# 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 Straight Line  
Referring to the actual line No. 8, the length of the straight line was set as 500 m, the track gauge was 1435 mm, the wheel-rail static coefficient of friction was 0.3, the initial irregularity was not considered on the rail surface, and the vehicle running speed was 70 km/h. The vehicle-track coupling model was used for calculation, and the corresponding wheel-rail stick-slip characteristic curves were obtained, as shown in Figures 12 and 13.  
Because the vehicle runs at a constant speed on the straight track, the traction force of the vehicle was constant, which was equal to the running resistance of the vehicle, and the motion state of the vehicle was also constant, therefore, the variation ranges of the wheel-rail creepages and adhesion coefficients were very small, as shown in Figures 12 and 13. The wheel-rail longitudinal stick-slip curves of the guiding wheelset and the driven wheelset on the straight line had similar shapes, but the ends of the two curves were different. The amplitudes of wheel-rail lateral stick-slip curves were consistent, but the variation range of wheel-rail lateral creepage of the driven wheelset was relatively large. With the increase of lateral creepage, the wheel-rail lateral adhesion coefficient remained unchanged, indicating that there was no wheel-rail torsional stick-slip vibration in the lateral direction. With the increase of longitudinal creepage, the wheel-rail longitudinal adhesion coefficient decreased first and then increased, that is, the wheel-rail longitudinal stick-slip curve had a negative slope phenomenon. However, the variation range of longitudinal creepage corresponding to the wheel-rail longitudinal stick-slip curve was very small, about 0.0000075, thus, the intensity of the wheel-rail longitudinal torsional stick-slip vibration was weak and it was not easy to form rail corrugation. If the traction behavior of the vehicle changes suddenly and the surface state of the straight rail is bad, the variation range of longitudinal creepage may be expanded, the wheel-rail longitudinal torsional stick-slip vibration will be intensified, and then rail corrugation will be generated, which may be the formation mechanism of rail corrugation on the measured straight section.  
Figure 12: Wheel–rail stick-slip relation curves of the guiding wheelset of straight line. (**a**) Wheel–rail longitudinal stick–slip curve, (**b**) Wheel–rail lateral stick–slip curve.  
Figure 13: Wheel–rail stick–slip relation curves of the driven wheelset of straight line. (**a**) Wheel–rail longitudinal stick–slip curve, (**b**) Wheel–rail lateral stick–slip curve.  
Through the analysis of the wheel-rail stick-slip characteristics on the straight line, it is found that the formation mechanism of rail corrugation on the straight line is different from that on the curve line. The formation of rail corrugation on the straight line is mainly related to the wheel-rail longitudinal torsional stick-slip vibration, while the formation of rail corrugation on the curve line is mainly related to the wheel-rail lateral torsional stick-slip vibration. This conclusion can well explain the corrugation situation on the measured line, and also verify the cause theory of rail corrugation described in Section 3.