Influence of railway wheel tread damage on wheel-rail impact loads and the durability of wheelsets

Dynamic wheel-rail contact forces induced by a severe form of wheel tread damage have been measured by a wheel impact load detector during full-scale field tests at different vehicle speeds.Based on laser scanning,the measured three-dimensional damage geometry is employed in simulations of dynamic vehicle-track interaction to calibrate and verify a simulation model.The relation between the magnitude of the impact load and various operational parameters,such as vehicle speed,lateral position of wheel-rail contact,track stiffness and position of impact within a sleeper bay,is investigated.The calibrated model is later employed in simulations featuring other forms of tread damage;their effects on impact load and subsequent fatigue impact on bearings,wheel webs and subsurface initiated rolling contact fatigue of the wheel tread are assessed.The results quantify the effects of wheel tread defects and are valuable in a shift towards condition-based maintenance of running gear,and for general assessment of the severity of different types of railway wheel tread damage.

Useful zero friction simulations for assessing MBS codes Pascal’s formula giving wheelsets frequency for zero wheel-rail friction

Present study provides a simple analytical formula,the“Klingel-like formula”or“Pascal’s Formula”that can be used as a reference to test some results of existing railway codes and specifically those using rigid contact.It develops properly the 3D Newton-Euler equations governing the 6 degrees of freedom(DoF)of unsuspended loaded wheelsets in case of zero wheel-rail friction and constant conicity.Thus,by solving numerically these equations,we got pendulum like harmonic oscillations of which the calculated angular frequency is used for assessing the accuracy of the proposed formula so that it can in turn be used as a fast practical target for testing multi-body system(MBS)railway codes.Due to the harmonic property of these pendulum-like oscillations,the squareω2 of their angular frequency can be made in the form of a ratio K/M where K depends on the wheelset geometry and load and M on its inertia.Information on K and M are useful to understand wheelsets behavior.The analytical formula is derived from the first order writing of full trigonometric Newton-Euler equations by setting zero elastic wheel-rail penetration and by assuming small displacements.Full trigonometric equations are numerically solved to assess that the formula providesω2 inside a 1%accuracy for usual wheelsets dimensions.By decreasing the conicity down to 1×10^(−4) rad,the relative formula accuracy is under 3×10^(−5).In order to test the formula reliability for rigid contact formulations,the stiffness of elastic contacts can be increased up to practical rigidity(Hertz stiffness×1000).

Influence of dynamic unbalance of wheelsets on the dynamic performance of high-speed cars

With further increasing in running speed of newer high-speed EMUs（electric multiple units）,higher demand for wheelset dynamic balance is required.In order to study the influence of the dynamic unbalance of wheelset on the stability,ride quality,and curving performance for a high-speed car,a detailed dynamic model of a high-speed EMU car is established using the software SIMPACK.The analysis results indicate that the dynamic unbalance of the wheelset significantly influences the dynamic performance of the high-speed car.The increase in dynamic unbalance of the wheelset will decrease the hunting critical speed,worsen the vertical ride quality,and increase the wheelset lateral force,derailment coefficient,and wheel unloading ratio.Therefore,in order to improve the stability,ride quality,and running safety of high-speed car,the values of dynamic unbalance of wheelset should be strictly controlled in manufacturing,and periodically monitored in operation.

Bifurcation and Stability Analysis of Time-Delayed Wheelset System under White Noise Excitation

Considering the impact of time delay in the lateral stiffness of the primary suspension and stochastic disturbances of equivalent conicity on the wheelset system, a stochastic time-delayed wheelset system is established. The wheelset system is transformed into a onedimensional Ito stochastic differential equation using central manifold and stochastic averaging methods. The analysis of the system's stochastic stability is conducted through the maximum Lyapunov exponent and singular boundary theory. The combination of the stationary probability density method and numerical simulation is employed to discuss the types and conditions of stochastic P-bifurcation in the wheelset system. The results indicate that changes in speed and time delay induce stochastic P-bifurcations in the wheelset system, while changes in noise intensity do not lead to stochastic P-bifurcations. Both time delay and equivalent conicity affect the critical speed of the wheelset system, and the critical speed gradually increases with the decrease of time delay and equivalent conicity.

