Wheel polygonization — periodic out-of-roundness of railway wheel treads — develops on heavy-haul electric locomotives as severe high-order (roughly 16th–25th) circumferential wear that triggers abnormal-vibration alarms and accelerates fatigue of unsprung components. A 2020 field-measurement study at a Chinese locomotive depot established the phenomenon's features and the effect of re-profiling, but explicitly left open the root cause and formation mechanism, including why locomotives in dedicated single-line service developed severe fixed-order polygonization and vibration from the start of service while structurally identical locomotives from the same depot running mixed lines showed almost none. Subsequent work (2020–2025 reviews and mechanism studies) has converged on a framework in which wear becomes fixed at excitation frequencies locked to resonances of the coupled vehicle–track system (the so-called fixing-frequency mechanism) — but the dominant excitation pathway (wheelset bending resonance, rail flexibility and P2 resonance, friction-induced vibration under wheel–rail slip, traction-drive harmonics/interharmonics exciting axle torsion, discrete tread irregularities, anti-slip control interaction) remains contested, and the line/operating-condition dependence is still unexplained quantitatively. The problem of establishing a validated, predictive formation mechanism for high-order polygonal wear of locomotive wheels therefore remains open.

Background

Polygonal wear (also called wheel polygonization or out-of-roundness, OOR) is a circumferential wear pattern on railway wheel treads in which the radius varies periodically around the wheel; it is characterized by its harmonic order NN, the number of wavelengths around the circumference, so a wheel of rolling circumference CC carries a wear wavelength of C/NC/N. 'High-order' polygonization (roughly N≥15N\geq 15, i.e. wavelengths around 150–250 mm on typical locomotive wheels of about 1.25 m rolling diameter, corresponding to a rolling circumference CC of roughly 3.9 m) excites the wheel–rail interface at the passing frequency N v/CN\,v/C at speed vv, which for heavy-haul locomotives at their typical operating speeds of roughly 65–75 km/h lands in the roughly 70–130 Hz band where many unsprung-mass and track resonances live. The result is damaging impact loading, abnormal-vibration alarms from the on-board abnormal vibration alarm system (AVAS) used by Chinese operators, and fatigue cracking of wheel rims, springs, dampers and gearboxes. Heavy-haul and high-power AC electric locomotives in China typically develop 16th–25th order wear (with 7th–8th order also reported), South African locomotives a pronounced 20th order, and metro and high-speed trains their own order families. The standard palliative is re-profiling (turning the wheel on a lathe, often an under-floor wheel lathe without lifting the locomotive), but poor re-profiling leaves residual high-order wear that regrows within weeks.

The prevailing explanatory framework is the 'fixing-frequency mechanism': circumferential wear becomes concentrated at orders whose passing frequency coincides with a resonance of the coupled vehicle–track system, so the wear pattern 'locks' to a fixed frequency and hence to a speed-dependent order. Candidate excitation pathways identified in the literature include: natural vibration of the wheelset — in particular its first bending mode near 81–84 Hz and lateral bending of the wheel disc near 122–132 Hz — which Tao, Wang, Wen, Guan and Jin (2018) proposed as the cause of the 17th–19th and 23rd–25th order wear of Chinese electric locomotive wheels; axle torsional vibration excited by wheel–rail stick–slip under saturated adhesion together with harmonics and interharmonics of the AC traction drive (variable-frequency drive, VFD), which Fröhling, Spangenberg and Reitmann (2019) identified for South African 20th-order polygonization; P2 resonance, the classical vertical resonance of the vehicle unsprung mass on the track stiffness; friction-induced vibration (self-excited vibration of the wheel–rail contact under slip); discrete tread irregularities such as wheel flats; and interactions with anti-slip traction control. Peng, Iwnicki, Shackleton and Song (2021) formulated general conditions for polygonal wear to grow: the phase relation between the instantaneous wear and the excitation governs whether a given order grows or decays. Long-term wear-evolution simulations (vehicle–track dynamics coupled with contact mechanics and a wear law such as the USFD (University of Sheffield) wear function, an Archard-type wear model relating material removal to local frictional power in the contact patch, iterated over many wheel revolutions) are the standard predictive tool, and their fidelity depends on how the flexibility of the wheelset and rails is modeled.

The immediate source of the present question is the field study of Yang, Ling, Liu, Wang and Zhai (2020), who measured wheel roughness across the fleet of a Chinese heavy-haul electric-locomotive depot ('Depot Y') and performed on-track vibration tests. They established that high-order polygonal wear is the root cause of the AVAS vibration alarms, determined the harmful wavelength and order ranges, and showed by tracking measurements how different re-profiling methods remove or fail to remove the wear. Crucially, they could not explain why some locomotives with fixed (dedicated single-line) routing — running mainly on one line, with alarms essentially from the start of service — suffered severe high-order polygonization, while structurally identical locomotives of the same depot running various lines showed little high-order wear and no alarms. The authors therefore left the formation mechanism of high-order polygonal wear of locomotive wheels open, stating that further experimental and theoretical analyses were under way. Later reviews (Tao, Wen, Jin and Yang 2020; Iwnicki, Nielsen and Tao 2023) confirm that the exact mechanism of wheel polygonization remained not fully understood, and the same group's 2024 follow-up still describes the sources of the resonance excitation as controversial and defers the line-specific question to future work. What is missing is a validated causal account that identifies the dominant excitation pathway, quantitatively predicts which orders grow — and how fast — for given line geometry, speed profile, traction/adhesion and re-profiling conditions, and explains the observed operating-condition dependence, thereby grounding prevention measures beyond symptomatic re-profiling.

Problem Statement

Determine the formation mechanism — the root cause — of high-order polygonal wear of locomotive wheels, to a validated and quantitative level. Specifically: identify which excitation pathway or combination of pathways (wheelset bending resonance; rail flexibility and P2 resonance or discrete sleeper-support excitation; friction-induced vibration under wheel–rail slip; traction-drive harmonics and interharmonics exciting axle torsion; discrete tread irregularities; interaction with anti-slip traction control) fixes the circumferential wear at the observed high orders (roughly 16th–25th), and demonstrate this causally rather than by frequency coincidence alone. The mechanism must explain and predict the documented operating-condition dependence, including why locomotives in dedicated single-line service developed severe high-order polygonization and abnormal vibration essentially from the start of service while structurally identical locomotives of the same depot running mixed lines developed little high-order wear, and how line geometry, speed profile, traction and adhesion conditions, and re-profiling quality govern which orders grow and how fast. The mechanism must be established as a predictive model of order-and-depth evolution validated against independent field or full-scale measurements: checked against such data, the model must reproduce the observed locked high orders (roughly 16th–25th) and the measured single-line versus mixed-line dependence to within the scatter of those measurements, over their full measurement interval; the 7th–8th order wear also reported on these locomotives forms a separate, lower-order family and lies outside this high-order validation target. Demonstrating the identified pathway or combination of pathways causally — rather than by frequency coincidence alone — requires at least one discriminating test — a targeted measurement, full-scale experiment, or dedicated simulation that separates the identified pathway or combination of pathways from the leading alternative predicting the same locked order (full pairwise separation of every candidate pathway is not required) — and the validated order-and-depth model. The operating-condition account need extend only as far as reproducing the measured single-line versus mixed-line dependence, and the validated mechanism grounds preventive measures beyond symptomatic re-profiling.

References

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