Vehicle-track Dynamics Research Articles

Development of vehicle-track coupled dynamics theory and engineering practice

<p indent="0mm">Railway vehicles running on track structures constitute an interactive and inseparable large-scale dynamics system. For a long time, studies on railway vehicle dynamics and on track structure vibration were carried out separately due to the complexity of wheel-rail nonlinear systems and the classification of disciplines, which consequently results in the classical theory system of separate vehicle dynamics and track dynamics. However, the dramatic increase of operating speed and hauling mass of modern railway transportation intensifies dynamic interactions between vehicles and tracks, and such complicated vehicle-track interaction problems fail to be handled by the classical subsystem dynamics theory. Therefore, it is necessary to break through the subsystem research framework and comprehensively investigate the vehicle-track interaction mechanism, so as to achieve the optimal dynamic performance design of the whole system. For this purpose, the vehicle-track coupled dynamics theory system is developed on the basis of absorbing the theoretical achievements of vehicle dynamics and track dynamics, which treats the vehicle subsystem and the track subsystem as a large integrated system by establishing a wheel-rail spatial dynamic coupling model. The vehicle-track coupled dynamics problems can be divided into three aspects: The vertical, lateral and longitudinal coupled dynamics. Generally, the vehicle-track vertical coupled dynamics mainly studies the train-track vertical interaction problem. The vehicle-track lateral coupled dynamics focuses on the stability and safety of vehicle lateral movement on the elastic-damping track structure. In recent years, with the development of long marshalling heavy-haul trains, especially running in the complex environment of long ramps in mountainous areas, the longitudinal impulse of vehicles in a train and its influence on the track system are aggravated, bringing prominent safety problems of the train and track system, which is exactly the mission of longitudinal coupled dynamics research. In view of these three aspects, the vehicle-track coupled dynamics model has undergone the development process from simple to complex, including the unified vertical coupled model, the vertical-lateral spatial coupled model, and the vertical-lateral-longitudinal three-dimensional coupled model. In this paper, the theory system of vehicle-track coupled dynamics will be briefly introduced, including the academic rationale and its formation process. Most of the emphasis is laid on the construction of the unified model of vehicle-track vertical coupled dynamics (namely the fundamental model), and the vehicle-track spatial coupled dynamics model and its recent development. Based on the theory and its simulation platform, an optimal matching design principle of the vehicle and track dynamic performance is proposed, providing a scientific solution for high safety and high stability design of the modern rail transportation system. The vehicle-track coupled dynamics theory ends the long history of separate investigations on vehicle dynamics and track dynamics, and opens up a new research field of railway large-scale system dynamics. As a new theory system, it is recognized worldwide that the vehicle-track coupled dynamics has become the fundamental method for research on railway engineering dynamics after nearly <sc>30 years</sc> of development. This theory has been widely applied to railway engineering practice and has successfully solved a series of key dynamics problems in tremendous railway engineering projects. For this, some practical engineering projects are selected to illustrate the application of the theory, including the investigations on the selection of the plane and vertical profiles design scheme for a Chinese high-speed railway line, the key parameters design for a high-speed railway with a design speed of <sc>400 km/h,</sc> the design of rail asymmetrical grinding profiles for a heavy-haul railway curved line, the safety control of a long heavy-haul train under crush conditions, and the vibration reduction and optimization design of floating slab tracks for metro railways. It is demonstrated that the vehicle-track coupled dynamics theory and its applications strongly support the remarkable development of Chinese railways.

A wheel–rail normal contact model using the combination of virtual penetration method and strip-like Boussinesq’s integral

This paper reports a new non-Hertz normal contact model for the engineering computations such as vehicle-track dynamics and wheel-rail damage prediction. The model is developed as a combination of virtual penetration method and Boussinesq’s integral. A first novel aspect is the proposed virtual penetration method to compensate the inconsistence introduced by this combination, (i) a ‘stepwise penetration scaling coefficient’ approach that adapts to the lateral contact boundary is presented; (ii) we propose a new formula for the longitudinal contact boundary to compensate the error introduced by the step-by-step increase of interpolated penetration. A second novelty is the use of strip-like Boussinesq’s integral for strip discretized contact patch to achieve the fast computation. On the one hand, it makes this model easier to convergence since it only considers the result in the center of each strip. On the other hand, we propose a fast method of generating influence coefficient matrix. Some numerical tests are evaluated by the CONTACT software and compared with KP method and STRIPES. In addition, the comparison of modeling approach and computational cost are discussed in detail.