Research on the influence of flexible wheelset rotation effect on wheel rail contact force

Purpose-Under the high-speed operating conditions,the effects of wheelset elastic deformation on the wheel rail dynamic forces will become more notable compared to the low-speed condition.In order to meet different analysis requirements and selecting appropriate models to analyzing the wheel rail interaction,it is crucial to understand the influence of wheelset flexibility on the wheel-rail dynamics under different speeds and track excitations condition.Design/methodology/approach-The wheel rail contact points solving method and vehicle dynamics equations considering wheelset flexibility in the trajectory body coordinate system were investigated in this paper.As for the wheel-rail contact forces,which is a particular force element in vehicle multibody system,a method for calculating the Jacobian matrix of the wheel-rail contact force is proposed to better couple the wheel-rail contact force calculation with the vehicle dynamics response calculation.Based on the flexible wheelset modeling approach in this paper,two vehicle dynamic models considering the wheelset as both elastic and rigid bodies are established,two kinds of track excitations,namely normal measured track irregularities and short-wave irregularities are used,wheel-rail geometric contact characteristic and wheel-rail contact forces in both time and frequency domains are compared with the two models in order to study the influence of flexible wheelset rotation effect on wheel rail contact force.Findings-Under normal track irregularity excitations,the amplitudes of vertical,longitudinal and lateral forces computed by the flexible wheelset model are smaller than those of the rigid wheelset model,and the virtual penetration and equivalent contact patch are also slightly smaller.For the flexible wheelset model,the wheel rail longitudinal and lateral creepages will also decrease.The higher the vehicle speed,the larger the differences in wheel-rail forces computed by the flexible and rigid wheelset model.Under track short-wave irregularity excitations,the vertical force amplitude computed by the flexible wheelset is also smaller than that of the rigid wheelset.However,unlike the excitation case of measured track irregularity,under short-wave excitations,for the speed within the range of 200 to 350 km/h,the difference in the amplitude of the vertical force between the flexible and rigid wheelset models gradually decreases as the speed increase.This is partly due to the contribution of wheelset's elastic vibration under short-wave excitations.For low-frequency wheel-rail force analysis problems at speeds of 350 km/h and above,as well as high-frequency wheel-rail interaction analysis problems under various speed conditions,the flexible wheelset model will give results agrees better with the reality.Originality/value-This study provides reference for the modeling method of the flexible wheelset and the coupling method of wheel-rail contact force to the vehicle multibody dynamics system.Furthermore,by comparative research,the influence of wheelset flexibility and rotation on wheel-rail dynamic behavior are obtained,which is useful to the application scope of rigid and flexible wheelset models.

Research on the strain gauge mounting scheme of track wheel force measurement system based on high-speed wheel/rail relationship test rig

Purpose-This paper aims to analyze the stress and strain distribution on the track wheel web surface and study the optimal strain gauge location for force measurement system of the track wheel.Design/methodology/approach-Finite element method was employed to analyze the stress and strain distribution on the track wheel web surface under varying wheel-rail forces.Locations with minimal coupling interference between vertical and lateral forces were identified as suitable for strain gauge installation.Findings-The results show that due to the track wheel web’s unique curved shape and wheel-rail force loading mechanism,both tensile and compressive states exit on the surface of the web.When vertical force is applied,Mises stress and strain are relatively high near the inner radius of 710 mm and the outer radius of 1110mmof the web.Under lateral force,high Mises stress and strain are observed near the radius of 670mmon the inner and outer sides of the web.As the wheel-rail force application point shifts laterally toward the outer side,the Mises stress and strain near the inner radius of 710 mm of the web gradually decrease under vertical force while gradually increasing near the outer radius of 1110 mm of the web.Under lateral force,the Mises stress and strain on the surface of the web remain relatively unchanged regardless of the wheel-rail force application point.Based on the analysis of stress and strain on the surface of the web under different wheel-rail forces,the inner radius of 870 mm is recommended as the optimal mounting location of strain gauges for measuring vertical force,while the inner radius of 1143 mm is suitable for measuring lateral force.Originality/value-The research findings provide valuable insights for determining optimal strain gauge locations and designing an effective track wheel force measurement system.

