Wheel-rail dynamic interaction in high-speed railway systems: a comprehensive review of stability, safety and wear evolution

In recent decades, the rapid development of high-speed railway (HSR) systems worldwide has been recognised as one of the strategic transportation solutions for meeting the increasing demand for fast, safe, and sustainable mobility (Su, Li, Su, Chang, & Liu, 2024; Doan Van & Lu, 2026). Along with the continuous increase in operating speeds and axle loads, more stringent requirements have been imposed on the dynamic stability, reliability, and operational safety of railway vehicles (Chi, Xiao, Nadakatti, Zhang, & Wang, 2024). In this context, the dynamic interaction between the wheel and rail has emerged as a central factor that directly governs vehicle vibration behaviour, ride quality, the level of wear and structural damage, as well as the risk of instability and accidents (Yang & Li, 2022). Therefore, a comprehensive investigation of the mechanisms, modeling approaches, and characteristics of wheel-rail (WR) dynamic interaction is considered essential for enhancing stability and ensuring the safety of HSR systems, while also providing an important scientific foundation for modern design, operation, and maintenance practices (Sun, Seyedkazemi, Nguyen, & Zhang, 2025a).

Although numerous studies have been conducted on WR dynamic interaction, this field still faces several significant challenges (Lu, Chen, Shi, & Li, 2024). First, the contact characteristics between the WR are inherently highly nonlinear and extremely complex, being simultaneously influenced by contact geometry, surface conditions, material properties, applied loads, and operating speeds, which makes the accurate modeling and prediction of dynamic responses particularly difficult (Montenegro & Calçada, 2023). In addition, the strong coupling and mutual interaction among system dynamics, wear processes, and operational safety issues may lead to increased dynamic forces, deterioration of ride quality, and potential instability risks (Wang, Zhou, Liu, Wang, & Jing, 2025). However, existing studies remain largely fragmented across individual aspects and lack a systematic and integrative perspective. Consequently, a comprehensive review is urgently required to integrate the underlying mechanisms, modeling approaches, and existing research findings, thereby clarifying the central role of WR dynamic interaction in enhancing stability and ensuring the safety of HSR systems (Zhang et al., 2023a, b).

Therefore, this paper aims to provide a comprehensive and systematic overview of WR dynamic interaction in HSR systems. Specifically, existing studies are classified into several major thematic categories, including contact mechanisms, dynamic characteristics, wear behaviour, and issues related to stability and operational safety. On this basis, modern modeling approaches, ranging from theoretical formulations and numerical models to multi-physics and multi-scale methods, are compared and evaluated in order to clarify their respective advantages, limitations, and ranges of applicability. Finally, through the synthesis and analysis of published research findings, existing research gaps are identified and potential future research directions are proposed, thereby contributing to the development of subsequent studies aimed at enhancing stability and ensuring the safety of HSR systems.

To ensure a systematic, this review adopted a structured literature retrieval and selection protocol. A comprehensive literature search was conducted across major academic databases (Web of Science, Scopus, IEEE Xplore, Elsevier, Springer, Google Scholar) using targeted Boolean logic (wheel-rail contact, wheel-rail interaction, high-speed railway, hunting stability, derailment safety, machine learning, AI, digital twin, multi-physics). The temporal scope primarily focused on publications between 2010 and 2026 to capture state-of-the-art technological breakthroughs, while foundational papers prior to 2010 were selectively retained to preserve theoretical continuity in contact mechanics. Through this systematic screening protocol, representative studies were curated and seamlessly integrated into the subsequent analytical framework.

To provide a clear logical framework for this comprehensive review, a technical roadmap is presented in Figure 1. Section 2 presents the theoretical foundations of WR contact. Section 3 introduces WR dynamic models, as well as rail and track infrastructure models. Section 4 discusses dynamic effects, WR wear, and their evaluation through experimental investigations. Subsequently, Section 5 presents research trends, existing research gaps, and potential future directions. Finally, Section 6 summarises the main conclusions.

The Hertzian contact theory, originally proposed by Heinrich Hertz in 1882, has remained the most widely adopted fundamental model for the analysis of WR contact (Hertz, 1982). This theory is established on several fundamental assumptions, in which the WR materials are considered to be linear elastic, isotropic, and free from plastic deformation throughout the contact process. The contact surfaces are assumed to be smooth, friction in the normal direction is neglected, and the contact deformation is considered small compared with the overall geometric dimensions of the WR. Under these assumptions, WR contact is characterised by an elliptical contact patch, within which the pressure distribution follows a parabolic law and the maximum pressure occurs at the centre of the contact region. The Hertzian contact theory exhibits broader applicability than many other failure criteria across various damage mechanisms, as illustrated below (Iwnicki, Björklund, & Enblom, 2009):

Where: p₀ is the maximum contact pressure, P is the normal contact load, E^* is the equivalent elastic modulus, R is the equivalent radius of curvature, and $F1(ξ)$ is the elliptic integral function associated with the contact ellipticity parameter $ξ$⁠, as illustrated in Figure 2.

Owing to its relatively simple formulation, the Hertzian model enables rapid calculations, making it well suited for multibody dynamics (MBD) simulations and readily integrable into commercial software packages such as SIMPACK, UM, and ADAMS/Rail (Bulduk & Metin, 2025). However, this model also presents certain limitations, as plastic deformation, residual stresses, and thermal effects are not considered, which results in reduced accuracy under conditions of high loads, prolonged high-speed operation, or complex localised contact regions such as wheel flange contact. Leban et al. (2024) presented a study in which a Hertz-type contact model was applied to a practical WR pair by utilising ultrasonic measurement data and vehicle dynamic analysis. It was confirmed that the Hertz model remains effective in predicting contact stresses and rail performance, particularly under standard loading conditions, although minor deviations were observed compared with non-Hertzian models in complex contact regions such as curved tracks. The results highlighted the significant role of this model in railway safety and performance management, while also supporting more efficient finite element (FE) simulations in WR design. Li, Qi, Wu, Ding, and Ding (2025c) developed a coupled dynamic model of a high-speed bogie turnout system that was established using a semi-Hertzian contact theory to accurately predict rail wear in turnouts. A profile updating step of 0.05 mm and an adaptive filtering algorithm were employed, achieving a matching accuracy of 89.91 % with field measurement data. Several wear models were compared, and the results demonstrated that the semi-Hertzian formulation outperforms the classical Hertz model in computational efficiency. Furthermore, a comprehensive rail grinding strategy based on longitudinal wear distribution was proposed, resulting in reductions of 52.56 % in lateral vibration and 30.43 % in vertical vibration when vehicles passed through the turnout.

In WR interaction simulations, the normal contact model is essential for accurately determining the contact forces and stress distribution. Although the linear elastic Hertzian model has been widely adopted due to its simplicity and computational efficiency, it is purely elastic assumptions become inadequate under conditions of high loads and high-speed operation. Consequently, elastic-plastic contact models have been developed to account for plastic deformation, residual stresses, and the accumulation of material damage, thereby enabling a more accurate representation of contact behaviour in regions subjected to high stress and complex localised contact conditions, particularly at the wheel flange contact (Jing, Zhou, & Wang, 2023). When the contact pressure exceeds the material yield limit, a localized plastic deformation zone is formed beneath the contact surface. This leads to a nonlinear stress distribution that no longer follows the symmetric elliptical pattern characteristic of Hertzian contact. Elastic-plastic models enable the determination of the size and location of the plastic zone while also describing the shakedown phenomenon, in which the material transitions to a repeated elastic response after several initial loading cycles (McMaster, Kosarieh, Liskiewicz, Neville, & Beake, 2023). This mechanism constitutes a key factor in the analysis of rolling contact fatigue (RCF) initiation.

Another important characteristic of elastic-plastic contact is the accumulation of residual deformation during rolling-sliding cycles. This residual deformation gradually modifies the contact surface geometry, leading to an expansion of the contact patch and changes in slip distribution as well as local friction conditions. In WR systems, these mechanisms are closely associated with progressive wear processes, strain hardening, and the formation of surface damage modes such as micro- and macro-spalling (Zhou, Li, Wen, Zhou, & Tao, 2024). Furthermore, modern elastic-plastic models also account for material inhomogeneity along the depth direction, arising from heat treatment processes, surface hardening, and strain hardening accumulated during service (Fu et al., 2024). The incorporation of advanced hardening laws and yield criteria enables a more accurate representation of the mechanical property evolution within the surface layer, which is the region most susceptible to the initiation of RCF cracks. Zhou et al. (2024) presented a three-dimensional FE model that was developed to analyse the elastic-plastic stress state of WR contact under cyclic loading. The model incorporated an improved cyclic plasticity law and demonstrated that, under repeated loading and local slip, stresses and plastic strains within the rail surface layer continuously accumulate with the number of cycles, particularly under partial slip conditions. This accumulation is clearly reflected by the increase in equivalent residual plastic strain and accumulated residual deformation, which can promote rail damage once the plastic limit of the material is exceeded. Three-dimensional elastic-plastic models are therefore required for the accurate prediction of contact stresses and RCF life. Spiryagin et al. (2023) reported that a WR contact model incorporating surface roughness and elastic-plastic material behaviour was developed and implemented within an MBD simulation framework for locomotive traction studies. Simulation results indicated that the combined consideration of surface roughness and elastic-plastic deformation reduces local stress concentrations at the junction between the wheel tread and wheel flange, particularly under high traction forces, thereby confirming the essential role of elastic-plastic models in accurately simulating WR interaction under realistic operating conditions. Skrypnyk, Nielsen, Ekh, and Pålsson (2019) described a surrogate modeling approach based on FE results that incorporates elastic-plastic material behaviour that was proposed to simulate normal WR contact in turnout regions. This surrogate model accurately reproduced the pressure distribution and contact area under high-load conditions while significantly reducing computational cost compared with the full FE model, demonstrating the potential for integrating elastic-plastic models into large-scale WR dynamic simulations. Owing to their capability to more realistically represent stress and deformation fields, elastic-plastic models play an important role in predicting wear and RCF, as well as in linking contact mechanics with maintenance strategies and wheel reprofiling practices. However, this high level of accuracy is accompanied by significant computational cost and the requirement for detailed material data, which means that elastic-plastic models are typically applied to local analyses or used as reference benchmarks for simpler models in large-scale simulations.

