# Maintenance Method for Rail Corrugation Considering Wheel-Rail Interaction Force
## 2 Materials and Methods
### Effect of Rail Grinding on Dynamic Track Response  
The track load (dynamic load, rail acceleration, rail and sleeper displacement) measurement results before and after rail grinding for trains operating in the section where rail corrugation occurred are shown in Figure 6a-f.  
As shown in Figure 6a, the results of measuring the track load before and after rail grinding showed that the peak value of the maximum response of the dynamic wheel load before rail grinding increased significantly due to the influence of the unevenness generated on the rail surface.  
As shown in Figure 6b, before rail grinding, the peak value of the maximum response of the rail acceleration was significantly increased due to the influence of the unevenness on the rail surface. On the other hand, after rail grinding, the unevenness was reduced,  
Figure 4: Measurement sensors.  
Figure 5: Examples of surface roughness measurement before and after grinding; (**a**) Section A-4; (**b**) Section B-4.  
and the peak value of the track response was significantly reduced compared to before rail grinding.  
The sleeper displacement and rail displacement are shown in Figure 6c-f, respectively. Before rail grinding, the peak value of the maximum response increased for the sleeper displacement and rail displacement due to the influence of unevenness on the rail surface. After rail grinding, the unevenness decreased, and the peak value of the track response decreased compared to before rail grinding.  
The maximum wheel loads and maximum accelerations of the rail measured on Sections A and B during the subway operations are presented in Figure 7. For Section A, the maximum wheel loads ranged from 120 to 154 kN before the grinding and were reduced to 61-80 kN after the grinding, which is approximately a 33-48% reduction, as shown in Figure 7a. The maximum accelerations of the rail also decreased from \(\pm\)30-40 m/s\({}^{2}\) to  
Figure 6: Examples of dynamic track response measurements on Section A: (**a**) wheel load; (**b**) acceleration of rail; (**c**) vertical displacement of sleeper; (**d**) detail of vertical displacement of sleeper; (**e**) vertical displacement of rail; (**f**) detail of vertical displacement of rail.  
\(\pm\)10 m/s\({}^{2}\) due to the grinding, as shown in Figure 7b. The maximum wheel loads and the maximum accelerations of the rail on Section B were larger than those on Section A but decreased to similar levels as on Section A after the grinding, as shown in Figure 7c,d.  
The maximum vertical displacements of the sleeper and rail on Section A were also reduced by the grinding, as shown in Figure 7e,f. Before the grinding, the maximum vertical displacements of the rail ranged from 2.5 to 2.7 mm, but they decreased to 2.1-2.3 mm after the grinding. The displacement of sleepers and rails due to rail grinding was reduced by approximately 18% and about 12%, respectively.  
Figure 7: Dynamic responses of track before and after grinding: (**a**) maximum wheel load (Section A); (**b**) maximum acceleration of rail (Section A); (**c**) vertical displacement of sleeper (Section B); (**d**) vertical displacement of rail (Section B); (**e**) maximum vertical displacement of rail on Section A; (**f**) maximum vertical displacement of sleeper on Section B.