# The Impact of Hollow Wear on the Stability of High-Speed Railway Vehicles
## 5 Discussion  
Based on the measured wheel profile, this paper examines how the hollow wear of wheels affects the geometric relationship between wheel-rail contact and the stability of the vehicle.  
With an increase in the vehicle's mileage, both the depth and width of the hollow wear intensifies, and the wheel equivalent conicity has nonlinear characteristics. And thus, the nominal equivalent conicity cannot accurately reflect the wheel-rail geometric contact relationship. It is more accurately depicted by using nonlinear equivalent conicity to reflect the contact relationship between worn wheel and rail.  
The critical speeds corresponding to different degrees of wheel hollow wear were obtained using the velocity-reducing method and the bifurcation configuration method. These methods indirectly assess the vehicle's stability by comparing the critical speeds with the vehicle's actual operating speed. The numerical results show that under the same wheel wear conditions, there is a certain difference in the critical speeds determined by the two methods. The bifurcation configuration method better reflects the transition process of the vehicle from stable operation to hunting instability. In addition, through the dynamic simulation of the vehicle system, the maximum vertical and lateral accelerations of the carbody and the lateral vibration acceleration of the bogie frame can be obtained. The data indicate that wheel tread hollow wear has a relatively small effect on the vertical vibration of the carbody, but a significant effect on the lateral vibration. This is because the contact points between the wheel and rail gradually spread to both sides of the hollow wear area, leading to increased lateral impacts between the wheel and rail. Slight hollow wear is not sensitive to speed, but when the hollow wear is severe, the lateral vibration acceleration of the bogie increases sharply. The conclusions drawn from the three methods show that as hollow wear intensifies, the critical speed of the vehicle decreases or the lateral acceleration of the bogie exceeds the limit. They are commonly used in suspension system design, wheel profile improvement, and vehicle system performance analysis.  
As the vehicle operates on the track, the sensors mounted on the body and bogie continuously capture the vibration acceleration data of both the body and frame in real time, allowing for intuitive monitoring of this information. The results from the simulation align with the actual functioning of the vehicle, demonstrating that hollow wear on the wheels considerably affects vehicle stability.  
In response to the vibration issues caused by hollow wear, the current practice of railway maintenance departments is to restore the standard profile of wheels through re-profiling. In the future, as an additive manufacturing method, the application of laser cladding technology in repairing hollow wear damage deserves further research.  
Figure 15: The lateral acceleration of the frame.  
**Author Contributions:** Conceptualization, L.Z. and J.H.; methodology, L.Z.; software, C.W.; validation, L.Z. and J.H.; formal analysis L.Z.; investigation, C.W.; resources, Z.L.; data curation, L.Z.; writing--original draft preparation, L.Z.; writing--review and editing, L.Z.; visualization, C.W.; supervision, J.H.; project administration, J.H. All authors have read and agreed to the published version of the manuscript.  
**Funding:** This research was funded by the National Natural Science Foundation of China (Grant No. 12393783), the Research and Development Project of Science and Technology of China Railway Corporation (N2023T011-B(JB)), and the Natural Science Foundation of Hunan Province (Grant No. 2021J40181).  
**Acknowledgments:** We would like to acknowledge the Central South University for providing the research facilities and laboratory space necessary for this study.  
**Conflicts of Interest:** The authors declare no conflict of interest.