Kalker's linear theory serves as a fundamental model for describing the tangential contact forces between the WR under conditions of micro-slip and small relative rotational motion. According to this theory, the longitudinal and lateral tangential forces, as well as the spin moment, are assumed to be linearly proportional to the creep quantities, thereby allowing the formulation of simple analytical expressions that can be readily integrated into MBD models (Tudorache, Oprea, Spiroiu, Craciun, & Arsene, 2025). A key assumption of this theory is that the contact patch operates predominantly in an adhesion state, with only a very small portion experiencing local slip. Under this condition, the tangential forces in the longitudinal and lateral directions, as well as the torsional moment, are linearly related to the relative creep components, which are characterised by creep coefficients dependent on the contact patch geometry, elastic modulus, Poisson's ratio, and the normal load (Jin, 2022). Consequently, Kalker's theory provides a compact representation with a clear physical basis for tangential WR interaction. An important advantage of the linear theory is the ability to decouple the normal and tangential contact problems, in which the normal contact problem is typically solved using the Hertz model, while the tangential problem is treated independently through creep coefficients. This approach allows straightforward integration into vehicle and train dynamic models, particularly in studies concerning motion stability, vibration behaviour, and guiding forces (Szeszycki, Bryk, & Stefańska, 2024). However, when creep and spin increase and local slip occurs, the linear assumption becomes no longer valid; therefore, nonlinear contact models are required to ensure adequate accuracy.

The nonlinear FASTSIM model is an efficient approximation method for describing tangential WR contact under conditions involving local slip. Based on Kalker's contact theory, FASTSIM accounts for the non-uniform distribution of adhesion and slip regions within the contact patch, thereby providing a more realistic representation of the nonlinear behaviour of tangential forces as creep increases. Owing to its simple computational algorithm and low computational cost, FASTSIM has been widely applied in MBD simulations of HSR systems, particularly in analyses related to stability, wear, and operational safety (Vollebregt & Voltr, 2023). Liu and Bruni (2024) extended the nonlinear FASTSIM model to accommodate non-Hertzian contact conditions, which commonly occur in practical WR interactions due to complex geometry and localised deformation. The extended FASTSIM formulation enables a more detailed representation of the distribution of adhesion and slip regions within the contact patch, thereby allowing a more accurate computation of tangential force distribution and dissipated energy under conditions of increased creep. The results indicated that the use of the extended FASTSIM model significantly improves the prediction capability for wear and RCF compared with linear models based on Hertzian assumptions, while still maintaining high computational efficiency suitable for integration into large-scale WR dynamic simulations. Chen, Sun, Ding, and Wang (2023) conducted a systematic evaluation of fast non-Hertzian contact models, including extended variants of FASTSIM, which was conducted when directly integrated into vehicle dynamic simulations. The results indicated that non-Hertzian approaches provide a more accurate representation of the actual contact patch geometry as well as the non-uniform distribution of adhesion and slip regions, particularly under conditions of complex WR geometry and varying loads. At the same time, these models maintain high computational efficiency, enabling their application in large-scale multibody simulations without significantly compromising numerical stability or computational time.

The nonlinear CONTACT model is a high-accuracy approach for describing WR contact based on Kalker's non-Hertzian contact theory. In this model, the normal and tangential stress distributions within the contact patch are solved directly, while the adhesion-slip regions and the actual contact geometry are determined in detail. As a result, CONTACT is capable of accurately representing complex contact conditions, particularly in cases involving large creep, non-elliptical contact geometries, or worn surfaces. However, due to its high computational cost, the CONTACT model is typically employed for detailed analyses or used as a reference benchmark for the evaluation and calibration of approximate models in railway dynamic simulations (Giner-Navarro, Gómez-Bosch, Alonso, & Baeza, 2023; Fang et al., 2023). Baeza, Bruni, Giner-Navarro, and Liu (2023) presented a linearised non-Hertzian tangential contact model that was proposed to describe WR interaction under time-varying unstable contact conditions. The model was developed based on Kalker's non-Hertzian contact theory and constructed with direct reference to the CONTACT algorithm, allowing the actual contact patch geometry and the non-uniform distribution of adhesion and slip regions to be considered. The results indicated that the model is capable of accurately reproducing tangential force responses under conditions of varying creep coefficients and complex contact geometries, while achieving significantly higher computational efficiency compared with the full nonlinear CONTACT model, thereby making it suitable for integration into large-scale WR dynamic simulations. Yang et al. (2022) employed a non-Hertzian contact model that was applied to analyse the dynamic interaction between locomotive wheels and the rail under conditions where the friction coefficient varies spatially and temporally. The model enables the direct determination of the normal contact pressure distribution, tangential forces, and the formation of adhesion-slip regions within the actual contact patch, thereby providing a more accurate representation of the nonlinear behaviour of WR contact compared with classical Hertzian assumptions. The results indicated that the consideration of non-Hertzian contact is essential for accurately describing dynamic force responses, particularly under conditions of high loads and unstable friction that are characteristic of railway operation.

The friction coefficient between the WR governs tangential forces, traction-braking capability, and the dynamic stability of railway vehicles. Fundamentally, the friction coefficient determines the adhesion limit within the contact patch, thereby directly influencing the distribution between adhesion and slip regions. When the friction coefficient increases, the maximum tangential force that can be transmitted through the contact also increases, which improves traction and braking performance; however, this simultaneously leads to increased contact stresses and wear rates, particularly under conditions of large creep or at wheel flange contact. Conversely, a low friction coefficient reduces the available tangential force, which may result in wheel slip, deterioration of running stability, and increased safety risks, especially during high-speed operation or under adverse weather conditions. Therefore, the friction coefficient is not merely a material parameter but also a key dynamic parameter that must be accurately modelled and properly controlled in WR interaction analyses, as well as in the design and operation of modern railway systems (White et al., 2024; Krishnan, Moraal, Li, & Yang, 2025).

Low-adhesion conditions in WR contact, commonly caused by rain, dew, fallen leaves, or rail surface contamination, represent a significant challenge for HSR operation. The reduction in the friction coefficient markedly decreases the available tangential force, leading to wheel slip, reduced traction-braking performance, and increased braking distances. At the same time, low adhesion alters the creep characteristics, causing the creep force to reach saturation earlier and become more sensitive to small variations in creep, thereby reducing the guiding capability of the wheelset and increasing the risk of dynamic instability, particularly under conditions of high-speed operation and heavy axle loads (Xiao, Wu, Yao, & Shen, 2022; Wu, Xiao, An, Wu, & Shen, 2022; Chang, Chen, Cai, & Wang, 2024).

Song et al. (2025) conducted WR contact experiments under large creep conditions with various surface environments, including water, oil, and contaminants simulating leaf layers. The results indicated that the presence of these environments significantly reduces the maximum adhesion coefficient while causing the tangential force to reach saturation earlier and become more sensitive to small variations in slip ratio. Low-adhesion conditions not only reduce the capability for traction-braking force transmission but also modify the dynamic characteristics of WR contact, thereby adversely affecting the operational stability of railway systems. Zhao et al. (2023) reported that the influence of unilateral local low-adhesion conditions on the transitional rolling-sliding contact between the WR was analysed. The results demonstrated that asymmetric adhesion loss significantly alters the distribution of tangential forces and creep within the contact patch, leading to an expansion of the slip region and increased temporal fluctuations of contact forces. These variations not only reduce the guiding capability of the wheelset but also promote the formation of wheel damage, particularly asymmetric wear and the initiation of RCF. Qiao et al. (2025) conducted experiments to evaluate the effectiveness of sand application in improving WR adhesion under low-friction conditions. The results indicated that sand application significantly increases the adhesion coefficient and shifts the saturation point of the tangential force toward a higher slip region, thereby reducing wheel slip and improving traction-braking force transmission, as illustrated in Figure 3. At the same time, the restoration of adhesion stabilises the distribution of adhesion-slip regions within the contact patch, contributing to improved guiding capability and enhanced operational safety of railway vehicles under adverse conditions.