Optimal allocation method of electric/air braking force of high-speed train considering axle load transfer

Reasonable distribution of braking force is a factor for a smooth,safe,and comfortable braking of trains.A dynamic optimal allocation strategy of electric-air braking force is proposed in this paper to solve the problem of the lack of consideration of adhesion difference of train wheelsets in the existing high-speed train electric-air braking force optimal allocation strategies.In this method,the braking strategy gives priority to the use of electric braking force.The force model of a single train in the braking process is analyzed to calculate the change of adhesion between the wheel and rail of each wheelset after axle load transfer,and then the adhesion of the train is estimated in real time.Next,with the goal of maximizing the total adhesion utilization ratio of trailer/motor vehicles,a linear programming distribution function is constructed.The proportional coefficient of adhesion utilization ratio of each train and the application upper limit of braking force in the function is updated according to the change time point of wheelset adhesion.Finally,the braking force is dynamically allocated.The simulation results of Matlab/Simulink show that the proposed algorithm not only uses the different adhesion limits of each trailer to reduce the total amount of braking force undertaken by the motor vehicle,but also considers the adhesion difference of each wheelset.The strategy can effectively reduce the risk and time of motor vehicles during the braking process and improve the stability of the train braking.

Train wheel-rail force collaborative calibration based on GNN-LSTM

Accurate wheel-rail force data serves as the cornerstone for analyzing the wheel-rail relationship.However,achieving continuous and precise measurement of this force remains a significant challenge in the field.This article introduces a calibration algorithm for the wheel-rail force that leverages graph neural networks and long short-term memory networks.Initially,a comprehensive wheel-rail force detection system for trains was constructed,encompassing two key components:an instrumented wheelset and a ground wheel-rail force measuring system.Subsequently,utilizing this system,two distinct datasets were acquired from the track inspection vehicle:instrumented wheelset data and ground wheel-rail force data,a feedforward neural network was employed to calibrate the instrumented wheelset data,referencing the ground wheel-rail force data.Furthermore,ground wheel-rail force data for the locomotive was obtained for the corresponding road section.This data was then integrated with the calibrated instrumented wheelset data from the track inspection vehicle.Leveraging the GNN-LSTM network,the article establishes a mapping relationship model between the wheel-rail force of the track inspection vehicle and the locomotive wheel-rail force.This model facilitates continuous measurement of locomotive wheel-rail forces across three typical scenarios:straight sections,long and steep downhill sections,and small curve radius sections.

FPGA Implementation of Extended Kalman Filter for Parameters Estimation of Railway Wheelset

It is necessary to know the status of adhesion conditions between wheel and rail for efficient accelerating and decelerating of railroad vehicle.The proper estimation of adhesion conditions and their real-time implementation is considered a challenge for scholars.In this paper,the development of simulation model of extended Kalman filter(EKF)in MATLAB/Simulink is presented to estimate various railway wheelset parameters in different contact conditions of track.Due to concurrent in nature,the Xilinx®System-on-Chip Zynq Field Programmable Gate Array(FPGA)device is chosen to check the onboard estimation ofwheel-rail interaction parameters by using the National Instruments(NI)myRIO®development board.The NImyRIO®development board is flexible to deal with nonlinearities,uncertain changes,and fastchanging dynamics in real-time occurring in wheel-rail contact conditions during vehicle operation.The simulated dataset of the railway nonlinear wheelsetmodel is tested on FPGA-based EKF with different track conditions and with accelerating and decelerating operations of the vehicle.The proposed model-based estimation of railway wheelset parameters is synthesized on FPGA and its simulation is carried out for functional verification on FPGA.The obtained simulation results are aligned with the simulation results obtained through MATLAB.To the best of our knowledge,this is the first time study that presents the implementation of a model-based estimation of railway wheelset parameters on FPGA and its functional verification.The functional behavior of the FPGA-based estimator shows that these results are the addition of current knowledge in the field of the railway.

