# Formation Mechanism of Metro Rail Corrugation Based on Wheel-Rail Stick-Slip Behaviors
## 4 Analysis of Wheel-Rail Stick-Slip Characteristics
### Wheel-Rail Stick-Slip Characteristics of Large Radius Curve  
This section focuses on the wheel-rail stick-slip characteristics of a large radius curve. Referring to the measured line Section 4, the line-type composition is the same as Section 4.1, the circle curve radius was set as 700 m, the track superelevation was 50 mm, the track gauge was 1435 mm, the wheel-rail static coefficient of friction was 0.3, the rail surface was free of initial irregularity, and the running speed of vehicle on the circular curve was 64 km/h. By model calculation, the corresponding wheel-rail stick-slip curves could be obtained, as shown in Figures 10 and 11. Figure 10: _Cont._  
Figure 9: Wheel–rail stick–slip relation curves of the driven wheelset of small radius curve. (**a**) Longitudinal stick–slip curve of the outer wheel-outer rail, (**b**) Lateral stick–slip curve of the outer wheel-outer rail, (**c**) Longitudinal stick–slip curve of the inner wheel-inner rail, (**d**) Lateral stick–slip curve of the inner wheel-inner rail. Figure 11: Wheel–rail stick–slip relation curves of the driven wheelset of large radius curve. (**a**) Longitudinal stick–slip curve of the outer wheel-outer rail, (**b**) Lateral stick–slip curve of the outer wheel-outer rail, (**c**) Longitudinal stick–slip curve of the inner wheel-inner rail, (**d**) Lateral stick–slip curve of the inner wheel-inner rail. Figure 10: Wheel–rail stick–slip relation curves of guiding wheelset of large radius curve. (**a**) Longitudinal stick–slip curve of the outer wheel-outer rail, (**b**) Lateral stick–slip curve of the outer wheel-outer rail, (**c**) Longitudinal stick–slip curve of the inner wheel-inner rail, (**d**) Lateral stick–slip curve of the inner wheel-inner rail. As can be seen from Figure 10, similar to the case of the small radius curve, on the large radius curve track, the lateral stick-slip characteristic curve of the inner rail-inner wheel of the guiding wheelset also appears as a negative slope phenomenon, which indicates that the lateral relative slip of the inner rail-inner wheel occurs, resulting in the lateral torsional stick-slip vibration, and it is easy to induce the formation of corrugation on the inner rail surface. However, compared with the adhesion coefficient of 0.0084 required for the lateral torsional stick-slip vibration of the inner rail-inner wheel of the guiding wheelset on the small radius curve, the adhesion coefficient of 0.044 required for the lateral torsional stick-slip vibration of the inner rail-inner wheel of the guiding wheelset on the large radius curve is higher, thus the vibration intensity is weak and the occurrence probability is relatively low. There is no obvious negative slope in the other wheel-rail stick-slip characteristic curves, which illustrates that it will not produce corresponding torsional stick-slip vibration and has little influence on the formation of rail corrugation. It can be seen from Figure 11 that the lateral stick-slip characteristic curves of the outer rail-outer wheel and inner rail-inner wheel of the driven wheelset have some negative slope sections, and the negative slope range corresponding to the lateral stick-slip characteristic curve of the outer rail-outer wheel is more than that of the inner rail-inner wheel, which indicates that the lateral torsional stick-slip vibration of the driven wheelset has a certain influence on the formation of inner and outer rail corrugations. However, because the adhesion coefficients of the outer rail-outer wheel and inner rail-inner wheel of the driven wheelset are higher, which are 0.066 and 0.052, respectively, the vibration intensity is weak and the occurrence probability is low.