The coupled vehicle-track system model represents a fundamental and effective approach for investigating WR dynamic interaction, in which the railway vehicle and the track structure are treated as an integrated dynamic system with bidirectional interaction through WR contact. In this framework, the equations of motion of both the vehicle and the track are formulated and solved simultaneously, allowing the two-way dynamic mechanisms to be fully represented. The WR contact force acts as the interface through which energy is transmitted and vibrations are excited between the vehicle and the track structure. In this process, rail deformation and vibration govern the dynamic response of the train, while the motion of the train determines the magnitude of dynamic loads and the level of track damage. Consequently, the coupled model is capable of accurately describing important phenomena such as nonlinear vibration, degradation of dynamic stability, amplification of contact forces, and the influence of rail geometric irregularities and high axle loads during high-speed operation. This approach thus establishes an essential theoretical foundation for analyses of stability, safety, wear, and structural durability in HSR systems (Narayanan, Vishwakarma, & Harsha, 2025; Cai, Zhong, Lau, Zhang, & Hou, 2024; Doan Van, Nguyen Huu, Vo Dinh, & Tran Cong, 2026). Ishchuk et al. (2023) described how the MBD framework was extended by incorporating flexible bodies in order to more accurately represent the influence of structural compliance on the overall dynamic response. The integration of flexible components, typically implemented through the FE method and model order reduction techniques, enables the interaction between structural vibrations and the nonlinear motion of the multibody system to be captured. The results indicated that deformation effects have a significant influence on dynamic WR loads, vibration responses, and motion stability, particularly under high-speed operating conditions or excitations induced by track geometric irregularities. Li, Chi, Guo, and Liang (2023) investigated the abnormal lateral vibration of an intercity electric multiple unit (EMU) carbody using a detailed MBD model, in which WR interaction and the characteristics of the yaw damper were consistently represented. The results indicated that the reduction of the equivalent WR conicity decreases the self-steering capability of the wheelset, while the unloading of the yaw damper force weakens the energy dissipation mechanism of the vibration. The combined effect of these two factors leads to dynamic instability within the operating speed range, resulting in large-amplitude carbody oscillations. The study confirms the importance of MBD models in simultaneously evaluating the influence of contact geometry and suspension parameters on running stability.

In MBD models of the vehicle-track system, system components can be represented either as rigid bodies or as flexible bodies depending on the required level of accuracy and the dynamic frequency range to be considered. The rigid body model assumes that components are non-deformable and considers only the translational and rotational motion of concentrated masses. Owing to its simplicity and computational efficiency, this approach is commonly applied to components such as the carbody, bogie, or wheelset in analyses of overall dynamic stability. In contrast, flexible body models allow elastic deformation and structural vibration modes to be considered and are typically applied to rails, sleepers, wheel axles, or carbody structures when accurate representation of high-frequency vibration phenomena and stress distributions is required. The combination of rigid and flexible bodies within a coupled model provides a balance between physical accuracy and computational cost while enabling a comprehensive representation of the dynamic interaction between the vehicle and the track under conditions of high-speed operation and high axle loads (Sun, Cai, Cheng, Hu, & Zhou, 2024a; Sharma, Sharma, Choi, & Lee, 2023; Pagaimo, Millan, & Ambrósio, 2023). Wikaranadhi and Handoko (2023) described an MBD model that was employed to analyse the curving performance of a long-rail transport train, in which the rail and track structure were represented with elastic properties in order to capture the realistic dynamic interaction between the vehicle and the track. The consideration of structural flexibility enabled a more accurate simulation of WR load distribution, relative motion between wheelsets, and the dynamic response of the train when negotiating small-radius curves. The results indicated that the coupled rigid-flexible MBD model is capable of capturing dynamic effects that are difficult to represent using purely rigid-body models, particularly in problems involving high loads, special geometries, and complex operating conditions.

Guan, Deng, and Wang (2023) presented an MBD model of a HSR that was developed in which the wheelset was represented as a flexible component, while the influence of polygonal wheel wear was also considered. The incorporation of wheelset flexibility enables a more accurate simulation of vibration transmission from WR contact to the axle-box bearing, particularly within the medium- and high-frequency ranges. The results indicated that structural deformation effects and geometric wear have a significant influence on the dynamic response and dynamic loading of the bearing. The standard deviation of the WR vertical force increases with the amplitude of polygonal wheel wear, as illustrated in Figure 4. These findings confirm the necessity of coupled rigid-flexible MBD models for vibration and component durability analyses in modern railway vehicle systems. Sun, Liu, Sun, Li, and Wang (2023b) utilised an MBD model of a six-axle heavy-haul locomotive with a broad gauge, in which the wheelset was represented with structural flexibility to evaluate the influence of elastic deformation on the overall dynamic characteristics. The results indicated that wheelset compliance has a noticeable effect on WR load distribution, vibration response, and motion stability indices, particularly under conditions of high axle loads and excitations caused by track irregularities. Compared with traditional rigid-body models, the MBD model incorporating flexible wheelsets provides a more accurate representation of dynamic effects in the medium and high-frequency ranges.

In the dynamic modeling of vehicle-track systems, the track infrastructure is considered a critical component that significantly influences the dynamic response and the distribution of WR forces. Two commonly adopted track structures are ballasted track and slab track. For ballasted track, the ballast layer is typically modelled as a distributed elastic-damping medium that absorbs vibrational energy and distributes loads from the rail to the subgrade, resulting in a relatively compliant system with effective attenuation of high-frequency vibrations. However, the nonlinear characteristics and the gradual stiffness degradation of ballast over time make the dynamic response of the system sensitive to repeated loading and operating conditions (Vale, 2021; Hu & Bian, 2022). Sayeed and Shahin (2023) presented a three-dimensional FE model that was employed to analyse the dynamic response of the ballast-subgrade track system under moving train loads. The ballast structure was modelled as a distributed elastic-damping medium, allowing the transmission and attenuation of vibrations from the rail to the subgrade to be represented. The results indicated that the stiffness and damping parameters of the ballast layer play a decisive role in determining vibration amplitudes, stress distribution, and the high-frequency dynamic response of the system, while also demonstrating the sensitivity of the dynamic behaviour to repeated loading and train speed. Farooq, Nimbalkar, Punetha, and Sheng (2024) investigated the rail response in both the vertical and lateral directions, as illustrated in Figure 5. The results showed that lateral displacement increases as the axle load varies from 20 to 40 tons. In addition, train speed was found to significantly affect the track structural layers. Specifically, lateral displacement increased to 5 mm at a train speed of 200 km/h compared with 3.9 mm at 70 km/h. Meanwhile, vertical displacement reached 6.5 mm at 200 km/h compared with 5 mm at 70 km/h, as shown in Figure 6.

In contrast, slab track employs a continuous concrete structure with high stiffness and is typically modelled using continuous elastic elements or FE formulations, allowing the rail geometry to be maintained more stably and reducing overall deformation during high-speed operation. Although slab track offers advantages in geometric stability and reduced maintenance requirements, it exhibits a more limited capability for vibration absorption compared with ballasted track, which may lead to increased dynamic responses and localised stresses if not properly designed (Alzabeebee, Alkhalidi, Obaid & Keawsawasvong, 2023, 2024). Vu, Jang, and Kang (2021) investigated the structural dynamic response and vehicle-track interaction of a prefabricated slab track system, which were evaluated using a coupled vehicle-track model. The analysis results indicated that although slab track reduces the overall structural deformation, the dynamic response and localised stresses in the rail and slab tend to increase if the elastic and damping characteristics of the intermediate layers are not properly selected. These findings highlight the importance of detailed slab track modeling in dynamic analyses in order to achieve a balance between geometric stability, vibration control, and structural durability. Aly, Elnaga, Soliman, and Diab (2024) presented a new design approach for slab track systems that was proposed, in which the concrete slab and intermediate elastic layers were modelled in detail to evaluate the influence of stiffness, thickness, and damping characteristics on rail deformation and WR force distribution. The results indicated that the appropriate selection and coordination of the elastic parameters of the slab track play a decisive role in controlling dynamic responses and localised stresses, particularly under high-speed operating conditions. These findings confirm that accurate modeling of slab track not only supports dynamic analysis but also provides an essential basis for the sustainable and safe design of modern railway systems.

