# Key Factors of the Initiation and Development of Polygonal Wear in the Wheels of a High-Speed Train
## 4 Discussion on the Calculated Results of High-Order Polygonal Wear  
Wheels with different diameters have different wavenumbers of high-order polygonal wear; however, their exciting frequencies are the same and, in general, they are in the range of 570-580 Hz (as shown in Section 2). The wheelset discussed has a bending mode of 576 Hz (as shown in Section 3.1). It is obvious that the modal frequency is close to the exciting frequency of the polygonal wear at 300 km/h. An experimental analysis of the mechanism of high-order polygonal wear of high-speed trains was conducted [12]; in that study, the authors suggested that the mechanism of polygonal wear is attributed to the excited resonance of the train-track coupling system in operation through the field tests. Therefore, the mechanism of the polygonal wear should be further investigated by developing the simulation model that involves the flexible deformation (bending deformation) of the wheelset in this paper. The numerical simulation uses the vehicle-track rigid-flexible coupling dynamical model described in Section 3.1, and the track random roughness is used as an exciting input (Figure 12a,b). The speed of the train is 300 km/h and the diameter of the wheel is 920 mm. The normal contact forces and creepages are calculated. Figure 12c,d shows the comparisons of the calculated results for the flexible wheelset and the rigid wheelset in the frequency domain. Figure 12: _Cont._  
As shown in Figure 12c, the normal force of the flexible wheelset is slightly smaller than that of the rigid wheelset in the considered frequency domain. The difference between the normal forces of the two types of wheelset models is relatively large at 132 Hz, which is the sleeper passing frequency. Figure 12d shows the obvious peaks of the lateral creepages at approximately 88, 132, 144, 286, 385, and 576 Hz, and there are large differences between the flexible and rigid wheelset at these frequencies. The flexible wheelset modes of 88, 144, 286, 385, and 576 Hz need to have remarkable contribution to the polygonal wear corresponding to the peaks. However, the tested results in Section 1 show that the dominant polygonal wear are in the 18 th to 20 th order, which are related to 576 Hz. Therefore, the numerical simulation of the present paper focuses on the influence of the wheelset vibration mode of 576 Hz only and the other modes (88, 144, 286, and 385 Hz) are excluded in the simulation program when calculating polygonal wear. The wear model described in Section 3 is used to calculate the wear loss along the circumference of the wheel with 50 circles rolling. In the calculation, the track random roughness is used as an exciting input. Figure 13a,b show the calculated results of the wear loss along the circumferences of the two wheels with 50 rolling circles. One is a flexible wheelset and the other is a rigid wheelset. Figure 14a,b indicate their irregularity spectra corresponding to Figure 13a,b, respectively. From the calculated result, it is found that the flexible deformation of the wheelset either greatly contributes or leads to polygonal wear generation. Figure 12: (**a**) Vertical irregularity; (**b**) Lateral irregularity; (**c**) Normal contact forces; (**d**) Lateral creepages. Figure 13: Results of wear loss along the circumferences of the two wheels with rolling of 50 circles. (**a**) Flexible wheelset and (**b**) Rigid wheelset. Note that Figure 12d shows the peaks of the lateral creepage at 88, 132, 144, 286, 385, and 576 Hz. Furthermore, the wheel circumference is approximately within the integral multiples of the wavelengths of the vibration at 144, 286, and 576 Hz, at 300 km/h and at the 920 mm wheel diameter. This is a basic condition for the generation of polygonal wear at 144, 286 and 576 Hz. The polygonal wear of the corresponding 5 th, 10 th, and 20 th orders should start at the same time and develop quickly. However, the calculated result, as shown in Figure 14a, does not show the polygonal wear of the 5 th and 10 th orders.