Research on Wheel Polygonal Wear Based on the Vehicle–Track Coupling Vibration of Metro

Abstract

Wheel polygonal wear of metro deteriorates the vibration environment of the vehicle system, potentially leading to resonance-induced fatigue failure of components. This poses serious risks to operational safety and increases maintenance costs. To address the adverse effects of wheel polygonal wear, dynamic tracking tests and numerical simulations were conducted. The modal analysis focused on the vehicle–track coupling system, incorporating various track structures to explore the formation mechanisms and key influencing factors of polygonization. Test results revealed dominant polygonal wear patterns of the seventh to ninth order, inducing forced vibrations in the 50–70 Hz frequency range. These frequencies closely match the P2 resonance frequency generated by wheel–rail interaction. When vehicle–track coupling is considered, the track’s frequency response shows multiple peaks within this range, indicating susceptibility to resonance excitation. Additionally, rail joint irregularities act as geometric excitation sources that trigger polygonal development, while the P2 force resonance mode plays a critical role in its amplification.

1. Introduction

With the rapid development of rail transit technologies, the exponential increase in passenger demand has imposed new technical requirements on urban rail systems [1]. In large-scale applications, numerous engineering and scientific challenges have emerged, with wheel polygonal wear being one of the most severe issues. This phenomenon disrupts the wheel–rail contact dynamics, intensifies wheel–rail interactions, and leads to abnormal vibrations and noise during train operations. Over time, such interactions result in uneven wear on wheels and rails, significantly affecting passenger comfort and the surrounding environment. Moreover, the persistent vibrations may induce fatigue failure or damage to key vehicle components [2,3], potentially jeopardizing normal operations and compromising driving safety. Consequently, an in-depth investigation into the mechanisms and impacts of wheel polygonal wear is urgently needed.

Wheel polygonal wear is an extremely complex process, and understanding the formation mechanism of this phenomenon holds significant theoretical importance and practical engineering value. Johansson and Andersson [4] proposed a train–track coupling dynamics model, integrating the long-term wear model to investigate wheel polygonal wear, and concluded that the P2 force resonance at approximately 40 Hz, along with the anti-resonance of the track in the vertical direction, contributes to the development of wheel polygonal wear. Tao [5] conducted field tests to study the metro wheel polygonal wear mechanism and found that the root cause of fifth- to eighth-order wheel polygonal wear with fixed wavelengths is attributed to P2 force resonance. Cai [6] et al. evaluated the harmonic characteristics of wheel–rail normal force by introducing swept frequency excitation into their vehicle–track coupling dynamics model. The results revealed that the vertical bending mode of rail between the front and rear bogie wheels significantly influences the dynamic response of wheel–rail forces and serves as a primary factor for high-order polygonal wear on high-speed train wheels. Yang [7] et al. performed field tests and simulation analysis on 13th- to 16th-order polygonal wear in metro vehicles, suggesting that P2 force resonance is primarily responsible for high-order polygonal wear while emphasizing that first-order bending vibration of wheelset exacerbates such phenomena. Qu [8] et al., through bench mode tests on rail sections between bogie wheelbases, confirmed the existence of local bending modes within these intervals, attributing them as causes for wheel polygonal formation due to resonant effects. Recent studies by scholars have made significant progress in understanding and addressing issues related to wheel polygonal wear [9,10].

Previous studies on the coupling relationship between vehicles and tracks in the context of wheel polygonal wear have primarily focused on simplified rail structures, often overlooking the impact of diverse track types. This study addresses that gap by developing vehicle–track coupling models that incorporate different track structures, based on dynamic tests of polygonal wear observed in metro systems. Initially, the characteristics of wheel polygonal wear and its correlation with track structure are identified through field measurement analysis. Subsequently, vertical coupling models corresponding to various track configurations are constructed to perform numerical simulations, modal analysis, and validation. These analyses reveal the interaction among wheel–rail dynamic response, low-order vertical bending modes of the rail, and the development of polygonal wear under coupled vibration conditions. The results demonstrate that the primary contributor to polygonal wear under vehicle–track coupling is the resonance mode induced by the wheel–rail P2 force.

