# Key Factors of the Initiation and Development of Polygonal Wear in the Wheels of a High-Speed Train
## 2 Characteristics of Polygonal Wear of High-Speed Wheels
Figure 5 denotes the diameter change in the wheels corresponding to the polygonal wear of different orders that occurred on this typical train. The wheels of the tested train had different diameters, and this was not done intentionally. This high-speed train was used as a test train for long-term follow-up investigations into the dynamic behaviours and wear states of wheels/rails. The diameters of the wheels of the train were different because of the wear and re-profiling caused by an increase in operational mileage. The polygonal wear and fatigue states of the wheels determine their metal cutting quantity during re-profiling. Therefore, the cutting quantities of the wheels in re-profiling were different. Figure 5 shows that the wheels with diameters of ~920 mm generated a 20 th-order polygonal wear; those with an 875 mm diameter produced 19 th-order wear; those with 830-840 mm diameters  
Figure 4: Results of the measured polygonal wear. formed 18 th-order polygonal wear. This clearly indicates that a decrease in the diameter leads to a decrease in the polygonal wear order. Furthermore, the measured results of the wheels of car 5 do not indicate polygonal wear in Figures 4 and 5 because the re-profiling of its wheels was conducted just before polygonal wear measurement. The exciting frequency of the polygonal wear is calculated as:  
\[f=\frac{v}{\pi D}\times n \tag{1}\]  
where \(f\) denotes the exciting frequency of the polygonal wear, \(v\) denotes the operating speed of the vehicle, \(D\) denotes the diameter of the wheel, and \(n\) represents the polygonal wear order. Equation (1) indicates that wheels with different diameters have different polygonal wear orders at the same exciting frequency. For the present test case, \(f\) is \(\sim\)570-580 Hz. This means that the wheels are excited in the frequency range of 570-580 Hz, and could produce the 18 th to 20 th order polygonal wear, corresponding to different wheel diameters. Therefore, it is necessary to clearly find where the 570-580 Hz vibrations are coming from (the vehicle or the track or their coupling resonance). That is the key to explaining the mechanism of initiation and development of high-order polygonal wear, and this will be further discussed later. The test results of the same train are shown in Figure 6. The first row in Figure 6 indicates the wheel diameter reduction from 920 to 830 mm; the second row denotes the polygonal wear described in the polar coordinate system corresponding to different wheel diameters; the third row illustrates the order of the polygonal wear, which is also called the roughness spectra of the polygonal wear. In the test, the train operation speed was 300 km/h. The interval of wheel re-profiling was 200,000 km. Figure 6 shows the states of polygonal wear at six different wheel diameters--920, 905, 875, 860, 840, and 830 mm. The nominal diameter of new wheels is 920 mm, and 830 mm is the diameter close to the end of the wheel use life. During service, the wheel diameter changes from large to small because of wear and re-profiling. Indeed, at wheel diameters of -920, 875, and 830-840 mm, a polygonal wear of the 20 th, 19 th, and 18 th orders occur, respectively. According to Equation (1), the passing frequencies of the polygonal wear of three different orders or the resultant exciting frequencies between the wheel and rail are -580 Hz at 300 km/h. Figure 6 further indicates that polygonal wear develops at a high rate at the three stages, at which the wheel diameters decreased in their whole use life, and they are,  
Figure 5: Polygonal wear of different orders corresponding to different wheel diameters. respectively, the initial stage of new wheel use, the wheel diameter near 875 mm, and the stage when the diameter is between 840 and 830 mm, in the present investigation case. Further, this phenomenon can be illustrated using Figure 5. For a wheel diameter around 905 and 860 mm, irregular wear with periodic character or equal-wavelength, or polygonal wear, is not serious.