# Key Factors of the Initiation and Development of Polygonal Wear in the Wheels of a High-Speed Train
## 1 Introduction  
Polygonal wear is uneven wear along the circumference of train wheels and its wavelength varies from a dozen centimetres to the entire circumference of the wheel [1; 2]. Polygonal wear with only one wavelength around the wheel circumference is called first-order polygonal wear (i.e., eccentric wear); that with two equal wavelengths is called second-order polygonal wear (i.e., elliptical wear); that with three equal wavelengths is called third-order polygonal wear, and so on. First-, second-, and third-order polygonal wear are considered low-order polygonal wear. In recent years, polygonal wear beyond the eighth order--defined as a high-order polygonal wear in the present research have often been detected on the wheels of high-speed trains, metro trains, and electric locomotives in China [2]. Polygonal wear increases wheel-rail interaction and has a considerable effect on the use life of the components of railway vehicles and tracks. Furthermore, it threatens operation safety [3]. Therefore, this problem has gradually become a matter of urgent public concern in the railway transportation industry in China, and globally, and thus, it has attracted the attention of many scholars over the last few years. [PERSON] identified polygonal wear phenomena on train wheels when he conducted research on the noise of intercity trains and studied the relationship between polygonal wear and noise in the frequency domain [4]. [PERSON] and [PERSON] reviewed the literature on wheel polygonal wear in 2000 and 2018, respectively, and in their review, they summarised numerical simulation models of polygonal wear and explanations on its initiation mechanism and development [2; 3]. [PERSON] developed a dynamics model of an ICE-1 high-speed Garman train to investigate the polygonal wear mechanism. In the model, the wheelset mass modelling included five parts (two wheels and three brake discs), and they were all regarded as rigid bodies [5; 6; 7]. Three-dimensional rotational spring-damper units were used as connections to characterize the bending and torsional properties of the wheelset. The results showed that the bending resonant modes of the wheelset were excited by the fluctuating vertical force of the wheel-rail, and this led to a scenario where the lateral creep force of the wheel-rail varied periodically and the polygonal wear occurred on the rolling circle of the wheel. Based on the [PERSON]'s simulation model, [PERSON] considered beam elements as connections instead of three-dimensional rotational spring dampers [8]. Then, the effect of rotational inertia, gravity, and the gyroscopic moment of the wheelset on the initiation of polygonal wear was considered. In addition, imbalance calculations and long-term wear simulation were performed. [PERSON] established a coupling dynamics model that included an elastic wheelset and two elastic rails to study the formation of polygonal wear [9]. The results showed that flexible deformations of the wheelset and rails, caused by their interaction, resulted in the initiation and development of polygonal wear. The first and second bending modes of the wheelset played an important role in initiating polygonal wear. This literature focused on the characteristics and mechanisms of low-order polygonal wear. [PERSON] proposed a finite element model of a wheelset's rolling contact with two rails using commercial finite element software to conduct research to identify the root cause of polygonal wear [10]. [PERSON] suggests that the self-excited vibration of the wheel-rail system leads to polygonal wear at a frequency of 150 Hz. A suitable sleeper support stiffness or wheel-rail friction coefficient can be controlled to limit the development of polygonal wear. [PERSON] et al. conducted extensive measurements of polygonal wear on electric locomotive wheels with radii of 1050-1200 mm at the average operation speed of 80 km/h [11; 12]. The measurement results showed that the dominant orders of the polygonal wear of locomotive wheels were 18 th, 19 th, and 24 th, and depended on wheel diameter.