In the dynamic modeling of vehicle-track systems, rail geometric irregularities and the stiffness of the track infrastructure are two key factors governing the dynamic response and WR forces. Rail irregularities act as sources of forced excitation, inducing vibrations in the wheelsets, bogies, and carbody, thereby increasing contact forces, vibration amplitudes, and wear rates, particularly during high-speed operation. Choi, Park, Chung, and Kim (2021) demonstrated that irregularities in rail geometry increase dynamic WR interaction forces even when the deviations are small, and the magnitude of this increase strongly depends on train speed. Moreover, carbody vibrations caused by rail irregularities and alternating wear may further amplify forced effects within the vehicle-track system, thereby reducing operational stability if not properly considered in MBD models (Wei et al., 2025). Meanwhile, the stiffness of the track structure and subgrade governs the transmission and attenuation of vibrations. Stiff structures such as slab track help maintain stable rail geometry but tend to increase dynamic forces and localised stresses, whereas more compliant structures such as ballasted track can reduce peak forces but are more prone to nonlinear behaviour and the accumulation of deformation over time (Xiao, Xu, Yang, Chen, & Hu, 2024; Chen, Pei, & Liu, 2025; Sun et al., 2024a, b). Han, Li, and Cheng (2025) identified the spatial non-uniformity of ballasted track stiffness constitutes an important source of dynamic excitation, which can produce vibration responses and WR force distributions similar to, or even indistinguishable from, the effects of rail geometric irregularities. Through the use of a two-dimensional multi-degree-of-freedom (MDOF) coupled vehicle–track model and a model-updating procedure based on measured dynamic data, localised reductions or increases in ballast stiffness were shown to cause significant variations in dynamic contact forces, thereby increasing the risk of misinterpreting track condition when rail geometry alone is considered. At the same time, studies on ballast stiffness irregularity have indicated that variations in infrastructure stiffness modify force distribution and vibration characteristics, leading to increases in contact forces beyond design limits if not properly controlled (Shi, Zhou, Xu, Zhang, & Guo, 2023). The interaction between rail geometric irregularities and the stiffness characteristics of the infrastructure may produce amplification or resonance effects, thereby directly affecting dynamic stability, structural durability, and the operational safety of HSR systems.

When trains operate at high speeds (above approximately 200–250 km/h), the vehicle-track-bridge system no longer responds independently but behaves as a complex coupled dynamic system. In this interaction, forces transmitted from the wheels pass through the rail to the bridge structure, while the deformation and vibration of the bridge affect vehicle motion and WR contact forces. At low speeds, the dynamic response is primarily governed by relatively simple relative motion; however, as speed increases, effects such as resonance vibration, amplified dynamic responses, and repeated reaction forces from the bridge to the rail and vehicle become more pronounced. These phenomena lead to significant changes in vibration levels, contact forces, localised stresses, and safety indices for both the train and the bridge structure. Numerous studies have shown that as operating speed increases, the coupled dynamic response causes rapid growth in bridge and vehicle accelerations and internal forces due to bidirectional interaction. The bridge may experience larger vibration amplitudes under HSR passage, and these vibrations are subsequently transmitted back to the vehicle system, thereby affecting motion stability and material durability (Ribeiro, Calçada, Brehm, & Zabel, 2022; Liu, Luo, Dai, & Tang, 2025b).

In their study König and Adam (2024) demonstrated that under the action of HSR, the longitudinal interaction among the rail, ballast, and bridge structure forms a bidirectional coupled dynamic system in which bridge vibration and deformation modify WR forces. At high speeds, these interaction effects significantly increase the dynamic response of both the bridge and the vehicle system; therefore, they cannot be neglected in the evaluation of operational stability and the structural durability of ballasted railway bridges. Tahiri, Khamlichi, Dkiouak, and Bezzazi (2024) clarified the dynamic response of a simply supported beam bridge influenced by the coupled interaction between the rail and the bridge. The results indicated that neglecting rail-bridge interaction may lead to an underestimation of the dynamic response, particularly at high speeds. Consequently, comprehensive modeling of the coupled interaction effects is required for accurate analysis of the safety and durability of railway bridges. Therefore, comprehensive modeling of this coupled interaction incorporating the structural responses of the bridge, rail, and train within a unified coupled system is required to ensure dynamic stability, operational safety, and the sustainable structural design of HSR lines.

Hunting motion in WR systems represents a system-level self-excited vibration sustained and amplified by internal dynamic forces without periodic external excitation. This mechanism originates from the nonlinear coupling among WR contact geometry, tangential creep forces, and suspension system dynamics. When a wheelset deviates laterally from its equilibrium position, the difference in rolling radii between the two wheels generates longitudinal and lateral micro-slip, producing tangential forces and spin moments that are out of phase with the oscillatory motion. Above a critical speed threshold, the contact forces supply positive energy to the oscillation, exceeding the dissipation capacity of suspension damping and leading to sustained limit-cycle oscillations. Consequently, hunting motion reflects the transition from dynamic equilibrium to system instability, serving as a primary determinant of HSR operational safety (Liang, Sun, Jiang, Pan, & Jiao, 2024; Zheng, Wei, Zeng, & Zhang, 2024; Li, Tan, Stichel, & Yao, 2025a).

In addition to wheelset hunting dynamics, friction-induced self-excited vibration represents another distinct mode of dynamic instability operating primarily at localized contact zones. Distinct from hunting motion driven by rolling-radius differences, this phenomenon is induced by velocity-dependent friction characteristics and transient slip transitions, particularly during braking operations (Xiaolu, Pengyu, Jiaxin, & Zongchao, 2021). Cui et al. (2021) identified that friction-induced self-excitation can sustain contact vibrations even under non-periodic conditions. When the tangential friction force becomes out of phase with oscillatory velocity, energy is continuously injected into the local system, establishing a feedback loop with rail surface wave-like irregularities that accelerates corrugation and uneven wear. Recognizing friction-induced chatter as a localized self-excitation mechanism separate from global vehicle hunting is crucial for addressing high-speed braking noise, contact fatigue, and localized wear evolution.

The determination of the critical speed in hunting stability analysis refers to identifying the velocity at which the dynamic equilibrium of the wheelset-bogie-carbody system transitions from a stable to an unstable state, leading to the onset of self-excited oscillations. From a theoretical perspective, the critical speed is typically determined by linearising the equations of motion around the straight-running equilibrium state and performing eigenvalue analysis. As the velocity increases, the influence of tangential forces modifies the effective stiffness and damping characteristics of the system, and at a certain speed, the real part of a pair of complex conjugate eigenvalues changes sign from negative to positive, indicating the loss of dynamic stability. In nonlinear models, the critical speed may also be identified through time-domain simulations by observing the transition from decaying oscillations to sustained limit-cycle oscillations when the operating speed exceeds a threshold. The critical speed strongly depends on WR contact geometry, tangential force characteristics, suspension stiffness and damping, as well as friction conditions and loading, and therefore plays a key role in the design, stability assessment, and the establishment of safe operating limits for HSR systems (Yu, Ma, Zhang, & Niu, 2022). Hou, Yang, Chen, Liu, and Wang (2024) reported that rail profile deviations have a direct influence on the critical speed of hunting oscillation by modifying WR contact geometry and tangential force characteristics. Under coupled parameter conditions such as suspension stiffness and damping, axle load, and friction coefficient, even small deviations in the rail profile may lead to significant shifts in the critical speed value. The analysis results indicated that when profile deviations increase the sensitivity of tangential forces to micro-slip, the real part of the complex conjugate eigenvalue pair becomes positive at a lower velocity, resulting in the earlier onset of self-excited oscillations. Zhang, Ling, Stichel, and Zhai (2024a) demonstrated that the integration of a bio-inspired damping mechanism into the bogie traction system suspension can significantly alter the effective damping characteristics of the vehicle system, thereby shifting the critical speed of hunting oscillation. Through eigenvalue analysis and time-domain simulations, it was shown that the proposed damping structure maintains the real parts of the complex conjugate eigenvalue pairs at negative values over a wider speed range, thereby increasing the critical speed and delaying the onset of self-excited oscillations. These findings confirm the key role of damping distribution and magnitude in controlling the critical speed and indicate that advanced suspension design solutions can significantly improve dynamic stability and safe operating limits for HSR systems.

The Nadal criterion is one of the classical and standard operational safety indices used to assess the risk of flange-climb derailment in WR interaction. It represents the relationship between the lateral force L and the vertical force V at the WR contact under conditions approaching derailment, expressed through the ratio L/V. According to the classical Nadal formulation (Huang, 2021), the safety limit is defined as:

Where: α represents the wheel flange angle (typically ranging from 60° to 75° for wheel profiles such as S1002 or LMA) and μ denotes the WR flange friction coefficient (generally assumed between 0.3 and 0.4 under dry conditions, or managed below 0.2 with flange lubrication).

The derailment coefficient thresholds vary across countries, with a limit of 0.8 adopted in Europe (TSI, 2002), Japan (RTRI, 2006), China (TB 10621, 2014), and 1.0 adopted in the United States (AAR, 2011). When the L/V ratio exceeds this limiting value, the lateral force becomes excessively large relative to the vertical load, allowing the wheel flange to climb onto the rail head and thereby leading to a risk of flange-climb derailment and loss of operational stability. Owing to its simplicity, the Nadal criterion has been widely applied in the design, testing, and dynamic safety assessment of railway vehicles, particularly in analyses related to stability and high-speed operation (Stoilov, Sinapov, Slavchev, Maznichki, & Purgic, 2024).

