Due to the combined effects of material properties, manufacturing tolerances, and complex operational conditions, the wheel-rail interface and suspension parameters of high-speed trains exhibit significant stochasticity, which fundamentally shapes dynamic performance distributions. To capture this stochasticity over a full reprofiling cycle, this study integrates multi-condition wear simulations with measured data to establish a stochastic wheel-profile database. A method combining Monte Carlo simulation, Latin hypercube sampling, and Kullback-Leibler divergence is proposed to predict dynamic performance distributions while balancing sampling efficiency and convergence control. Analysis of the coupled effects of stochastic wheel-rail and suspension parameters shows that dynamic performance distributions evolve significantly with mileage. In the later service stage, key indicators such as the lateral Sperling index exhibit left-skewed and heavy-tailed distributions, with broader spreads and increased tail risk as mileage accumulates. The proposed method enables quantitative evaluation of long-term dynamic performance evolution and operational safety risk.

This paper presents a thorough bifurcation analysis of a 17 degrees-of-freedom high-speed train lateral dynamics model subject to delayed yaw feedback control, incorporating nonsmooth wheel-rail interaction. The control force provided by actuators replacing the yaw dampers is modeled as a polynomial function of the state variables. First, the eigenvalue analysis can be applied to identify the critical delay at which a Hopf bifurcation destabilizes the control systems with two actuators. Next, a single-parameter bifurcation diagram is obtained using the delay as the bifurcation parameter. From this, the critical delay and hunting frequency of the linear terms in the wheel-rail contact geometry are calculated. Then, the influence of feedback gains on the critical delay, hunting frequency, first Lyapunov coefficient, hunting amplitude, and control force is explored. Finally, the hunting stability of the passive system and the active system with various delay is compared under distinct wheel conicities and running speeds. These findings indicate that active control can stabilize a system that is inherently unstable when passive. While a moderate increase in delay enhances stability, excessive delay will once again lead to instability. In actively controlled vehicle systems, hunting stability can be improved more effectively through the careful choice of both linear and nonlinear feedback gains.

This study investigates frequency-selective stiffness (FSS) yaw dampers versus conventional dampers featuring the same bidirectional-flow structure for railway vehicle stability analysis. Unlike traditional designs, FSS dampers feature enhanced frequency-dependent dynamic characteristics, with dynamic stiffness varying substantially across different excitation frequencies, whereas conventional dampers exhibit only minor frequency-dependent variations. Bench tests were conducted on both damper types with identical static force-velocity characteristics. Results demonstrate that the FSS damper achieves 43.8% lower dynamic stiffness and 23.5% lower dynamic damping at carbody hunting frequencies, while maintaining comparable high dynamic stiffness at bogie hunting frequencies. A nonlinear damper model incorporating frequency- and amplitude-dependent behaviour was developed and validated against experimental data. Vehicle dynamics simulations reveal that the FSS damper provides superior carbody stability for 300 km/h-class vehicles under low-conicity scenarios. However, at 350 km/h, the carbody stability index approaches the threshold due to reduced dynamic damping - a limitation stemming from the damper's design principle. Parametric analysis suggests that maintaining adequate dynamic damping or reducing dynamic stiffness can improve carbody stability at ultra-high-speeds. Under high-conicity conditions, both damper types demonstrate comparable bogie stability. These findings demonstrate that FSS dampers offer effective solutions for balancing carbody and bogie stability, though careful parameter optimisation is essential for ultra-high-speed applications.

