Dynamic Vehicle Track Interaction Research Articles

Multibody simulation benchmark for dynamic vehicle-track interaction in switches and crossings: modelling description and simulation tasks

This paper presents the final description for the S&C Benchmark that was launched at the IAVSD 2019 conference held in Gothenburg, Sweden and completed by eighteen participants by the end of 2020. The purpose of this paper is to allow for the replication of the Benchmark exercise after publication for those who wish to do so in the future, and it includes a link to the repository containing all necessary input data. The original task description, including a description of the Benchmark submission, is presented in full. The results from the Benchmark are available in [Bezin Y, Pålsson BA, Kik W, et al. Multibody simulation Benchmark for dynamic vehicle-track interaction in switches and crossings: results and method statements. Submitted to VSD, 2021].

Vehicle running instability detection algorithm (VRIDA): A signal based onboard diagnostic method for detecting hunting instability of rail vehicles

In recent years, significant research transpired on onboard monitoring of various phenomena arising in dynamic vehicle-track interaction. One key issue being monitoring of vehicle hunting instability. Current hunting detection standards are appropriate for certification tests of vehicles, but incapable to monitor the health of the vehicle and track subsystems influencing the hunting instability. This paper proposes a signal based procedure for accurately triggering Hunting/No-Hunting alarm by conforming to requirements of onboard monitoring. A new method is conceived to reveal coherence among lateral and longitudinal accelerations during vehicle hunting. Furthermore, an index which amalgamates phase and amplitude information of lateral and longitudinal axlebox accelerations is introduced to detect coupled modes in lateral and yaw directions, i.e. hunting modes. Several simulations based pragmatic case studies are performed to assess the efficacy of the proposed procedure. The proposed method outperforms traditional hunting detection procedures by detecting more Hunting/No-Hunting occurrences. The proposed method contributes towards digitalization of rail vehicles through condition-based and predictive maintenance.

Calibration and validation of a freight wagon dynamic model in operating conditions based on limited experimental data

This article presents an efficient methodology for the calibration and validation of a numerical model of a freight wagon based on a dynamic test under real operation conditions. The dynamic test takes place during a regular journey of the train and involved the installation of on-board accelerometers and LVDTs, whose number and location was conditioned by the space occupied by the goods and constraints associated with loading and unloading the wagon. The data derived from the dynamic test was used for the identification of carbody's modal parameters, namely the frequencies, mode shapes and damping coefficients and to extract accelerations and displacements time-histories. A three-dimensional (3D) FE numerical model of the freight wagon was developed and calibrated using a genetic algorithm. The methodology proves efficiency and robustness in precisely estimating three numerical parameters, besides a significant upgrade in relation to the model before calibration. Model validation involved the comparison between numerically simulated results, based on a vehicle-track dynamic interaction analysis, and the experimental observations. An excellent agreement between experimental and numerical after updating time-histories was obtained, especially for the carbody responses, whose behaviour is governed by lower frequencies (below 3.5 Hz), in which the calibration process was focused.

Evaluation of Numerical Simulation Approaches for Simulating Train–Track Interactions and Predicting Rail Damage in Railway Switches and Crossings (S&Cs)

Switch and crossing (S&C) faults are a major cause of track-related delays and account for a significant proportion of maintenance and renewal budgets for railway infrastructure managers around the world. Although various modelling approaches have been proposed in the literature for the simulation of vehicle–track dynamic interaction, wheel–rail contact and damage prediction, there is a lack of evaluation for combining these approaches to effectively predict the failure mechanism. An evaluation of S&C modelling approaches has therefore been performed in this article to justify their selection for the research interests of predicting the most dominant failure mechanisms of wear, rolling contact fatigue (RCF) and plastic deformation in S&C rails by recognising the factors that influence the accuracy and efficiency of the proposed modelling approaches. A detailed discussion of the important modelling aspects has been carried out by considering the effectiveness of each individual approach and the combination of different approaches, along with a suggestion of appropriate modelling approaches for predicting the dominant failure mechanisms.