The wheel unloading ratio is an important safety index used to evaluate the reduction of the vertical force acting on a wheel during operation, reflecting the risk of loss of WR contact and potential derailment, WR separation occurs at 1. From a mechanical perspective, this ratio represents the relative decrease of the dynamic wheel load compared with the static wheel load, which commonly arises from vertical vibrations and rolling motions of the vehicle system induced by rail irregularities, bridge vibrations, centrifugal forces in curves, or nonlinear WR dynamic interaction. When the wheel unloading ratio becomes large, the normal force maintaining WR contact is reduced, thereby increasing the L/V ratio and the risk of flange climbing, particularly under conditions of high-speed operation and heavy axle loads (Magalhães et al., 2024). The wheel unloading ratio limits vary across national standards, with a limit of 0.9 specified in the United States (AAR, 2011) and Europe (CEN, 2010), while China (TB 10621, 2014) specifies a limit of 0.6. In HSR turnout regions, WR contact conditions are strongly influenced by the redistribution of dynamic loads caused by geometric discontinuities and complex load transmission mechanisms. Among the safety indices, the wheel unloading ratio is a key parameter used to quantify the reduction of the vertical contact force between the wheel and rail, thereby reflecting the risk of contact loss. Wang, Shen, Huo, Wang, and Qin (2025a) reported that large wheel unloading ratios frequently occur in sensitive regions of turnouts, demonstrating intensified dynamic interaction and reduced contact stability. When combined with WR force indices in multivariate analyses, the wheel unloading ratio provides direct information regarding the proximity to unsafe operating conditions, confirming its essential role in comprehensive safety assessment and condition classification of HSR turnouts. Furthermore, the L/V ratio and the wheel unloading ratio evaluated according to international standards are illustrated in Figure 7, where both values remain below the safety limits.

Rail height irregularities in turnout regions introduce localised geometric excitation, resulting in the redistribution of dynamic loads and significant modification of WR system responses. The analysis results indicated that as the reduction in rail height increases, the vertical vibration of the wheelset and the WR contact forces tend to increase, accompanied by a decrease in the vertical contact force acting on the wheel (Ma et al., 2025). Consequently, the wheel unloading ratio becomes a sensitive indicator that directly reflects the degradation of contact stability and the increasing risk of approaching unsafe conditions in turnout regions. The simultaneous evaluation of the unloading ratio and WR forces enables the adverse effects of rail geometric irregularities on HSR operational safety to be effectively identified. Therefore, the wheel unloading ratio serves not only as a direct measure of contact safety but also as a key index used in combination with the Nadal criterion and MBD analysis to evaluate the stability and operational safety of HSR systems.

The wheel profile is one of the most important parameters governing WR dynamic interaction and has a direct influence on stability, wear, and operational safety. From a geometric perspective, the wheel profile determines the equivalent rolling radius, effective conicity, and the position and shape of the contact patch between the WR, thereby influencing creep characteristics and the tangential forces generated when the wheelset experiences lateral displacement. Profiles with high conicity enhance the self-steering capability and stability at low speeds but may reduce hunting stability at high speeds due to increased sensitivity of tangential forces. Conversely, profiles with low conicity or those optimised for high-speed operation improve the critical speed and reduce hunting oscillations but may increase the risk of flange contact and localised wear in sharp curves. In addition, profile variations caused by wear during service continuously modify WR contact conditions, leading to changes in dynamic and safety-related indices (Song et al., 2024). Dai, Qu, Huang, and Wu (2023) identified the wheel profile directly determines the effective conicity and WR contact characteristics, thereby governing the critical speed and hunting stability of railway vehicles. The results indicated the existence of a limiting profile threshold beyond which the vehicle system may lose dynamic stability even when suspension parameters remain unchanged. Sun et al. (2025a, b, c) focused on optimising the wheel tread profile in order to regulate the effective conicity and the geometry of the WR contact patch, thereby improving the dynamic stability of trains at high speeds. The results demonstrated that the optimised profile increases the hunting critical speed and reduces the lateral oscillation amplitude of the wheelset while maintaining appropriate steering capability in curves. Hou, Chen, and Cheng (2022) highlighted that the wear process continuously modifies the wheel profile, leading to changes in effective conicity and WR contact conditions throughout service. These changes result in a reduction of the critical speed and an increase in hunting oscillations, directly affecting the dynamic stability of HSR. Specifically, as illustrated in Figure 8, the lateral vibration acceleration of the carbody varies at different operating distances, with a maximum recorded value of 0.5 m/s², while the dominant vibration frequency remains approximately 1.7 Hz. These findings highlight the necessity of considering the evolution of wheel profile wear in simulations, stability assessments, and vehicle maintenance strategies.

Therefore, the wheel profile is not only an initial geometric parameter but also a dynamic factor that must be considered simultaneously in design, simulation, and maintenance management to ensure the stability and safety of HSR systems.

Suspension system parameters in the dynamic analysis of railway vehicles include the stiffness, damping coefficients, and nonlinear characteristics of the primary and secondary suspension elements, which play a crucial role in governing vibration response, hunting stability, and WR contact forces. The primary suspension influences the filtering of high-frequency vibrations and the distribution of WR forces, whereas the secondary suspension determines ride comfort and the overall stability of the vehicle. Excessively high stiffness may increase dynamic forces and reduce the ability to accommodate rail geometric irregularities, while excessively low stiffness may lead to large vibration amplitudes and reduced stability at high speeds. Similarly, damping serves to dissipate vibrational energy; if not properly selected, the system may enter a state of self-excited oscillation or exhibit excessive response to track-induced excitations (Yao, Chen, Li, & Li, 2023; Dumitriu & Apostol, 2023). Recent studies have indicated that the primary suspension stiffness and the lateral damping of the secondary suspension have a significant influence on the hunting critical speed, exhibiting substantial variations when these parameters are modified, which leads to considerable changes in motion stability at high speeds (Bustos, Tomas-Rodriguez, Rubio, & Castejon, 2023). Sensitivity analyses have shown that secondary suspension parameters and inter-car connections also shape the lateral vibration response at operating speeds, confirming that appropriate selection and adjustment of the suspension system are prerequisites for maintaining operational safety (Bustos, Rubio, Castejon, & Garcia-Prada, 2025). Furthermore, adaptive nonlinear damping solutions in the secondary suspension have been demonstrated to enhance hunting stability, highlighting the importance of designing suspension damping systems that are compatible with operating conditions and WR interaction characteristics (Jin et al., 2020). Therefore, the optimisation of suspension system parameters is a prerequisite for achieving a balance among dynamic stability, operational safety, and passenger comfort in HSR systems.

The Archard model is one of the classical wear models widely used to estimate material loss in sliding contact systems, including WR wear in railway engineering. Fundamentally, the model assumes that material loss is proportional to the accumulated frictional energy at the contact interface, meaning that a portion of the work generated by tangential contact forces during sliding motion is converted into wear. The basic Archard equation is expressed as follows (Yan, Jin, Ma, Zhang, & Zhou, 2023):

Where: V denotes the accumulated wear volume; k is the wear coefficient characterizing the material pair; N represents the normal force acting on the contact patch; S is the accumulated sliding distance; and H denotes the material hardness.

In WR interaction, the Archard model is employed as a fundamental formulation to simulate wear evolution over time based on the normal and tangential forces obtained from MBD simulations or physical contact analyses. The accumulation of wear leads to modifications of surface geometry, altering the WR profiles and consequently affecting creep forces, contact locations, and the stability indices of the system. Therefore, the Archard model is not merely a formulation for estimating material loss but also serves as a link between friction mechanisms, contact forces, and the time-dependent evolution of contact geometry, thereby supporting comprehensive analyses of phenomena such as hunting oscillations, increased dynamic forces, and variations in critical speed during HSR operation (Myśliński & Chudzikiewicz, 2022).

Energy-based wear models represent a modern approach for describing WR wear, in which the amount of material loss is assumed to be proportional to the frictional energy dissipated within the contact patch, namely the work of the tangential force and the relative sliding velocity. This approach directly reflects the influence of adhesion-slip distribution and actual contact conditions, thereby enabling a more accurate representation of nonlinear operating conditions such as low adhesion, large local slip, or wheel flange contact. Owing to their clear physical basis and their compatibility with nonlinear contact models such as FASTSIM and CONTACT as well as MBD frameworks, energy-based wear models are particularly suitable for analysing uneven wear and accelerated wear processes in HSR systems, although parameter calibration based on experimental data is still required and the computational cost is higher than that of the traditional Archard model (Myśliński & Chudzikiewicz, 2023). Li, Wei, Chen, and Xu (2015) point out that wear in heavy-load operation is closely associated with the frictional energy dissipated within the contact patch, which is represented by the work of tangential forces and relative slip. The accumulation of wear significantly modifies the contact geometry, leading to changes in the size and position of the contact patch as well as the stress distribution over the service period. Pacheco et al. (2024) reported that comparative analyses indicated that wear indices based solely on geometric parameters are insufficient to fully represent wear mechanisms under practical operating conditions of freight vehicles. In contrast, indices directly related to contact conditions and the level of frictional energy dissipation within the WR contact patch provide a more accurate representation of uneven wear distribution and the evolution of wheel profiles over time. These results confirm that wear indices grounded in energy and dynamic considerations are more suitable for evaluating wheel wear under heavy-load operating conditions.

