Wheel-rail Interaction Research Articles

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.

Challenges and methodology for pre-processing measured and new rail profiles to efficiently simulate wheel-rail interaction in switches and crossings

This paper describes a methodology developed to systematically pre-process rail profile data from switches and crossings for railway vehicle dynamics simulation. The methodology accepts two data sources, unworn geometries from CAD drawings or worn geometries from digitised track measurements. The method addresses key challenges with the relative positioning and quality improvement of the input data and explains the necessary steps to ensure compatibility with the interpolation schemes used to represent the rail profile in certain multibody software. The case studies presented show how small misalignments in the processed digitised measurements affect simulation results and how simulations can help understand the qualitative evolution of switches and crossings rail profiles in a used track. This paper concludes that one of the most challenging tasks remains the automation of rail pre-processing for measured data because it is difficult to correct vertical and lateral misalignments of the profile cross-sections without a reference system.

Dynamic performance evaluation of ballastless track in high-speed railways under subgrade differential settlement

Ballastless tracks are widely used to provide high rail smoothness in high-speed railways. However, the differential settlement inevitably develops in the subgrade soil, which poses a great threat to the track performance and riding quality via the train-rail dynamic interaction. Since the ballastless tracks are extremely difficult to repair during the maintenance window, it is quite necessary to carry out preventive maintenance to keep the track in good conditions. In order to relate the railway performance with the profiles of subgrade differential settlement, a three-dimensional train-ballastless track-subgrade model was developed incorporating 64 combinations of settlement wavelengths and amplitudes at the roadbed surface. The numerical results were first verified with the measured velocity responses at the concrete base in the Beijing-Tianjin high-speed railway. Then the dynamic responses of the train-track system caused by subgrade differential settlement were analyzed, including the dynamic displacement of train wheels and track structure, wheel-rail interaction forces and car body accelerations. Railway performance was further evaluated as track degradation, lower riding comfort and risk of train safety based on these indicators at different settlement profiles. Results show that increasing settlement amplitudes result in stronger dynamic wheel-rail interaction and vibration of car body. However, critical settlement wavelengths of 10 m and 10–20 m are found to exist where the wheel-rail interaction forces and accelerations of the car body reach their peak values, respectively. It also reveals that the current design limits on the subgrade settlement of high-speed railways are infeasible for infrastructure managers to evaluate the railway status or organize the maintenance works. Moreover, the wheel-rail interaction forces are more credible to determine the railway status than the car body acceleration.

Polygonal wear mechanism of high-speed wheels based on full-size wheel-rail roller test rig

The polygonal wear of train wheels is common. It increases the wheel-rail interaction force drastically and adversely affects the safety and comfort of the train. The mechanism of the initiation and development of polygonal wear warrants further study. This study performed a high-speed rolling test based on the full-size wheel-rail roller test rig to reproduce the entire process of the generation and development of the polygonal wear on the tested wheelset of CL60 steel in the laboratory. The mechanism of the initiation and development of polygonal wear was analyzed using the test results, the bending resonance of wheelset was considered as an important cause of the polygonal wear in this paper. The basic condition for the polygonal wear formation and its high rate of development was verified. The evolution process of polygonal wear was studied in-depth, and the relationship between axle-box acceleration and polygonal wear was revealed. Effective countermeasures against the development of polygonal wear were proposed. Variable speed operation could mitigate the development of polygonal wear in this paper. The results obtained in this study may provide reference for the further study of the effective countermeasures against the development of polygonal wear.

Algorithm for inverse determination of derailment coefficient by using instrumented wheelsets

The main indicator of the running safety of railway vehicles is the ratio between lateral and vertical forces in the wheel-rail interaction, known as derailment coefficient. Its exact determination has a huge significance in the development and certification phases of railway vehicles. The most reliable determination of wheel-rail interaction forces is based on experimental testing, by using instrumented wheelsets, which is otherwise prescribed in appropriate international regulations. This paper presents a unique algorithm for inverse determination of wheel-rail interaction forces, i.e., derailment coefficient, based on the measurement signals obtained from instrumented wheelsets. The blind signal separation (BSS) and method of independent component analysis (ICA) are applied. Verification is carried out on the example of the wheelset of freight wagon, based on the wheel's FEM model. The obtained results confirmed a high efficiency and accuracy of the developed algorithm, whereby estimated error of inverse identification is less than 5%.