Combining wavelet analysis of track irregularities and vehicle dynamics simulations to assess derailment risks

Guaranteeing operational safety is mandatory for railways worldwide. As track deteriorates, its geometry deviates from ideal conditions (e.g. perfectly aligned and levelled), which creates undesired vibration and oscillations to the vehicle, increasing dynamic loads and derailment risk. Although current standards establish nominal limits for the track geometry, such point-wise comparisons may overlook relevant track features that can lead to unsafe conditions. The proposed investigation is a contribution to the study of the response of the rail vehicle to the track quality, aimed at identifying track irregularities that produce high track forces and unsafe vehicle responses. To fulfil this aim, Wavelet Analysis is combined with Vehicle Dynamics Simulations to evaluate how the track irregularities, filtered in various wavelength ranges and reconstructed with different wavelets and coefficients' amplitudes, impact vehicle safety in terms of the Nadal safety criterion Y/Q. The simulations demonstrate that defects occurring in some scales/frequencies are more harmful than others, and the similarity between the geometric defects and the shape of the wavelets may be used to identify track locations that require maintenance. These findings suggest that it is possible to create ‘stamps’ of track irregularities that can be used by infrastructure managers to improve their maintenance strategies.

Investigation on energy-regenerative shock absorber with adjustable damping and power for freight wagons

Due to lack of power supply, the onboard monitoring and intelligent devices applied in unpowered freight wagons require manual periodic battery replacement. Converting and utilizing local vibration energy is an effective means to realize the self-power of nearby onboard devices. In this paper, a compact energy-regenerativeshockabsorber with nut-screw transmission and novel unidirectional rotation converter is proposed for harvesting energy from suspension vibration of freight wagons. In addition, an interface circuit with voltage control loop implements the adjustment of system damping and power. With two given policies of control loop reference value, the absorber presents two mechanical characteristics: variable damping and constant damping. The overall system is modelled with dynamic characteristic of diodes considered, and the numerical simulation errors in absorber reaction force and the power obtained by DC/DC are reduced by 48% and 66%. In lab tests, the maximum average efficiencies of DC/DC converter and the whole system are 87.66% and 42.6%. A maximum charging power of 9 W is obtained at the normal suspension vibration excitation, and the average charging power can achieve 87% of that at ideal impedance matching. Meanwhile, the system damping characteristics and power generation capacity under the influence of voltage control loop and external excitation are investigated systematically. By vehicle-track dynamics analysis, the influence law of absorber on freight wagon vibration characteristics is revealed versus different circuit loads. This energy-regenerative damping system possesses adjustable damping and power by the control of circuit load, which will have notable superiority in adapting to the mechanical constraints and power requirements of more engineering application scenarios.

Integration of a dissipative contact force model into vehicle–track dynamics for analysing wheel–rail dynamic interaction under short-wavelength irregularity

Wheel–rail dynamic interaction under short-wavelength irregularity which has a detrimental effect on the service life of vehicle and track components, is of crucial importance to be estimated accurately. Aiming at this, dissipative contact force models are integrated into a validated vehicle–track coupled dynamics model, which enables to consider the energy dissipation at the wheel–rail interface. Wheel–rail interactions for different dissipative contact force models are evaluated, and the Hu–Guo model is selected as the most suitable one for wheel–rail interaction analysis. The wheel–rail interactions for the Hu–Guo model and Hertz theory are analysed under different track irregularities including sinusoidal rail corrugation and rail welded joints. The simulation results indicate that the Hu–Guo model has little effect on the normal interaction at low frequencies, but reduces the contact force fluctuation amplitude obviously at high frequencies above 600 Hz, with a more significant reduction at the resonance peak of high frequency range. The Hu–Guo model has an obvious contact force phase lead compared with the Hertz theory at higher frequencies above 1250 Hz. The Hu–Guo dissipative contact force model is needed for the wheel–rail interaction analysis at high frequencies above 600 Hz.

