Vehicle-track Coupling Dynamics Research Articles

Assessment of random dynamic behavior for EMUs high-speed train based on Monte Carlo simulation

A novel statistical method was developed to obtain a dynamic response with irregular line excitations and independent uncertain parameters. The proposed approach combines a three-dimensional vehicle-track coupling dynamics model and uncertainty parameters. Moreover, a new method is used to treat the dynamic indices: derailment coefficient, vertical/lateral wheel/rail force, vertical/lateral car body acceleration, and wheel reduction ratio. The model is validated by comparing simulations (deterministic) results with field measurements, which provide excellent agreement with limited data. According to the findings, the results reveal that the high vibration effect arises when the uncertainty parameter in the dynamic system exists. The total fit effects, the consistency of the vehicle safety, and the tail fit effects are determined for selecting the best method. Therefore, regarding the approach, the lognormal and extreme maximum distribution values may be the appropriate assumed distribution for dynamic safety under limited data.

A modified Hertzian-based wheel-rail contact model for vehicle system dynamics simulation

This paper develops a modified Hertzian-based wheel-rail contact model (MHM) to improve the robustness and accuracy of the traditional Hertzian contact model in vehicle-track coupling dynamics simulation. First, the wheel-rail non-Hertzian contact area is estimated based on the virtual penetration (VP) area, and an equivalent ellipse of the non-Hertzian contact area is calculated. Then, taking the equivalent elliptical contact patch as the input, the wheel-rail normal problem is solved by using Hertzian contact theory. Finally, considering the effect of the non-elliptical contact patch on Kalker’s linear coefficient, a modified Shen–Hedrick–Elkins model is proposed. The computation accuracy, robustness, and efficiency of the developed MHM are assessed by comparing it with a robust Kalker variational method (RKVM), a VP-based non-Hertzian contact model RNHM, and two traditional Hertzian-based models. The comparison results show that the MHM improves the computational robustness and accuracy of the traditional Hertzian-based contact models. MHM achieves almost the same computational accuracy as the RNHM, but its computational efficiency is 2.4 times faster than RNHM. The developed MHM is an ideal model for vehicle-track coupling dynamics simulation.

Investigation of rail damage considering impact at a welded joint under wet condition

PurposeThe purpose of this study is to develop a transient wheel–rail rolling contact model to primarily investigate the rail damage under wet condition when the train passes through the welded joints.Design/methodology/approachThe impact force induced by welded joints is obtained through vehicle–track coupling dynamics. The normal and tangential wheel–rail contact pressures were solved by elastohydrodynamic lubrication (EHL) theory and simplified third-body layer theory, respectively. Then, the obtained tangential pressure and normal pressure were applied to the finite element model as moving loads, simulating cyclic loading. Finally, the shakedown map and critical plane method were used to predict rolling contact fatigue (RCF) and the initiation of fatigue cracks.FindingsThe results indicate that RCF will occur and fatigue cracks are more prone to appear on the subsurface of the rail, specifically around 2.7 mm below the rail surface in the vicinity of the welded joint and its heat-affected zone.Originality/valueThe cosimulation of numerical model and finite element model was implemented. The influence of surface roughness and fluids was considered. In this model, the normal and tangential wheel–rail contact pressure, the stress and strain and the rail fatigue cracks were obtained under a rail-welded joint excitation.

Solving coupled differential equation groups using PINO-CDE

As a fundamental mathematical tool in many engineering disciplines, coupled differential equation groups are being widely used to model complex structures containing multiple physical quantities. Engineers constantly adjust structural parameters at the design stage, which requires a highly efficient solver. The rise of deep learning technologies has offered new perspectives on this task. Unfortunately, existing black-box models suffer from poor accuracy and robustness, while the advanced methodologies of single-output operator regression cannot deal with multiple quantities simultaneously. To address these challenges, we propose PINO-CDE, a deep learning framework for solving coupled differential equation groups (CDEs) along with an equation normalization algorithm for performance enhancing. Based on the theory of physics-informed neural operator (PINO), PINO-CDE uses a single network for all quantities in a CDEs, instead of training dozens, or even hundreds of networks as in the existing literature. We demonstrate the flexibility and feasibility of PINO-CDE for one toy example and two engineering applications: vehicle-track coupled dynamics (VTCD) and reliability assessment for a four-storey building (uncertainty propagation). The performance of VTCD indicates that PINO-CDE outperforms existing software and deep learning-based methods in terms of efficiency and precision, respectively. For the uncertainty propagation task, PINO-CDE provides higher-resolution results in less than a quarter of the time incurred when using the probability density evolution method (PDEM). This framework integrates engineering dynamics and deep learning technologies and may reveal a new concept for CDEs solving and uncertainty propagation.