Correction method for measurement data of wheel-rail lateral force based on estimation of lower limit of load center position

Instrumented wheelsets are widely used in the railway industry for the purpose of measurement of the wheel-rail interaction forces, which are crucial factors in a running safety assessment. The lateral force, which is the lateral component of the wheel-rail interaction forces, is measured using bending strains induced in the wheel web in the popular configuraions of instrumented wheelset. In this principle of lateral force measurement, the measurement accuracy descreases when the load center position is shifted laterally since the wheel load, which is the vertical component of the interaction forces, also induce the bending strains. In this research, an estimation method for the lower limit of the load center position using a simple calculation to eliminate a part of the measurement error associated with the wheel load.

Dynamic Wheel-Rail Force-Based Track-Irregularity Evaluation for Ballasted Track on Serviced Railway by Adjacent Excavation

This study investigates a load-based, track-irregularity-analysis technique for ballasted tracks on a serviced railway line with respect to excavation work conducted in adjacent sites. A numerical analysis and field measurements (railbed-settlement-monitoring sensor, track-geometry-measurement system, wheel-load measurements) were analyzed comparatively to demonstrate the correlation between the track irregularities and the Wheel-Rail interaction force. In this way, we highlight the necessity for load-based track-irregularity-management methods. The analyzed results show that the maximum dynamic wheel load was measured in the range of approximately 10 m before and after the location where the maximum track irregularities occurred, and that even if the maintenance criteria of track irregularities were satisfied, the design dynamic wheel load could still be exceeded depending on the train speed, thus indicating that track damage can be caused by the impact load.

Coupled dynamic behaviours of the brake system considering wheel–rail interactions

ABSTRACT During vehicle operation, the brake system is influenced by wheel–rail interactions. To investigate the dynamic behaviours of the brake system, we propose a novel dynamic model of the brake system by considering the coupling effects between the disc–pad and the wheel–rail subsystems. Using the established model, the nonlinear coupled dynamic behaviours including wheel–rail adhesion characteristics, wheel–disc torsional vibrations and disc–pad stick–slip vibrations were comprehensively explored. The results showed that braking conditions remarkably influenced the longitudinal slip rate. The wheelset and brake units affect each other, and the wheels on one wheelset influence each other when they are asynchronous. The brake system is stable in the wheel–rail stick state, but becomes unstable in the wheel–rail stick–slip state or slip state. The limit cycle analysis showed that the brake pad stick–slip vibrations were easier to occur at a large slip rate.

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.

Failure analysis of fatigue damage for fastening clips in the ballastless track of high-speed railway considering random track irregularities

In order to study the influence of wheel-rail random dynamic interaction on the fatigue damage for fastening clips, a three-dimensional (3-D) high-speed railway vehicle-track coupling random dynamics model is established based on the random theory of the probability density evolution method (PDEM). The number theoretic method (NTM) and stochastic harmonic functions (SHF) are employed to generate the representative random track irregularities. Furthermore, a refined finite element model of WJ-8 fastening system is established, and the stress time history results of the clips are obtained based on the co-simulation analysis. Eventually, the rain-flow counting is introduced to study the influence of random track irregularities on fatigue damage of fastening clips combined with cumulative damage theory and the S-N curve of the clips. The results show that, the dynamic characteristics and stochastic probability evolution mechanism of the vehicle-track random system considering random track irregularities, as well as the evolution characteristics of the fatigue failure probability of clips with service time are accurately reproduced based on PDEM. Significantly, the fatigue damage of fastening clips caused by one vehicle passing by follows the lognormal distribution with a mathematical expectation of 2.35 × 10-8 and a variance of 1.48 × 10-12. The 95% confidence interval of mathematical expectation is [7.05 × 10-9, 5.89 × 10-7] and the 95% confidence interval of variance is [1.37 × 10-13, 1.59 × 10-11]. Additionally, the longer the service time of the fastening system, the more serious the fatigue damage of the clips and the greater the fatigue failure probability.

