Track Dynamic Model Research Articles

A refined track dynamic model considering the bending properties of iron pad: Proposal and validation

Iron pads are crucial components in rail fastening systems, characterized by their load-bearing and force-transmitting capabilities. This study presents and validates a track dynamic model considering the bending properties of iron pad, offering a comprehensive analysis of their dynamic performance under train loads. The primary aim is to employ iron pads as key elements for monitoring and detecting potential defects throughout the track’s service life. Initially, the construction of the track dynamic model is outlined, followed by an in-depth explanation of how the iron pads integrate with the track model. This involves introducing an enhanced Kelvin-Voigt three-element model and elaborating on the parameter selection for the spring element using a nonlinear spring model that accounts for voids and their relevant conditions. Subsequently, a systematic comparative analysis is performed to evaluate the accuracy of simulating iron pads using solid, shell, and beam elements, along with a proposed strain correction method. Finally, the established model and methods are employed to simulate and analyze the dynamic response of iron pads under typical defect conditions. These results indicate that iron pads can effectively reflect the failure conditions of the railway track system, making them ideal sensing elements for the dynamic monitoring of track structures. The enhanced model developed in this study holds significant theoretical and practical value, contributing to the safety monitoring and defect analysis of railway operations.

Multi-objective optimisation of a metro wheel profile to reduce wheel flange wear and RCF considering the distribution density of wheel−rail contact points

In this study, the problem of severe wheel flange wear and tread rolling contact fatigue (RCF) of metro wheels with two wheel profiles, i.e. the LM-30 profile and the DIN5573-30 profile, is investigated. The contact characteristics of the two profiles are compared to analyse the causes of wheel flange wear and RCF. Indices combining the density distribution of contact points are proposed to evaluate the wheel flange wear and RCF. The optimisation region of the wheel profile is defined by eight arc parameters, which is derived from the tangency of the arcs. A back-propagation neural network is constructed as a surrogate model for the design variables and the objective function. Four intelligent optimisation algorithms are compared and used to solve the optimisation problem. The vehicle—track dynamic model and the wheel wear and RCF prediction model are used to verify the performance of the optimised profile. The results show that the critical speed of the optimised profile is between that of the LM profile and that of the DIN5573 profile, and the curving performance of the optimised profile is significantly improved. At the same time, the optimised wheel profile can reduce wheel flange wear and tread RCF.

Parametric investigation of railway fastenings into the formation and mitigation of short pitch corrugation

Short pitch corrugation has been a problem for railways worldwide over one century. In this paper, a parametric investigation of fastenings is conducted to understand the corrugation formation mechanism and gain insights into corrugation mitigation. A three-dimensional finite element vehicle–track dynamic interaction model is employed, which considers the coupling between the structural dynamics and the contact mechanics, while the damage mechanism is assumed to be differential wear. Various fastening models with different configurations, boundary conditions, and parameters of stiffness and damping are built up and analysed. These models may represent different service stages of fastenings in the field. Besides, the effect of train speeds on corrugation features is studied. The results indicate: (1) Fastening parameters and modelling play an important role in corrugation formation. (2) The fastening longitudinal constraint to the rail is the major factor that determines the corrugation formation. The fastening vertical and lateral constraints influence corrugation features in terms of spatial distribution and wavelength components. (3) The strengthening of fastening constraints in the longitudinal dimension helps to mitigate corrugation. Meanwhile, the inner fastening constraint in the lateral direction is necessary for corrugation alleviation. (4) The increase in fastening longitudinal stiffness and damping can reduce the vibration amplitudes of longitudinal compression modes and thus reduce the track corrugation propensity. The simulation in this work can well explain the field corrugation in terms of the occurrence possibility and major wavelength components. It can also explain the field data with respect to the small variation between the corrugation wavelength and train speed, which is caused by frequency selection and jump between rail longitudinal compression modes.