2. Field Test of Vehicle System

2.1. Polygonal Measurement

To investigate the distribution characteristics and evolution patterns of polygonal wear on metro vehicle wheels, a comprehensive tread wear test was conducted on vehicles operating along a specific metro line. The study summarized the observed wear characteristics and underlying patterns. Four identical trains operating on the same line were selected to represent different stages of wheel wear, designated as Train A, Train B, Train C, and Train D. All trains share a nominal rolling circle radius of 0.42 m. The trains were chosen such that their operating mileage since the last wheel re-profiling increases sequentially, with Train A having the shortest mileage and thus exhibiting the best-preserved wheel tread profile. Figure 1 presents both the manifestation of wheel polygonal wear and the corresponding wheel tread roughness measurements [11].

Figure 2 presents the average wheel tread roughness for all wheels from each of the four trains, as obtained from the wear test. Comparative analysis reveals that Train A maintains a favorable roughness profile, exhibiting no significant polygonal wear aside from the first-order eccentricity component. In contrast, the other three trains display distinct signs of eighth-order polygonal wear in addition to the first-order eccentricity. Among them, Trains B and C show relatively moderate roughness levels, with maximum average amplitudes of 9.7 dB Re 1 μm and 14.7 dB Re 1 μm, respectively, both remaining below the 15 dB Re 1 μm threshold. Train D, which has the longest operating mileage since its last wheel re-profiling, demonstrates the most severe polygonal wear, with average amplitudes approaching 25 dB Re 1 μm, and peak values for individual wheels reaching up to 30 dB Re 1 μm during testing. These results suggest that low-order polygonal wear, particularly eighth-order components, predominantly characterizes metro vehicle wheel wear within the studied range, and that such wear becomes increasingly pronounced with cumulative operating mileage.

In response to the polygonal wear observed in the metro train wheel tests, Train D was selected for wheel re-profiling, and a comparative analysis of wheel roughness before and after re-profiling was conducted. Figure 3 presents the comparison results for a representative wheel exhibiting a typical eighth-order polygonal pattern. In this figure, the black thin solid lines represent the roughness results of all eight wheels from a selected vehicle in Train D, while the red and blue thick solid lines correspond to a representative eighth-order polygonal wheel before and after re-profiling, respectively. As shown in Figure 3a, before re-profiling, the wheel profiles exhibited distinct polygonal shapes with significant fluctuations in the irregularity amplitude, clearly identifying polygonal orders in the range of 7–9. For the representative eighth-order polygonal wheel, the re-profiling process led to a marked improvement in profile roundness, with a substantial reduction in the irregularity amplitude. Figure 3b shows the corresponding roughness levels, indicating that polygonal irregularities were more severe before re-profiling, particularly the prominent eighth-order component, which exhibited roughness amplitudes exceeding 20 dB Re 1 μm. However, the roundness levels of each lower order have significantly decreased after wheel re-profiling within an acceptable range, the roughness level amplitude of the eighth-order wheel polygon has also decreased to near 0 dB Re 1 μm, and no evident polygonal phenomenon was observed.

The results of the polygonal wear test on the wheels of Train D indicate that most of the wheels show significant polygonal wear. Statistical data shows that out of a total of 48 wheels, nearly 35 exhibit obvious polygonal wear, accounting for approximately 73%. These polygons are mainly concentrated in low order, mostly manifested as eighth order. The order of wheel polygonal wear often serves as a critical characteristic parameter that determines the excitation frequency associated with such wear phenomenon. For metro vehicles operating at speeds of 50–70 km/h, the eighth-order polygonal wheels correspond to the characteristic frequency range of 42.1–58.9 Hz [12,13].

$$f_{\mathrm{OOR}}={\displaystyle \frac{N_{\mathrm{OOR}}V}{2\pi R_{\mathrm{w}}}}={\displaystyle \frac{8\times (50~70)/3.6}{2\pi \times 0.42}}$$

(1)

where $f_{\mathrm{OOR}}$ is the characteristic frequency of wheel polygonal wear; $V$ is vehicle operating speed; $R_{\mathrm{w}}$ is wheel radius; and $N_{\mathrm{OOR}}$ is polygon wear order.