For high-speed bogie, the traction motor contributes to a large mas to the bogie system then influences the running stability. This study proposed to actively control the suspension parameters of the traction motor to enhance the running performance of the high-speed bogie. A simplified vehicle dynamics model was firstly built with nonlinear wheel/rail contact integrated, then a root locus analysis was performed to examine the relationship between the motor suspension frequency and critical speed of the vehicle system. Based on this, the necessity of active control on the motor suspension was elaborated, and it was pointed out that the active suspension control can adjust the suspension frequency of traction motor to increase the critical speed of the vehicle system under different wheel/rail conicity states. Furtherly, bifurcation analysis is carried out to show that the active control may affect the vehicle bifurcation characteristics. According to the calculations, with fixed lateral damping ratio of the motor, the linear critical speed of the system has increased by 4.8% -24.6%, with fixed lateral damping of the motor, the linear critical speed of the system has increased by 1.9% -30.9%, and possible impact of time delay and countermeasures were explained. Furtherly, optimization can be performed using the nonlinear control laws with the cubic terms concerned.

After two decades of leapfrog development, China has built the world's largest 350 km/h high-speed railway operation system. CR400 high-speed train, as the core equipment of this system, its wheel-rail dynamic characteristics directly affect the operational quality of the railway network. Based on a four-month in-service tracking test covering over 230,000 km on the Beijing-Shanghai high-speed line, this study identifies fixed-frequency peaks in vertical axlebox acceleration around 45 Hz, 350 Hz, 580 Hz, and 820 Hz, amplitudes of which surge nonlinearly with speed. Wheel roughness measurements reveal a distinctive "dual-peak order" polygonization pattern: dominated by the 10 similar to 12th order (similar to 350 Hz, wavelength 240 similar to 290 mm) with a co-developing 17 similar to 18th order (similar to 580 Hz, 160 similar to 170 mm), markedly different from the existing CRH380 trains. Through finite element simulations and wear evolution analyses, we establish that these frequencies correspond to intrinsic wheel-rail coupling modes (P2, B2, B3, B4), with the low-damping and frequency-stable B2 and B3 modes acting as the physical origins driving periodic wheel wear. To explain why low-order polygons become dominant despite the presence of both B2 and B3 excitations, we propose PolyFilter, a novel spatial convolution-based model that, for the first time, abstracts the abrasive block as a mechanical low-pass filter. The analysis reveals that the current 125-mm-long abrasive block operates in a severely ineffective trace-grinding mode against the 10-12th-order polygon at 350 km/h, nullifying their intended suppression effect while allowing the B3-excited high-order components to be partially suppressed. This geometric selectivity, rooted in the fundamental mismatch between block length and polygon wavelength, provides the first quantitative explanation for the selective evolution of polygon orders observed in field tests. Accordingly, two targeted countermeasures are proposed: (1) frequency-shifted arrangement of high-frequency vibration-absorbing fasteners to detune resonant excitation; and (2) increasing abrasive block length to achieve effective "span-grinding". These countermeasures offer both theoretical insight and practical pathways for ensuring safe, reliable, and cost-efficient operation of high-speed trains exceeding 350 km/h, including the CR400 and the under-development CR450.

This study examines the dynamical behavior of a railway bogie with yaw actuators under delayed displacement and velocity feedback control. First, the time delay is regarded as a bifurcation parameter to analyze stability switches and Hopf bifurcations. Next, analytical criteria for bifurcation direction and periodic solution stability are derived using the normal form theory and center manifold theorem. Furthermore, bifurcation analysis reveals the influence of key parameters on stability switches, Hopf frequency, global view of periodic motions, and global structure of Hopf bifurcations, including a Hopf-Hopf bifurcation through crossed Hopf branches. Notably, distinct critical delays generate periodic solutions with varying Hopf-related frequencies. Ultimately, numerical simulations validate that growing delay induces multiple stability switches and Hopf bifurcations, eventually causing instability, with hunting stability potentially being maintained under certain high-delay regions.

