# Key Factors of the Initiation and Development of Polygonal Wear in the Wheels of a High-Speed Train
## 1 Introduction
The initiation mechanism of the polygonal wear of the locomotive wheels is not captured in this paper. [PERSON] et al. studied the mechanism of the ninth-order polygonal wear in wheels of metro trains with a linear induction motor using a detailed site test and observation [13]. They found that the resonant frequency of the first wheelset bending matched the exciting frequency of the ninth-order polygonal wear. When the first wheelset bending mode was excited, the period of lateral creepage and force between wheel and rail occurred. Furthermore, the ninth-order polygonal wear gradually appeared. [PERSON] et al. studied the mechanism of polygonal wear of high-speed train wheels through extensive field tests [14]. The operation speed of the tested train was 250 km/h, and the diameter of the wheels was 860 mm. The results showed that the mechanism of wheel polygonal wear of high-speed trains could be attributed to the excited resonance of the train-track coupling system in operation and changing the operating speed could suppress the development of polygonal wear effectively. In [13; 14], the authors conducted many experiments to investigate the mechanism of high-order polygonal wear, but both studies lacked in-depth theoretical research and numerical simulation. [PERSON] et al. studied the root cause of high-order polygonal wear [15]. Their study concluded that there was a \(\sim\)650 Hz bending mode of the rail segment between the front and rear wheelsets of the same bogie. This bending mode was identified as the primary contributor to polygonal wear. However, in the literature [15], the exciting frequency of the polygonal wear is 550-600 Hz, which does not match the bending mode frequency very well. The conclusions of this paper lack experimental verification. [PERSON] et al. presented a detailed investigation into the mechanism of metro wheel polygonal wear using on-site experiment numerical simulations [16]. The measurement results showed that more than 70% of the metro wheels had sixth- to eighth-order polygonal wear. In this paper, P2 resonance was suggested as the main contributor to polygonal wear, and the flexibility of the wheelset was also found to influence the formation of polygonal wear. However, this is not enough to explain the higher order polygonal wear, which occurred in high-speed conditions. The literature discussed above provides a certain understanding of wheel polygonal wear problems. However, thus far, consistent understanding on the mechanism of polygonal wear is lacking. To understand the mechanisms of the initiation and development of high-order polygonal wear of railway wheels clearly, this paper conducts a detailed investigation into the high-order polygonal wear of the high-speed trains in China via extensive experimental analysis and numerical simulation. The remainder of this manuscript is organised as follows: Section 2 analyses the data measured from more than 1000 sets of polygonal wheels in the field and provides information on the important relationship between polygonal wear order and wheel diameter size. Section 3 presents a simulation model to predict the initiation and development of polygonal wear. In Sections 4 and 5, the model is used to verify the key conditions of initiation and the development of high-order polygonal wear and to calculate the relationship between polygonal wear and high-speed development, train operation speed, and wheel diameter change.