Optimisation of slab track design considering dynamic train–track interaction and environmental impact

Modern railway tracks for high-speed traffic are often built based on a slab track design. A major disadvantage of slab track compared to conventional ballasted track is that the environmental impact of the construction is higher due to the significant amount of concrete required. In this paper, the dimensions of the rectangular cross-sections and the types of concrete used in slab tracks are optimised with the objective to minimise greenhouse gas emissions, while considering the constraint that the design must pass the static dimensioning analysis described in the European standard 16432-2. The optimised track design is also analysed using a three-dimensional (3D) model of vertical dynamic vehicle–track interaction, where the rails are modelled as Rayleigh–Timoshenko beams and the concrete parts are represented by quadratic shell elements. Wheel–rail contact forces and the time-variant stress field of the concrete parts are calculated using a complex-valued modal superposition for the finite element model of the track. For the studied traffic scenario, it is concluded that the thickness of the panel can be reduced compared to the optimised design from the standard without the risk of crack initiation due to the dynamic vehicle load. In parallel, a model of reinforced concrete is developed to predict crack widths, the bending stiffness of a cracked panel section and to assess in which situations the amount of steel reinforcement can be reduced. To reduce the environmental impact even further, there is potential for an extended geometry optimisation by excluding much of the concrete between the rails.

On the modelling of normal wheel-rail contact for high-frequency vehicle–track dynamics analyses

ABSTRACT A transient wheel–rail rolling contact (RC) model and a vehicle–track coupled dynamics (CD) model are separately developed for a Hertzian contact in elasticity to calculate normal wheel–rail interactions at high frequencies. Short-wave irregularities with a wavelength of 20 ~ 400 mm are considered for a speed of 50 ~ 500 km/h. Results of 180 cases show that contact forces predicted by the CD model are significantly different from those by the RC model, suggesting that ignored or greatly simplified structural and wheel-rail flexibilities, transient effects, finite contact patch, etc. in the CD approach, play important roles in high-frequency interactions. Using the RC predictions as reference, a modified non-linear Hertzian spring is developed to improve the accuracy of the CD model. Such a modification provides references for determination of contact spring and contact filter effect at high frequencies, even though not applicable in a direct way.

Design method of worn rail grinding profile based on Frechet distance method

Due to the large volume and high running density of railway freight lines, rail deterioration occur frequently. Thus, it is necessary to grind the rail in time to improve the wheel-rail relationship. The profile data of the worn rail were measured at different measuring points in a section, and the Frechet distance method was adopted to analyze the data. The representative profile reflecting the overall condition of rail wear in this section is obtained. Combined with NURBS curve theory, a fitting algorithm in which the rail profile with certain discrete points was established. Taking the reduction of the amount of grinding material removed as the objective function, setting wheel-rail matching characteristics, and the reduction of rail wear as the constraint conditions, a calculation model for rail grinding profile was established. The dynamic characteristics of standard profile CN75 and g grinding profile OP75 were analyzed by the vehicle track dynamics model. The results showed that compared with the standard profile CN75, the amount of grinding material removed of the grinding profile OP75 is reduced by 44.7%, and the height reduction of the rail top is reduced by 0.39 mm. After [Formula: see text] km of running, the wear amounts of grinding profile OP75 is about 36.1%–36.5% less than that of standard profile CN75.In the small curve section, the derailment coefficient of grinding profile OP75 is reduced by 11.7% compared with that of standard profile CN75. The dynamic performance is improved. The grinding target profile has better dynamic characteristics and is beneficial to reduce wheel-rail wear.