In China's Electric Multiple Units (EMUs) operations, EMUs primarily operating on Line B (Vehicle B) exhibit hunting when running on Line A at the end of the wheel reprofiling cycle, while EMUs mainly operating on Line A (Vehicle A) remain stability on both lines. Simulations of EMU dynamics and wheel wear prediction throughout the entire wheel reprofiling cycle were conducted, revealed that the primary cause of the worn wheel profile differences is the disparity in rail profiles. Specifically, the inner and outer rail shoulders of left Rail B are lower than those of Rail A. On the right side, the inner rail shoulder of Rail B is lower than that of Rail A, and the rail top is 2-3 mm outward compared to Rail A. This wheel-rail difference creates excessive equivalent conicity when Vehicle B operates on Line A, ultimately causing hunting motion during cross-line operations. Based on these findings, it is recommended to unify the rail profiles of both lines to the existing profile of Line B, frequently alternate EMU operating routes between the two lines, or adopt thin-flange tread profiles such as the P8 tread to enhance the hunting stability of EMUs.

To optimize the vibration phenomenon of rail vehicles, this paper refers to the "flutter theory" used in dynamic research of aircraft, bridges, and other fields to analyze vibration. This article first conducted eigenvalue correlation research on a two-degree-freedom system, studied the conditions for flutter occurrence through eigenvalue analysis and time-domain analysis, and combined two cases to illustrate the situation of flutter in actual physical systems. Afterward, this article calculated the influence of damping on flutter, and innovatively analyzed the wheel-rail contact system using flutter theory, calculated the impact of factors like suspension stiffness, equivalent conicity, and wheel-rail creep coefficient on flutter, and combined dynamic equations to analyze how the operating speed of the system affects the damping term, thereby affecting the flutter situation. The results indicated that there is a possibility of flutter in the lateral dynamics model of wheel-rail contact. If the lateral stiffness of the primary suspension, equivalent conicity, creep coefficient of the system, and track gauge are too high, it will cause flutter. In the defined system, when the lateral stiffness exceeds 1.65 * 106 N m-1, or the equivalent conicity exceeds 0.375, or the creep coefficient exceeds 1.04 * 107, or the half of the rolling circle span exceeds 0.57 m, the system will experience flutter, while the longitudinal stiffness below 2.25 * 107 N m-1 will also cause flutter and an increase in the operating speed of the system will have a negative impact on flutter suppression. Under the set parameter conditions, when the operating speed is greater than 483.9 kmh-1, the damping term will be insufficient to suppress flutter, and flutter will reappear in the system. Therefore, when designing a rail transit system, it is necessary to pay attention to the eigenvalues and avoid eigenvalue degeneracy and flutter phenomena by adjusting parameters.

The EN and Area methods are commonly reported procedures for evaluating dynamic damper characteristics, both predominantly relying on time-domain data of damper force and displacement, with the EN method established as a standard in EN13802. However, these time-domain approaches do not fully utilize all experimental data and have inherent limitations that can impact the accuracy of the results. To address this challenge, this study introduces a calculation method based on the Fast Fourier Transform (FFT), which shifts the analysis from the time domain to the frequency domain, allowing for more reliable determination of phase angle, dynamic stiffness, and damping. Comparative analysis of dynamic test results on typical hydraulic dampers reveals that traditional time-domain methods lead to abnormal fluctuations in dynamic stiffness at low frequencies due to inaccuracies in phase angle calculations. In contrast, the frequency-domain method delivers more reliable results. Among the tested methods (EN, Area, and FFT), the FFT method aligns most closely with the standard EN method, showing discrepancies of less than 10%, and demonstrates greater robustness under noisy conditions. In comparison, the Area method exhibits higher sensitivity to sampling frequency variations, resulting in less reliable outcomes. This study provides practical insights for enhancing damper performance evaluation and recommends the frequency-domain method as a reliable tool for dynamic characteristic analysis, particularly in applications where noise resilience is required, while the EN method remains suitable for low-noise conditions.

