Wheel-rail Contact Forces Research Articles

An efficient physical-based method for predicting the long-term evolution of vertical railway track geometries

The dynamic wheel-rail contact forces resulting from the interaction between vehicle and track are responsible for the local track settlement. If these local settlements vary along the track, geometric irregularities develop further amplifying the dynamic loading of the track caused by the interaction between the vehicle and track. In this work, an efficient vehicle-track interaction (VTI) model is presented for predicting the long-term evolution of vertical track settlement during operation. The VTI model has two interacting components – vehicle and track. The vehicle model describes the vertical dynamics of an 8th of a car. The track model considers an elastic rail on discrete (sleeper) supports. Each sleeper location can have its own stiffness, relative height and settlement characteristics. Dependent on the distribution of stiffness and settlement behaviour along the track together with the initial track geometry, each sleeper settles dependent on the number of load cycles (vehicle passes). The track model is initialized with measured vertical track geometry data and static track deflection data at the beginning (day 0) for two types of track sections in the field, a track section where concrete sleepers with Under Sleeper Pads (USP) are used and a track section where only concrete sleepers are used. Using the same settlement model parameters (constant along the track) for the two tracks, the physical-based VTI model can predict the different track geometry quality evolution for both tracks over 350 days. Finally, the VTI model is used to assess the track geometry deterioration when the track/vehicle properties are changed. The prediction strength of the fast VTI model based on the physical understanding can assist in designing and optimizing tracks and in supporting of maintenance activities.

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.

Identification of vertical wheel-rail contact force based on an analytical model and measurement and its application in predicting ground-borne vibration

Wheel-rail interaction plays an important role in the study of railway engineering. The wheel-rail contact forces (WCFs) are the key factors in the models addressing wheel-rail interaction. However, it is sometimes difficult to be measured, so an indirect identification methodology is proposed in this paper. Based on an analytical model and measurement, the vertical WCF can be determined. Using measured rail accelerations as input data, a calculation program is developed. The vertical WCF and the excitation forces transmitted from the vehicle-rail system to the roadbed can be obtained. The latter forces are used to predict the train-induced ground-borne vibrations. A case study of predicting ground-borne vibration in Beijing Metro is presented to verify the effectiveness of this method. The results show that the vertical WCF can be obtained efficiently and accurately, and the predicted ground-borne vibrations have good agreement with the measured ones.

Optimization on the Crosswind Stability of Trains Using Neural Network Surrogate Model

Under the influence of crosswinds, the running safety of trains will decrease sharply, so it is necessary to optimize the suspension parameters of trains. This paper studies the dynamic performance of high-speed trains under crosswind conditions, and optimizes the running safety of train. A computational fluid dynamics simulation was used to determine the aerodynamic loads and moments experienced by a train. A series of dynamic models of a train, with different dynamic parameters were constructed, and analyzed, with safety metrics for these being determined. Finally, a surrogate model was built and an optimization algorithm was used upon this surrogate model, to find the minimum possible values for: derailment coefficient, vertical wheel-rail contact force, wheel load reduction ratio, wheel lateral force and overturning coefficient. There were 9 design variables, all associated with the dynamic parameters of the bogie. When the train was running with the speed of 350 km/h, under a crosswind speed of 15 m/s, the benchmark dynamic model performed poorly. The derailment coefficient was 1.31. The vertical wheel-rail contact force was 133.30 kN. The wheel load reduction rate was 0.643. The wheel lateral force was 85.67 kN, and the overturning coefficient was 0.425. After optimization, under the same running conditions, the metrics of the train were 0.268, 100.44 kN, 0.474, 34.36 kN, and 0.421, respectively. This paper show that by combining train aerodynamics, vehicle system dynamics and many-objective optimization theory, a train’s stability can be more comprehensively analyzed, with more safety metrics being considered.