Long-term simulation strategies in studies of WR wear evolution and profile degradation aim to describe the cumulative changes in contact geometry and the dynamic response of the system over extended service periods, rather than analysing only instantaneous conditions. Since wear and RCF develop much more slowly than dynamic oscillations, long-term simulations are typically implemented through a multi-iteration strategy. First, the vehicle-track dynamic problem is solved over a short time interval to determine contact forces, creep, and energy distribution. These quantities are then used as inputs for wear or fatigue models to update the surface geometry of the WR. Finally, the contact conditions are updated and the cycle is repeated for subsequent operational time steps. This approach enables the nonlinear relationship between profile evolution, WR force distribution, and dynamic stability to be captured, where profile degradation may alter contact conditions, increase localised wear, or trigger new instability mechanisms (Wang, Yang, Tao, & Wen, 2024). Wen, Yang, Tao, and Wen (2025) presented a predictive model for locomotive wheel wear evolution based on thermo-mechanical coupling, in which wear is determined from the frictional energy dissipated within the contact patch and is consequently associated with the temperature generated during rolling-sliding processes. Through a long-term simulation strategy involving iterative cycles of dynamic analysis, wear calculation, and profile updating, the degradation of wheel geometry with accumulated operating distance is represented in a cumulative and nonlinear manner. Comparison with experimental data indicated that the model is capable of reasonably reproducing the evolution of wheel profiles as well as the influence of wear on contact conditions and dynamic responses under heavy-load operation. Li, Li, Yu, Li, and Sun (2024a) described how the influence of time-varying WR wear on the dynamic response of railway vehicles was investigated, in which profile degradation was described as an accumulative process and sequentially updated during simulation. The study clarified the nonlinear relationship among wear evolution, changes in WR contact conditions, and variations in dynamic indices such as wheel forces, accelerations, and motion stability. The results indicated that wear not only modifies the contact geometry but may also amplify dynamic responses and reduce operational safety when accumulated beyond certain thresholds. Long-term simulation, therefore, is essential for predicting WR service life, optimising maintenance strategies, and evaluating the operational safety of railway systems, particularly under conditions of high axle loads and high speeds.

During the evolution of WR wear and profile degradation, contact geometry directly determines the distribution of contact pressure, normal forces, and tangential forces within the contact patch. As wear progresses, material removal alters the WR profiles, leading to shifts in the contact location and modifications in the size and shape of the contact patch, which may evolve from the classical Hertzian elliptical form to non-standard configurations or multiple contact points. These changes modify the local stress distribution, creep levels, and tangential forces, thereby strongly affecting the dynamic response, hunting stability, safety indices such as the L/V ratio, and the risk of derailment. At the same time, variations in contact geometry feed back into the wear and RCF mechanisms, creating a nonlinear feedback loop among wear evolution, contact geometry, and system dynamics (Han, Wei, & Yang, 2024).

Zhang, Pun, Hiew, and Yan (2025a) observed that wear at the movable switch point significantly modifies WR contact geometry, as reflected by the shift in contact location and the variation in the size and shape of the contact patch over the service period. This geometric degradation leads to a more uneven distribution of contact pressure and tangential forces, increasing localised stresses and altering the dynamic characteristics of the wheelset when passing through the turnout. The simulation results were validated against field measurements, as illustrated in Figure 9. The study therefore confirmed that wear is not only a consequence of dynamic interaction but also an active factor that alters contact geometry, generating a nonlinear feedback loop among wear, geometry, and WR forces, particularly pronounced under heavy-load railway conditions. Major, Németh, Jóvér, and Fischer (2025) highlighted that the effective contact radius between the WR is a key geometric parameter governing the size of the contact patch, the pressure distribution, and the characteristics of tangential forces. Accurate determination of the contact radius through numerical methods enables a more precise representation of non-Hertzian contact conditions arising from profile deviations, wear, or high loads. The results emphasise that variations in contact geometry, reflected by changes in the contact radius, have a direct influence on dynamic responses and the accuracy of WR interaction models. Therefore, accurate simulation of wear evolution and profile degradation, together with the associated changes in contact geometry, is a fundamental requirement for predicting the service life, safety, and operational performance of WR systems.

Hunting instability induced by wear arises as a direct consequence of changes in WR contact geometry during service. As wear develops, particularly in the form of hollow wear or uneven wear, the WR profiles are altered, resulting in significant variations in equivalent conicity and contact conditions. These changes modify the characteristics of creep forces and the self-steering moment of the wheelset, thereby reducing the energy dissipation capability of the system. Within a certain speed range, especially when wear increases the effective conicity, the critical speed for hunting is reduced, causing self-excited oscillations to occur earlier and with larger amplitudes (Gao et al., 2025; Li, Dai, Guo, & Chi, 2024b). Gao et al. (2025) introduced a new wheel wear index based on WR contact parameters, particularly the variation of equivalent conicity and the distribution of the contact patch, which was proposed. The results indicated that progressive wear significantly modifies contact geometry, thereby altering the characteristics of creep forces and the self-steering moment of the wheelset. These changes lead to a reduction in the hunting critical speed and an increased tendency toward dynamic instability, confirming that wheel wear directly governs hunting stability through the mechanism of contact geometry alteration. Zhang, Hu, Wang, and Liu (2025b) observed that hollow wear on the wheel tread significantly modifies contact geometry and the WR contact relationship. This alteration leads to a wider and more uneven distribution of contact points, and in some cases multiple contact patches may occur, resulting in increased lateral forces and influencing the dynamic stability of the vehicle. Moreover, simulation results indicated that when hollow wear becomes severe, the hunting critical speed decreases while the lateral vibration amplitude increases rapidly. These findings confirm that changes in contact geometry induced by wear constitute a decisive factor contributing to the degradation of stability and operational safety in HSR. Therefore, wear is not only a matter of geometric degradation and structural service life but also an important factor inducing dynamic instability, directly affecting the safety and operational limits of HSR vehicles.

The degradation of operational safety in railway systems results from the combined effects of unfavourable changes in system dynamics, contact geometry, and structural conditions occurring during long-term service. When factors such as WR wear, profile degradation, increased rail irregularities, or variations in suspension characteristics arise, the dynamic response of the vehicle-track system is amplified, leading to increased WR contact forces, particularly lateral forces and wheel unloading. This deterioration adversely affects operational safety indices such as the L/V ratio, the wheel unloading ratio, and the amplitude of hunting oscillations, thereby increasing the risk of derailment, loss of motion stability, and structural damage. In high-speed operation, safety degradation exhibits nonlinear characteristics and may occur abruptly when the system exceeds critical thresholds of dynamic stability (Hu, Li, Sun, & Dou, 2025).

Braga, Costa, Ambrósio, Frey, and Andrade (2024) highlighted that the degradation of operational safety in railway vehicles results from the combined effects of wheel profile variation, changes in WR contact conditions, and the nonlinear dynamic response of the vehicle system. Through a data-driven approach and surrogate modelling, safety indices such as the L/V ratio, the wheel unloading ratio, and hunting stability were systematically evaluated, clarifying the relationship among wear evolution, dynamic variation, and operational risk, particularly under high-speed conditions and near stability thresholds. The management of WR conditions plays a central role in maintaining the operational safety of modern railway systems. The gradual degradation of WR profiles due to wear, RCF, and surface defects modifies contact geometry and the dynamic response of WR interaction, leading to increased lateral forces, wheel unloading, and deterioration of safety indices such as the L/V ratio and hunting stability. Consequently, condition management strategies based on monitoring, coupled modelling, and risk assessment are not only intended to extend structural service life but also serve as key tools for early detection of safety degradation and for supporting proactive operational and maintenance decision-making (Ekberg, Kabo, & Lundén, 2023). The evaluation of train operational safety under seismic excitation represents a typical challenge due to the sudden and nonlinear increase of ground motion inputs acting on the WR system. Ground vibrations transmitted through the track structure and the vehicle rapidly modify WR contact forces, leading to wheel unloading, increased L/V ratios, and an expanded derailment risk domain. Under sinusoidal excitation with a frequency of 1 Hz and an amplitude of 0.4 g, the occurrence of wheel flange climbing leading to derailment can be clearly observed, as illustrated in Figure 10 (Zhu, Zhou, Zheng, Gong, & Tang, 2024). Therefore, the degradation of operational safety is not merely the result of a single parameter but rather the manifestation of complex interactions among wear, system dynamics, and operating conditions, which must be evaluated through coupled models and comprehensive safety indices in the design and operation of modern railway systems.

