###### Abstract  
This study presents a method for determining the optimal gear ratio in electric trains by examining the effects of motor efficiency, wheel wear, and relative damage to the input and output shafts of the reduction gear. In electric trains, reduction gears and wheels are critical for converting the driving motor's torque and determining the motor's operational point, which in turn affects efficiency and durability. Over time, wheel wear from regular use and periodic profiling reduces the wheel radius, causing an effective increase in the gear ratio, which impacts the motor efficiency and load distribution across drivetrain components. This study models the dynamic behavior of the vehicle's drivetrain system using MATLAB/Simulink and incorporates real-world data on wheel wear to address the problem. Through simulations with varying gear ratios, it analyzes changes in motor efficiency and uses Miner's rule to assess the relative damage on the reduction gear's input and output shafts. The results enable the identification of a gear ratio that balances motor efficiency and reduces cumulative fatigue damage, which is especially important for maintaining long-term drivetrain durability. This approach provides a systematic way to enhance the overall performance and lifespan of electric train systems by selecting a gear ratio that optimally aligns efficiency and durability. miner's rule; revolution counting method; motor efficiency; gear ratio; quantified damage; longitudinal train dynamics; pareto optimal point; utopia point; Euclidian distance +
Footnote †: journal: Applied sciences  
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travel distance of electric trains requires efforts to simultaneously improve both drivetrain efficiency and durability. This study aims to determine the optimal reduction gear ratio to maximize the total travel distance, selecting an urban electric train as the research subject. To achieve this goal, a dynamic performance model of the target train and a MATLAB/Simulink-based performance simulator were developed. Using real driving data from the urban electric train, the simulator comprehensively analyzed changes in relative damage to the input and output shafts of the reduction gear and variations in the motor efficiency under different gear ratios. Damage analysis methods for the drivetrain can be classified into quantitative, detailed analysis methods, and qualitative methods that assess trends in relative damage. As an example of quantitative damage analysis, [PERSON] et al. (2018) proposed a fatigue life testing method using small samples and validated the simulation's effectiveness through finite element modeling using ABAQUS and fatigue life analysis with FE-SAFE, ultimately providing a quantitative fatigue life prediction [1]. Another example is the study by [PERSON] and [PERSON] (2014), who used a modified Lundberg-Palmgren model that incorporated geometric parameters, misalignment, and combined loading effects to predict the fatigue life of bearings. The authors validated their methodology by comparing it with experimental results [2]. Such studies demonstrate the need for sufficient experimental data and material information for quantitative fatigue life predictions. Consequently, in the early stages of development, where detailed data on components may not be fully available, qualitative analysis of relative damage is often more practical than quantitative damage analysis. This study applies [PERSON]'s rule as a method for analyzing relative damage. By applying this rule, the cumulative fatigue damage for each shaft was calculated according to the gear ratio, and based on this, the relative durability damage of the drivetrain was evaluated. Additionally, changes in the motor operating points were analyzed to assess variations in transmission efficiency within the drivetrain system.