Influence of unsupported sleepers on the dynamic stability of ballasted bed based on wheelset impact tests

The unsupported sleeper can change the load characteristics of ballast particles and thus affect the dynamic stability of a ballasted bed.In this work,a laboratory test was constructed on a ballasted track containing unsupported sleepers.The ballasted track was excited by a wheelset,and the influence of unsupported sleepers on the dynamic stability of a ballasted bed was studied.The results show that the main frequency of the sleeper vibration appeared at 670 Hz,and the first-order rigid vibration mode at the frequency of 101 Hz had a significant effect on the condition without the unsupported sleeper.When the sleepers were continuously unsupported,the vibration damping effect of ballasted bed within the frequency range of 0–450 Hz was better than that at higher frequencies.Within the frequency range of 70–250 Hz,the vibration damping effect of the ballasted bed with unsupported sleepers was better than that without the unsupported sleeper.Owing to the excitation from the wheelset impact,the lateral resistance of the ballasted bed with unsupported sleepers whose hanging heights were 30,60,and 90 mm increased by 37.43%,12.25%,and 18.23%,respectively,while the lateral resistance of the ballasted bed without the unsupported sleeper remained basically unchanged.The unsupported sleeper could increase the difference in the quality of the ballasted bed between two adjacent sleepers.In addition,test results show that the hanging height of the unsupported sleeper had little effect on the lateral resistance of a ballasted bed without external excitation,but had an obvious effect on the rate of change of the lateral resistance of a ballasted bed and the acceleration amplitude of the sleeper vibration under the wheelset impact.

Research on hunting stability and bifurcation characteristics of nonlinear stochastic wheelset system

A stochastic wheelset model with a nonlinear wheel-rail contact relationship is established to investigate the stochastic stability and stochastic bifurcation of the wheelset system with the consideration of the stochastic parametric excitations of equivalent conicity and suspension stiffness.The wheelset is systematized into a onedimensional(1D)diffusion process by using the stochastic average method,the behavior of the singular boundary is analyzed to determine the hunting stability condition of the wheelset system,and the critical speed of stochastic bifurcation is obtained.The stationary probability density and joint probability density are derived theoretically.Based on the topological structure change of the probability density function,the stochastic Hopf bifurcation form and bifurcation condition of the wheelset system are determined.The effects of stochastic factors on the hunting stability and bifurcation characteristics are analyzed,and the simulation results verify the correctness of the theoretical analysis.The results reveal that the boundary behavior of the diffusion process determines the hunting stability of the stochastic wheelset system,and the left boundary characteristic value cL=1 is the critical state of hunting stability.Besides,stochastic D-bifurcation and P-bifurcation will appear in the wheelset system,and the critical speeds of the two kinds of stochastic bifurcation decrease with the increase in the stochastic parametric excitation intensity.