2.2. Dynamics Testing and Analysis

Train D, which exhibited the most severe polygonal wear among the tested vehicles, was selected for vehicle dynamics testing. The test was conducted under two operating conditions: before and after wheel re-profiling. Acceleration sensors were installed on key structural components of the vehicle, including the carbody and bogie, to monitor structural vibrations during operation. Dynamic responses were captured using a real-time tracking data acquisition system, as illustrated in Figure 4a. The vibration signals were primarily collected through acceleration sensors securely mounted on the train components using high-strength adhesive. The measurement range for the axlebox sensors was set to 100 g, while sensors at other locations had a range of 18 g. All sensors were sampled at a frequency of 2000 Hz. The specific installation positions of the acceleration sensors on the bogie are shown in Figure 4b,c. To analyze the collected vibration acceleration data, both Fast Fourier Transform (FFT) and Short-time Fourier Transform (STFT) techniques were employed. FFT was used to extract the vibration amplitude-frequency characteristics, while STFT enabled time-frequency analysis to capture transient vibration features and their evolution over time.

As shown in Figure 5a, the time-domain signals of vertical vibration acceleration collected from vehicle dynamics tests at the wheelset axlebox and carbody floor before wheel re-profiling are presented, with a maximum operating speed maintained within the range of 70 km/h. It can be seen that, in most cases, the vertical vibration acceleration on the axlebox and carbody is kept within 0.1 g and 20 g, respectively, but it increases significantly at certain moments. It can be seen that during these times, the vehicle is subjected to vertical excitation, resulting in increased vertical vibration, which may be related to the track it is passing through at these times. Based on the acceleration signals collected from the stability vibration measurement points arranged on the carbody, we perform 0.5–40 Hz bandpass filtering on the vibration acceleration signal and calculated the vertical stationarity index according to the stationarity index formula in GB/T 5599 [14]:

$$W_{\mathrm{z}}=3.57\sqrt[10]{{\displaystyle \frac{A^3}{f}}F(f)}$$

(2)

where $A$ is the vibration acceleration; $f$ is the matching frequency; and $F(f)$ represents the frequency weighted function.

The calculated results of the Sperling ride comfort (stability) index based on the dynamic test data are presented in Figure 5b. At an operating speed of 70 km/h, the vehicle’s vertical stability index exceeded the excellent threshold of 2.5 during certain time intervals, with the most severe cases approaching the critical limit of 3. This observation is consistent with the time-domain analysis results of the vibration acceleration signals. Additionally, Figure 5b includes the time-frequency diagram of the axlebox vertical acceleration, derived from processing the vibration time-domain signal using STFT, where the blue solid line represents the vertical stability index, and the red dashed line indicates the limit value of excellent stationarity, which is 2.5.

The analysis reveals that within the frequency range below 200 Hz, the axlebox experiences distinct abnormal vibrations at multiple time intervals, rather than throughout the entire duration of the dynamic test. These localized vibration events suggest a strong correlation with specific track sections encountered by the vehicle. The main excitation frequencies associated with the abnormal vibrations are concentrated in the 30–80 Hz range and exhibit a clear periodic pattern. Correlating these findings with the vehicle stability index, it is evident that the periods of abnormal vibration align with the intervals during which the vertical Sperling index exceeded the acceptable standard. This indicates that the observed abnormal axlebox vibrations are the primary contributors to the degradation of ride stability during operation.

To further identify the specific frequencies associated with the abnormal vertical vibrations observed at the axlebox, a representative time period containing these abnormal vibrations was selected from the vibration acceleration time-domain signal for amplitude-frequency analysis. For comparison, a separate time segment without abnormal vibrations was also selected. The amplitude-frequency analysis results are shown in Figure 5c. It is evident that during periods of abnormal vibration, the amplitude of the vibration signal is significantly higher than during normal operation. Multiple prominent frequency peaks are observed in the vibration spectrum, especially at 52.9 Hz and 59.4 Hz. These peaks exhibit clear periodicity, aligning well with the findings from the previous time-frequency analysis.