Dynamic Behavior in Transition Zones and Long-Term Railway Track Performance

Transition zones between embankments and bridges or tunnels are examples of critical assets of the railway infrastructure. These locations often exhibit higher degradations rates, mostly due to the development of differential settlements, which amplify the dynamic train-track interaction, thus further accelerating the development of settlements and deteriorating track components and vehicles. Despite the technical and scientific interest in predicting the long-term behavior of transition zones, few studies have been able to develop a robust approach that could accurately simulate this complex structural response. To address this topic, this work presents a three-dimensional finite element (3D FEM) approach to simulate the long-term behavior of railway tracks at transition zones. The approach considers both plastic deformation of the ballast layer using a high-cycle strain accumulation model and the non-linearity of the dynamic vehicle-track interaction that results from the evolution of the deformed states of the track itself. The results shed some light into the behavior of transition zones and evidence the complex long-term response of this structures and its interdependency with the transient response of the train-track interaction. Aspects that are critical when assessing the performance of these systems are analyzed in detail, which might be of relevance for researchers and practitioners in the design, construction, and maintenance processes.

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.

Case study: Understanding the formation of squat-type defects in a metropolitan railway

Squat-type defects are becoming an increasing issue in rail transportation systems. In this work, a root-cause analysis was carried out to identify the main causes leading to squat formation in a metropolitan railway. Several inspection visits were carried out after the first squat appeared in December 2017 in order to collect evidence from the field. The Corrugation-Analysis Trolley (CAT) was used to perform spectral analysis and a number of rail sections were extracted from critical locations of the railway for laboratory analysis of the microstructure. Four root-causes for squat formation were identified, namely: rail corrugation derived from resonance frequencies induced by vehicle-track dynamic interaction, increase of traffic, problems related to maintenance management and inadequate rail grinding. The analysis of data from the field revealed a clear correlation between the formation of squat-type defects and the presence of a White Etching Layer (WEL) on the surface of the rail, whose formation was shown to be most likely induced during the rail grinding operations as it was verified after a controlled grinding experiment. The increase of traffic over the last 15 years, as well as rail corrugation, which was linked with the introduction of new vehicles to the system, were also considered key factors for squat formation.

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.

Load and response quantification of direct fixation fastening systems for heavy rail transit infrastructure

Ballastless track (i.e. slab track) systems are used extensively in passenger rail applications for improved track stability, alignment control, vibration, and life cycle cost (LCC) benefits. These systems regularly rely on Direct Fixation (DF) fasteners to connect the rail to the structure. Field performance observations have indicated that even under similar track geometry and train operating conditions, the DF fasteners useful life varies widely. Meanwhile, a review of literature reveals that there is limited prior research to guide optimization of DF fastener designs for heavy rail transit. Therefore, researchers at the University of Illinois at Urbana-Champaign (UIUC) conducted a field investigation at three sites on a United States legacy heavy rail transit system to quantify wheel-rail interface loading demands and DF fastener response. Track response variance across similar track geometry was found. Wheel loads ranged between 2.7 to 18.2 kip (12.0 to 81.0 kN) and 0.9 to 12.4 kip (4.0 to 55.2 kN) for vertical and lateral loads, respectively. Lateral rail head displacements ranged between −0.05 to 0.16 inches (−1.27 to 4.06 mm) while dynamic lateral stiffness ranged from 42 to 62 kip/in. (7.3 to 10.8 kN/mm), indicating a low stiffness ratio for the DF fastener studied. Differences in behavior are attributed to dynamic vehicle-track interaction, the relationship between balanced and operating speeds, and differences in track gauge between sites. A comparison of vertical loading results with two additional heavy rail transit agencies shows Burr distributions that accurately represent the loading demands. Results from this study provide quantitative information that can be leveraged to improve heavy rail transit DF fastening system design and development of representative design validation testing protocols.

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.

Effect of Rail Pad Stiffness on Vehicle–Track Dynamic Interaction Excited by Rail Corrugation in Metro

Rail corrugation can cause intense dynamic interaction between train and track, which can reduce riding comfort and lifespan of track structure, and even threaten running safety. Instead of investigating the root cause and growth of corrugation, this case study aims to investigate possible solutions to the excess train–track dynamic interaction excited by rail corrugation in a metro track through both numerical analysis and field experiments. Numerical analysis was performed based on a vehicle–track coupled dynamical model with field-measured rail corrugation information from two curves. The numerical analysis results indicated that rail pad stiffness was the key factor affecting wheel–rail contact force in the studied direct fixation type transit track system. Rail pads with a lower stiffness could reduce the wheel–rail interaction; however, softer rail pads will also increase the rail displacement. Therefore, both the wheel–rail contact force and rail displacement need to be considered while determining the optimal rail pad stiffness. New rail pads with a stiffness of 35 MN/m, which are softer than the original rail pads with a stiffness of 50 MN/m, were recommended for the track in this study. Through field validation and long-term monitoring, new rail pads have been proven to effectively reduce the vehicle–track dynamic interaction and ease the development of rail corrugation to a certain extent. Compared with regular rail grinding, using rail pads with the appropriate stiffness can save transit agencies a tremendous amount of time and cost. The observations from this case study can benefit transit facing rail corrugation problems.