Investigations on wagon–track interaction and running safety with unsupported sleepers

Unsupported sleeper defects are not rare for the ballasted track. Based on the status quo of the railway in Kosovo, this paper presents a study on the wagon–track interaction and running safety risk with unsupported sleepers. A three-dimensional wagon–track dynamic model is first developed and validated through a full-scale field experiment. The dynamic response features of wagon and track components are respectively presented and analysed under the sleeper hanging condition. Parameter studies and safety analysis are then conducted with different wagon speeds, including gap height, unsupported quantity, wagon load, and asymmetric effects of the unsupported sleeper. The results indicate that unsupported sleepers will induce wheel–rail impact and significantly exacerbate the vibrations of the wagon and track. The wavelength corresponding to the dominant frequency for the wagon vertical acceleration (ACC) is equal to the wheelbase. Moreover, adjacent ballasts of the unsupported zone exhibit maximal displacements and ACCs, which could be the compelling evidence to explain the extension of the unsupported zone. The derailment risk is typically higher when the unsupported sleepers are asymmetrically distributed compared to the scenarios with symmetrically unsupported sleepers. Additionally, the combined effects of unsupported sleepers and wheel flat will further deteriorate the wagon running safety. The presented results can provide a significant reference for the wagon speed increase and track maintenance in Kosovo and other countries with deficient railway infrastructure.

Towards time-domain modelling of wheel/rail noise: Effect of the dynamic track model

Transient events in railway rolling noise, such as the characteristic impulsive noise at switches and crossings, can significantly contribute to the perceived annoyance, despite being difficult to detect in the standard frequency-domain methods to analyse rolling noise. Studying these transient effects and their perception requires predicting the noise in the time domain. While several time-domain approaches exist for predicting the dynamic interaction of wheel and rail, predicting the associated rolling noise with adequate accuracy is computationally costly. The lack of a model for transient noise and the need for studying its perception was recently identified. Aiming for a comprehensive time-domain radiation model that includes the wheel and track contributions to rolling noise, this work focuses on the track radiation. The modelling approach taken here is based on a 2.5D formulation for the acoustic radiation and moving Green’s functions in the air. The computational cost, which lies mainly in the 2.5D BE calculations, is addressed by pre-calculating acoustic transfer functions. These transfer functions can be combined with different dynamic track models. Different dynamic track models in turn affect radiated sound field in different ways. Here, the sound fields produced by six different track models are compared, including different support types and analytical and numerical rail models. Several descriptors of the sound field are analysed. In terms of the radiated sound power and radiation efficiency, modelling the rail as a simple beam leads to similar results as elaborate numerical models up to about 5 kHz. In terms of the track-side sound pressure, simple beam models can provide similar results only up to 2.5 kHz. Euler-Bernoulli (E-B) beams seem unfit for time-domain predictions of the radiated noise as they over-estimate the bending wave speed at high frequencies. The results also show that the standard track decay rate (TDR) and the decay of acoustic sound pressure along the track are comparable.

Comprehensive efficient vertical and lateral track dynamic model to study the evolution of rail corrugation in sharp curves

• A highly accurate and fast model is developed for the study of rail corrugation. • Experimental receptances are precisely fitted using RFP and genetic algorithms. • Lateral system dynamics is added to the model preserving short computational times. • The model has been validated with experimental measurements. This paper addresses a time/space domain model, extremely efficient in terms of computation, which combines the vertical and lateral dynamics of the track to predict undulatory wear depending on track and vehicle parameters. As it is known, this is a source of noise and vibration that can provoke very high levels. The model is obtained from the transformation of a model in the frequency domain to the time/space domain by means of the rational fraction polynomials method. Multiobjective genetic algorithms are used to minimize the error in fitting receptances and to ensure the stability of the system. This model includes the vertical wheel-rail dynamic interaction with a Hertzian spring, and the FASTSIM algorithm is used to study tangential contact. The model is validated with the experimental corrugation measurements taken on a metro line.