Vibro-acoustic characteristics of a rail transit viaduct paved with trapezoidal sleeper track

To investigate the effects of a trapezoidal sleeper track (TST) on the vibration and noise of rail transit viaducts, the wheel–rail interaction model was first built according to the vehicle–track coupling dynamics theory. Subsequently, the vibration responses of the viaduct were analyzed using the beam–slab finite element method, and its radiated noise was calculated using the acoustic boundary element method. The modeling method was verified based on the test data of a 3 × 40 m continuous rigid frame bridge. Taking the Jialing River Bridge of Chongqing Rail Transit Line 9 as the background, the control effects of the TST on the vibration and noise of the viaduct and the effective laws of different track parameters on the bridge noise were analyzed. Results show that the simulated and measured values are in good agreement; for example, the modeling methods are reliable; the radiated noise of the viaduct is influenced by the vibration responses under the action of train load, which are jointly determined by dynamic wheel–rail force (external excitation) and displacement admittance (self-vibration characteristics); compared with embedded sleeper track (EST), the TST can reduce the overall vibration acceleration level and sound pressure level of the box girder web plate by 13.9 dB and 7.8 dB, respectively; the stiffness of the damping path is the primary factor influencing the noise of the elevated box girder, followed by the sleeper thickness and the fastener stiffness; taking the bottom plate as an example, the stiffness of the damping pad is reduced by 1 and the overall sound pressure level can be reduced by approximately 3 dB; the sleeper thickness is increased by 1, and the overall sound pressure level can be reduced by 1–2 dB; and the fastener stiffness is reduced by 1, and the noise reduction is within 1 dB.

Study on dynamic characteristics of urban rail transit vehicle considering faulty axle-box bearings under variable speeds

Axle-box bearing is the key component of urban rail transit vehicles, and its performance status seriously affects the operation safety and stability of the train. Therefore, analyzing the dynamic response of a vehicle system by considering axle-box bearings is the premise of ensuring its safety. Besides, vehicles generally run under the condition of variable speeds, which leads to more complex dynamic response for the vehicle system. Accordingly, studying the influence of faulty axle-box bearings on the vehicle system under variable speeds can reflect the running situation of trains more realistically. In this paper, a dynamics model of axle-box bearings is considered in the vehicle-track coupling model, and the dynamic response of the vehicle system with faulty bearings under variable speeds is analyzed. Firstly, a vehicle-track coupling dynamics model considering axle-box bearings is established, which considers the coupling effect between axle-box bearings and other vehicle components. The bearing inner race is fixedly connected with the axle shaft, and the bearing outer race is fixedly connected with the axle-box housing. Then, an outer race defect model and an inner race defect model of axle-box bearings are respectively established to simulate the internal fault excitation which is often generated in the running process of train bearings. Finally, considering faulty axle-box bearings and variable speeds, the dynamic response of the vehicle system is simulated by the proposed model, whose effectiveness is validated through the theoretical analysis and field tests. The test results show that the axle-box bearing with an outer or inner race defect has a certain influence on the dynamic response of the vehicle system under variable speeds.