Improving Wheelset Stability of Railway Vehicles by Using an H∞/LPV Active Wheelset System

The complexity of railway vehicle structures has been part of an evolutionary process for almost two hundred years. Challenges such as increased weight, increased maintenance, higher costs and energy consumption have become common. The vision for future railway vehicles is to reduce complexity, hence enable simpler structures and reduce maintenance and cost, and of course various research challenges arise from this. In fact, a number of papers in the railway engineering literature have presented practical ways to control steering of railway vehicles to improve performance. The model of the railway wheelset is highly nonlinear, mainly due to the nature of the wheelset structure and the related wheel-rail contact forces involved during operation. In this paper, the simplest design in terms of retrofitting, the actuated solid-axle wheelset is considered, we investigate actively controlled wheelsets from a Linear Parameter Varying (LPV) control aspect. We use the grid-based LPV approach to synthesize the H∞ / LPV controller, which is self-scheduled by the forward velocity, as well as the longitudinal and lateral creep coefficients. The aim of the controller is to reduce the lateral displacement and yaw angle of the wheelset. Simulation results show that the proposed controller ensures the achievement of the above targets in the considered frequency domain up to 100 rad/s.

Failure simulation, test and optimization of slide plate at metro turnouts

The wheel-rail contact relationship in turnout is more complicated than that in regular track, which will increase the dynamic wheel-rail interaction. The slide plate, being important component of turnout, is prone to produce fatigue damage under the cyclic action of wheel-rail contact force. In this paper, an investigation and analysis has been done on the fatigue damage of welded slide plate, tongue depressor fracture and weld separation. The structural optimization schemes are proposed for various failure modes. The fatigue performance of slide plate for two schemes is evaluated and compared by simulation. The strength performance of slide plate for two schemes is compared by laboratory test. In simulation, two models were established to analyse the wheel-rail dynamic interaction of vehicle-track system and stress characteristics of slide plate, respectively. The fatigue life of the slide plate for two schemes were evaluated and compared, based on the fatigue damage theories. During the test, the ultimate strength of tongue depressor and bond strength between the slide platform and the base plate for two schemes, were tested and compared. The simulation and test results showed that the fatigue and strength performance of slide plate have increased reasonably after optimization. It can provide reference for design of slide plate.

Influence of the railway vehicle properties in the running safety against crosswinds

The aim of the present study consists of evaluating the influence of the most relevant geometric, mechanical and aerodynamic vehicle properties in the risk of derailment caused by crosswinds. To achieve this objective, a vehicle-structure interaction model is used to carry out non-linear dynamic analyses to assess the train-track coupling behaviour in the presence of winds. By computing the wheel-rail contact forces, the derailment risk is evaluated based on the unloading criterion, as suggested by the European Norm EN 14067–6 (2016), for several scenarios with different train and wind speeds. The wind is simulated with a stochastic model that allows the generation of turbulent wind time-histories based on power spectral density functions. The reference vehicle adopted in this work corresponds to the European InterCity Express 3 (ICE-3) train, whose original properties were parameterized in order to evaluate their influence in the vehicle's stability. The parametric study focused on several properties of the vehicle, namely the carbody mass, height of the gravity centre, aerodynamic coefficients, and stiffness and damping of the suspensions. Apart from the suspensions' properties, which prove to have a negligible influence in the vehicle's stability, the remaining parameters have a significant impact in the running safety against crosswinds.

Wheel-rail rolling contact behavior induced by both rail surface irregularity and sleeper hanging defects on a high-speed railway line

In this study, a wheel-rail transient rolling contact model capable of accounting for the nonlinear displacement-force properties of hanging sleepers is proposed. The sleeper hanging status affected by rail irregularities is an input for an analysis of the wheel-rail contact behavior and related rail degradation in terms of plastic deformation and rolling contact fatigue. The results indicate that the severity of sleeper hanging is significantly affected by the geometric characteristics and the relative position with respect to the sleepers of the rail surface irregularity. The sleeper hanging defects aggravate the wheel-rail impact and increase the wheel-rail contact force amplitude, contact patch size, pressure, and von Mises stress, thus exacerbating the plastic deformation of the rail material. It was also found that the sleeper hanging defects rarely affect the distribution of the adhesion-slip states and rolling contact fatigue. The knowledge gained can serve as guidance for evaluating the condition and conducting the maintenance of ballasted railway tracks.