Time delay in active control has a significant impact on the hunting stability of railway bogies and needs to be studied theoretically. This paper investigates the Hopf bifurcation characteristics of an actuated bogie governed by linear and nonlinear feedback control with multiple time delays. The lateral and longitudinal actuator forces are formulated as state-dependent nonlinear delay functions. At first, the local stability of the trivial equilibrium and the existence of Hopf bifurcation are evaluated by considering the feasible combinations of the two delays as bifurcation parameters. Furthermore, some explicit formulae for identifying the direction of Hopf bifurcation and the stability of bifurcated periodic solutions are derived using the normal form method and center manifold theorem. To end with, the lateral and longitudinal actuator delays are individually fixed to examine their interplay, thereby uncovering the dynamic impact of the remaining delay. The study reveals how variations in individual parameters affect two critical delays and demonstrates the significant influence of feedback gains and time delays on bifurcation behaviour. Importantly, distinct delay scenarios in the control strategy are shown to significantly influence passenger comfort and operational safety through their impact on hunting amplitudes and stability thresholds. Numerical simulations conducted using the bifurcation analysis tool DDE-BIFTOOL corroborate the theoretical findings. The derived analytical criteria provide a fundamental reference for stability assessment and suspension control design in railway bogies.

The parameters of traditional yaw dampers are typically determined during the vehicle dynamics design stage based on specific wheel and rail profiles. However, dampers with fixed parameters often struggle to effectively mitigate hunting motions due to the significant variations in wheel-rail contact conditions encountered during operation. Unlike the traditional method of adjusting dynamic damping, the goal of this work is to propose an innovative on-off yaw damper that can realize switchable low and high dynamic stiffness, and thus has the ability to suppress both low-frequency carbody hunting and high-frequency bogie hunting under different wheel-rail conicity conditions. First, the working principle of the damper is detailed, highlighting switchable dynamic stiffness in two selectable modes. A physical model is then developed to study the damper’s dynamic characteristics under different combinations of excitation frequency and amplitude. The results reveal a substantial difference in dynamic stiffness between the two modes, with a 74% variance, while dynamic damping remains largely unaffected. A new parameter, termed dynamic stiffness difference, is introduced to describe the frequency-dependent stiffness property of the damper, and its sensitivity to damper parameters is explored, providing insights for design optimization. Finally, numerical simulations demonstrate that the on-off yaw damper significantly improves both low and high conicity stability, thereby enhancing overall vehicle stability across a wide range of wheel-rail contact conditions.

This paper presents a theoretical study of hunting bifurcation behavior in high-speed rail vehicles under modal coupling and compares it to the traditional uncoupled system. A dynamic simplified model that integrates the lateral and yaw motions of the rigid bogie and the lateral motion of the carbody is established to evaluate the modal coupled effect between the carbody and bogie. The stability and Hopf bifurcation of the trivial equilibrium are first analyzed qualitatively using the normal form theory. The linear stability analysis then reveals that modal coupling introduces a new unstable region known as carbody (primary) hunting, which is absent in the uncoupled system that only exhibits bogie (secondary) hunting. The double-parameter Hopf bifurcation analysis is further carried out, which considers the influence of suspension parameters on the bifurcation speed and stability region. Our findings indicate that the dynamical behavior of the coupled system can closely match that of the uncoupled system with suitable parameter configurations, effectively reducing primary hunting and enhancing the overall hunting stability of rail vehicles.

Yaw dampers are critical for suppressing hunting instability in railway vehicles, yet their performance is significantly affected by installation flexibility, often neglected in conventional modelling approaches. This study investigates yaw damper installation stiffness effects on damper dynamic characteristics and bogie stability through an integrated methodology combining finite element (FE) analysis, experimental validation, and multibody dynamics simulation. A detailed FE model was developed to characterise mounting system stiffness. Results reveal that mounting bracket stiffness is 25 MN/m when considering full-vehicle structural assembly-substantially lower than commonly assumed rigid conditions. A physical damper model incorporating installation flexibility was constructed and validated through test rig experiments under varied support stiffness conditions. Three vehicle modelling approaches were compared: conventional rigid multibody system (MBS), rigid MBS with equivalent support stiffness, and flexible-rigid coupled MBS. Analysis indicates that equivalent support stiffness modelling achieves comparable accuracy to flexible approaches with substantially reduced computational cost. Extensive vehicle dynamics simulations using the validated equivalent stiffness approach demonstrate that insufficient damper support stiffness significantly degrades bogie stability, particularly under high-speed and high wheel-rail conicity conditions. These findings underscore the necessity of accurately modelling yaw damper installation conditions and provide practical guidance for improving stability assessment methodologies in high-speed rail applications.

