# Formation Mechanism of Metro Rail Corrugation Based on Wheel-Rail Stick-Slip Behaviors
## 5 Conclusions  
Based on the actual measurement on-site, the occurrence situation of rail corrugation was investigated first. Then, the formation mechanism of rail corrugation was explained from the theory of the wheel-rail contact stick-slip by analyzing the curve passing form of a single wheelset. Finally, the vehicle-track space rigid-flexible coupling model is used to study the relationship between the wheel-rail stick-slip characteristics and rail corrugation, and the wheel-rail contact stick-slip theory was verified. The following conclusions can be drawn:  
(1) The results of field investigation show that most of the rail corrugations occur on the inner rail surface of curve tracks with a radius less than 700 m, and the smaller the curve radius is, the more serious the rail corrugation is.  
(2) The analysis of the curve passing form of single wheelset shows that the wheel-rail lateral torsional stick-slip vibration is the main reason for the corrugation on the curve track, while the corrugation on the straight track may be related to the wheel-rail longitudinal torsional stick-slip vibration.  
(3) Based on the vehicle-track space rigid-flexible coupling model, the wheel-rail stick-slip characteristics on tracks with different curve radii were studied. On the small radius curve track, the lateral torsional stick-slip vibration of the inner rail-inner wheel of the guiding wheelset induces the generation of inner rail corrugation, and the lateral torsional stick-slip vibration of outer rail-outer wheel of the driven wheelset may also occur, but the intensity is weak and the probability is low. Therefore, on the small radius curve, the inner rail is worn seriously, while the outer rail is worn slightly or not. On the large radius curve track, the lateral torsional stick-slip vibration of inner rail-inner wheel of the guiding wheelset is also easy to cause the inner rail corrugation, but the degree of the inner rail corrugation is decreased compared with that on the small radius curve track. Corrugation is still not easy to be formed on the outer rail of a large radius curve, but if the rail surface is not smooth, it may cause the appearance of the outer rail corrugation. The formation mechanism of rail corrugation on the straight line is different from that on the curve line, which is mainly related to the wheel-rail longitudinal torsional stick-slip vibration. If the traction behavior of the vehicle changes suddenly [38] and the surface condition of the straight rail is not good [39], the wheel-rail longitudinal torsional stick-slip vibration may be aggravated, which may further lead to rail corrugation.  
(4) The conclusions of this paper can well explain the rail corrugation phenomenon on the curve and straight tracks, and also verify the theory of rail corrugation caused by wheel-rail contact stick-slip characteristics.  
Conceptualization, methodology, software, validation, formal analysis, investigation, writing-original draft preparation, writing-review and editing, Z.W. ([PERSON]): conceptualization, resources, writing-review and editing, supervision, project administration, funding acquisition, Z.L. ([PERSON]). All authors have read and agreed to the published version of the manuscript.  
This study was funded by the National Natural Science Foundation of China, grant number 11772230.  
Not applicable.  
Data Availability StatementAll data, models, and code generated or used during the study appear in the submitted article.