A finite element methodology to model flexible tracks with arbitrary geometry for railway dynamics applications

The dynamic analysis of railway vehicles requires an accurate representation of the vehicle, the track geometry and structure, and their interaction. Generally, flexible track models with curved geometries represent the rails with straight beam elements, which results in a piecewise linear representation of the rails. Consequently, the wheel-rail contact mechanics are not properly captured, and the wheel-rail contact forces present spurious high-frequency oscillations. This work proposes a novel approach to model flexible railway tracks with arbitrary geometries, in which the correct geometry in the wheel-rail contact mechanics is assured by modeling the rails as Timoshenko curved beam elements. This approach improves both the geometric representation of the rails and the accuracy of the wheel-rail contact forces calculation. A realistic operation scenario in which a multibody model of a railway vehicle runs on a flexible track with a curved geometry is used here to demonstrate the novel aspects of this work and then discuss the improvements over the conventional approaches. The results show that the proposed methodology greatly improves the computation of the wheel-rail interaction forces and prevents spurious oscillations from propagating to the vehicle.

Indirect identification of wheel rail contact forces of an instrumented heavy haul railway vehicle using machine learning

Rail car safety and stability are important factors for good performance. The most used safety index to quantify railway safety is the ratio between the lateral and vertical wheel rail contact forces (L/Q). This study aims to use machine learning (ML) models to evaluate the viability of estimating the wheel rail contact forces from sensors in a regular instrumented railway vehicle (IRV). A virtual model of a BRA1 railway vehicle was created to generate an artificial dataset with variables measured with the actual BRA1 vehicle plus different variables measured by other IRVs found in the literature. The desired output variable is the L/Q ratio for each wheel of the leading bogie. Exploratory data analysis was done to clarify the correlation between the variables while model explainability techniques were applied to evaluate the contribution of these input variables to the output (L/Q). A total of 24 embedded machine learning models were trained and optimized using the tree-based pipeline optimization tool (TPOT) to generate a ML pipeline capable of producing an accurate L/Q ratio as the output for different cases of sampling rate, input variables and track irregularities. The results show that machine learning models can predict the wheel rail contact forces indirectly – without using instrumented wheelsets – with the highest mean squared error being equal to 0.01113.

Rail-wheel contact forces and track irregularity estimation from on-board accelerometer data

Rolling stock approval protocols, such as UIC 518, demand monitoring of lateral and vertical forces at rail-wheel contact. Continuous monitoring through on-board instrumentation needs algorithms to convert the on-board sensor data into rail-wheel forces and track irregularities. In this work a Feed Forward Neural Network architecture, for fast and accurate estimation of rail-wheel forces and track irregularities from data obtained from a cluster of accelerometers mounted on the rolling stock, is presented. Simulation study is conducted for a passenger coach running over numerically generated set of one hundred rail tracks, each with a different irregularity. Power spectral density (PSD) function of ERRI B176 is used for creating rail irregularities. Multi-body rail coach model consists of wheel-sets, axle-box, bogie, bolster and car body. The input comprises acceleration, yaw and roll rate data from axle-box, bogie and car body, to produce contact forces and rail irregularities as outputs. Goodness of fit between actual and estimated values is illustrated through point-by-point graphs of actual and estimated track forces and irregularities. R-Squared () values, representing the fraction by which the variance of errors are less than the variance of actual values, are computed as indices of the accuracy of estimates.

Design, calibration and validation of a wheel-rail contact force measurement system in V-Track

An innovative downscale test rig called V-Track has been constructed for wheel-rail contact experiments under impact loading conditions. In this paper, a force measurement system termed a dynamometer was developed in V-Track to measure the wheel-rail contact forces. The dynamometer consists of four 3-component piezoelectric force sensors and was mounted between the wheel assembly and the steel frame of V-Track, enabling it to measure the forces transmitted from the wheel-rail interface to the frame. Static tests were first carried out to calibrate the dynamometer in three directions. Then, several tests were performed in V-Track to examine the reliability and validity of the dynamometer for measuring the wheel-rail contact forces under running conditions. Experimental results show that the dynamometer is capable of reliably and accurately measuring these forces. Utilizing the measurement results from the dynamometer, the control of the wheel-rail contact forces in V-Track has also been achieved.