Stochastic Analysis on the Resonance of Railway Trains Moving over a Series of Simply Supported Bridges

Resonance problems encountered in vehicle-bridge interaction (VBI) have attracted widespread concern over the past decades. Due to system random characteristics, the prediction of resonant speeds and responses will become more complicated. To this end, this study presents stochastic analysis on the resonance of railway trains moving over a series of simply supported bridges with consideration of the randomness of system parameters. A train-slab track-bridge (TSB) vertically coupled dynamics model is established following the basic principle of vehicle-track-coupled dynamics. The railway train is composed of multiple vehicles, and each of them is built by seven rigid parts assigned with a total of 10 degrees of freedom. The rail, track slab, and bridge are considered as Euler–Bernoulli beams, and the vibration equations of which are established by the modal superposition method (MSM). Except for the nonlinear wheel-rail interaction based on the Hertz contact theory, the other coupling relations between each subsystem are assumed to be linear elastic. The number theory method is employed to obtain the representative sample point sets of the random parameters, and the flow trajectories of probabilities for the TSB dynamics system are captured by a probability density evolution method (PDEM). Numerical results indicate that the maximum bridge and vehicle responses are mainly dominated by the primary train-induced resonant speed; the last vehicle of a train will be more seriously excited when the bridges are set in resonance by the train; the resonant speeds and responses are rather sensitive to the system randomness, and the possible maximum amplitudes predicted by the PDEM are significantly underestimated by the traditional deterministic method; optimized parameters of the TSB system are preliminary obtained based on the representative point sets and imposed screening conditions.

Resonance of railway vehicles induced by floating-slab tracks: mechanism and countermeasures

For a railway vehicle moving over a series of floating-slab (FS) tracks with identical spans at a constant speed, track-induced resonance on the railway vehicle could occur when any of the frequencies of the FS track coincides with any of those implied by the wheel loads. Under this condition, the wheel–rail interaction will be aggravated and the ride comfort of railway vehicles will be deteriorated. This paper presents an experimental and numerical investigation of the mechanism and countermeasures for the resonant response of a metro vehicle induced by eccentric wheels travelling on FS tracks. The characteristics of the resonant response of the metro vehicle are revealed through the field tracking tests. A vehicle–track model considering the FS tracks and eccentric wheels is developed to analyse the resonant mechanism. Several countermeasures, including optimal design of FS track structure and elimination of wheel eccentric wear, are proposed to restrain the resonant vibration. The results show that the resonance caused by the eccentric wheels moving over FS tracks is the root causes for the ride comfort reduction of the metro vehicle. The field tests validate that re-profiling eccentric wheels can significantly eliminate the resonance phenomenon and enhance vehicle dynamics performances.

Consistent Tangent Stiffness of a Three-Dimensional Wheel–Rail Interaction Element

Consistent tangent stiffness plays a crucial role in delivering a quadratic rate of convergence when using Newton’s method in solving nonlinear equations of motion. In this paper, consistent tangent stiffness is derived for a three-dimensional (3D) wheel–rail interaction element (WRI element for short) originally developed by the authors and co-workers. The algorithm has been implemented in finite element (FE) software framework (OpenSees in this paper) and proven to be effective. Application examples of wheelset and light rail vehicle are provided to validate the consistent tangent stiffness. The quadratic convergence rate is verified. The speeds of calculation are compared between the use of consistent tangent stiffness and the tangent by perturbation method. The results demonstrate the improved computational efficiency of WRI element when consistent tangent stiffness is used.

Study of constitutive relation of rail decarburized layer

Rail decarburized layer has significant impact on the wear and rolling contact fatigue in the wheel-rail interaction. Due to the lack of constitutive relation of rail decarburized layer, it is impossible to analyse accurately the influence of rail decarburized layer on wheel-rail contact. To obtain the constitutive relation of this layer of decarburized non-uniform material, nano-indentation experiments were carried out at different vertical positions in the decarburization layer on a rail specimen with decarburization thickness of 0.55 mm. Young’s modulus and hardness were determined using Oliver and Pharr method. Axisymmetric two-dimensional finite element models were established in ABAQUS to simulate the nano-indentation loading process and the power law elastic–plastic stress–strain relationships were obtained for material at different vertical positions in the rail decarburized layer. A set of dimensionless functions were proposed for Young’s modulus, hardness, yield stress and strain hardening exponent at arbitrary depth in a rail decarburized layer or in a decarburized layer treated by rail pre-grinding. The results show that the Young’s modulus and hardness decrease from the rail bulk to the surface of the decarburized layer. The Young’s modulus and hardness near the surface are 11% and 35% lower than those in the rail bulk, respectively. However, the yield stress exhibits an increasing trend from rail bulk to the decarburized surface, where yield stress is 20% higher than the rail bulk. Analysis shows that the main reason that causes the reduction of hardness at the decarburized layer surface is the reduction of Young’s modulus but not the yield stress.

