Vehicle-track Coupling Dynamics Research Articles

Dynamic behavior of resilient wheels at a rail weld joint

The aim of this paper is to investigate the dynamic response of the resilient wheel equipped on the intercity train at the rail weld. A vehicle-track coupling dynamics model with resilient wheels is developed. A rigid multi-body system with 55 degrees of freedom is utilized to model the vehicle system. The rubber layer of the resilient wheel is modeled as a three-directional spring-damper unit between the wheel rim and the wheel core. For the track sub-model, the rails were modelled as Euler Beam and supported by concrete sleepers modelled as mass block. The vehicle and track motion equations are represented as mass-stiffness-damping matrixes. The accuracy of this modeling method at low frequencies is verified via the comparison between the field measured data and numerical results. The dynamic results of the rigid wheel are compared with those of the resilient wheel. Results show that the dynamic wheel-rail force of the rigid wheel is slightly higher than that of the resilient wheel. Furthermore, the mass factor is introduced to investigate the effect of the rubber layer position on the tire acceleration and the wheel-rail impact force. The numerical simulation results are expected to provide references for resilient wheel application into the intercity train.

Hydraulic damage characteristics of cracks adjacent to sleepers of concrete slab

In order to investigate the hydraulic damage characteristics of cracks adjacent to twinblock sleepers and estimate its fatigue life, an analytical expression of the hydrodynamic pressure in cracks under the external load was derived, and a hydraulic fracturing model of twinblock sleeper has been established based on the vehicle-track coupling dynamics theory and fracture mechanics theory. In addition, a laboratory test was conducted to verify the hydrodynamic pressure expression. It was observed that the computed results are in good consistent with the experimental results. The value of the hydrodynamic pressure in the crack peaks when the wheelset is close to the cracking area, while the hydrodynamic pressure is zero when the wheelset or the bogie reaches the damaged area. Numerous factors affect the hydrodynamic pressure and the effective stress intensity factor, including the train speed, crack opening, and crack length. In comparison, the hydrodynamic pressure and the effective stress intensity is more sensitive to the crack opening. The initial crack length is the main factor affecting the fatigue life of the crack. If the initial crack length is long enough, the critical fracture length can be easily reached under the coupling effect of the train load and water.

In-Service Detection and Quantification of Railway Wheel Flat by the Reflective Optical Position Sensor.

Railway wheel tread flat is one of the main faults of railway wheels, which brings great harm to the safety of vehicle operation. In order to detect wheel flats dynamically and quantitatively when trains are running at high speed, a new wheel flat detection system based on the self-developed reflective optical position sensor is demonstrated in this paper. In this system, two sensors were mounted along each rail to measure the wheel-rail impact force of the entire circumference by detecting the displacement of the collimated laser spot. In order to establish a quantitative relationship between the sensor signal and the wheel flat length, a vehicle-track coupling dynamics analysis model was developed using the finite element method and multi-body dynamics method. The effects of train speed, load, wheel flat lengths, as well as the impact positions on impact forces were simulated and evaluated, and the measured data can be normalized according to the simulation results. The system was assessed through simulation and laboratory investigation, and real field tests were conducted to certify its validity and correctness. The system can determine the position of the flat wheel and can realize the quantification of the detected wheel flat, which has extensive application prospects.

Dynamic evaluation of elastic bar in track transition section of fast-metro system

In China, the rapid development of fast-metro system, along with many dynamic problems in track transition section, threatens the safe operation of the metro system. Aiming at this practical issue, this article presents an evaluation on the dynamic behaviors of elastic bars in track transition section of the fast-metro system. Primarily, an effective global–local method for evaluating the performance of elastic bar is proposed based on vehicle–track-coupled dynamics, in which two important models are established, namely, the vehicle–track transition section–coupled dynamic model and the three-dimensional finite element model of elastic bar. Then, the dynamic property of elastic bar in track transition section of the fast-metro system is evaluated employing the proposed method, focusing on the fastener force, dynamic displacement of elastic bar, and stress of elastic bar. Finally, fatigue analysis is conducted to evaluate the service life of elastic bar in track transition section. Results show that the proposed global–local method is effective to evaluate the dynamic behaviors of elastic bar in track transition section in fast-metro system. Impact appears when vehicles run through the track transition section and it mainly influences the two fasteners on each side. Operational direction of vehicle has little influence on amplitude of displacement of elastic bar. When the vehicle runs at 120 km/h, maximum stress of elastic bar is 1050 MPa, which occurs inside the rear toe. From the perspective of long-term service, traditional track transition section is not suitable for fast-metro system, which should be redesigned.