According to the theoretical calculation formula for wheel polygonal wear frequencies, these peak frequencies correspond to the characteristic frequencies of seventh- and eighth-order wheel polygons. To further explore the relationship between the abnormal vibrations induced by wheel polygons and the track structure, a field survey of the metro line was conducted during the testing process. It was found that the track structure along the line primarily comprises floating slab track and trapezoidal sleeper track. As illustrated in Figure 5a,b, the analysis of vehicle dynamic responses across different track structures indicates that abnormal vibrations predominantly occurred when the vehicle passed through sections with floating slab track. This suggests a strong correlation between wheel polygon-induced vibrations and specific track structures. These findings highlight that the severity and manifestation of polygonal-induced vibrations are not solely dependent on wheel condition but are also influenced by the underlying track structure. Further investigation into this coupling effect between wheel polygon characteristics and track structure is warranted.

3. Formation Analysis of Wheel Polygonal

3.1. Modal Analysis of Track Structure

When integrating the vehicle and track systems for coupled dynamic analysis, wheel polygonal wear emerges as a critical internal issue within the vehicle–track coupling system. As the vehicle traverses different sections of track, variations in track structure cause corresponding changes in the dynamic response of the integrated system. During the formation of polygonal wear on the wheel tread, the primary driving factor is the fluctuation in the vertical wheel–rail contact force. Therefore, when constructing the finite element (FE) model for dynamic analysis, particular emphasis is placed on the vertical structural characteristics of the coupled system.

To reflect the actual conditions of the metro line, finite element models corresponding to different track structure types, specifically floating slab track and trapezoidal sleeper track, were established for analysis. A vertical vehicle–track coupling model was developed based on measured system parameters [15]. As shown in Figure 6a,b, the floating slab track system is supported by steel springs and employs DTVI2 fasteners. Due to the rigid connection between the track slab and the short rail sleeper, they are treated as a single unit in the model, with the steel spring support between the track slab and the subgrade represented as a spring-damping element. The trapezoidal sleeper track system uses ZX-3 fasteners. The longitudinal beam sleeper in this structure can be regarded as a continuous track slab, and the rubber damping layer beneath it is similarly modeled using spring-damping elements. Figure 6c,d illustrate the finite element models of both track types created using software HyperMesh 2019, along with their respective vertical system coupling models incorporating the metro vehicle. The key parameters used in modeling the metro vehicle and track systems are listed in

Table 1. Main parameters of the metro vehicle and track system.

System	Parameter	Symbol	Value	Unit
Vehicle system	Nominal radius of wheel	R0	0.42	m
	Half distance between two bogie frames	lc	6.3	m
	Half distance between two axles of wheelset	lw	1.15	m
	Mass of carbody	Mc	24,937	kg
	Mass of bogie frame	Mf	1830	kg
	Mass of wheelset	Mw	1231	kg
	Vertical stiffness of primary suspension	Kp	1.5	MN/m
	Vertical stiffness of secondary suspension	Cp	2	kN·s/m
	Vertical damping of primary suspension	Ks	0.4	MN/m
	Vertical damping of secondary suspension	Cs	60	kN·s/m
Track system	Density of concrete	ρs	2500	kg/m3
	Young’s modulus of concrete	Es	0.35 × 1011	Pa
	Poisson’s ratio of concrete	υs	0.22	-
	Vertical stiffness of DTVI2 fastener	Kf1	50	MN/m
	Vertical stiffness of ZX-3 fastener	Kf2	60	MN/m
	Vertical stiffness of steel spring	Kd1	10	MN/m
	Vertical damping of steel spring	Cd1	20	kN·s/m
	Vertical stiffness of rubber damping	Kd2	20	MN/m3
	Vertical damping of rubber damping	Cd2	10	kN·s/m3
	Longitudinal spacing of steel spring	Lx	1.2	m
	Transverse spacing of steel spring	Ly	1.8	m

.