Field measurements and WR force estimation are essential steps for acquiring realistic dynamic response data and calibrating numerical models. Chen, Gong, Ge, Chen, and Wang (2024) introduced a WR force estimation method based on the STF-SCKF-NE algorithm (strong tracking filter-square-root cubature Kalman filter-noise estimator), in which the contact force is not measured directly but is inferred from measured kinematic signals of the vehicle system. By combining a nonlinear dynamic model with an improved Kalman filter that accounts for noise and modeling uncertainties, the method enables accurate reconstruction of both vertical and lateral WR forces under real operating conditions. The results indicated that force estimation based on measured acceleration and motion signals provides an effective tool for evaluating contact safety, calibrating numerical models, and monitoring the condition of WR systems in high-speed operation. Mal et al. (2021) described a WR contact force estimation approach based on a nonlinear dynamic model of the vehicle system, in which the contact force was reconstructed from measured motion signals rather than directly measured. The method exploits the nonlinear relationship among acceleration, displacement, and contact force, enabling accurate reconstruction of WR force components under complex operating conditions. Milošević, Pålsson, Nissen, Nielsen, and Johansson (2024) introduced an inverse method based on Green's functions that was proposed to simultaneously reconstruct WR contact forces and track irregularity characteristics in turnout regions using acceleration signals measured on sleepers. By exploiting the dynamic relationship between contact excitation and track structural response, the method enables time-varying WR forces to be identified without the need for direct force sensors. The results demonstrated that field acceleration signals, when combined with appropriate mechanical models, can provide reliable information for contact safety assessment and calibration of vehicle-track interaction models.

Because vehicle-track dynamic models contain numerous uncertain parameters, model calibration based on experimental data is an essential step to ensure reliable predictive capability. This process is typically carried out by comparing characteristic quantities obtained from simulations and measurements, followed by iterative adjustment of model parameters to minimise discrepancies. After calibration, the model must be validated using independent datasets or under different operating conditions in order to assess its generality and applicability for safety analysis and real operational prediction. Solonenko et al. (2025) presented a vehicle-track dynamic model incorporating the viscoelastic characteristics of the track infrastructure, which was developed, and parameter calibration was performed using experimental measurement data. Quantities such as system acceleration and dynamic responses were compared between simulation and experimental results to adjust the stiffness and damping parameters of the model, thereby reducing discrepancies and improving predictive reliability. This validation process demonstrated that the integration of real measurement data is a prerequisite for ensuring the accuracy and practical applicability of the model in safety analysis and operational assessment. Zhang, He, Shen, Dollevoet, and Li (2024d) reported that a three-dimensional FE model was developed to represent WR interaction in detail within the high-frequency range and was comprehensively validated using data obtained from the V-Track test rig. Acceleration signals, stresses, and dynamic responses of the rail were directly compared with simulation results to evaluate the capability of the model to reproduce contact phenomena and vibration transmission. Silva et al. (2021) described how calibration of a freight waggon dynamic model was performed using dynamic test data obtained under various loading scenarios. Indices such as natural frequencies, vibration modes, and acceleration responses were compared between simulations and experimental measurements to iteratively adjust the stiffness and damping parameters of the suspension system.

The increasing operating speeds, the demand for life-cycle cost (LCC) optimisation, and the objective of intelligent railway operation are driving the field of WR dynamic interaction to shift from purely mechanical models toward integrated multidisciplinary systems based on data-driven methods and adaptive control. Three major development directions have emerged, including artificial intelligence (AI) and machine learning (ML), multi-physics and multi-scale modelling, and active suspension systems together with intelligent WR interfaces, as summarised in Table 1.

Data-driven and AI methods are increasingly being employed to predict dynamic instability phenomena, particularly hunting oscillations, in WR systems. Instead of relying solely on traditional mechanical models, which often require numerous assumptions and high computational cost, AI-based approaches directly exploit data collected from sensors or numerical simulations to learn complex nonlinear relationships among operating conditions, contact geometry, and the dynamic response of the system. ML and deep learning algorithms such as random forest, ML, CNN, RNN, or hybrid 2DCNN-GRU models enable early identification of instability trends and prediction of critical speeds or related safety indices without the need to solve the full set of dynamic equations (Amin, Najeh, Sridharan, Ghoul, & Karim, 2025; Bris-Peñalver, Verdecia-Peña, & Alonso, 2026). Yang et al. (2024) introduced a hybrid model combining thermo-frictional principles with ML algorithms that was developed to enable early detection of axle bearing anomalies. The physical model predicts the expected temperature under given operating conditions, while the data-driven model compensates for deviations caused by complex real-world factors. This approach demonstrates the potential of integrating mechanics and AI for condition monitoring and early warning of instability. Sun et al. (2021) detailed a hunting detection method based on vibration signal analysis that was proposed instead of directly solving the dynamic equations. Time-frequency features extracted from acceleration and displacement signals were used to identify the transition from damped oscillations to self-excited vibrations.

Similarly, data-driven and AI-based approaches for anomaly detection are becoming increasingly important. The core concept of this approach is to exploit large volumes of data continuously collected from sensors installed on vehicles and infrastructure to learn the “normal” behaviour of the system under stable operating conditions. Based on this learned baseline, algorithms such as AE, IF, OC-SVM, and LSTM are employed to identify abnormal deviations in spatial or temporal domains. A key advantage of these methods lies in their capability to model complex nonlinear relationships without requiring fully labelled fault data, making them well suited for real-time monitoring applications (Jin & Kang, 2024; Sun et al., 2025a, b, c). Recently, ML approaches have been effectively applied to the early detection of dynamic instability states, particularly small-amplitude bogie hunting. Studies on ML-based hunting identification methods have demonstrated that vibration signal features obtained from acceleration sensors can be exploited to distinguish stable states from near-instability conditions with high accuracy (Guo, Zhang, Shi, & Zeng, 2024). Bernhard, Haener, and Frey (2024) employed interferometric radar image sequences (InSAR) from the TerraSAR-X satellite to detect rail geometric anomalies through the analysis of micro-deformation over time. By exploiting long-term observation data and interferometric time-series processing, the method enables the identification of regions experiencing subsidence, displacement, or abnormal accumulated deformation without the need for direct field access. Baldyga, Barański, Belter, Kalinowski, and Weichbroth (2024) provided a comprehensive review of anomaly detection methods in railway sensor data environments, which were systematically reviewed and experimentally evaluated, including both traditional statistical techniques and ML models. Through performance comparisons using real-world datasets, the study indicated that unsupervised and semi-supervised learning models are capable of effectively detecting subtle deviations in vibration signals and system states, even when fault data are not fully labelled. Consequently, data-driven anomaly detection not only supports early warning and predictive maintenance but also contributes to improving reliability, operational safety, and operational efficiency of vehicle-track systems, particularly under high-speed operating conditions and variable environmental environments.

Thermo-mechanical coupling is a complex physical phenomenon arising from time-varying temperature at the contact surface and its feedback influence on the mechanical state. When the wheel rolls, friction generates significant localised heat within the contact patch; this heat is not only dissipated over time but also alters the mechanical properties of the materials. Variations in temperature and stress interact with each other, as temperature affects contact forces and moments, while mechanical deformation influences heat distribution and subsequent heat generation. Numerical models typically employ coupled mechanical and thermal equations within a multi-physics framework, where the dynamic equilibrium equations are solved simultaneously with the energy equation. In this formulation, the heat source is determined by local frictional work and is transferred through material components according to mechanisms of conduction, convection, and radiation (Wei, Han, Yang, Wu, & Chen, 2024; Li, Wei, Yang, & Li, 2025b). Han, Wei, and Liu (2023) observed that heat generation due to sliding friction between the WR is often accompanied by lateral displacement of the wheel, resulting in two-point contact conditions, as illustrated in Figure 11. The results indicated that at a sliding speed of 2 m/s and an axle load of 30 tons, with a sliding distance of 200 mm, the temperature at the centre of the contact region near the rail gauge corner reached 547.7 °C, while the temperature at the rail crown reached 813 °C, as shown in Figure 12. Yang et al. (2026) presented a thermo-mechanical coupled modeling framework that was developed to describe the temperature evolution within the WR contact region during braking. The heat source was directly determined from local frictional work associated with tangential forces and creep and was subsequently coupled with the heat transfer equation to calculate the temporal distribution and diffusion of heat within the WR. The results indicated that the contact temperature increases rapidly during intense braking, thereby modifying the stress state and contact conditions. He, Yang, Zhang, Dollevoet, and Li (2025) observed that heat generated under high slip ratios during both braking and acceleration accelerates the wear process; therefore, an FE model was developed and validated through experimental testing. The results demonstrated that at a temperature of 360 °C and under different slip ratios, the maximum deviation between simulation and experimental results was less than 9.9 %, confirming the reliability of the simulation outcomes.