Design method of LM thin flange wheel profile based on NURBS

The maintenance strategies of the worn wheels have an important impact on maintenance cost of railway. LM worn wheels of heavy haul wagons are often re-profiled to their original standard form, and this excessive removal of material could reduce the wheel service life. A new LM wheel profile reconstruction method was established by taking into account the geometrical characteristics of the LM wheel profile and applying the Non-Uniform Rational B-Spline theory. The design of LM thin flange re-profiling wheel can be accomplished by using Particle Swarm Optimization method which handles multiple objectives including train operation safety concerns, and minimizing material removal. A new wheel profile with a flange thickness of 32 mm can be designed by the integration of vehicle-track coupling dynamics model, and the results showed that the mean wear work is reduced by 55.97% compared with the original standard profile. Under the optimized wheel profile, the root mean square value of the lateral force and the maximum contact stress is reduced, and the amount of material removed is decreased. The design method can provide support for the LM wheel re-profiling maintenance, by designing the thin flange profiles of a flange thickness of 28∼33 mm.

Study on an elastic lever system for electromagnetic energy harvesting from rail vibration

Energy harvesting from rail vibration is a promising approach to solve the power supply problem in remote and off-grid areas. The major issue of current energy harvesting techniques and devices is the limited power generating capacity. In this paper, the authors put forward an elastic lever system to enhance the performance of an electromagnetic energy harvester. A vehicle-track coupling dynamics model is established to simulate the service condition of the energy harvester. The Power Amplification Factor (PAF), which is defined as the ratio between the output power with and without a lever system, is introduced to quantify the Enhanced Energy Harvester (EEH). It is found that the PAF can be greater than n2 with a leverage ratio of n. Simulation shows that the output power can be magnified by 430 times with an elastic lever system with a leverage ratio of 10. The amplification effect of the output power comes from two aspects, one is the magnifying effect of leverage itself and the other is the resonance effect. Additionally, it is found that a single EEH will increase the wheel-rail contact force slightly, which indicates the EEH is impractical for use as an approach for rail vibration reduction. Nevertheless, it will not have a significant negative effect on rail vibration.

Vibration reduction performance of rubber concrete backfill layer in high-speed railway tunnel

A novel approach to reduce vibration was put forward by applying rubber concrete as backfill layer of the high-speed railway tunnel, and its feasibility was analyzed based on the vibration isolation theory. A three-dimensional spatial coupling model of vehicle-track-tunnel-rock mass was established by means of vehicle-track coupling dynamics theory. The dynamic response of the vehicle, track, and tunnel structure under common and rubber concrete backfill layer was compared. The vibration reduction performance and the characteristics of rubber concrete were discussed. The change in tunnel vibration under different elastic modulus and damping ratios of backfill layer was analyzed, and the vibration reduction effect of rubber concrete combined with damping cushion was studied. Results show that the influence of the rubber concrete backfill layer on the dynamic indices of vehicle and track structure can be neglected. Because of the application of rubber concrete, the vibration acceleration of tunnel decreases by about 40%, and 4–8 dB can be reduced in the corresponding frequency of 100–200 Hz. With decrease in the elastic modulus and increase in the damping ratio, the vibration of the tunnel decreases gradually. Moreover, the influence of damping ratio is more significant than that of elastic modulus. The combination of rubber concrete backfill layer and damping cushion demonstrates a superior effect in reducing vibration, which decreases the vibration level by 3–5 dB compared with setting the damping cushion only. The article is expected to provide theoretical guidance for the application of rubber concrete in the high-speed railway.

Matching performance of CHN60N rail with various wheel profiles for Chinese high-speed railway

The matching of wheel profile with rail profile is the key issue in design of high-speed railway, it directly affects the vehicle dynamics performance during travelling and the wear behavior of wheel/rail. The matching performance of wheel profiles LMA, S1002CN and XP55 widely used in Chinese high-speed railway with CHN60N rail was analyzed in the study in terms of wheel/rail contact geometry, wheel/rail rolling contact and vehicle-track coupling dynamics. The results indicate that: By comparing the matching performance of the three wheel profiles with CHN60 rail, S1002CN profile matches best with the CHN60N rail. XP55 profile is not applicable to CHN60N rail.