A Hybrid Method for Vehicle–Track Coupling Dynamics by Analytical and Finite Element Combination Technique

Globally, rail transit is developing toward higher speeds, larger axle weights, and greater environmental friendliness. The more and more complex wheel–rail interaction will result in the dynamic responses of vehicles, tracks and other structures needing more in-depth theoretical research. However, most existing models for dynamic simulations of the vehicle–track coupling system need to extend the model on both sides of the concerned region to eliminate the boundary effect. To a certain extent, this kind of process method increases the computational effort. To overcome this disadvantage, a hybrid model combined with the analytical method and finite element method was proposed. The moving support system (including transition nodes) was specially established referring to the analytical solution of rail deflection based on the Winkler elastic foundation beam theory to realize the combination of the two methods. Two examples were presented to verify the stability and accuracy of the proposed model. The comparison results show that simulation results of vertical wheel–rail forces and track vibrations are almost consistent with the existing model. Furthermore, the calculation efficiency was discussed and certificated under different long-marshalling trains, with an obvious speedup factor that could be more than 2.5 for 16-marshalling train. The proposed model has a wide application prospect in the vehicle–track coupling analysis of long-marshalling trains, especially for heavy haul railways with hundreds of vehicles.

Research on an Identification Method for Wheelset Coaxial Wheel Diameter Difference Based on Trackside Wheelset Lateral Movement Detection

The wheelset coaxial wheel diameter difference is one of the most common wheel faults of railway vehicles. The existence of the wheelset coaxial wheel diameter difference may lead to the off-load operation of vehicles, resulting in abnormal wheel tread wear, leading to the deterioration of the wheel–rail contact relationship, resulting in the deterioration of the vehicle’s operating stability and comfort, and even leading to an increase in the derailment coefficient, affecting the running safety. In order to monitor the freight car wheelset coaxial wheel diameter difference online, a vehicle–track coupling dynamics model based on a trackside detection method was established, and the response of rail lateral displacement under the condition of the wheelset coaxial wheel diameter difference was analyzed. The results show that the existence of the wheelset coaxial wheel diameter difference can lead to a deviation in the vehicle’s run, with an increase in the wheelset coaxial wheel diameter difference and an increase in the lateral offset of wheelset increases. The impact of vehicle unbalance loading on the lateral movement of the wheelset is much smaller than that of the wheelset coaxial wheel diameter difference. The existence of the wheelset coaxial wheel diameter difference can be better reflected by detecting the wheelset’s lateral displacement. On straight line, the variation of lateral displacement has no infection of vehicle speed, but shows a quadratic growth trend with the wheelset coaxial wheel diameter difference. Based on this, the mapping relationship between the wheelset coaxial wheel diameter difference and wheelset lateral displacement can be obtained. Through a mapping relationship, the size of the wheelset coaxial wheel diameter difference can be reversed precisely through the detection of a trackside lateral movement monitoring system. The reliability of the identification method was verified with a specific test on the trackside monitoring system.

Refined nonlinear fractional derivative model of vehicle-track coupling dynamics

The coupled vehicle-track system (CVTS) dynamics have been extensively investigated for decades. However, the calculation accuracy of prevailing vehicle-track coupling models needs to be improved in the high frequency range due to the inappropriate model simplification and neglect of material nonlinearity. In this study, we propose a refined numerical model of the CVTS that considers the nonlinear properties of the railpads and primary suspension using the fraction derivative Zener model. Furthermore, we more realistically simulate the wheelset, rail and railpad configuration with the elastic axle, solid finite element and surface-support models, respectively, and improve the computation efficiency by employing the mode superposition method. The results demonstrate that the refined CVTS model is more accurate than the classical model in simulating vehicle-track coupling dynamics above 2 kHz. In particular, there are significant differences in the dynamic response of the elastic wheelset model compared to the rigid model over a broad frequency range, with an 11% difference in the bogie acceleration response at the first dominant frequency. When the railpads are modeled using the surface-support model, the rail acceleration differences exceed 41% near 1 kHz and 44% near 2650 Hz, compared to the point-support model. Additionally, the rail response at various locations across the rail cross section can be calculated using the finite element method in this refined model. Overall. the proposed CVTS model provides high accuracy and efficiency for random vibration analysis, especially in the high frequency domain.