Dynamic track model of miscible CO2 geological utilizations with complex microscopic pore-throat structures

Monitoring field-scale CO2 geological utilizations is of paramount importance but challenging due to the complexities in microscopic heterogeneity. In this paper, complex geological characterizations and fluid properties are specifically analysed and a prediction model is developed, which is capable to track the dynamic behaviour of miscible CO2 multiphase flow in microscopically-heterogeneous porous media. More specifically, first, pore-throat sizes and distributions were characterised from the constant-rate mercury injection and the CO2-displacement seepage resistance was evaluated from a capillary bundle model. The differences of seepage resistance caused from the throat changing and coupling diffusion-dissolution effects and viscosity-resistance reductions were specifically studied in the process of continuous miscible CO2 displacement. Accordingly, a comprehensive mathematical model was developed with the time-node analysis method and validated through comparison with the experimental results. The leading edge of CO2 displacement as well as the timing of gas breakthrough and displacement completion are determined to be different with varying throat sizes. It is further found that the gas breakthrough time and the time required to complete the displacement are reduced with increasing throat size and their differences also decrease. Moreover, the interval area of injection and production wells could be characterised as pure CO2, diffusion and pure oil zones, whose positions could be dynamically tracked from the recovery performance. The calculated oil recovery and gas-oil ratio from the developed model share good agreement with experimental results, with deviations of 2.2 and 0.7%. Such the validated mathematical model is then applied to successfully predict the dynamic performance of an actual reservoir (H3).

Three-Dimensional Vehicle–Curved Track Dynamic Model Based on FEM and DEM

In this work, a systematic vehicle–curved track dynamic model is presented, in which the vehicle is modeled as a multi-rigid-body system. The track structure is modeled by finite element method with curved rail beam element considered in geometry. To obtain accurate dynamic behavior of railway ballasted track, the resistance characteristics of ballast bed are revealed by introducing the discrete element method. Besides, a two-step iterative-update method is improved to solve the multi-nonlinearity of the vehicle–curved track dynamic interaction. To improve the computational efficiency, and the improved infinite cyclic calculation method is introduced. Apart from the model validations, the application of this model in engineering practices, such as the vehicle-induced vibration of the continuously welded rail (CWR), has been revealed, and some conclusions are drawn from the numerical studies.

Active steering control based on preview theory for articulated heavy vehicles.

This paper investigates the active steering control of the tractor and the trailer for the articulated heavy vehicle (AHV) to improve its high-speed lateral stability and low-speed path following. The four-degree-of-freedom (4-DOF) single track dynamic model of the AHV with a front-wheel steered trailer is established. Considering that the road information at the driver’s focus is the most clear and those away from the focus blurred, a new kind controller based on the fractional calculus, i.e., a focus preview controller is designed to provide the steering input for the tractor to make it travel along the desired path. In addition, the active steering controllers based on the linear quadratic regulator (LQR) and single-point preview controller respectively are also proposed for the trailer. However, the latter is designed on the basis of the articulation angle between the tractor and trailer, inspired by the idea of the driver’s single-point preview controller. Finally, the single lane change maneuver and 90o turn maneuver are carried out. And the simulation results show that compared with the single-point preview controller, the new kind preview controller for the tractor can have good high speed maneuvering stability and low speed path tracking ability by adjusting the fractional order of the controller. On this basis, three different AHVs with the same tractor are simulated and the simulation results show that the AHV whose trailer adopts the single-point preview controller has better high-speed lateral stability and low-speed path tracking than the AHV whose trailer adopts the LQR controller.