Dynamic Analysis of Vehicle Track Coupling Based on Double Beam Track Model

The rail was considered as double Timoshenko beam in this paper, applied to the vehicle track coupling dynamics model; the Hertz nonlinear method is used to calculate the wheel rail contact force. Wheel rail vertical force and response of vehicle are calculated by using the model under random irregularity and single harmonic excitation; at the same time, wheel rail force and vertical acceleration response of 3‐order, 10‐order, and 19‐order wheel polygon were calculated. The results show that, under the excitation of random irregularity, the wheel rail vertical force of two models was very close in the low frequency band, and the response of the double beam model in the high frequency band of 200–1000 Hz is larger than the single beam model, and the acceleration and displacement responses of the double beam model are relatively close. Under a single harmonic excitation, the double beam model has a shorter wheel rail force attenuation time than that of the single beam model. And wheel rail force peak value of double beam model is 9% larger than that of single beam model. Similarly, the vertical displacement of the double beam model increased by 2.6%. Under the 3‐order and 10‐order wheel polygon excitation, vertical wheel rail peak force of double beam is, respectively, 37.5% and 50% larger than single beam model; the vertical frame acceleration amplitude is 1 g and 1.7 g; under the 19‐order polygon wheel excitation, the difference of the wheel rail force between two models is very small, and the amplitude of acceleration of bogie is 2.3 g. And double beam model has more advantage in analyzing high frequency problems such as wheel polygonization.

Time-domain model for wheel-rail noise analysis at high operation speed

This paper develops a numerical model for wheel-rail noise analysis in the time-domain. This model for wheel-rail noise is based on vehicle-track coupling dynamics considering the effect of flexible wheelsets and track, and a transient wheel-rail noise prediction method. This model can approximatively characterize the components of vibration and noise in the frequency range up to 3.5 kHz. The wheel-rail forces are calculated and shown in both time and frequency domains by using the vehicletrack coupling dynamic model. Then the vibration and sound of the flexible wheelset are calculated by the transient finite elementboundary element (FE-BE) prediction model at 300 km/h, in which the effects of random irregularity and discrete supporting excitation are considered. The numerical results calculated by using the present model are discussed. The present model is also used to calculate the effect of corrugation with wavelengths of 40 mm to 300 mm on wheel-rail noise. The numerical results can be useful for academic research and engineering application to railway noise and vibration.

Finite-infinite element coupled analysis on the influence of material parameters on the dynamic properties of transition zones

Based on the theory of vehicle-track coupling dynamics, a plane stress finite-infinite element model of a high-speed railway subgrade-bridge transition zone is proposed. With this model, the influence of 2 simultaneously varied subgrade material parameters on the dynamic response of the vehicle-track-subgrade system in a high speed railway transition zone with the slab track is investigated. The results indicate that the influence of the dynamic elastic modulus of the graded broken stone on the dynamic response of the vehicle system is larger than that of the dynamic elastic modulus of the subgrade bed surface layer. The recommended dynamic elastic moduli of the subgrade bed surface layer and the graded broken stone are chosen as 4000MPa and 2000MPa, respectively.

An investigation of subgrade differential settlement on the dynamic response of the vehicle–track system

The construction of non-ballasted slab railway track on existing subgrade soils, or on embankments, is at an early stage of development on Chinese railways. Developing appropriate standards for the allowable amount of subgrade differential settlement that takes into account the dynamic response of the train–track system is one of a number of issues that need to be addressed. To inform the development of such standards, a model based on the theory of vehicle–track coupling dynamics, which considers the weight of the track structure, was created to investigate how differential settlement, in terms of the amplitude, wavelength and position of the settlement along the track, can affect various railway performance-related criteria, including ride quality, stability, vehicle safety and potential damage to the wheel of the train and the rail (i.e. forces at the wheel–rail contact and in the fasteners). The performance of the model was favorably compared with other widely used models described in the literature. The analysis of the study to inform design standards using the developed model demonstrated that the magnitude of the differential settlement influences passenger comfort the most compared with other performance criteria. For the considered CRTS I track, there exists a particular wavelength (8 m for the specific conditions considered) that results in all measures of performance being at their maximum values. Furthermore, the longitudinal position of the settlement waveform in relation to the joints between two concrete slabs, a factor which is not considered in design standards, was shown to influence component deterioration, passenger comfort and safety. The greatest propensity to cause component damage occurs when the beginning or end of the differential settlement waveform corresponds with the inter-slab joint of a concrete base. Accordingly, it is recommended that current design standards should be modified to specify appropriate combinations of amplitude, wavelength and position of the differential settlement to give acceptable measures of performance.