A comparison of track model formulations for simulation of dynamic vehicle–track interaction in switches and crossings

This paper compares different track model formulations for the simulation of dynamic vehicle–track interaction in switches and crossings (S&C, turnouts) in a multi-body simulation (MBS) environment. The investigations are an extension of the S&C simulation Benchmark with the addition of a finite element model of a 60E1-760-1:15 turnout. This model constitutes a common reference from which four different track formulations are derived: co-running, modal superposition, finite element incorporated into the MBS model and finite element coupled to MBS using a co-simulation approach. For the different track models, the difference in modelling technique, results, simulation time, and suitability for different simulation tasks is compared. A good agreement is found between the different track model formulations for wheel–rail contact forces and rail displacements. This study found a better agreement between co-running and structural track models compared to previous studies in the prediction of wheel–rail contact forces. This appears to be due to the increased complexity of co-running track model used in this study together with a tuning of the co-running track model to the reference model in a wider frequency range. For the reader interested to reproduce the results in this paper, the reference track model is available for download.

Development and validation of a wear prediction model for railway applications including track flexibility

The simultaneous prediction of wheel surface wear is one of the most challenging tasks in the railway field, which requires the knowledge of vehicle–track dynamics, rolling contact mechanics, and other tribological phenomena. In this paper, a new model for predicting wheel profile wear is presented to study in detail the characteristics of wear in the railway. The model is able to consider the effect of track flexibility on wheel wear evolution. The proposed modelling approach includes a vehicle–track coupled model for vehicle dynamical simulation, the local contact model for wheel–rail interaction, and an energetic approach for surface wear evaluation. The whole model has been validated by the comparison with experimental data coming from Chinese high-speed railway lines. The results show that the new model assures high computational efficiency as well as reaches a good prediction accuracy. The proposed model allows the investigation of the role played by different track parameters related to track flexibility on the wheel and rail wear evolution. The influence of the fastener and railpad stiffness on the wheel wear evolution is presented, using the proposed model.

Multibody simulation benchmark for dynamic vehicle–track interaction in switches and crossings: results and method statements

A Benchmark of railway multibody dynamics software application to switches and crossings (S&C) is presented, comparing all major commercially available software and a few independent codes. Two different representative S&C have been implemented, using the Manchester Benchmark passenger vehicle. The final results show that all software offer a reliable and efficient way to understand the kinematic and dynamics forces between the wheels and the track elements. The highest challenges are found when modelling a combination of multiple rails in simultaneous contact with a wheel (check-stock or switch-stock), large longitudinal variations in rail shape (crossings) and high lateral steering forces (diverging cases in tight radius). In those cases, the codes able to account for the exact relative motion of each wheels with respect to each rails independently are the most apt. The most significant variations between software are found in the contact prediction with an influence on the detailed contact tangential and normal forces. The user variability is found to be very small, with the most time-consuming and error prone being the task of handling the input data for the variable rails definition. All software could benefit from improvements to assist the user and ensure higher reliability and efficiency generally.

A reliability assessment approach for slab track structure based on vehicle-track dynamics and surrogate model

The reliability assessment of rail infrastructure is directly related to the safety and effectiveness of railway transportation and critical for railway management department. This paper presents an approach for service reliability analysis of slab track from the point of view of the vehicle-track system operational safety. The vehicle-track dynamics is simulated by the established finite element model (FEM) and the limit state function (LSF) is defined on the danger of derailment. To reflect the real state of track geometric condition, the track irregularity spectrums (TISs) are extracted from the measured track irregularity data and fitted by the seven-parameter formula. Then, a set of time series can be obtained from the TISs using a binary wavelet-based inversion method and then input to the FEM to obtain the value of LSF. Finally, Monte Carlo simulation (MCS) is used in the calculation of track reliability. To overcome the slow convergence of the vehicle-track models, this study develops a surrogate model based on support vector machine (SVM). It is validated that the established SVM can well approximate the relationship between the track irregularities to the derailment coefficients in terms of small error and high correlation. More importantly, the efficiency is more than 1000 times higher than traditional FEM. This is a pioneering study to incorporate vehicle-track dynamics into the reliability assessment of slab track in service. For a 1024-m section of slab track, results show that its reliability index can satisfy the requirement in specifications.

