Wheel-rail Forces Research Articles

High-speed vehicle–slab track coupled vibration analysis of the viscoelastic-plastic dynamic properties of rail pads under different preloads and temperatures

The viscoelastic-plastic dynamic properties of rail pads were are not adequately accounted for in the traditional vehicle–track coupled dynamic model. To investigate the influence of the viscoelastic-plastic dynamic properties of rail pads on the high-speed vehicle–track coupled vibrations, we obtained the viscoelastic-plastic dynamic properties of rail pads first by a series of laboratory tests, after which we described these properties theoretically by a modified Fractional Derivative Zener (FDZ) model and a traditional Berg friction model. A modified vertical vehicle–slab track coupled dynamic model was established by introduction of the modified FDZ and traditional Berg models for rail pads to investigate the influence of the viscoelastic-plastic dynamic properties of the rail pads on the high-speed vehicle–slab track coupled vibration responses under various preloads and temperatures. The FDZ and Berg models for rail pads improved the calculation accuracy of the high-speed vehicle–slab track coupled vibration responses, compared with the traditional KV model for rail pads, especially in the dominant high frequency range. The dynamic plastic properties of the rail pads effectively suppressed the high-frequency wheel-rail forces and yet increased the high-frequency vibration responses of the track substructures under the rail. Low temperatures and increased preloads on rail pads had a similar effect on the vehicle–track coupled vibrations. Increasing the preload on rail pads or decreasing the temperature increased the wheel-rail random excitation energy and its dominant frequencies, increased the vibration responses of the wheel-set and the track substructure under the rail, and decreased the vibrations of the rail at nearly all frequencies. Highlights The dynamic viscoelasticity and plasticity of rail pad under preloads and temperatures were tested. A modified FDZ model for the dynamic viscoelastic properties of rail pads was proposed. The dynamic plastic properties of rail pads can decrease the high-frequency wheel-rail forces. The dynamic plastic properties of rail pads can increase the high-frequency vibration under the rail. Low temperatures and increased preloads on rail pads had a similar effect on vehicle/track vibration.

A High-Precision Method for Dynamically Measuring Train Wheel Diameter Using Three Laser Displacement Transducers.

Wheel diameter is a significant geometric parameter related to the safe operation of trains, and needs to be measured dynamically. To the best of the authors’ knowledge, most existing dynamic measurement methods and systems do not meet the requirement that the wheel diameter measurement error for the high-speed vehicle is less than 0.3 mm. In this paper, a simple method for dynamically and precisely measuring train wheel diameter using three one-dimensional laser displacement transducers (1D-LDTs) is proposed for the first time, and a corresponding measurement system which was developed is described. The factors that affect the measurement accuracy were analyzed. As a main factor, rail deformation caused by the wheel-rail interaction force at low (20 km/h) and high (300 km/h) speeds was determined based on the combination of multi-body dynamics and finite element methods, and the effect of rail deformation on measurement accuracy is greatly reduced by a comparative measurement. Field experiments were performed to verify the performance of the developed measurement system, and the results of the repeatability error and measurement error of the system were both less than 0.3 mm, which meets the requirement of wheel diameter measurements for high-speed vehicles.

Investigating the Effect of Some Train and Track Parameters on Contact-impact Forces in the Vicinity of a Rail Breakage

Broken rails or welds are the main causes of derailment in railway networks. Therefore, a wheel-rail interaction model, which precisely estimates contact-impact forces in the presence of broken rails, can have a significant effect on derailment risk reduction. This paper attempts to present contact-impact forces in the vicinity of broken rails by employing a detailed 3D finite element model. The model is verified using a field test carried out on a ballasted railway track. Effects of train speed, gap length, axle load and railpad and ballast characteristics are studied on rail-wheel contact forces as well as on railpad and ballast forces. Results suggest that increasing the train speed from 60 km/h to 110 km/h would increase dynamic impact force from 2.46 to 4.11. It is also observed that increasing axle load results in an increase in the wheel-rail impact forces and in railpad and ballast forces, while leading to a reduced dynamic impact factor. Furthermore, investigating the effect of the track parameters demonstrates that ballast stiffness is the most important characteristic of the track, which has a reverse effect on dynamic impact forces. Moreover, unloading length increase and consequently derailment risk increase is highly sensitive to increasing train speed.