In-situ test on impact loads of a five-module 100% low-floor tram and the prediction of damage characteristics of a pile-plank-supported tram track

To mitigate the differential settlement of the soft soil foundation and to reduce the maintenance work of the embedded tram track, an innovative pile-plank-supported tram track configuration is proposed and utilized in Shanghai Tram Line T1/T2. Since this is the first application of this new structure in tram track projects, the dynamic properties and service performance of this structure are still not clear. In this work, an in-situ test on the dynamic performance of the pile-plank-supported ballastless tram track is carried out. The contact forces between the independently rotating wheelset of a five-module 100% low-floor tram and the channel rail of tram track are measured and investigated as well as the vertical acceleration of the plank. The measured wheel-rail contact forces are employed as a loading condition for a track-subgrade coupling model. The influence of multi-factors (i.e. dynamic loading, thermal conditions and subgrade settlement) on the tram track damage is investigated. The results indicate that the long-term service performance of the pile-plank-supported tram track is stable under the dynamic tram loads.

Optimising the location of wagon gravity centre to improve the curving performance

ABSTRACT The location of wagon gravity centre (WGC) has a significant effect on the wheel-rail contact force. For the sake of improving the curving performance of a freight wagon, it is necessary to optimise the location of WGC by shifting the position of cargo or adopting the balance weight. This paper proposes a data analysis methodology that demonstrates the safe distribution scope of WGC based on the results of dynamics simulations. A general model of the loaded wagon is built using the multibody dynamics software VI-Rail. The simulation conditions are designed to achieve the analog of vehicle running circumstances in reality. The simulation results under various conditions provide us full evidence to demarcate the safe locations of WGC and derive the Pareto-optimal solutions. The methodology presented in the paper can be applied to an arbitrary case of railway freight transportation to promote the vehicle running safety.

Stochastic dynamic analysis of vehicle-bridge coupled systems with nonlinear Hertz contacts by explicit time-domain method

ABSTRACT Vibration analysis of vehicle-bridge coupled systems has received considerable attentions over the past two decades. This work is dedicated to the stochastic dynamic analysis of vehicle-bridge coupled systems with nonlinear Hertz wheel-rail contacts subjected to random track irregularities. An explicit time-domain method (ETDM) is proposed for efficient nonlinear dynamic analysis of vehicle-bridge coupled systems with a dimension-reduced iteration scheme focusing on the nonlinear wheel-rail contact forces. The high-efficient ETDM is further utilised to implement the numerous nonlinear dynamic analyses required in the Monte-Carlo simulation (MCS) for obtaining the response statistics of the vehicle-bridge coupled systems. A numerical example involving a single-wheel vehicle traversing a simply-supported beam with nonlinear Hertz wheel-rail contacts considering random track irregularities is presented to demonstrate the computational accuracy and efficiency of the proposed method, and an engineering application involving a four-wheel vehicle moving across the Egongyan suspension bridge is further analysed to indicate the effectiveness of the proposed method for large-scale engineering problems.

A simplified analysis framework for assessing overturning risk of high-speed trains over bridges under crosswind

This technical note addresses the overturning risk assessment of high-speed trains over multi-span simply supported bridges under crosswind. A train-bridge coupled system is established to estimate the wheel–rail contact forces from which the overturning risk of train is assessed. The estimation is also compared to that without consideration of bridge vibration. The result shows that the loss of vertical wheel–rail contact force is primarily caused by the crosswind. The influence of track irregularities and bridge vibration on overtuning risk of train is secondary. The bridge deformation can be approximately estimated as static deformation under moving train weight thus a sophisticated dynamic analysis of coupled train and bridge system can be avoided. When the external excitation due to deformation of multi-span bridge has a frequency close to the vertical domain frequency of train system, resonant effect is observed which increases the influence of the bridge deformation on train performance.