Wheel–rail impact loads and axle bending stress simulated for generic distributions and shapes of discrete wheel tread damage

Wheel–rail impact loads generated by discrete wheel tread irregularities may result in high dynamic bending stresses in the wheelset axle, leading to a decrease in component life and an elevated risk for fatigue failure. In this paper, a versatile and cost-efficient method to simulate the vertical dynamic interaction between a wheelset and railway track, accounting for generic distributions and shapes of wheel tread damage, is presented. The wheelset (comprising two wheels, axle and any attached equipment for braking and power transmission) and track with two discretely supported rails are described by three-dimensional finite element (FE) models. The coupling between the two wheel‒rail contacts (one on each wheel) via the wheelset axle and via the sleepers is considered. The simulation of dynamic vehicle–track interaction is carried out in the time domain using a convolution integral approach, while the non-linear wheel–rail normal contact is solved using Kalker's variational method. Wheelset designs that are non-symmetric with respect to the centre of the axle, track support conditions that are non-symmetric with respect to the centre of the track, as well as non-symmetric distributions of tread damage on the two wheels (or irregularities on the two rails) can be studied. Time-variant stresses are computed for the locations in the wheelset axle which are prone to fatigue. Based on Green's functions for stress established using the wheelset FE model, this is achieved in a post-processing step. An extensive parametric study has been performed where wheel–rail impact loads and axle stresses have been computed for different distributions and sizes of tread damage as well as for different train speeds.

Probability of instant rail break induced by wheel–rail impact loading using field test data

ABSTRACT The probability of an instant rail break, initiated at a single pre-existing rail foot crack due to a severe wheel impact loading, is predicted using statistical methods and a time-domain model for the simulation of dynamic vehicle–track interaction. A linear elastic fracture mechanics approach is employed to calculate the stress intensity at the crack in a continuously welded rail subjected to combined bending and temperature loading. Based on long-term field measurements in a wayside wheel load detector, a three-parameter probability distribution of the dynamic wheel load is determined. For a faster numerical assessment of the probability of failure, a thin plate spline regression is implemented to develop a meta-model of the performance function quantifying the stress intensity at the crack. The methodology is demonstrated by investigating the influence of initial crack length, fracture toughness and rail temperature difference on the risk for an instant rail break.

Investigation on rail corrugation grinding criterion based on coupled vehicle–track dynamics and rolling contact fatigue model

Based on the measured spectra of rail roughness and track structures longitudinal roughness, the rail grinding limit is studied with the help of an established coupled dynamic metro vehicle–track model and a rolling contact fatigue model. The results indicate that metro rail grinding control should be regulated according to corrugation wavelength range and operating speed. Based on the rolling contact fatigue model, longer wavelength of rail corrugation has less influence on the wheel rolling contact fatigue. For the metro lines with a maximum operating speed of 80 km/h, the average levels of rail corrugation in the wavelength ranges of 30–65 mm, 65–125 mm, and 125–250 mm should be less than 5.4, 24.8, and 33.8 dB re 1 μm, respectively; for the ones with the operating speed of 80–120 km/h, the corresponding average corrugation levels in the three wavelength ranges should be less than 4.4, 9.8, and 29.8 dB re 1 μm, respectively.

On-Line Learning and Updating Unmanned Tracked Vehicle Dynamics

Increasing levels of autonomy impose more pronounced performance requirements for unmanned ground vehicles (UGV). Presence of model uncertainties significantly reduces a ground vehicle performance when the vehicle is traversing an unknown terrain or the vehicle inertial parameters vary due to a mission schedule or external disturbances. A comprehensive mathematical model of a skid steering tracked vehicle is presented in this paper and used to design a control law. Analysis of the controller under model uncertainties in inertial parameters and in the vehicle-terrain interaction revealed undesirable behavior, such as controller divergence and offset from the desired trajectory. A compound identification scheme utilizing an exponential forgetting recursive least square, generalized Newton–Raphson (NR), and Unscented Kalman Filter methods is proposed to estimate the model parameters, such as the vehicle mass and inertia, as well as parameters of the vehicle-terrain interaction, such as slip, resistance coefficients, cohesion, and shear deformation modulus on-line. The proposed identification scheme facilitates adaptive capability for the control system, improves tracking performance and contributes to an adaptive path and trajectory planning framework, which is essential for future autonomous ground vehicle missions.