Study on the numerical optimization of rail profiles for heavy haul railways

The aim of this paper is to study the optimization of the rail profile for heavy haul railways. A numerical model is developed, where the rail profile is parameterized as a generalized function for a series of independent variables. A well-designed formula, which characterizes the conformance between wheel and rail profiles around contact point for all possible wheel–rail contact situations, is considered as the objective function. During the construction of the objective function, a wheel–rail contact geometry algorithm is implemented to detect contact point positions quickly. Linear and nonlinear constraints are introduced in order to meet some necessary conditions. Then, the optimization of rail profile can be transformed into a typical mathematical nonlinear optimization problem with single objective, multivariables, and multiconstraints. In order to solve this problem effectively and efficiently, the sequential quadratic programming algorithm combined with Lagrange function, quasi-Newton method is employed. At each major iteration, a quasi-Newton approximation is made of the Hessian matrix of the Lagrangian function using BFGS updating method. This is then used to generate a quadratic programming subproblem whose solution is for forming the search direction for the iteration of independent variables. Finally, the R75 rail profile, prevalently used in China’s heavy haul railways, is optimized using the developed model to better match the LM wheel profile. A modified rail profile is put forward and compared with the original rail profile systematically in wheel–rail contact geometry relationship, vehicle–track dynamic behaviors, and wear developments. A vehicle–track coupling dynamics model and a wheel–rail wear prediction model are respectively established to conduct the comparative study. According to the calculation results, the optimized rail profile is proved to have superior performances and, thus, can be considered a better choice to match LM wheel for China’s heavy haul railways, which is of practical value for the design and preventive grinding of heavy haul rails. In addition, this application example validates the rationality of the developed numerical optimization model. It can also be used for the optimization of other rail profiles.

Study on the subgrade deformation under high-speed train loading and water–soil interaction

It is important to study the subgrade characteristics of high-speed railways in consideration of the water–soil coupling dynamic problem, especially when high-speed trains operate in rainy regions. This study develops a nonlinear water–soil interaction dynamic model of slab track coupling with subgrade under high-speed train loading based on vehicle–track coupling dynamics. By using this model, the basic dynamic characteristics, including water–soil interaction and without water induced by the high-speed train loading, are studied. The main factors-the permeability coefficient and the porosity-influencing the subgrade deformation are investigated. The developed model can characterize the soil dynamic behaviour more realistically, especially when considering the influence of water-rich soil.

Effect of track irregularity on the dynamic response of a slab track under a high-speed train based on the composite track element method

Slab tracks are common track structures in high-speed railways. In this study, a vehicle/slab track interaction model is developed based on vehicle–track coupling dynamics theory, and composite track elements are used to rapidly model the finite element equations of the slab track based on the stationary value theory of total potential energy. In the model, the rail is represented as a discretely-supported infinite beam, the slab and the base are considered as continuously-supported free beams, and the connections of the track structure are modelled as viscoelastic spring–damping elements. The composite track element method effectively derives the equations of motion with high or low degrees of freedom by increasing or decreasing the number of track elements; therefore, it can be applied to the dynamic analysis of the track and to investigate the dynamic responses of the slab track system, including the rail, pad, slab, Cement asphalt mortar (CA mortar) and base. The equations of motion of the vehicle system are also proposed using the finite element method. The vehicle system and the slab track system interact through the vertical wheel/rail force, which is approximated using Hertz contact theory. The dynamic responses of a slab track subjected to moving vehicle loads are analysed using dynamic simulations and are compared with another classic simulation method. The effects of random track irregularity and vehicle velocity on the dynamic responses of the slab track system are discussed.

