the Pareto optimal points for each gear ratio, a utopia point was established where relative damage to both the input and output shafts is minimized, and the average energy efficiency is maximized. The optimal gear ratio was determined as the value minimizing the distance between each Pareto optimal point and the utopia point. This innovative approach to gear ratio optimization provides a practical and impactful method for enhancing both the performance and longevity of railway vehicles.  
Conceptualization, S.K., W.L., J.J. and D.K.; methodology, S.K. and W.L.; software, S.K. and W.L.; validation, S.K. and W.L.; formal analysis, S.K. and W.L.; investigation, S.K., W.L., J.J., and D.K.; resources, S.K. and W.L.; data curation, S.K. and W.L.; writing--original draft preparation, S.K. and W.L.; writing--review and editing, S.K., W.L., J.J. and D.K.; visualization, S.K. and W.L.; project administration, W.L.; and funding acquisition, W.L. All authors have read and agreed to the published version of the manuscript.  
The APC was funded by the Korea Agency for Infrastructure Technology Advancement (KAIA) grant funded by the Korean government (MOLIT) (no. RS-2021-KA164547, Development of Self-Powered and Wireless Safety Monitoring Technology for Railway Power Supply Systems).  
Not applicable.  
The original contributions presented in this study are included in the article and further inquiries can be directed to the corresponding author.  
The authors declare no conflicts of interest.