# Maintenance Method for Rail Corrugation Considering Wheel-Rail Interaction Force
## 1 Introduction  
Recently, various rail surface damages have occurred in urban railways during operation, with an increasing trend in rail corrugation. This issue has caused problems such as reduced riding quality and track impact. Maintenance for rail corrugation has largely relied on visual inspections by inspectors, with qualitative evaluations of the rail's condition. Consequently, the appropriate extent of rail grinding has not been evaluated, but grinding has instead been performed repeatedly without proper assessment. In Korea, [PERSON] [1] conducted field measurements on the Seoul Metropolitan subway for research on rail corrugation, analyzing its causes using frequency analysis based on the collected data. [PERSON] [2] studied appropriate rail surface management methods by analyzing wheel-rail interaction and examining the impact of rail grinding on the dynamic track interaction force through field measurements. [PERSON] [3] proposed a correlation existing between the rail surface quality index and track dynamic force, considering train load, and suggested a draft for a general railway rail grinding standard. [PERSON] and [PERSON] used the rail roughness value on a high-speed railway line using a vehicle-track dynamic interaction force analysis program to calculate the track impact leveland rail bending stress according to the roughness depth. They proposed a high-speed railway rail surface defect management standard [4]. [PERSON] studied the characteristics of the field measurement data on rail corrugation in the sharp curve section of the Gyeongbu High-Speed Railway and proposed a management measure for these sections [5]. [PERSON] and [PERSON] analyzed the correlation between the automatic operation mode of urban railway electric trains and rail corrugation resulting from traction and braking forces [6]. [PERSON] evaluated rail polishing effectiveness and performed wheel-rail interaction force analysis based on measured roughness data, predicting actual train passing tonnage [7]. [PERSON] et al. analyzed the types and causes of corrugation occurring on the rail surface. They also analyzed the occurrence status and characteristics of rail corrugation occurring in high-speed railway sections [8]. [PERSON] et al. [9] conducted indoor tests on used and new rails in the Seoul Metro operating section and proposed the optimal amount of grinding and grinding cycle for urban railway rails based on the test results. It was suggested that initial grinding be performed when the thickness is 0.3 mm or more, and maintenance grinding be performed when a rail defect occurs. [PERSON] [10] conducted related research to develop a rail corrugation measurement system and analysis software. The analysis was based on the weight, measurement speed, size, resolution, and measurement range of rail corrugation measurement systems used overseas. [PERSON] [11] examined the change in surface roughness through rail grinding in a high-speed railway operation section and analyzed the optimal number of rail grinding cycles by comparing the quality and effect based on the number of grinding cycles with international standards. The effects of roughness on the wheel-rail interaction force were analyzed using a dynamic wheel-rail model. As a result, a rail surface management method that takes into account the characteristics of the operating track can reduce rail surface defects and track damage by reducing dynamic track interaction forces. Overseas studies on rail corrugations have also been conducted. [PERSON] analyzed dynamic loads generated by initial roughness, which, in connection with driving, friction elasticity, and creep at the wheel-rail contact point, cause deformation of the initial wavelength. He further noted that the wheel-rail contact direction acts vertically and horizontally, with corrugation progressing due to dynamic loads [12]. [PERSON] et al. [13] conducted time and frequency studies on rail roughness in a curved ballasted track in the Paris Reseau Express Regional commuter train network.