Since the view that the localized rail third-order bending mode can cause high-order polygonization (mainly 18–23) of high-speed train wheels was put forward in 2017, many scholars have attempted to link a connection between the localized rail bending modes and wheel polygonization phenomenon and polygonal wheel passing frequency. This paper first establishes a flexible track model considering the structural and parametric characteristics of fasteners, verifies the model by using vehicle tracking test data, then investigates the influence of fastener parameter matching on the localized rail bending modes, and obtains the following conclusions: (1) There is nearly a 1:1 mapping relationship between the localized rail bending modal frequency and polygonal wheel passing (PWP) frequency, which supports that the localized rail bending mode is one of the causes of wheel polygonization. (2) The iron plate of the fastener system plays a role of dynamic vibration absorber in the vehicle-rail coupled system, and the fastener parameters significantly influence the localized rail bending modal vibration. Finally, this paper proposes a design principle of a high-frequency vibration-absorbing fastener, which provides a feasible solution to mitigate the localized rail bending modal vibration and high-order wheel polygonization. Meanwhile, it points out that this measure may induce other high-frequency vibration problems, e.g., aggravating modal vibration above 800 Hz. Further, this paper proposes a concept of differentiated arrangement of fasteners, suggesting that different high-frequency vibration-absorbing fasteners be installed in different sections of the whole line to make the localized rail bending modal frequency of the whole line disordered, thus disrupting and further mitigating the development of the wheel polygonization.

High-speed trains in China are characterized by high operating speeds, extensive constant-speed sections, prolonged durations of continuous operation, and reliance on ballastless track systems with limited structural variations, resulting in frequent occurrences of high-order wheel polygonization. To fundamentally solve this issue, researchers have conducted in-depth studies on the formation mechanism behind this special phenomenon. However, the academic community has not yet reached a consensus after a decade of research since the systematic study was initiated in 2014. Current studies propose four main mechanisms for high-order wheel polygonalization of high-speed trains, all originating from Southwest Jiaotong University (SWJTU): (A) vibration of bogie components; (B) friction-induced self-excited vibration; (C) resonance of the wheel-rail system triggered by the third-order bending modal vibration of a rail segment restrained by the bogie (rail B3 modal vibration); and (D) joint action of rail B3 modal vibration and frequency shift. This paper first sorts out the controversial points existing in these four mechanisms, and then systematically proves the following two points through vehicle tracking tests, rail modal tests, and dynamics simulation analysis: (1) The rail B3 mode is the fundamental factor leading to the high-order wheel polygonization, and there is no significant frequency shift between the B3 modal frequency and the eventually formed polygonal wheel passing frequency (PWP frequency). (2) The parameter-matching characteristics of the fastener system significantly regulate the B3 modal vibration, with optimized parameter-matching relationships proving effective in suppressing wheel polygonization. This research not only clarifies the formation mechanism of high-order wheel polygonization in high-speed trains but also provides an innovative theoretical foundation and engineering solution for addressing this persistent issue.

In this paper an active bogie stability scheme combining a dynamic vibration absorber (DVA) and an actuator is proposed for high-speed trains, and a control strategy is presented by transforming the actuating force into a virtual part of hybrid DVA whose characteristic frequency and damping can be adjusted. Firstly, a simplified model of the lateral bogie dynamics is established for control system design, and the optimal value of the characteristic frequency and damping of the hybrid DVA are theoretically investigated from the perspective of bogie stability. Then the strategy of active stability is introduced by using the idea of adaptive vibration absorber, and a method for auto-tuning the optimal value of the DVA suspension is proposed. To realize this auto-tuning strategy a method to detect the bogie instability and its frequency is presented. At last, the feasibility of the adaptive vibration absorber is verified by comparing it to a passive one using a co-simulation model of a railway vehicle, and the effect of time delay in the control system on bogie stability is also analyzed.

