# Key Factors of the Initiation and Development of Polygonal Wear in the Wheels of a High-Speed Train
## 5 Key Conditions of Initiation and Development of Polygonal Wear  
### Integral Multiple Condition  
The research results show that periodically fluctuating creepage (or slip) can lead to the initiation and development of polygonal wear, and the resonance of the coupling system of train and track can cause periodically fluctuating load and creepage of the wheel-rail. If the circumference of the wheel is nearly an integral multiple of the wavelength of the excited system resonance, it is regarded as a key condition for initiating the high-rate development of polygonal wear. This is called an integral multiple condition. As shown in Figure 16[12], the basic condition for wheel polygonal wear generation is more rigorous than that for rail corrugation formation because the rail is infinitely long and the corrugation in its development can extend infinitely along with its track. However, the perimeter of the rolling wheel is finite, and uneven wear along the wheel circumference will be superimposed circularly. The referenced start points of the uneven wear on the wheel running surface when the wheel rolls have different phases if the perimeter cannot be divided exactly by the wavelength of the uneven wear caused by the resonance. If so, the uneven wear or wheel polygonal wear develops very slowly. In the other case, wheel polygonal wear can develop very quickly. This case indicates that the changes in wheel perimeter because of the wear and re-profiling is nearly an integral multiple of the wavelength \(\lambda\) of the excited resonance of the wheel-rail system. In the following analysis case, the effect of the wheelset mode of 576 Hz on the development of polygonal wear was analysed under conditions where the operating speed was 300 km/h and the wheel diameter was 900 mm and 920 mm. Figure 17 shows the effect of the diameter difference. When the wheel had a 900 mm diameter at 300 km/h, its circumference was not an integral multiple of the wavelength (\(v\) = 300 km/h and \(f\) = 576 Hz), and when the wheel had a 920 mm diameter, at 300 km/h, the integral multiple condition was nearly satisfied. Thus, the calculated wear loss along  
Figure 16: Description of basic condition for wheel COR generation [12]. the circumferences of the two wheels with 50 rolling cycles showed a large difference at the 20 th order of polygonal wear, as shown in Figure 17.  
As shown in Figure 17, 20 th order polygonal wear occurs on wheels with two different diameters. However, it is obvious that polygonal wear is more serious on the wheel with a diameter of 920 mm, that satisfies the integral multiple condition nearly. Figure 18 shows the polygonal wear results obtained by superposing the uneven wear at different wheel rolling cycles (5 cycles, 25 cycles, and 50 cycles). Figure 18a,b indicates the results of the wheels with diameters of 920 mm and 900 mm, respectively. As shown in Figure 18a, it is obvious that the wear loss along the circumference with a wear superposition of different cycles has nearly the same phase, and the polygonal wear increased gradually and rapidly. As shown in Figure 18b, for a wheel with a diameter of 900 mm, the polygonal wear does not increase considerably, and it appears similar to the polygonal wear pattern of each cycling \"rotating\" or \"shifting\" around the circumference. Superposing the uneven wear of each cycling with different initial phases eliminates their peaks and valleys. This is because the referenced start points of the uneven wear at each rolling cycle have different phases if the perimeter is not an integral multiple of the wavelength of the uneven wear. If so, the polygonal wear develops very slowly. Figure 17: Calculated wear loss along the circumferences of wheels with two different diameters. Figure 18: Polygonal wear results obtained by superposing the uneven wear of the wheels rolling with cycles, (**a**) \(D\) = 920 mm, (**b**) \(D\) = 900 mm. The wheel diameter is an important parameter that can determine whether the wheel satisfies the integral multiple condition.