Turning dynamics analysis of a heavy articulated vehicle by the vehicle planar dynamic model with two steering input signals

The vehicle planar single track dynamic model with two input steering angle parameters is derived by using Lagrange's method with the basis of equations for calculating the tire's force components. Dynamic analysis of a heavy articulated vehicle in case of turing is carried out by the vehicle planar dynamic model, in which two input steering angles are taken into account. Simulation with the selected velocity value to make sure that the stability according to the friction conditions at all axles of the vehicle is satisfied. Turning spacing, lateral forces at each axle of the vehicle are determined and analyzed for all three different cases of steering angles, respectively with steering angle of the semi-trailer is in the same direction, in the opposite direction and is locked or not steered in comparision with the steering angle of the tractor. The obtained results show that the derived model could employ to determine the planar kinematic and dynamic parameters, and analyze the dynamic safety features of an articulated vehicle, too. In addition, the derived mathematical model could also employ to develop a computational model that controls the planar articulated vehicle dynamics.

A Validated Train-Track-Bridge Model with Nonlinear Support Conditions at Bridge Approaches

A bridge approach, an essential component connecting a relatively rigid bridge and a more flexible track on subgrade soil, is one of the most common types of track transition zones. The tracks on a bridge deck often undergo significantly lower deformations under loading compared to the approach tracks. Even though there have been numerous efforts to understand and remediate performance deficiencies emerging from the differences in stiffness between the bridge deck and the approach, issues such as differential settlement and unsupported hanging crossties often exist. It is often difficult and expensive to try different combinations of mitigation methods in the field. Therefore, computational modeling becomes of vital importance to study dynamic responses of railroad bridge approaches. In this study, field instrumentation data were collected from the track substructure of US Amtrak’s Northeast Corridor railroad track bridge approaches. After analyses and model implementation of such comprehensive field data, an advanced train-track-bridge model is introduced and validated in this paper. Nonlinear relative displacements under varying contact forces observed between crosstie and ballast are adequately considered in the dynamic track model. The validated model is then used to simulate an Amtrak passenger train entering an open deck bridge to generate typical track transient responses and better understand dynamic behavior trends in bridge approaches. The simulated results show that near bridge location experiences much larger transient deformations, impact forces, vibration velocities and vibration accelerations. The validated track model is an analysis tool to evaluate transient responses at bridge approaches with nonlinear support; it is intended to eventually aid in developing improved track design and maintenance practices.

Research on the Vibration Characteristics of a Track’s Structure Considering the Viscoelastic Properties of Recycled Composite Sleepers

In order to investigate the vibration characteristics of a composite sleeper-ballasted track and provide a basis for further popularization, a vehicle–track dynamic coupling model is established and the viscoelastic properties of the composite sleeper are considered. The power flow method is employed to reveal the power flow distribution characteristics of the composite sleeper. The results show that the viscoelastic properties of the composite sleeper have little influence on the rail power and have a greater influence on the power flow of the sleeper and ballast bed in some frequency ranges. The viscoelastic properties of the composite sleeper can effectively improve the calculation accuracy of the track structure’s power flow. Compared with the type-III pre-stressed concrete sleepers widely used in China, composite sleepers consume more energy in the vibration process due to their own physical characteristics, which reduces the power flow transmitted downward and relieves vibration on the ballast bed, especially in the ranges of 80–125 Hz and 250–400 Hz. The temperature change mainly affects the power flow of the composite sleeper in the frequency range above 50 Hz. As the temperature increases, the modulus of the composite sleeper decreases and the vibration reduction effect of the ballast bed is improved.

Influence of motion characteristics of dual stealth aircraft on monopulse radar performance

In view of the difficulties to effectively evaluate the influence of penetration of dual stealth aircraft formation on monopulse radar angle tracking error under different flight speeds, the dynamic track model of the dual stealth aircraft under different navigation speeds is established for the first time, and the acquisition method of the dynamic Radar cross section of the dual stealth aircraft formation under different navigation speeds is proposed; the dynamic signal-to-noise ratio of the dual stealth aircraft under different navigation speeds is used as a reference and the model of single pulse radar angle tracking error is established. This paper analyzes the influence of the formation motion characteristics of dual stealth aircraft on the angle tracking error performance of monopulse radar. It is the first time to conclude that the acceleration of the navigation speed of dual stealth aircraft will increase the angle tracking error of monopulse radar when there is no interference.