Influence of differential deterioration of random track irregularity at different wavelengths on high-speed train safety

ABSTRACT To reveal the influence of differential deterioration of random irregularity at different wavelengths on train safety. Based on the vehicle-track coupling dynamics and the optimized wavelet theory, irregularity samples of typical wavelengths with different deterioration degrees are reconstructed, Henceforth, the postures of the vehicle during the whole derailment process is simulated, during which the derailment risks are revealed. The research shows that the wavelength range of most potential threat to train safety is less than 1 m and greater than 32 m to speed-up line. Train derailment posture is sudden and the safety margin of Nadal criterion is appropriate when the wavelength of track irregularity is less than derailment posture mutation wavelength (DCMW). By contrast, when the wavelength is greater than DCMW, derailment posture is a gradual process, and the safety margin of Nadal criterion is too large. The results can provide theoretical guidance for the fine maintenance and safety monitoring of track geometric.

Multiobjective optimisation of rail profile at high speed

In this paper, a multiobjective optimisation method considering the rail profile at high speed is presented. Based on nonuniform rational B-spline (NURBS) theory, a parameterised model of the rail profile is constructed to determine the variables. The wear index, wheel–rail lateral force and contact stress are selected as the objective function. Based on multibody dynamics theory is applied to establish the vehicle–track coupling dynamic model of the high-speed train CRH380A. An improved NSGA-II algorithm called CN-NSGA-II is proposed in this study. The multi-objective optimisation problem of rail profile is improved by the vehicle–track coupling dynamics model and CN-NSGA-II algorithm. The Pareto front solution is calculated, and the TOPSIS algorithm is used to select the optimal solution and obtain the optimised profile. The analysis of the objective function values of the CN60 profiles and the optimised profile indicate that the maximum wheel–rail lateral force of the left and right wheels of the steering wheelset decreases by 13.3% and 13.71%, the maximum contact stress decreases by 10.35% and 3.21%, and the maximum wear number decreases by 36.09% and 11.4%. The new optimised rail profile can effectively reduce the wheel–rail lateral force, contact stress and wear number in high-speed running conditions.

Rail corrugation detection using one-dimensional convolution neural network and data-driven method

Rail corrugation is a very common wear phenomenon occurring on rail surface, especially on sharp curves, and is one of the main excitation sources of noise and vibration during railway transportation. Timely monitoring of rail corrugation is of great benefit to make scheduled maintenance and save maintenance costs. This paper proposes a novel method combining deep learning and data-driven fusion algorithms to detect rail corrugation on metro lines. First, a one-dimensional convolutional neural network (1DCNN) is constructed to intelligently identify the state of rail corrugation and classify its wavelength. Then, a vehicle–track coupling dynamics model considering the flexibilities of the wheelsets and track structure is established to simulate the dynamic response of the axle box under the excitation of rail corrugation. Next, the depth characteristics of rail corrugation can be calculated using the Kriging surrogate model (KSM) and particle swarm optimization (PSO) algorithms. Finally, a series of field tests are carried out and the feasibility of the proposed method has been verified based on the field measurement data. The results demonstrate that the 1DCNN–KSM–PSO data-driven method can efficiently and quantitatively detect the severity of rail corrugation with a relative error less than 15% and an average error of 6.75%.

Research on rail wear of small radius curve in EMU depot

PurposeWith the help of multi-body dynamics software UM, the paper uses Kik–Piotrowski model to simulate wheel-rail contact and Archard wear model for rail wear.Design/methodology/approachThe CRH5 vehicle-track coupling dynamics model is constructed for the wear study of rails of small radius curves, namely 200 and 350 m in Guangzhou East EMU Depot and those 250 and 300 m radius in Taiyuan South EMU Depot.FindingsResults show that the rail wear at the straight-circle point, the curve center point and the circle-straight point follows the order of center point > the circle-straight point > the straight-circle point. The wear on rail of small radius curves intensifies with the rise of running speed, and the wearing trend tends to fasten as the curve radius declines. The maximum rail wear of the inner rail can reach 2.29 mm, while that of the outer rail, 10.11 mm.Originality/valueWith the increase of the train passing number, the wear range tends to expand. The rail wear decreases with the increase of the curve radius. The dynamic response of vehicle increases with the increase of rail wear, among which the derailment coefficient is affected the most. When the number of passing vehicles reaches 1 million, the derailment coefficient exceeds the limit value, which poses a risk of derailment.