Wheel-rail wear simulation and rail cant optimisation based on railway vehicle dynamics

A numerical prediction model for the wheel-rail wear development on heavy-haul railway is established herein, and a corresponding program is written using MATLAB. Using Archard's material wear theory, wear distributions in the wheel-rail contact patch and along the rail profile are evaluated via vehicle-track dynamics simulation and wheel-rail rolling contact analysis. The established model is employed to study the influences of rail cant on the wheel-rail wear distribution and development. The following main conclusions are drawn. On straight railway section, the wheel-rail contact region and wear distribution become unreasonable when the rail cant exceeds 1/20. On curved section, the influences of rail cant on the wear of the inner and outer rails are different. The changes of rail cant also obviously impact the changing rules of wear with the vehicle speed. A rail cant of 1/30 is recommended for the curved section of heavy-haul railway.

Wheel-rail wear simulation and rail cant optimisation based on railway vehicle dynamics

A numerical prediction model for the wheel-rail wear development on heavy-haul railway is established herein, and a corresponding program is written using MATLAB. Using Archard's material wear theory, wear distributions in the wheel-rail contact patch and along the rail profile are evaluated via vehicle-track dynamics simulation and wheel-rail rolling contact analysis. The established model is employed to study the influences of rail cant on the wheel-rail wear distribution and development. The following main conclusions are drawn. On straight railway section, the wheel-rail contact region and wear distribution become unreasonable when the rail cant exceeds 1/20. On curved section, the influences of rail cant on the wear of the inner and outer rails are different. The changes of rail cant also obviously impact the changing rules of wear with the vehicle speed. A rail cant of 1/30 is recommended for the curved section of heavy-haul railway.

Simulation of vertical dynamic vehicle–track interaction using a three-dimensional slab track model

When improving track design, a better understanding of the track’s damage modes is needed, and the railway industry is then dependent on the availability of accurate simulations of the dynamic vehicle–track interaction. In the present study, the vertical dynamic interaction between a travelling railway vehicle and a slab track is simulated in the time domain by using an extended state-space vector approach. A three-dimensional slab track model is launched where the rails are modelled using Rayleigh–Timoshenko beam elements and the concrete panel and roadbed are represented by using either shell or solid finite elements. From the parameterised track model, which is developed in Abaqus using Python scripts, the system matrices are exported to Matlab where the simulation of the dynamic vehicle–track interaction is performed. A complex-valued modal superposition technique is employed, which reduces the computational cost of the simulation. In a post-processing step, calculated wheel–rail contact forces from the dynamic analysis are used as input to the Abaqus track model where various track responses are evaluated. In particular, the time history of principal stresses is determined at critical locations in the concrete panel. Also the influence of the speed of the vehicle on the wheel–rail contact forces, and the influence of a transverse culvert below the track (modelled as a local increase of the foundation bedding modulus) on the track stiffness variation at the rail level, are investigated. A mesh convergence study for a range of track responses has been conducted including investigations of when to use linear or quadratic elements and shell or solid elements. Finally, the presented three-dimensional models have been compared to an alternative two-dimensional model to determine in what situations a two-dimensional model is sufficient.

Numerical investigation on the dynamic behaviour of derailed railway vehicles protected by guard rail

Train derailment can cause not only damage to the train itself but also secondary damage to surrounding structures. For this reason, guard rails are commonly used to prevent secondary damage caused by derailed trains on high-risk lines. In this paper, a 3D vehicle-track dynamics simulation model and a collision contact model were used to investigate the post-derailment dynamic behaviours of the train as well as the effectiveness of guard rail protections. Variables studied include derailer oblique angle, the gap between running rail and guard rail, the effect of derailing speed on the posture, and impact force after derailment. The study shows that the oblique angle has a strong influence on the dynamic derailment behaviours. At a large gap, the bogie generates a noticeable distortion, which is very detrimental to the derailed vehicles. It was found that when the gap is 200 mm, the derailed wheelsets roll on the sleepers stably. And high derailing speeds can also cause significant impact forces. These simulations further the theory of train running posture and impact response, and can inform good railway design and maintenance. This is particularly true for tracks on which guard rails are installed to reduce secondary damage.