Efficient evaluation of bridge deformation for running safety of railway vehicles using simplified models

The running safety of high-speed trains over bridges is a great concern in bridge design. Typically, the running safety of vehicles is evaluated by vehicle–track simulations that are computationally expensive and unfamiliar to bridge designers. This study investigates simplified vehicle–track models for assessing the running safety of vehicles on deformed bridges. Four types of simplified vehicle models along with four types of simplified wheel–track models are investigated. The predicted wheel–rail forces are compared with those simulated by the detailed vehicle–track program. In these simulations, typical bridge deformations are taken as excitations to the dynamic system. It is found that omitting the rail vibration leads to large wheel–rail response errors. The wheel–rail constraint model gives similar wheel–rail responses to those obtained by the Hertz contact model. A vehicle–track model with five degrees-of-freedom is adequate for assessing wheel–rail forces. Furthermore, an analytical solution to the wheel–rail forces running over an angular rotation was obtained. These simplified vehicle–track models provide an efficient way to assess the running safety of vehicles on deformed bridges when using probabilistic or optimal analyses that require a large number of simulations.

Dynamic behaviour of the track in transitions zones considering the differential settlement

Transition zones in railway tracks are the locations with considerable changes in supporting structures. Because of the difference in the structures or material properties, the differential settlement always present. The structural vibration caused by the hanging sleepers is often observed in transition zones, which leads to significant amplification of dynamic responses between the ballast and sleeper, aggravating the track degradation.In order to explain the high degradation rate of the track in transition zones, a 3D dynamic (explicit) Finite Element model of transition zones has been used. It considers that the rapid compaction of ballast tracks occurs after a few months of operation, while the track on the engineering structure barely settles, resulting in the appearance of hanging sleepers in transition zones. Therefore, the model can study the differential settlement and the stiffness variation between the ballast track and the engineering structure at the same time. Nonlinear contact elements are used to model the interface between sleepers and ballast so that the behaviour of hanging sleepers can be better studied.The results show that the differential settlement plays a more important role in track degradation than the stiffness variation. The dynamic behaviours are different in the embankment-bridge and bridge-embankment transitions. The location that the maximum wheel-rail interaction force appears does not correspond to that of the maximum ballast stress. The results explain the degradation mechanism and provide guidance for maintenance.

Dynamic reliability evaluation of vehicle–track coupled systems considering the randomness of suspension and wheel–rail parameters

The ride quality and running safety of high-speed trains are directly influenced by uncertainties of some key parameters, such as the damping and stiffness coefficients of suspension systems, wheel–rail coefficient of friction and wheel–rail profiles. Dynamic reliability problems of vehicle–track coupled systems under the influence of the above random parameters are studied in this article. An efficient numerical method is presented by combining a prediction-based iterative solution technique with subset simulation method. The solution efficiency of deterministic responses is improved by means of efficient prediction of wheel–rail forces, and the number of deterministic solutions required is reduced by expressing a small failure probability as a product of large conditional probabilities. The accuracy and the efficiency of the present method are verified by comparing with the direct Monte Carlo simulation. The failure probability distribution curves of the lateral ride index on straight track and the derailment coefficient during curve negotiation are obtained and the reliability sensitivity analyses are also carried out. The main conclusions are given as follows: the reliability of the system is higher when the randomness of the parameters with greater sensitivity is not considered; the increase of the damping of anti-yaw damper or the wheel–rail coefficient of friction will improve the ride quality on straight track, but will lower the running safety when negotiating a curved track.

차륜-레일 상호작용력을 고려한 고속철도의 레일연마효과 분석에 관한 연구

본 연구에서는 고속철도 운영선에서 레일연마에 따른 레일표면요철의 변화수준을 계측하고 레일연마횟수에 따른 연마효과 및 연마품질의 수준을 국제규정과 비교하여 적정연마횟수를 검토하였다. 또한 레일표면요철이 동적 차륜/레일 상호작용력에 미치는 영향을 차륜-레일의 동역학 모델을 이용하여 검토하고 이를 선행 연구결과와 비교분석하였다. 본 연구결과를 이용하여 차륜/레일 상호작용력의 발생수준에 근거한 적정 레일연마방안(레일표면요철관리방안)을 도출하였다.

Study on effect of wheel polygonal wear on high-speed vehicle-track-subgrade vertical interactions

Wheel polygonal wear, as a form of wheel surface damage, is of great concern and potential threat to the deterioration and safety of railway systems. The experimentally measured polygonal wear can be treated as a superimposed wave with different harmonic orders, phases and wave depths, accordingly various frequency components are included. Most of the previous research is focused on vehicle-track vibrations caused by wheel polygon, while its influence on subgrade performance is rarely referred. With this consideration, a vertical model for vehicle-track-subgrade dynamic interactions is established by the Green function method with high accurateness and efficiency. In the numerical analysis, three types of excitations are considered, i.e., the measured polygon, the harmonic polygon and the track random irregularity. Numerical results show that the short wavelength excitation originated from the measured wheel polygon induce high-frequency wheel-rail interactions, which intensify the wheel and rail vibrations and have additional effects on the vibration modes of the displacement and stress curves of the subgrade surface; with the increased polygon order and wave depth, the wheel-rail vertical forces, wheel unloading rates, fastener forces and rail accelerations are significantly exacerbated; the vertical displacement and stress of the subgrade system are mainly affected by the lower orders of wheel polygon.