The Influence of Track Structure Parameters on the Dynamic Response Sensitivity of Heavy Haul Train-LVT System

Background: In order to study the applicability of Low Vibration Track (LVT) in heavy-haul railway tunnels, this paper carried out research on the dynamic effects of LVT heavy-haul railway wheels and rails and provided a technical reference for the structural design of heavy-haul railway track structures. Methods: Based on system dynamics response sensitivity and vehicle-track coupling dynamics, the stability of the upper heavy-haul train, the track deformation tendency, and the dynamic response sensitivity of the vehicle-track system under the influence of random track irregularity and different track structure parameters were calculated, compared and analyzed. Results: Larger under-rail lateral and vertical structural stiffness can reduce the dynamic response of the rail system. The vertical and lateral stiffness under the block should be set within a reasonable range to achieve the purpose of reducing the dynamic response of the system, and beyond a certain range, the dynamic response of the rail system will increase significantly, which will affect the safety and stability of train operation. Conclusions: Considering the changes of track vehicle body stability coefficients, the change of deformation control coefficients, and the sensitivity indexes of dynamic performance coefficients to track structure stiffness change, the recommended values of the vertical stiffness under rail, the lateral stiffness under rail, the vertical stiffness under block, and the lateral stiffness under block are, respectively 160 kN/mm, 200 kN/mm, 100 kN/mm, and 200 kN/mm.

Effects of Wheel-Rail Impact on the Fatigue Performance of Fastening Clips in Rail Joint Area of High-Speed Railway

In order to study the effects of wheel-rail impacts on the fatigue damage of the fastening clips at the rail joints of a high-speed railway, field tests were carried out on the wheel-rail impacts at the rail joints of a high-speed railway in China. On the basis of the track irregularities at the rail joints obtained from field measurements, a nonlinear vehicle-track coupling dynamics three-dimensional (3D) model with consideration of Timoshenko beam elements and a refined finite element model of WJ-8 fastening system were constructed. And combined with the theory of cumulative damage and the method of fatigue analysis, the effects of wheel-rail impact at the rail joints on the fatigue life of fastening clips were analyzed. The results showed that the impacts of the wheel-rail in the joint area caused high-frequency fluctuations in the stress-time curves of the clips, which significantly increased the amplitude of stress cycle and increased a lot of stress cycles, of which the amplitudes were reached at a large level; the clips in the area where a rail joint was located suffered the most serious fatigue damage and had the shortest fatigue life; in the actual operation line, besides the clips in the rail joint area, it is also necessary to be concerned about the fatigue performance of fastening clips near the rail joint area.

Research on the evaluation criteria for safety state of train operation based on the scaled model

To accurately predict the train operation state through the test results of the scaled vehicle-track test platform, based on the similarity theory and vehicle-track coupling dynamics theory, the similarity criterion of vehicle-track coupling dynamics system was proposed, and the dynamics models of vehicle-track system in scaled and full scale were established. The running characteristics of wheels under the critical state of derailment were analyzed, and a dynamic evaluation criterion of relative wheel-rail displacement (DEC-RWRD) was proposed. The results show that based on the proposed similarity criterion, the predicted displacement responses of the scaled vehicle-track model is consistent with that of the full scale vehicle. The differences in the accuracy of different train safety evaluation criteria by the scaled vehicle-track model are investigated, and the accuracy of the evaluation can be improved by DEC-RWRD. The combination of DEC-RWRD and the existing train dynamic monitoring methods can realize the prediction and the evaluation of trains’ operation safety by the scaled vehicle-track test platform. The results can provide theoretical support for the dynamic evaluation of the safety status of high-speed train operation under severe line conditions and the experimental study of the whole process of derailment.