Wear-fatigue interaction represents a complex damage mechanism in which surface wear and RCF interact throughout the service life. Wear modifies the contact geometry and the near-surface stress state, which may remove layers of material that have accumulated fatigue damage and thereby slow crack propagation. Conversely, if wear is insufficient, subsurface fatigue cracks may develop and propagate, eventually leading to spalling or shelling. In the opposite direction, the initiation and propagation of fatigue cracks increase surface roughness and heterogeneity, which intensifies local slip, tangential forces, and the wear rate. This interaction is governed by factors such as axle load, friction coefficient, material properties, and thermal conditions within the contact region (Akama, 2025; Yang, Ling, Wang, & Zhai, 2023; Chen et al., 2024). Silva et al. (2023) conducted numerical simulations using the Universal Mechanism software, which was used to simulate wheel wear until the onset of RCF. The results indicated that when the wheel wear depth reached 2 mm, RCF began to develop due to high contact pressure. Zhang et al. (2023a, b) described how the wear-fatigue interaction mechanism was clarified through experimental investigation of RCF crack growth initiated from surface defects under different conditions of load, friction coefficient, and slip level. The results demonstrated that surface wear may remove material layers that have accumulated fatigue damage, thereby slowing crack propagation; however, under conditions of high friction and large slip, stress concentration may be intensified, accelerating crack growth. Zeng et al. (2024) demonstrated that the relationship between wear and RCF was further clarified through dry rolling-sliding experiments on vanadium microalloyed wheel steel. The results showed that at low slip levels, subsurface fatigue damage dominates, characterised by the initiation and propagation of RCF cracks. In contrast, at higher slip levels, increased wear may remove material layers containing accumulated damage, thereby altering the morphology and growth rate of cracks. The study emphasised that the balance between wear rate and fatigue damage accumulation determines the dominant failure mode and is strongly dependent on loading and slip conditions within the WR contact.

Active suspension systems represent an advanced control strategy in railway vehicles, in which sensors, controllers, and actuators are employed to generate control forces in real time, rather than relying solely on fixed elastic-damping characteristics as in passive suspension systems. Owing to their adaptive capability, active suspension systems reduce vibrations, mitigate hunting oscillations, improve load distribution, and enhance stability. When combined with optimal and intelligent control methods, these systems can adapt to nonlinear WR contact conditions and infrastructure-induced disturbances, thereby improving operational safety and ride quality (Shi, Zeng, & Qu, 2023). Zhang, Ling, and Zhai (2024b) described how the role of active suspension in improving hunting stability was clarified through an adaptive nonlinear damping control strategy applied to the secondary suspension. Instead of employing fixed damping characteristics as in passive systems, the control model adjusts the damping force according to the actual vibration state of the system, thereby improving energy dissipation capability and expanding the domain of dynamic stability. Simulation results indicated that the critical speed was significantly increased and the lateral vibration amplitudes of both the bogie and the carbody were markedly reduced, particularly at high operating speeds. Nitish and Singh (2023) introduced an active suspension control strategy based on a PID (Proportional-Integral-Derivative) controller that was presented. By adjusting the pole locations of the closed-loop system, the dynamic response was improved through increased damping and reduced transient time, thereby decreasing carbody vibration amplitude and enhancing ride comfort. The results demonstrated that the active suspension system reduces acceleration and dynamic forces compared with the traditional passive configuration, thereby improving vehicle stability under excitations induced by track irregularities. Zhang, Ling, Zhai, and Wang (2024c) outlined an active suspension configuration that was proposed to enhance train safety under strong crosswind conditions. The model accurately represents the influence of time-varying wind loads, based on which the active controller generates real-time compensating forces to suppress lateral rolling oscillations and redistribute wheel loads. The results indicated that the active suspension significantly reduces the wheel unloading ratio and the carbody vibration amplitude compared with passive suspension systems, thereby improving operational safety margins and rollover resistance of HSR under severe operating conditions.

The adaptive WR interface actively or semi-actively adjusts contact conditions in order to maintain an optimal operating state under varying operational conditions. Instead of treating WR contact as passive and fixed, the adaptive approach considers it as a dynamic interface that can be regulated through measures such as modifying suspension characteristics, controlling tangential forces, regulating the friction coefficient, optimising WR profiles, or integrating intelligent control algorithms based on sensor data. The objective is to maintain an optimal balance among dynamic stability, steering capability, wear behaviour, and operational safety, particularly under high-speed operation, low-adhesion conditions, or when WR profiles degrade over time. The adaptive interface enables the system to respond flexibly to variations in load, friction, and contact geometry, thereby mitigating adverse phenomena (Stichel, Persson, & Giossi, 2023). Zhang, Zhu, Wang, Tian, and Zhou (2025c) emphasised that the WR interface was highlighted as a dynamic contact system that requires real-time monitoring and regulation. Through an online parameter estimation approach, the WR adhesion coefficient was continuously identified based on operational signals, enabling timely detection of changes in friction conditions caused by moisture, surface contamination, or slip states. This approach provides a foundation for adaptive traction and braking control strategies aimed at maintaining optimal WR contact conditions, reducing slip risk, and improving stability and operational safety under varying service conditions. Gan, Wang, Lu, and Ou (2025) pointed out that the capability of adaptively controlling the WR interface through accurate estimation of adhesion states under nonlinear conditions was emphasised. By employing an improved nonlinear Kalman filter to identify adhesion coefficients and slip states in real time, the system can adjust traction and braking forces accordingly, maintaining operation near the optimal adhesion region and preventing unstable slip. This approach effectively transforms WR contact from a passive interface into an actively monitored and controlled system. Gan et al. (2025) identified adhesion optimisation was highlighted as an active regulation mechanism of the WR interface within permanent magnet motor traction systems. Through optimisation algorithms and traction torque adjustment based on the actual adhesion state, the system maintains operation close to the optimal adhesion limit while suppressing slip and tangential force oscillations. This approach enhances traction efficiency, dynamic stability, and operational safety, particularly under variable adhesion conditions at high speeds. This is considered an important development direction for intelligent railway systems, where control, monitoring, and prediction are integrated to optimise WR interaction throughout the entire service life.

Although significant progress has been achieved in the modeling and monitoring of WR dynamics, considerable research gaps still remain, as summarised in Table 2.

First, the lack of large-scale and publicly available experimental datasets significantly limits the calibration, validation, and cross-comparison of models across different studies. Most field measurement data are internally stored by railway operators and manufacturers, resulting in many models being validated only on limited datasets or under controlled experimental conditions. This constraint reduces the generalisability and reliability of these models when applied to the diverse operating conditions of HSR systems. In addition, a trade-off exists between model accuracy and computational cost. Multi-physics models, highly nonlinear contact models, or long-term wear evolution simulations provide high fidelity but require substantial computational resources, making them difficult to implement in real-time analysis or within iterative optimisation frameworks. Conversely, reduced-order or surrogate models offer high computational efficiency but may neglect important nonlinear mechanisms that influence stability and operational safety. The development of hybrid modeling frameworks or the integration of mechanics-based models with AI approaches represents a promising direction for balancing accuracy and computational feasibility. Finally, the need for standardisation of safety indices for HSR systems is becoming increasingly urgent. At present, several indices such as the L/V ratio, the wheel unloading ratio, and the hunting critical speed are used concurrently, yet a unified evaluation framework regarding their thresholds and conditions of application has not been established. This lack of consistency creates difficulties in comparing results across different studies, integrating them into real-time monitoring systems, and developing unified technical standards. Therefore, establishing a comprehensive set of safety indices with a clear physical basis and tailored to high-speed operating conditions will provide an essential foundation for design, risk assessment, and the implementation of future digital railway systems.

As synthesized throughout this manuscript, this review systematically evaluates WR dynamic interactions in HSR regimes. To provide actionable guidance for the community, the key conclusions are explicitly delineated into solved domains:

1. Classical contact mechanics under nominal quasi-static and moderate-speed conditions are now fully mature and computationally standardized. Similarly, single-regime wear depth prediction under steady-state rolling contact can be reliably simulated using traditional Archard formulations.

2. Significant domain-specific controversies remain unresolved in high-speed operating environments. The strict applicability boundaries of the classical Nadal criterion versus modern dynamic derailment metrics under high-speed transient wheel-climbing remain debated, as Nadal's formulation often yields overly conservative or physically inaccurate margins when lateral dynamic oscillations dominate. The physical mechanism governing the rapid degradation of adhesion under wet, oily, or extreme micro-slip conditions cannot be captured by static friction laws, leading to conflicting numerical predictions of high-speed hunting instability.

3. A persistent trade-off exists between localized sub-surface thermal-stress FE models and global macro-vehicle dynamics, where real-time simulation without significant accuracy loss remains an unfulfilled challenge.

4. Comparative synthesis reveals that while AI and ML surrogate models drastically reduce computation time, purely data-driven black-box architectures suffer from severe extrapolation failures outside their training domain. Consequently, future developments must shift toward more advanced neural network architectures to overcome these existing limitations.

5. Future HSR digital twin paradigms must transcend conceptual frameworks by focusing on three concrete breakthroughs: low-latency reduced-order physics-data hybrid models for real-time wear-fatigue health monitoring; open-access high-speed experimental benchmarks for standardized model validation, and multi-physics thermal-tribo-dynamic coupled frameworks operating across micro-to-macro spatial scales.