Improving rail vehicle dynamic performance with active suspension

Today,it is difficult to further improve the dynamic performance of rail vehicles with conventional passive suspension.Also,simplified vehicle respectively running gear layouts that significantly could reduce vehicle weights are difficult to realize with modern requirements on passenger vibration comfort and wheel and rail wear.Active suspension is a powerful technology that can improve the vehicle dynamic performance and make simplified vehicle concepts possible.The KTH Railway group has,together with external partners,investigated active suspensions both numerically and experimentally for 15 years.The paper provides a summary of the activities and the most important findings.One major project carried out in close collaboration with the vehicle manufacturer Bombardier and the Swedish Transport Administration was the Green Train project,where a 2-car EMU test bench was used to demonstrate different active technologies.In ongoing projects,a concept of single axle-single suspension running gear is developed with active suspension both for comfort improvement and reduced wheel wear in curves.The results from on-track tests in the Green Train project were so good that the technology is now implemented in commercial trains and the simulation results for the single-axle running gear are very promising.

Research on fatigue evaluation method of high-speed train axle based on axle box acceleration

As a key safety component of the high-speed train, fatigue fracture of the axle would lead to major accidents such as derailment or overturning. The complexity of the axle dynamic stress test seriously enhances the difficulty of axle fatigue damage analysis. In this paper, the dynamic stress test of the high-speed train axle was carried out,the axle box acceleration was monitored on-track during the test, and the relationship between the axle stress spectrum and acceleration was analyzed on-track. The results show that the relationships between the axle equivalent stresses and the Root Mean Square(RMS) values of the axle box vertical acceleration and lateral acceleration exhibit a strong joint probability density distribution. The concept of the virtual surface density of wheel-rail contact is also proposed to realize the purpose of using axle box acceleration to deduce axle equivalent force. The results quantify the relationship between axle box acceleration and axle equivalent force, provide a new method for predicting the axle damage using the acceleration RMS values, and open up a new approach for structural health monitoring of high-speed train axles.

Effects of wheelset vibration on initiation and evolution of rail short-pitch corrugation

The initiation and evolution of short-pitch corrugation in Beijing metro line 4 was studied from the viewpoint of wheelset vibration.A three-dimensional elastic model was set up.Numerical simulations were undertaken with this model to analyze the corrugation by the wheelset vertical vibration and torsional vibration.Based on numerical results,the relation between rail corrugation and wheelset vibration,and the relation between the position of electromotor and wheelset vibration were indicated.It is found that avoiding the wheelset-rail resonance is one method of controlling the rail short-pitch corrugation and solving the vibration and noise problem in metro lines.

Safety evaluation for railway vehicles using an improved indirect measurement method of wheel–rail forces

The wheel-rail force measurement is of great importance to the condition monitoring and safety evaluation of railway vehicles. In this paper, an improved indirect method for wheel-rail force measurement is proposed to evaluate the running safety of railway vehicles. In this method, the equilibrium equations of a suspended wheelset are derived and the wheel-rail forces are then be obtained from measured suspension and inertia forces. This indirect method avoids structural modifications to the wheelset and is applicable to the long-term operation of railway vehicles. As the wheel-rail lateral forces at two sides of the wheelset are difficult to separate, a new derailment criterion by combined use of wheelset derailment coefficient and wheel unloading ratio is proposed. To illustrate its effectiveness, the indirect method is applied to safety evaluation of rail- way vehicles in different scenarios, such as the cross wind safety of a high-speed train and the safety of a metro vehicle with hunting motions. Then, the feasibility of using this method to identify wheel-rail forces for low-floor light rail vehicles with resilient wheels is discussed. The values identified by this method is compared with that by Simpack simulation for the same low-floor vehicle, which shows a good coincidence between them in the time domain of the wheelset lateral force and the wheel-rail vertical force. In addition, use of the method to determine the high-frequency wheel-rail interaction forces reveals that it is possible to identify the high-frequency wheel-rail forces through the accelerations on the axle box.