Research on dynamics of a new high-speed maglev vehicle

The levitation bogie of the TR-series maglev vehicle is redesigned by adding an intermediate buffer layer between the levitationbogie and the levitation module to improve the curve negotiation capacity of the high-speed maglev vehicle and reduce the vertical coupleddynamic effect of the vehicle and the track beam. As the existing TR08 maglev vehicle dynamic model has been verified by experiments, anew type of dynamic model of maglev vehicle is constructed by transplanting the functional module of TR08 model. The vehicle-elastic trackbeam coupled dynamic model and the vehicle-curved track dynamic model are established. Simulation analyses of the dynamic response ofvehicles and track beams show that: the curve negotiation capacity of the new-type maglev vehicle is better than that of TR08 type maglevvehicle; the resonance effect does not occur between the vehicle and the track beam; the vertical dynamic displacement of the track beammid-span decreases by 23% compared with the TR08 type; the redesigned levitation bogie structure and the track beam have less dynamicinteraction, indicating that the working environment of the electromagnet in the new maglev vehicle has been improved, which can effectivelyreduce the burden of electrical decoupling of the control system.

Qualitative Prediction Model for Dynamic Behavior of Ballasted Tracks

Theoretical, experimental, analytical, and statistical evaluations were performed to predict and assess the dynamic behavior of a ballasted track, such as the track support stiffness, track impact factor, or dynamic wheel–rail forces. Field measurements were then performed to evaluate the dynamic behavior of the ballasted track and its components. A qualitative prediction model was then developed to predict and assess track performance as a function of dynamic wheel-rail force and variation in track support stiffness. The developed two-degree-of-freedom dynamic track model can define the rail pad and ballast stiffness ranges based on designed and measured values. Using the proposed model, qualitative analysis results are presented as a discrete space of various track responses and parameters, rather than as single values. The proposed model was then validated using field measurements, which demonstrated that the proposed model predicted the vertical rail displacement and rail bending stress within approximately 2–5% of the obtained field measurements. Overall, the developed qualitative prediction model allows the dynamic response of in-service ballasted tracks to be estimated as a function of the rail pad and ballast stiffness using only a simple field measurement.

Near Time Optimal Trajectory Generation for Over-Actuated Vehicles using Nonlinear Model Predictive Controller

Abstract The generation of time dependent paths is crucial for autonomous driving. While relatively simple models are sufficient for normal driving situations, more complex models are required the closer the trajectory is planned towards the handling limits. This paper considers a near time optimal trajectory generation for combined longitudinal and lateral dynamics for an over actuated vehicle. A nonlinear model predictive controller which accounts for actuator constraints is used to generate these trajectories. The predictive model is a reduced dynamic double track model with three degrees of freedom. The resulting trajectories show the ability of following a reference path with the use of all available actuators up to the handling limits.

Dynamic response of vehicle and track in long downhill section of high-speed railway under braking condition

The dynamic behaviors of vehicle and track in long and downhill section of high-speed railway are studied under braking condition. A vehicle–track dynamic interaction model is constructed based on two longitudinal vehicle–track interaction models. In the model, the vehicle is considered as a 21-degree-of-freedom multi-rigid body system composed of a car body, two bogies, and four wheels; using the finite-element method, the track is modeled as a Euler beam; the “circular track” method is proposed to reduce the degree of freedom of the model for the simulation of long-distance track; two longitudinal wheel–rail interaction models are considered: the Polach creep theory (suitable for simulating condition of large creep resulting from heavy braking) and the longitudinal rigid-contact theory. The dynamic responses of the substructures during vehicle braking calculated by the models based on the Polach creep model and longitudinal contact model show little difference, but the Polach creep model can fully consider the motion of the wheels and large wheel–rail creep in the braking process and can accurately analyze the wheel–rail interface damage. The results of dynamic interaction between wheel and rail under different conditions suggest that large braking torque will cause some or all of the wheels to slide and then cause the damage of wheel–rail interface. The grade will lead to the increase in braking distance and time and also extend the sliding time of locked wheels, increasing the risk of damage of the wheel–rail interface. The braking torque should be kept below a reasonable value, so that the braking distance and braking time can be as short as possible without the occurrence of wheel sliding along the track. A reasonable braking torque under the dry track and wet track conditions should be 7 and 4 kN m respectively, according to the calculation in this article.

