# The Impact of Hollow Wear on the Stability of High-Speed Railway Vehicles
## 1 Introduction  
The stability, safety, and comfort of the vehicle are crucial for the operation of railways as an efficient mode of transportation. Under high-speed, heavy-load, and long-term service conditions, the wear of wheel tread continuously intensifies. As the vehicle travel distance increases, lateral acceleration alarms on the bogies occur frequently during operation. Through maintenance of the vehicle, it is found that the wheels that reported the alarm exhibit varying degrees of hollow wear. Hollow wear primarily occurs in the vicinity of the nominal rolling circle on the tread of the wheel. This phenomenon is commonly observed in high-speed trains and subways,attributed to the significant curvature radius of the railway and the high flatness of the rails. [PERSON] [1; 2] conducted a comprehensive survey of wheel profiles for over 6700 wheels across a wide range of freight vehicles operating in North American freight railways. The survey revealed that a significant proportion of these wheels exhibited hollow wear shapes, and 45.5% of the wheels had hollow wear less than 0.25 mm, while 6.2% had wear exceeding 3 mm. Dynamic analysis further demonstrated that such hollow wheel shapes impair the steering ability of bogies, leading to increased rolling resistance and higher lateral forces between the wheels and rails. [PERSON] [3] monitored a certain number of EMUs in China over a certain period. The wheel wear data indicated that 69.29% of the wheels displayed hollow wear surpassing a depth of 0.2 mm. The lateral axle box acceleration spectra measured above the wheels indicated that, compared with new wheels, wheels with hollow wear had much higher amplitudes in the frequency range of 6-9 Hz. [PERSON] [4] developed a multibody dynamic model for the vehicle and examined how the instability was affected by the 'false wheel flange' resulting from hollow wear. Hollow wear not only affects the lateral stability of the vehicle, but also increases the stress in the contact area between the false flange of the wheel and rail, exacerbating rolling contact fatigue and plastic deformation of the wheel rail material [3; 5]. [PERSON] [6] explored how hollow wear influences the variability and vibrations experienced by a wagon, taking into account the importance of both single- and dual-point wheel-rail contact as key factors. Particularly, the presence of a hollow design resembling a false flange greatly enhances the extent of lateral movement in the wheelset, while erosion at the base of the wheel flange amplifies this problem. The above research indicates that different types of railway vehicles generally have hollow wear on the wheel tread after long-term operation, but the depth of hollow wear is different. Moreover, the impact of hollow wear on vehicle stability is not fixed, and is influenced by various factors such as railway environment, vehicle speed, and suspension system parameters. Considering the operating cost of railways, a certain level of hollow wear is allowed. However, once the wear reaches the specified threshold, it is necessary to repair the wheel profile through mechanical processing. In general, for low-speed wagons, a larger range of hollow wear values may be allowed, but high-speed EMUs are more sensitive to the wheels' geometric deviations than freight wagons. Therefore, hollow wear has a greater impact on the stability of vehicles at high speeds. The methods and standards for judging vehicle stability are not uniform. [PERSON] [7] revealed the characteristics of the lateral acceleration value or frequency spectrum of the bogie axle box through numerical simulation and actual testing. By measuring the vertical and lateral forces between the wheel and rail, the lateral force of the wheel axle, derailment coefficient, wheel load reduction rate, and other indicators, calculations can be performed to intuitively evaluate the stability of the vehicle [8; 9].