In the finite element model, Beam188 elements are employed to simulate the rails, with simply supported boundary conditions applied at both ends. The fastener systems and track support components are modeled using Combin14 spring-damping elements, while the track slab and other structural components are represented using Solid185 solid elements [16]. Within the vehicle–track vertical coupling model, the vertical contact stiffness at the wheel–rail interface is linearized and simulated using spring elements. According to Hertzian contact theory, the vertical contact stiffness is influenced by the curvature radii of the wheel and rail contact surfaces, the elastic moduli of the materials, Poisson’s ratios, and the normal load. For metro vehicles, the linearized vertical contact stiffness generally falls within the range of 1225–1524 MN/m [17]. In this analysis, a representative stiffness value of 1500 MN/m is adopted for simulation. Furthermore, the suspension isolation effect of the vehicle system is considered. The carbody is modeled as a concentrated mass load, with an unsprung mass of approximately 1300 kg per wheel and a single wheel static load of 50 kN. An external excitation force of 1000 N is applied, and the frequency domain analysis is conducted up to a maximum frequency of 1200 Hz, ensuring coverage of the relevant dynamic response range.

Due to the fact that the wheel polygonal characteristic frequency vibration of the 50–70 Hz on vehicles occurs within a specific track structure section, a modal analysis of the track under vehicle–track coupling is necessary to determine the vibration modes of different track structure types. To verify the accuracy of the coupling modal analysis model, acceleration sensors were installed on typical floating slab track and trapezoidal sleeper track sections for on-site modal testing. Comparing the test data with the coupling modal frequencies calculated by the model, the results show that in the floating slab track section, the main vibration frequency of the track system is about 58.9 Hz, which is highly consistent with the P2 force resonance mode identified in the model, with a frequency error of less than 5%, and the corresponding vibration mode shape is basically the same. The constructed coupling system model has good credibility and can be used for a modal analysis of vehicle track coupling systems under multiple non-track structures in the future.

Then, import the finite element model of the vehicle–track coupling system based on different track structures into software ANSYS R17.1, and perform a modal analysis on the floating slab track and trapezoidal sleeper track under the vehicle–track coupling state [18,19,20].

Table 2. Partial vertical modes of floating slab track under vehicle–track coupling.

Order	Vibration Mode	Frequency/Hz	Modal Shape
1	Wheel–rail P2 force resonance	59.647
2	First-order vertical bending	103.482
3	Second-order vertical bending	141.378
4	Third-order vertical bending	141.827
5	Fourth-order vertical bending	172.866

illustrates the vertical vibration modes and corresponding frequencies of the floating slab track in the coupling state, including the wheel–rail P2 force resonance mode and the first four-order vertical bending modes, the redder the color, the greater the deformation amplitude, while MX and MN represent the maximum and minimum amplitudes, respectively. It is observed that the resonance frequency of the wheel–rail P2 force is 59.647 Hz, which refers to the vertical dynamic load caused by the relative motion between the unsprung mass of the vehicle system and the track structure during the wheel–rail contact process. While the frequencies of the first four-order vertical bending modes displayed are all above 100 Hz, the modal characteristics they exhibit are determined by the mutual coupling between the rail and the floating slab. Comparing these vertical vibration modes of the track under coupling state, it can be found that the frequency of wheel–rail P2 force resonance, which closely aligns with the characteristic frequency of wheel polygonal compared to other vertical bending modes. Consequently, when an excitation near this frequency occurs, it easily triggers mode excitation and leads to resonance [21,22,23]. This may be the cause of the abnormal vertical vibration of the vehicle.

Similarly, a modal analysis was conducted on the trapezoidal sleeper track under the vehicle–track coupling condition. The analysis identified the wheel–rail P2 force resonance mode as well as the first four vertical bending modes. The corresponding vertical vibration modes and their frequencies are summarized in

Table 3. Partial vertical modes of trapezoidal sleeper track under vehicle–track coupling.