Vehicle-track dynamic interaction analysis of a metro vehicle

In this paper, comparison of results between the self-programming model (considering the track flexibility) and SIMPACK model (considering only fastener support) is carried out. The wheelset vibration is more obviously for the self-programming model as the track flexibility is considered. For the traditional dynamic calculation, the SIMPACK multi-rigid-body model is acceptable. Two kinds of harmonic vibrations in the car body for a metro car, which were found in the service operations, are reproduced by using self-programming model. High tread conicity leds to the harmonic vibrations in the car body about 4.8Hz. Reducing wheel conicity can improve the bogie hunting stability, and solve this problem. Another harmonic vibration with the frequency of about 2.2Hz in the car body is caused by the constant excitation wavelength in the track, which causes vibration transmited through the primary and secondary suspensions to the carbody. To reduce this harmonic vibration, more advanced suspensions are needed.

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.

Simulation of wheel–rail impact load and sleeper–ballast contact pressure in railway crossings using a Green's function approach

A method for the simulation of dynamic vehicle–track interaction and evaluation of measures to improve the design of railway crossings is presented. To accurately represent the high-frequency dynamics and non-linear contact conditions of the vehicle–track system, the vertical interaction between a wheelset and the crossing is simulated in the time domain using a Green's function approach based on extensive finite element models of track and wheelset in combination with an implementation of Kalker's variational method to solve the non-Hertzian, and potentially multiple, wheel–rail contact. Both wheels of the wheelset in simultaneous contact with the crossing rail and the outer rail are considered. Rigid and flexible wheelset models are compared. The sampled contact geometry of the crossing, including the discrete irregularity between the wing rail and the crossing nose, is used to determine a three-dimensional surface geometry between each pair of adjacent rail cross-sections. A parameter study is performed to investigate the influence of crossing design on the maximum vertical wheel–rail contact force and the contact pressure generated at the sleeper–ballast interface. It is concluded that a design with a combination of increased sleeper width, softer rail pads and implementation of under sleeper pads (USP) will reduce the track stiffness gradients in the crossing panel and mitigate the risk of differential track settlement by lowering the sleeper–ballast contact pressure.

Wheel–rail impact loads and noise generated at railway crossings – Influence of vehicle speed and crossing dip angle

Wheel–rail impact loads and noise at railway crossings are calculated by applying a hybrid prediction model. It combines the simulation of non-linear vertical dynamic vehicle‒track interaction in the time domain and the prediction of sound pressure level using a linear frequency-domain model. The two models are coupled based on the concept of an equivalent roughness spectrum. The time-domain model uses moving Green's functions for the linear vehicle and track models, accounting for wheel structural flexibility and a discretely supported rail with spatially-varying beam properties, and a non-Hertzian wheel–rail contact model. Three-dimensional surface geometry of the wheel and crossing is accounted for in the solution of the wheel–rail contact. The hybrid model is compared against field measurements and is demonstrated by investigating the influence of vehicle speed and crossing geometry on the radiated impact noise. Based on simulation results, it is concluded that the impact loads and noise can be mitigated by reducing the effective dip angle at the crossing, which is determined by the vertical trajectory of the wheel when making the transition between wing rail and crossing nose.

Prediction of plastic deformation and wear in railway crossings – Comparing the performance of two rail steel grades

Railway crossings are subjected to a severe load environment leading to damage and degradation of rail profiles. The damage is the result of the high magnitudes of contact pressure and slip generated in the wheel–rail contacts during each wheel transition between wing rail and crossing nose. In this paper, numerical predictions of the long-term accumulation of plastic deformation and wear are presented and compared for two rail grades used in crossings. The comparison is performed using a framework that includes simulations of dynamic vehicle–track interaction, wheel–rail contact and rail damage. A load sequence generated by means of Latin hypercube sampling, taking into account variations in worn wheel profile, vehicle speed and wheel–rail friction coefficient, is considered. A Hertzian-based metamodel for wheel–rail normal contact accounting for inelastic material response is used for the simulation of wheel–rail contact. The methodology is demonstrated by calculating the plastic deformation for one cross-section of the crossing nose using an Ohno-Wang cyclic plasticity model, while wear is predicted by means of the Archard model for sliding wear. For the studied conditions and after the simulation of 41400 load cycles, representing an accumulated traffic load of 0.8 MGT, it is concluded that the fine-pearlitic rail grade R350HT experiences half of the ratchetting strain compared to the austenitic hot-rolled manganese steel Mn13. Based on a wear model calibrated for Mn13, the maximum wear of the studied cross-section is about 2% of the maximum plastic deformation.