Random vibration analysis of tram-track interaction on a curve due to the polygonal wheel and track irregularity

The vibration performance of a tram vehicle running on the curved track is influenced by the speed of the running vehicle, the geometry of the track, the roughness of the wheel and rail, and environmental characteristics. This paper investigates the random vibration analysis of tram-track interaction on a curved track due to the polygonal wheel and track irregularity by the pseudo excitation method (PEM). The dynamic behaviour of tram-track interaction on a curve is modelled using the finite element method (FEM) and multi-body system (MBS). The field tests were carried out to acquire the rail vibration and deformation response, and also measuring the polygonal wheel wear profile to analyse and validate the dynamic behaviour tram-curved track model. The influence of the polygonal wheel on the vibration of tram-curved track coupled system and the wheel-rail contact responses are investigated by considering the wheelset flexibility. The results are illustrated through comparison between with and without the polygonal wheel in terms of time and frequency domain. The numerical results suggest that the wheelset flexibility under the polygonal wheel wear excitation would aggravate the vibration mode of the rail, car-body and axle-box, and also increase the dynamic wheel-rail contact force and creepage.

Comparison of wheel–rail contact models in the context of multibody system simulation: Hertzian versus non-Hertzian

The calculation of the wheel–rail contact forces is one of the most difficult yet time-consuming processes in multibody system (MBS) simulations for a vehicle-track interaction system. The classical combination of the Hertzian model with the FASTSIM algorithm is the most widely used model in MBS code for railway application and the ‘exact’ solver CONTACT is seldom used due to its high computational cost. A trade-off solution between accuracy and computational efficiency is the simplified and approximate non-Hertzian approach. This paper attempts to compare the influence on MBS simulation for rail vehicle system dynamics of the varied combinations of the classical contact models (i.e. Hertz model and FASTSIM), well-known simplified non-Hertzian model (Kik–Piotrowski model) recently developed improved simplified non-Hertzian models i.e. Extended Kik–Piotrowski and Kalker Book of Tables for Non-Hertzian contact (KBTNH), and the CONTACT algorithm. The results show that all non-Hertzian approaches deviate from the classical Hertzian solutions in both local contact and global dynamics and the KBTNH model provides better agreement with CONTACT than the FASTSIM algorithm for non-elliptic contact conditions considered in this study. A detailed analysis of the causes and influences of the difference due to varied contact models is presented.

A New Switch and Crossing Design: Introducing the Back to Back Bistable Switch

A new track swtich and crossing (S&C), the back to back bistable (B2B) switch, is proposed that has shown potential to significantly reduce the wheel/rail contact forces through the switch due to its more continuous wheel/rail contact interface and more uniform track stiffness arising from the elimination of the crossing nose. This offers a major reduction on maintenance cost of future S&Cs. The paper explains the concept and identifies the design guidelines for a current layout and uses vehicle/turnout dynamic modelling to predict wheel rail forces through a switch to identify performance improvements relative to a conventional S&C. Both multi-body simulation (MBS) and Finite Element (FE) model have been developed to account for dynamic and thermal analysis. The new design has shown improvements in lateral and vertical wheel-rail contact forces and less relative rail displacements due to thermal effect compared to the conventional S&C.

Moving Element Analysis of High-Speed Train-Slab Track System Considering Discrete Rail Pads

This paper presents a study of the dynamic behavior of a coupled train-slab track system considering discrete rail pads. The slab track is modeled as a three-layer Timoshenko beam. The study is carried out using the moving element method (MEM). By introducing a convected coordinate system moving at the same speed as the vehicle, the governing equations of motion of the slab track are formulated in a moving frame-of-reference. By adopting Galerkin’s method, the element stiffness, mass and damping matrices of a truncated slab track in the moving coordinate system are derived. The vehicle is modeled as a multi-body with 10 degrees of freedom. The nonlinear Hertz contact model is used to account for the wheel–rail interaction. The Newmark integration method, in conjunction with a global Newton–Raphson iteration algorithm, is employed to solve the nonlinear dynamic equations of motion of the vehicle–track coupled system. The proposed MEM model of the system is validated through comparison with available results in the literature. Further study is then made to investigate the vehicle–track system accounting for track irregularities modeled as short harmonic wave forms. Results showed that irregularities with short wavelengths have a significant effect on wheel–rail contact force and rail acceleration, and the dynamic response of the track structure does not increase monotonously with the increase of the vehicle speed.