Order	Vibration Mode	Frequency/Hz	Modal Shape
1	Wheel–rail P2 force resonance	108.615
2	First-order vertical bending	188.672
3	Second-order vertical bending	189.338
4	Third-order vertical bending	193.165
5	Fourth-order vertical bending	203.816

. The results indicate that under the influence of vehicle–track coupling, the vertical bending modes of the trapezoidal sleeper track exhibit significant changes, with mode frequencies markedly higher than those observed for the floating slab track structure. In particular, the frequency of the wheel–rail P2 force resonance mode is approximately 108.615 Hz. In addition, the vertical bending modes, primarily formed by the coupled interaction between the rail and the longitudinal sleeper, occur at frequencies above 188 Hz. These mode frequencies are substantially higher than the characteristic frequency range of wheel polygonal excitation, typically between 50 and 70 Hz. As a result, it becomes difficult for polygonal-induced excitation to trigger resonance within this track structure. This explains the observed absence of prominent polygonal characteristic frequencies when the vehicle operates on sections composed of trapezoidal sleeper track.

3.2. Formation of Wheel Initial Polygonal

Based on the modal analysis of vertical vibration of the track under the vehicle–track coupling state, it can be concluded that the abnormal vertical vibration in the range of 50–70 Hz (wheel polygonal characteristic frequency) that occurs in the vehicle is related to the wheel–rail P2 force resonance mode of the coupling state. However, this is only an internal factor; resonance will only occur when subjected to external excitation within the same range. Therefore, there must be an external factor that excites the wheel–rail P2 force resonance mode within the coupling system, and the excitation frequency range coincides with it [24,25]. For example, in the floating slab track section, the excitation frequency should be around 60 Hz, while it should be around 108 Hz for the trapezoidal sleeper track section. Therefore, we conducted research on the possible external disturbances of the metro line, especially the track irregularities that are directly related to the vehicle–track coupling system. As shown in Figure 7a, the measured track vertical irregularity results are presented, and it can be clearly seen that there is a significant periodic excitation along the track. Through field research, it was found that this excitation is caused by rail joint welds, distributed at equal intervals of 25 m. Due to the difficulty of continuously superimposing the random irregularities on the actual track surface in the circumferential direction of the wheel, the rail joint weld is used as the main excitation input for the vertical irregularities of the track. Figure 7b shows the simulated rail joint weld input, which is fitted based on the measured irregularities, and it is a concave weld seam with a maximum amplitude of about 2.5 mm and an excitation spacing of 25 m.

However, the formation of wheel polygonal wear is a result of the accumulation of long-term wheel–rail wear, and the onset of final polygonal wear also stems from an initial occurrence. This initial polygonal wear is caused by the wheel–rail vertical excitation, which arises from defects in the wheel tread or periodic excitation on the track. Obviously, when the vehicle is running on the track with this rail vertical irregularity, the joint welds will cause periodic wheel–rail collisions when vehicles pass through, thereby inducing rail–wheel P2 force resonance mode. Based on the measured results of rail vertical irregularity, a rail joint weld excitation digital model with a vertical amplitude of 2.5 mm was constructed for vertical impact simulation. Figure 7c shows the variation curve of the wheel–rail vertical impact force. It can be seen that the rail–wheel P2 force resonance frequency is about 62 Hz, which is close to the results obtained from the modal simulation of the vehicle–track coupling state in the previous text. Meanwhile, according to the analysis results of dynamic experiments, in sections with specific track structures (floating slab track), the rail–wheel P2 force resonance frequency is close to the wheel polygonal characteristic frequency, around 60 Hz. This alignment corresponds to the abnormal vibration observed in vehicles running through these sections, thus confirming that it serves as a direct cause for wheel polygonal wear.

