# The Impact of Hollow Wear on the Stability of High-Speed Railway Vehicles
## 3 Impact of Hollow Worn Wheel on Vehicle Stability
### An Evaluation of Vehicle Stability Using the Lateral Vibration Acceleration Method  
In order to monitor the safe operating status of vehicles, an alarm system is installed at the end of the bogie, and acceleration sensors are installed on the bogie frame that measures wheel-rail forces to provide a basis for speed limit processing. The acceleration of lateral vibration in the bogie frame is often utilized to assess the vehicle's lateral stability. As outlined in the Chinese national standard GB/T 5599-2019 [25], which details the criteria for evaluating dynamic performance and identifying tests for vehicles, real-time sampling of vibration acceleration above the axle box is carried out continuously within the maximum speed range during testing. Subsequently, the collected data undergo filtering using a band-pass filter set to a frequency range of 0.5 to 10 Hz. If the peak acceleration exceeds or reaches 8 m/s\({}^{2}\) six consecutive times, it indicates that the continuous lateral vibration of the bogie cannot converge, thereby determining that the bogie is laterally unstable. The maximum and average vibration accelerations at various speeds are derived from the lateral and vertical accelerations recorded at specific measurement points. Beyond these, the vehicle's operational stability and safety are gauged through additional indicators. The vertical and lateral forces that interacted between the wheel and rail are ascertained using force-measuring wheels [26]. The dynamic performance of the vehicle is evaluated by assessing whether the lateral force on the wheel axle, the derailment coefficient, and the wheel load reduction rate conform to the requisite standards [27]. The force acting laterally on the axle of the wheel must adhere to Equation (8):  
\[H_{max}\leq 0.85\times\left(1.5+\frac{P_{st1}+P_{st2}}{2}\right) \tag{8}\]  
where \(P_{st1}\) and \(P_{st2}\) are the static load of the left and right wheels, respectively; \(H_{max}\) is the peak value of the lateral force on the wheel axle. The derailment coefficient should comply with  
\[\frac{Q}{P}\leq 1.2 \tag{9}\]  
where \(Q\) is the lateral force exerted by the wheel at the climbing rail side on the rail, and \(P\) is the vertical force exerted by the wheel on the rail on the same side. The wheel load reduction rate should comply with  
\[\frac{\Delta P}{\overline{P}}\leq 0.65 \tag{10}\]  
where \(\Delta P\) is the load reduction of the wheel, and \(\overline{P}\) is the average wheel load on the side where loading or unloading occurs. The vehicle dynamics performance is shown in Figure 11 as the vehicle speed is gradually increased from 160 km/h to 300 km/h on a straight track, with a speed sampling step of 20 km/h. Figure 11a,b show the maximum vertical and lateral acceleration values of a carbody measured within this speed range. At the same speed, the difference in the maximum vertical acceleration among the five worn wheels is very small, but the difference in the maximum lateral acceleration is significant, especially for the worn wheels W4 and W5, which exhibit much greater lateral acceleration than the other wheels. This indicates that wheel hollow wear has a minor impact on the vertical vibration of the vehicle, but it has a significant effect on the lateral vibration. Figure 11: Vehicle dynamics performance. Figure 11c-e, respectively, depict the curves of wheel axle lateral force, derailment coefficient, and wheel load reduction rate as functions of speed for the five worn wheels. As the speed increases, the common characteristic of the wheel axle lateral force and derailment coefficient curves is that the slopes of the curves for worn wheels W4 and W5 are large, showing a significant difference from other tread surfaces. This indicates that once hollow wear reaches a certain depth, it significantly influences the lateral forces involved in the interaction between the wheel and rail. At the same time, the rate of wheel load reduction does not show a strong sensitivity to hollow wear, and no clear causal connection exists between the two.