Yaw dampers are usually tuned according to the nominal static force-velocity (F-V) characteristics specified by the vehicle manufacturer. However, in the low-speed region, the static F-V curve often varies significantly among damper suppliers due to a lack of standardised specifications. This variability underscores the necessity of accounting for nonlinearities in the analysis and understanding their relationship with the dynamic behaviour of yaw dampers and their impact on overall vehicle stability. To address these issues, we developed and validated a simplified physical damper model that incorporates these undefined nonlinearities through rig testing. Using this model, simulations were performed to investigate how these nonlinearities affect dynamic damper characteristics and vehicle stability. Our findings indicate that undefined nonlinearities in the low-speed region of the static F-V curve significantly influence the dynamic stiffness and damping of yaw dampers, particularly at small amplitudes and low frequencies. These effects have a pronounced impact on carbody stability in conditions with low wheel-rail conicity and significantly affect passenger's comfort. The insights gained from this study offer valuable implications for the design, optimisation and standardisation of yaw dampers in high-speed trains.

A two-degree-of-freedom nonlinear high-speed railway wheelset model with two time delays in the lateral and yaw dampers is studied. The aim is to investigate the effect of time delays on stability and Hopf bifurcation characteristics of the wheelset model. The local stability of the trivial equilibrium under different time delay conditions is qualitatively analyzed. Analytical studies reveal that the wheelset model undergoes stability switches with the variation of the time delays. The stability switches correspond to Hopf bifurcations that occur when the time delays cross critical values. Furthermore, properties of Hopf bifurcation including direction and stability of bifurcating limit cycles are studied by using the normal form theory and the center manifold theorem. Our findings indicate that time delays in both lateral dampers and yaw dampers influence the stability and direction of Hopf bifurcation. Additionally, the numerical results show that time delays in the lateral and yaw dampers not only affect the amplitude of the hunting motion of the wheelset but also the periodic and chaotic motions. If the time delays gradually increase, the wheelset will vibrate irregularly with large lateral displacements. The analytical results presented in this paper offer a theoretical reference for the stability design of wheelsets.

Wheelsets are important components of railway vehicles, and their health directly affects running safety, operation efficiency, and passenger comfort, so it is particularly important to timely detect or further isolate wheelset defects. Till now, researchers have carried out a great deal of work on methods for wheelset fault diagnosis, and this paper systematically surveys these representative works. Based on the inspection environment, the scene of inspection devices, and the passage speed of vehicles, the fault diagnosis methods in the surveyed works are first summarized into three major categories, i.e., in-workshop methods, wayside methods, and on-board methods. To further summarize, according to the disciplinary knowledge on which the inspection devices rely, incl., acoustics, optics, mechanics, electromagnetism, and thermology, the three major categories are sub-categorized. Then, the advantages and disadvantages of each category are summarized and compared, and the development trends and major problems to be solved are discussed. Finally, the following challenges and potential directions are pointed out: (1) Artificial intelligence (AI) technology, incl., deep learning (DL), has gradually been introduced into wheelset fault diagnosis, but most of the current research only stays at the theoretical level, resulting in the engineering value of AI technology not being reflected. (2) The relationship between the defect size, the fault features in signals, and the running safety of the vehicle is required to be established, and the on-board inspection devices need to realize the real sense of intelligence, which cannot violate the original intention of reducing costs and improving efficiency. (3) More reasonable thresholds of defects and standards for the definition of faults should be customized according to the characteristics of the vehicles themself and the service environment of the train, to take into account the running safety and maintenance economy. (4) Reliable and highly intelligent diagnostics using multi-sensor fusion technology and AI technology is a challenge for researchers to address. (5) High automation of the inspection process and high integration of inspection devices are the future development direction. (6) In-workshop methods, wayside methods, and on-board methods need to be applied synergistically, and combined with AI technology, to achieve the comprehensive and preventive maintenance of wheelsets.