In order to conduct practical verification and more intuitively demonstrate the impact of rail irregularity (rail joint weld) on the vehicle vertical vibration, and to reveal the correlation between rail excitation, wheel–rail P2 force resonance, and wheel polygonal wear, dynamic comparative tests were conducted on sections with good rail irregularity status on the metro line, with no obvious rail joint weld [26]. The train is in the state before wheel re-profiling, and the driving speed was 70 km/h. The statistical analysis results of the mean maximum and root mean square (RMS) values of vertical vibration acceleration at each measuring point during the testing process are shown in Figure 8. It can be seen that when there is periodic vertical rail irregularity, the average maximum and RMS values of vertical vibration acceleration at each measuring point on the vehicle are significantly higher than when there is no obvious rail irregularity, including axlebox, frame-end, air spring seat, and carbody bottom. Among them, the amplitude difference in vertical acceleration on the axlebox is the largest through comparison. Under the condition of good rail irregularity, the mean maximum and RMS values of vibration acceleration decrease from 11.23 g and 3.74 g, respectively, to 3.98 g and 1.07 g, about a 64.3% and 71.1% decrease. It can be seen that the irregularity of the rail joint welds on the track is the external factor that triggers the occurrence of wheel–rail P2 force resonance on vehicles, resulting in increased vibration on the carbody. In addition, under both operating conditions, the mean maximum vertical vibration acceleration of the carbody is less than 1 g, and the RMS value does not exceed 0.5 g. It can be seen that the suspension system of the vehicle has a good damping effect on the vibration generated by wheel–rail impact and, when the vibration is transmitted to the carbody, it has little effect on its elastic vibration. On the contrary, the carbody elastic vibration during vehicle operation also has little effect on the wheels. When studying the wheel polygonal vibration, the elasticity of the carbody can be simplified, as mentioned in the previous modeling and analysis.

In summary, in the vehicle–track coupling state, the wheel–rail P2 force resonance mode is related to the track structure, the floating slab track and trapezoidal sleeper track on this metro line are 59.647 Hz and 108.615 Hz, respectively. When there is periodic vertical fixed excitation (rail joint weld) on the track, it will excite the wheel–rail P2 force resonance mode during vehicle operation, with a frequency of about 62 Hz, which is close to the P2 force resonance frequency of the floating slab track, causing resonance and exacerbating wheel surface wear, resulting in initial irregularity. At the same time, under the influence of polygonal excitation feedback, these irregularities are further exacerbated, ultimately leading to the formation of wheel polygonal wear. For the eighth-order polygonal wear of metro vehicles, the periodic irregularity excitation of the track is the inducing source, and the fundamental factor for its formation lies in the wheel–rail P2 force resonance mode under the vehicle–track coupling state. Therefore, in order to effectively control the wheel polygonal wear, it is necessary to maintain the optimal state of the rail and wheel surface to minimize the vertical impact force between them. In addition, careful management of the structural parameters of vehicles and tracks is crucial to prevent resonance between the wheel–rail vertical force frequency and the bending mode frequency of the track under the vehicle–track coupling system, including P2 force resonance.

4. Conclusions

In response to the abnormal vibrations induced by wheel polygonal wear and its potential threat to operational safety, this study conducted field dynamic tests and established vehicle–track vertical coupling models for different track types. A modal analysis was then performed to investigate the formation mechanism of wheel polygonal wear in metro vehicle operations.

(1)

Distinct seventh-order to ninth-order polygonal wear patterns were observed on the wheel tread, with corresponding abnormal vertical vibration frequencies at the axlebox matching the polygonal excitation frequencies.

(2)

The wheel’s polygonal wear characteristics are influenced by the underlying track structure, and their dominant frequency components closely align with the P2 resonance frequency arising from wheel–rail interaction.

(3)

A modal analysis of the vehicle–track coupling system revealed multiple peaks in the track frequency response curve within the same range, confirming a strong correlation with the polygonal wear excitation frequencies.

(4)

For eighth-order polygonal wear, the irregularity at rail joints acts as a localized excitation source, while the P2 force resonance under coupled vibration conditions plays a key role in amplifying and sustaining the wear process.

These findings contribute to understanding the mechanism behind polygonal wear formation and provide a theoretical basis for engineering countermeasures. Potential mitigation strategies include reducing unsprung mass and optimizing track structural design to avoid P2 resonance conditions.