Analysis of steering performance of differential coupling wheelset

In order to improve the curving performance of the conventional wheelset in sharp curves and resolve the steering ability problem of the independently rotating wheel in large radius curves and tangent lines, a differential cou- pling wheelset （DCW） was developed in this work. The DCW was composed of two independently rotating wheels （IRWs） coupled by a clutch-type limited slip differential. The differential contains a static pre-stress clutch, which could lock both sides of IRWs of the DCW to ensure a good steering performance in curves with large radius and tangent track. In contrast, the clutch could unlock the two IRWs of the DCW in a sharp curve to endue it with the characteristic of an IRW, so that the vehicles can go through the tight curve smoothly. To study the dynamic performance of the DCW, a multi-body dynamic model of single bogie with DCWs was established. The self-centering capability, hunting stability, and self-steering performance on a curved track were analyzed and then compared with those of the conventional wheelset and IRW. Finally, the effect of coupling parameters of the DCW on the dynamic performance was investigated.

Effect of wheelset flexibility on wheel–rail contact behavior and a specific coupling of wheel–rail contact to flexible wheelset

The fexibility of a train＇s wheelset can have a large effect on vehicle–track dynamic responses in the medium to high frequency range.To investigate the effects of wheelset bending and axial deformation of the wheel web,a specifi coupling of wheel–rail contact with a fexible wheelset is presented and integrated into a conventional vehicle–track dynamic system model.Both conventional and the proposed dynamic system models are used to carry out numerical analyses on the effects of wheelset bending and axial deformation of the wheel web on wheel–rail rolling contact behaviors.Excitations with various irregularities and speeds were considered.The irregularities included measured track irregularity and harmonic irregularities with two different wavelengths.The speeds ranged from 200 to400km/h.The results show that the proposed model can characterize the effects of fexible wheelset deformation on the wheel–rail rolling contact behavior very well.

A Nondestructive Instrumented Wheelset System for Contact Forces Measurements

A nondestructive continuous instrumented wheelset design is proposed based on strain gauges placing inside of the wheel web and wireless telemetry system. The signal feature analysis including frequency contents and high order harmonic ripples is also carried out. The strain gradient decoupling method for vertical and lateral force identification is proposed based on the strain distributions under respective loads. The method implements minimum crosstalk effects and insensitive to the varying contact points. The KMT telemetry system is adopted for wireless inductive powering and signal transferring. The drilling holes on the wheel and axles are avoidable to ensure the integrity and long-term using of the wheelset. Bridging and demodulating schemes for lateral and vertical force are designed respectively as they have dramatic differences at the dynamic signal features. High order harmonic ripple analysis and error estimation are gotten by independent waveforms. Based on the data form calibration test rig, it is indicated that the high order ripple amplitudes are below 10% of the demodulation amplitudes and fulfill designed requirements.

ANALYSIS OF CREEP FORCES OF WHEEL/RAIL

The effects of structure elastic deformations of wheelset and track on creep forces of wheel and rail are investigated.Finite element method is used to calculate the influence coefficients expressing the relations between structure elastic deformations of wheelset and track and the corresponding loads in the rolling direction and the lateral direction of wheelset,respectively.The influence coefficients of wheelset and track are used to revise some of the influence coefficients obtained with the formula of Bossinesq and Cerruti in Kalker's theory of three dimensional elastic bodies in rolling contact with non Hertzian form.The theory of Kalker and the modified theory of Kalker are respectively employed to analyze creep forces of wheelset and track.The numerical results obtained show a great influence of structure elastic deformations of wheelset and track on the creep forces.Therfore it is not reasonable that wheel and rail are treated as elastic half space in the analysis of wheel and rail in rolling contact,and the present theories of rolling contact based on the assumption of elastic half space need to be further improved

Dynamic Analysis of Railway Vehicles Subjected to Linear Creep Forces

The behavior of the system of an unrestrained wheelset traveling on a straight track and subjected to linear creep forces between wheel and track is analized qualitatively. The presence of two eigenvalues of a relatively large negative real part is confirmed. So there exist rapidlydecaying terms in time response of the system and the stiffness in the equations of motion. The modal truncation is given to eliminate the contribution of the stiffness to system response, thereby speeding up numerical simulation of the wheelset motion.