# Formation Mechanism of Metro Rail Corrugation Based on Wheel-Rail Stick-Slip Behaviors
## 1 Introduction  
Rail corrugation is a kind of periodic wavy wear, which frequently occurs on the running surface of a rail. Corrugation will not only excite the high-frequency dynamic load of the wheel and rail, leading to the deterioration of vehicle and track components, but also produces high-level noise and vibration, affecting the living environment of residents along the line. Rail corrugation has always been one of the urgent problems to be solved in the railway industry. If the corrugation phenomenon can be avoided without treatment, it can save a lot of human and material resources [1; 2; 3; 4]. For more than 100 years, railway researchers have carried out a large number of experiments and simulation studies on rail corrugation, and put forward many theories to explain it. Most of them attribute the causes of rail corrugation to the resonance of the vehicle-track system (such as the resonance of the wheel-rail dynamic force P2 [5; 6; 7; 8], bending/torsion resonance of the wheelset [9; 10; 11], the pinned-pinned resonance of track structure [12; 13; 14], etc. ), or the unstable self-excited vibration of wheel-rail system [15; 16; 17; 18]. To date, rail corrugation is still an active research field. In 2009, based on the literature investigation, [PERSON] [19] corrected rail corrugation to a frequency-fixed phenomenon and divided rail corrugation into the following six types: roaring rails, rutting, other P2 resonance, heavy haul, light rail, and trackform-specific. [PERSON] et al. [20; 21; 22; 23] considered that the friction self-excited vibration of wheel-rail system was the cause of rail corrugation under the condition of creep force saturation, and systematically studied the influencing parameters of rail corrugation. By analyzing the correlation between the passing frequency of rail corrugation and the natural frequency of the track, [PERSON] et al. [24] concluded that thenatural vibration characteristics of the track structure and vehicle passing speed were the key reasons for the occurrence of rail corrugation. [PERSON] et al. [9] studied the causes of rail corrugation in the small radius curve section with Cologne egg fasteners using field tests and numerical simulations; they found that the lateral vibration of the rail caused by the lateral mode of the wheelset was one of the causes in this section. Based on the vehicle-floating slab track coupling model, [PERSON] et al. [25] proposed the limit value of rail corrugation of metro floating slab track from the aspects of vehicle operation safety, stability, and vehicle-track dynamic interaction. Through field investigation, test, and numerical analysis, [PERSON] et al. [26] found that the rail corrugation of Cologne egg fastener track was related to the vertical bending vibration of the track structure, and the values of fastener stiffness and damping had a great influence on the rail corrugation. [PERSON] et al. [27] investigated the phenomenon of wavelength-fixed corrugation on the shear-type damping fastener track, and the results indicated that the phenomenon is related to the vertical dynamic responses of rail under the specific track form. [PERSON] et al. [28] established a three-dimensional finite element model with dynamic friction rolling contact, analyzed the system responses of track structure vibration mode, wheel-rail contact force, and rail wear, and obtained that the longitudinal vibration mode of track structure may be the dominant factor leading to the formation of short pitch corrugation. Vibration is the macroscopic manifestation of the vehicle-track system. As rail corrugation occurs in the wheel-rail contact zone, it is closely related to the wear of rail material. Therefore, it is more convincing to study the microscopic wheel-rail contact behaviors to reveal the formation mechanism of rail corrugation. For metro lines, rail corrugation mostly occurs in the small radius curve sections, and the corrugation of the inner rail is more serious than that of outer rail [29; 30].