A spectral evolution model for track geometric degradation in train–track long-term dynamics

ABSTRACTIn this work, a new insight is put forward to characterise the evolution of track irregularities from viewpoint of spectral analysis. The main novelty lies in a proposal of regarding the geometric deterioration of track irregularities equivalently as the evolution of power spectral densities (PSD), and consequently, the stationarity of track irregularities and a robust dynamic assessment can be guaranteed. Besides a systematic framework integrating the train–track dynamic model, track irregularity PSD evolution model and the Pseudo-excitation method is developed to predict the uncertain responses of system components long-termly. In the PSD evolution method developed, we have departed from the conventional strategies trying to characterise the evolution of time-domain track irregularities from perspectives of physical-mechanical methods and elastic-plastic deformation. Instead, a statistical and mathematical model is proposed to randomly estimate the evolution of track irregularities with a guarantee of the stationarity of track geometries. In this model, the deterioration of time domain track irregularities is equivalently transformed as the evolution of PSD at frequency domain. A mathematical relationship between dynamic loads and PSD evolutions is constructed, in which the model parameters are defined by the statistical results and a Levenberg–Marquard iterative formula. Apart from predicting the long-term evolution of track irregularity amplitude and the track quality index, the PSD evolution model can be perfectly united with the train–track interaction model and a pseudo-excitation method to reveal the long-term evolution of system behaviours no matter on response amplitudes or on their characteristic frequencies against different confidence intervals.

Effects of Pier Deformation on Train Operations within High-Speed Railway Ballastless Track–Bridge Systems

The deformation of a bridge foundation (i.e. pier) for a ballastless track of a high-speed railway may cause additional irregularities within the track, thereby affecting train operation. By using a unit slab ballastless track bridge system as the research object, this study built a finite element model and a train–track dynamic interaction model. The additional rail deformation caused by the vertical or lateral deformation of a bridge pier was calculated by the finite element model, and then the effects on train operation due to the additional rail deformation were analyzed by the train–track dynamic model. It was found that the lateral deformation of a single pier should be of the most concern for the management and control of a high-speed railway. Specifically, when a pier suffered settlement and lateral deformation concurrently, the evaluation indices of train operation were primarily affected by the magnitude of the lateral deformation, and were only slightly affected by the settlement.

Simulation investigation of tractive energy conservation for a cornering rear-wheel-independent-drive electric vehicle through torque vectoring

Although electric vehicle fully exhibits its comparative merits of energy conservation and environmental friendliness, further improvement of its traction energy efficiency lacks comprehensive investigations in the past. In this paper, the effect of the torque vectoring on traction energy conservation during cornering for a rear-wheel-independent-drive electric vehicle is investigated. Firstly, turning resistance coefficient and energy conservation mechanism of torque vectoring are derived from the single track dynamic model. Next, an optimal torque vectoring control strategy based on genetic algorithm is proposed, with the consideration of the influence of the operation-point change of the in-wheel motors, to find out the best torque vectoring ratio offline. Finally, various simulation tests are conducted to validate the energy conservation effect after Simulink modelling. The results verify that though the optimization of the operating region of the motors is the main part for tractive energy conservation, the contribution of torque vectoring itself can reach up to 1.7% in some typical cases.