Effect of Rail Vehicle–Track Coupled Dynamics on Fatigue Failure of Coil Spring in a Suspension System

In a rail vehicle, fatigue fracture causes a significant number of failures in the coil spring of the suspension system. In this work, the origin of these failures is examined by studying the rail wheel–track interaction, the modal analysis of the coil springs and the stresses induced during operation. The spring is tested experimentally, and a mathematical model is developed to show its force vs. displacement characteristics. A vertical 10-degree-of-freedom (DOF) mathematical model of a full-scale railway vehicle is developed, showing the motions of the car body, bogies and wheelsets, which are then combined with a track. The springs show internal resonances at nearly 50–60 Hz, where significant stresses are induced in them. From the stress result, the weakest position in the innerspring is identified and a few guidelines are proposed for the reduction of vibration and stress in rail vehicles.

Analysis of parameters on the wheel–rail P2 force of subways

An experiment of falling wheels was performed in this study along with full-field tests, for a type of subway train on four subway lines. The results confirmed that 40–80 Hz vibration signals on the ground and train are caused by the wheel–rail P2 force. Vehicle–track-coupled dynamics models were created where the single-layer elastic support model, double-layer elastic support model and floating slab track model were considered. The results were validated by available experimental data and three types of theoretical models: Jenkins, Winkler and double-beam model. This shows that the amplitude of the P2 force increases with larger suspended rail joint angle, higher train speed, heavy unsuspended mass and stronger fastener stiffness. Besides, both fastener damping and the vertical stiffness of primary suspension enabled control of the amplitude of the P2 force in a limited interval. Supporting stiffness of track and unsprung mass played a key role in the frequency of the P2 force. However, the vertical stiffness of the primary suspension had a reduced effect on the frequency of P2 force as compared with the supporting stiffness. Thus, for an effective change to the supporting stiffness, the fastener stiffness could be changed accordingly.

Dynamic performance of locomotive electric drive system under excitation from gear transmission and wheel-rail interaction

Development of railway transportation capabilities towards high-power, high-speed and heavy axle-load makes the dynamic interactions between the electric drive subsystem and the mechanical subsystem of a locomotive more intensive and complicated, which may threaten the locomotive operational safety. However, the included dynamics mechanism and influencing law have not been revealed completely. Based on the co-simulation method and vehicle-track coupling dynamics, a model which enables considering dynamic interactions between the electric drive subsystem and the mechanical subsystem of a locomotive through an electromagnetic coupling interface and motor control subsystem is developed in this paper. By using this co-simulation model, the dynamic responses of the mechanical subsystem and the electric drive subsystem are analysed under complicated dynamic excitation, such as the time-varying gear mesh stiffness and the track geometric irregularity. The results indicate an obvious interaction between the electric drive subsystem and the mechanical subsystem, where the vibration status of the major mechanical components can be reflected by the electric current signals. Besides, the characteristic frequencies of the gear transmission can be extracted from the frequency spectrum of the traction motor current signals, which provides the possibility for condition monitoring and fault diagnosis of the locomotive mechanical components through the electrical signals.

Dynamic behavior of resilient wheels at a rail weld joint

The aim of this paper is to investigate the dynamic response of the resilient wheel equipped on the intercity train at the rail weld. A vehicle-track coupling dynamics model with resilient wheels is developed. A rigid multi-body system with 55 degrees of freedom is utilized to model the vehicle system. The rubber layer of the resilient wheel is modeled as a three-directional spring-damper unit between the wheel rim and the wheel core. For the track sub-model, the rails were modelled as Euler Beam and supported by concrete sleepers modelled as mass block. The vehicle and track motion equations are represented as mass-stiffness-damping matrixes. The accuracy of this modeling method at low frequencies is verified via the comparison between the field measured data and numerical results. The dynamic results of the rigid wheel are compared with those of the resilient wheel. Results show that the dynamic wheel-rail force of the rigid wheel is slightly higher than that of the resilient wheel. Furthermore, the mass factor is introduced to investigate the effect of the rubber layer position on the tire acceleration and the wheel-rail impact force. The numerical simulation results are expected to provide references for resilient wheel application into the intercity train.