Multi-objective optimisation of transition zones between slab track and ballasted track using a genetic algorithm

The vertical dynamic vehicle–track interaction in a transition between ballasted track and slab track is simulated in the time domain using an extended state-space vector approach. A complex-valued modal superposition technique is applied for the linear, time-invariant and non-periodic finite element model of the railway track. By considering a multi-objective optimisation problem solved by a genetic algorithm, the maximum dynamic loads on the track structure are minimised with respect to the selected design variables. To reduce the risk of long-term degradation of track geometry due to ballast/subgrade settlement, the transition zone is designed to minimise the influence of the track stiffness gradient between the two different track forms. The methodology is demonstrated by minimising the maximum wheel–rail contact force and the maximum pressure between sleeper/panel and foundation, while the selected design variables are distributions of rail pad stiffness and sleeper spacing adjacent to the transition. From the solution of the optimisation problem, non-dominated fronts are obtained illustrating potential for a significant reduction of the dynamic loads. It is shown that the optimised design leads to a more uniform distribution of load on the foundation reducing the risk of differential track settlement. The influences of the length of the transition zone and direction of travel on the maximum dynamic loads are investigated. Prescribed irregularities in longitudinal level may be accounted for but have been neglected in the optimisation as the optimised design would be more influenced by the given irregularity than by the stiffness gradient.

Differential wear modelling – Effect of weld-induced material inhomogeneity on rail surface quality

A methodology is introduced to enable prediction of differential wear along the rail due to the presence of geometrical imperfections and microstructural inhomogeneities. The method incorporates vehicle-track dynamic interaction, wheel-rail contact and wear modelling in order to predict long-term longitudinal rail profile evolution. The effect of different contact and wear modelling features on the results is investigated. As a case study, the differential rail wear due to material inhomogeneity caused by rail head weld repairs is considered. It is concluded that, regardless of the magnitude of hardness variation within the heat affected zone, the long-term surface degradation can be minimized by limiting the length over which the variation occurs.

Parallel Co-Simulation Method for Railway Vehicle-Track Dynamics

This paper introduces a new parallel co-simulation method to study vehicle-track dynamic interactions. The new method uses the transmission control protocol/internet protocol (TCP/IP) to enable co-simulation between a detailed in-house track dynamics simulation package and a commercial vehicle system dynamics simulation package. The exchanged information are wheel-rail contact forces and rail kinematics. Then, the message passing interface (MPI) technique is used to enable the model to process track dynamics simulations and vehicle dynamics simulations in parallel. The parallel co-simulation technique has multiple advantages: (1) access to the advantages of both in-house and commercial simulation packages; (2) new model parts can be easily added in as new parallel processes; and (3) saving of computing time. The original track model used in this paper was significantly improved in terms of computing speed. The improved model is now more than ten times faster than the original model. Two simulations were conducted to model a locomotive negotiating a section of track with and without unsupported sleepers. The results show that the vertical rail deflections, wheel-rail contact forces and vehicle suspension forces are evidently larger when unsupported sleepers are present. The simulations have demonstrated the effectiveness of the proposed parallel co-simulation method for vehicle-track dynamic interaction studies.

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

ABSTRACTThe vertical dynamic interaction between a railway vehicle and a slab track is simulated in the time domain using an extended state-space vector approach in combination with a complex-valued modal superposition technique for the linear, time-invariant and two-dimensional track model. Wheel–rail contact forces, bending moments in the concrete panel and load distributions on the supporting foundation are evaluated. Two generic slab track models including one or two layers of concrete slabs are presented. The upper layer containing the discrete slab panels is described by decoupled beams of finite length, while the lower layer is a continuous beam. Both the rail and concrete layers are modelled using Rayleigh–Timoshenko beam theory. Rail receptances for the two slab track models are compared with the receptance of a traditional ballasted track. The described procedure is demonstrated by two application examples involving: (i) the periodic response due to the rail seat passing frequency as influenced by the vehicle speed and a foundation stiffness gradient and (ii) the transient response due to a local rail irregularity (dipped welded joint).