Analysis of Local Vibration for High-Speed Railway Bridge Based on Finite Element Method

Based on the theory of vehicle track coupling dynamics, the local vibration of the high-speed railway box girder is analyzed by the Finite Element Method and the model is simulated with the solid elements. Through the study of vibration characteristics of the selected 6 sensitive points, the local vibrations in different parts of the box girder are figured out. It is compared the response of the time domain and frequency domain in different parts of the cross section on different train speeds. Furthermore, the influence of track irregularity of local vibration response is analyzed. The results show that the track irregularity is the main factor causing local vibration. At last, the effects of local vibration on the boundary conditions are discussed. The response of top panel, floor panel and web panel were different and the flange panel was similar between the simple supported beam and the fixed beam.

The effect of the frequency-dependent stiffness of rail pad on the environment vibrations induced by subway train running in tunnel

The influence of the frequency-dependent stiffness of rail pad on the frequency distribution of vibrations created by a subway train running in tunnel is investigated using a frequency-domain algorithm. The theoretical approach combines vehicle–track coupling dynamics and spectrum analysis using the finite element method. The proposed approach is validated by a comparison with measured data. The comparison further shows that the theoretical approach and the selection of calculation parameters are reasonable and they create high calculation accuracies in the considered frequency range. Compared with a constant stiffness pad, the frequency-dependent stiffness of rail pad has little effect on vibrations below the one-third octave center frequency of 25 Hz; however, it significantly changes the vibrations observed above that center frequency. It is also found that simply increasing the constant stiffness of rail pad can lead to predictions of the vibration that have only a small error in either the low-frequency or high-frequency domains.

Multiobjective Optimization of CRH3 EMU Wheel Profile

The wheel-rail wear problems inherent to railway operation have become increasingly prominent and serious, as they have been proven to be the main factors which affect safety, stability of electric multiple units (EMUs), and wheel-rail maintenance cost. The multiobjective optimization model of CN wheel profile proposed in this study was constructed in effort to reduce the wheel wear of CRH3. Reconstruction of the CN profile based on the nonuniform rational B spline (NURBS) curve theory was designed. Twenty vertical coordinates of the CN profile were selected as design variables, the first wheelset mean wear workand the wheel-rail lateral force were employed as the objective functions, and the wheel geometry, maximal contact pressure, and the derailment coefficient were chosen as the constraint conditions. Particle swarm optimization (PSO) was applied to complete the optimization model combined with the vehicle track coupling dynamics model. Analysis results indicated that the optimized CN-Opti profile possesses more favorable, comprehensive, dynamic, and effective characteristics than the traditional CN profile.

The Research on Environment Vibration due to Subway with Rail Pads of Frequency-Dependent Stiffness

Based on Vehicle-Track Coupling Dynamics and the spectrum analysis technique of the Finite Element Method, a frequency-domain method of environment vibration due to subway is put forward and frequency-range distribution of ground acceleration is discussed. Compared with the measured data, the result shows that after considering frequency-dependent stiffness of rail pad, the error is less than 0.3dB in the frequency range of 0-30 Hz, but it is up to 11.8 dB in the frequency range of 50-100 Hz. And the frequency-domain distribution of ground vibration changes too. Thus, the frequency-dependent stiffness of rail pads is not negligible in the prediction of environment vibration generated by subway.

Dynamic responses of bridge-approach embankment transition section of high-speed rail

Based on the vehicle-track coupling dynamics theory, a new spatial dynamic numerical model of vehicle-track-subgrade coupling system was established considering the interaction among different structural layers in the subgrade system. The dynamic responses of the coupled system were analyzed when the speed of train was 350 km/h and the transition was filled with graded broken stones mixed with 5% cement. The results indicate that the setting form of bridge-approach embankment section has little effect on the dynamic responses, thus designers can choose it on account of the practical circumstances. Because the location about 5 m from the bridge abutment has the greatest deformation, the stiffness within 0–5 m zone behind the abutment should be specially designed. The results of the study from vehicle-track dynamics show that the maximum allowable track deflection angle should be 0.09% and the coefficient of subgrade reaction (K 30) is greater than 190 MPa within the 0–5 m zone behind the abutment and greater than 150 MPa in other zones.