# Maintenance Method for Rail Corrugation Considering Wheel-Rail Interaction Force
## 4 Criteria of Rail Surface Roughness  
For the wheel-rail interaction force to be managed stably, the analytical dynamic wheel load due to rail corrugation wear should not be greater than the design dynamic wheel load. The rail surface roughness limits for different train speeds are presented in Figure 11. The maximum dynamic wheel load design value (121 kN) was calculated by multiplying the static wheel load of 80 kN by the impact factor of 1.513, and the rail surface roughness limit values were found to be approximately 1.0 and 0.8 mm when the train speed was 90 to 100 km/h. The impact factor was calculated using the formula presented in previous studies [22,30]. As the rail surface roughness increased, the dynamic wheel-rail interaction force was linearly proportional. In addition, the analysis results for the dynamic wheel-rail interaction force considering train speeds of 60 to 100 km/h showed that the slope of the increase in dynamic wheel-rail interaction force increased rapidly as the speed increased. In previous studies, [PERSON] [27] suggested that rails should be ground if the average rail roughness level of a track section exceeds the acceptable criterion. Therefore, the faster the train speed, the more conservatively the rail surface roughness must be managed. Owing to stably managing the wheel-rail interaction force below a certain level, it is desirable to plan and perform rail grinding before rail corrugation wear reaches the rail surface roughness limit. In this study, the upper and lower limits of rail surface roughness according to train speed are presented as results of wheel-rail interaction force analysis in Figure 12.  
Figure 11: Calculation of rail surface roughness management criteria (limit values) considering wheel–rail interaction force. Figure 10: Estimated and measured dynamic wheel loads: (**a**) Section A (before); (**b**) Section A (after); (**c**) Section B (before); (**d**) Section B (after). Figure 12: Calculation of rail surface roughness management criteria (upper and lower limits) considering wheel–rail interaction force: (**a**) train speed (V = 70 km/h); (**b**) train speed (V = 80 km/h); (**c**) train speed (V = 90 km/h); (**d**) train speed (V = 100 km/h). In actual track management sites, when the upper and lower limits of the rail surface roughness management standards are reached, priority or lower-priority rail grinding must be performed. However, it is realistically difficult to precisely control rail grinding during rail grinding work. In this study, the upper and lower limits of rail surface roughness according to train speed are presented in Figure 12 based on the results of wheel-rail interaction force analysis. The criteria for setting the lower limit of the rail surface roughness were applied to the (\(\pm\)) standard deviation value of the analysis model verified through this study. The (+) standard deviation value was excluded because it exceeded the maximum dynamic wheel load design value, and the (\(-\)) standard deviation was applied. The rail surface roughness value was calculated when the (\(-\)) standard deviation value was subtracted from the dynamic wheel load upper limit value (121 kN). As shown in Figure 12a, when the train speed is 70 km/h, the lower limit of the rail surface roughness is 0.095 mm, so the grinding should be performed according to the actual lower limit. However, in the field, if the rail grinding capacity is 0.02 mm per pass, it is desirable to grind five passes to remove 0.1 mm. Figure 12b shows that when the train speed is 80 km/h, four passes should be grinded to remove 0.08 mm. Figure 12c,d show that when the train speed is 90 and 100 km/h, three passes should be grinded to remove 0.06 mm. In addition, to promote the efficiency and convenience of rail grinding, it is also good to calculate the rail grinding pass numbers for the upper and lower limits of rail surface roughness by the train speed of the corresponding line.