Research on probability statistics of train running safety indices based on pseudo-excitation method

In order to explore the random nature of high-speed railway train operation safety indices, the pseudo-excitation method, extreme value theory, and non-stationary harmonic superposition theory are used in this paper to study the statistics of train operation safety indices. The pseudo-excitation load formulation for track irregularity is obtained by the pseudo-excitation method, and the resulting non-stationary random vibration problem is transformed into a deterministic time history problem. The pseudo-excitation method is used to establish the dynamic equations of motion, and the separation iteration method is used to solve the equations, so as to obtain the power spectral density of the wheel-rail interaction forces. The wheel-rail interaction forces are obtained by using a modulation function and the harmonic superposition method. By fitting an extreme value distribution, the maximum values of the train running safety indices are explored. The proposed numerical approach is validated experimentally using the data from a 24.6 m long simply supported concrete bridge by studying the extreme value distributions of driving safety indices. Additional numerical simulation are conducted for varying train speeds and bridge spans. The results show that the Gumbel distribution can fit the extreme value of driving safety parameters for different speeds and different bridge span lengths. It is observed that the higher the speed, the sharper the extreme value distribution of train running safety indices, and the larger the train running safety index values corresponding to 99.87% confidence level. The corresponding extreme values at the 99.87% confidence level are greater than the maximum value of each time-domain sample.

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.

Dynamic Influence of Wheel Flat on Fatigue Life of the Traction Motor Bearing in Vibration Environment of a Locomotive

Wheel flat can cause a large impact between the wheel and rail and excites a forced vibration in the locomotive and track structure systems. The working conditions and fatigue life of the motor bearings are significantly affected by the intensified wheel–rail interaction via the transmission path of the gear mesh. In this study, a fatigue life prediction method of the traction motor bearings in a locomotive is proposed. Based on the L−P theory or ISO 281 combined with the Miner linear damage theory and vehicle–track coupled dynamics, the irregular loads induced by the track random irregularity and gear mesh are considered in this proposed method. It can greatly increase the accuracy of predictions compared with the traditional prediction models of a rolling bearing life whose bearing loads are assumed to be constant. The results indicate that the periodic impact forces and larger mesh forces caused by the wheel flat will reduce the fatigue life of the motor bearings, especially when the flat length is larger than 30 mm. Using this method, the effects of the flat length and relatively constant velocity of the locomotive are analyzed. The proposed method can provide a theoretical basis to guarantee safe and reliable working for motor bearings.

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.

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.

Testing research on frequency-dependent characteristics of dynamic stiffness and damping for high-speed railway fastener

In this paper, the Vossloh W300 fastener currently used in China's high-speed railway is taken as the research object. Combined with the requirements of ISO 10846 series standards and the knowledge of the author, to the best of the authors knowledge, the first high-frequency dynamic stiffness test system for elastic elements of rail fastener has been successfully developed and built. By taking the influence of preloading into consideration, the vertical and lateral dynamic frequency-dependent stiffness and loss factor of high-speed railway W300 fastener at 5~1250 Hz were obtained through the 1:1 test model coupling test method for the first time. Referring to the prediction method of high-speed railway wheel-rail vibration and noise, and factoring in the high-speed rotating, the infinite length of plate track structure and high-speed movement of sound source to wheels, the Kelvin - Voigt simulation sub-model of fastening system was added to predict and analyze the difference between the total sound pressure levels of the wheel and rail that is relative to the standard point under the constant stiffness and frequency-dependent stiffness of fastener. The results indicate that the frequency-dependent characteristics of fastener stiffness have significant impact on the spectrum of wheel-rail interaction forces, total sound pressure levels of rail and wheel-rail. The total sound pressure level of the wheel-rail relative to standard point, which factors in the frequency-dependent stiffness of fastener was approximately reduced 2.6 dB, that is, the frequency-dependent stiffness of fastener can rectify the overestimation of wheel-rail sound pressure level by stiffness coefficient.