Analysing the correlation between vehicle responses and track irregularities using dynamic simulations and measurements

Track irregularities play a key role in vehicle response, but it is not uncommon to find irregularities with similar statistical characteristics giving very different vehicle behaviour. It is therefore important to find a consistent way of describing track irregularities, which better matches the vehicle behaviour to facilitate an efficient track maintenance and vehicle acceptance testing. Various proposals have been made to resolve this issue, although with limited success. In the present paper, a methodology to break down the track–vehicle interaction into steps, by analysing the irregularity–response correlation in detail, is applied to both the measured and simulated data of a passenger coach. The results show a very good agreement and a high correlation coefficient between the vertical axle box acceleration and the second spatial derivative of the vertical track irregularities when analysing the simulated data, but not for the measured data. Parameter variations are carried out through simulations, in which the vertical track stiffness, vehicle unsprung mass, vertical primary suspension and different combinations of track irregularities are varied. The results show that track stiffness mainly affects the axle box acceleration whereas the primary vertical suspension stiffness and unsprung mass predominantly affect the vertical wheel–rail forces. Therefore, it is important to understand the influence of track stiffness, especially with the help of the measured data, and the methods that reduce its influence should be investigated in future works.

A study of formation of high order wheel polygonalization

High frequency and high magnitude wheel-rail impact forces caused by high order wheel polygonalization have been associated with service failures of different structural components in high-speed rail vehicles. In this study, a long-term wear iterative scheme was developed to identify primary contributors of high order wheel polygonalization and its propagation over the service period. The wear model was formulated by integrating an Archard wear model to a coupled vehicle/track dynamic model of a high-speed railway car. The effects of different vehicle and track parameters such as the flexibilities of wheelset and rail, vehicle speed, wheelbase, and rail pad stiffness and damping on the wheel wear were further investigated. The bending vibration mode of the rail segment between two wheelsets, regarded as three half wavelength bending vibration mode near 650 Hz, was identified as the primary contributor to high magnitude wheel/rail contact force in the 500–800 Hz frequency range. This represented a nearly fixed-frequency loading condition. Variations in the vehicle speed and the track could help distribute wheel circumferential irregularities over a broader range of wavelength and thereby mitigate the growth rate of wheel polygonalization of a single order. It is further shown that the wheelset flexibility and higher rail pad stiffness accelerate the wheel wear and more likely contribute to the lower order wheel polygonalization. Increasing the rail pad damping could effectively reduce the rate of growth of high order wheel polygonalization.

Study on Vertical Dynamic Characteristics of Composite Sleeper Ballasted Track in Tunnels

In order to study the vertical dynamic characteristics of the composite sleeper ballasted track in tunnels, this paper establishes a dynamic model based on the finite element method, and compares the dynamic response of vehicle, wheel and rail systems, track systems and backfill layer with the type-III concrete sleeper. The research results show that the composite sleeper ballasted tracks’ acceleration of the car body and the wheel-rail force are smaller than that of the type-III sleeper. It can meet the safety of the train and passenger comfort. Because the composite sleeper has good elasticity, The rail displacement and acceleration, the sleeper displacement and acceleration of the composite sleeper are slightly larger than the type-III sleeper ballasted track, but the effect is not great. The composite sleeper has good elasticity and large damping, so that the acceleration of the track bed and the backfill layer is less than that of the type-III sleeper ballasted track. This shows that the composite sleeper has vibration damping characteristics for the track bed and the backfill layer.

A Numerical Analysis of Ground Vibration Induced by Typical Rail Corrugation of Underground Subway

A two‐step approach is used to establish a numerical prediction model to study the impact of typical rail corrugation on ground vibration from an underground subway. In the first step, a vehicle‐track‐tunnel rigid‐flexible coupling subsystem is established based on a lumped mass model dynamics and finite element analysis cosimulation method to simulate the generation of vibration. In the second step, a track‐tunnel‐soil three‐dimensional (3D) finite element subsystem is built to simulate the propagation of the vibration. The ground vibration response is obtained by applying the wheel‐rail force calculated from the first step. A section of Chengdu Metro Line 3 is studied, and the accuracy of the numerical prediction model is then verified by comparison with in‐situ measurement. Based on that, the impact of corrugation on wheel‐rail interaction and ground vibration is investigated by taking rail corrugation in typical subway sections and track geometry irregularities as system input excitation. In addition, to further analyze the sensitivity between different wavelength components in the rail corrugation samples and ground vibration, the measured rail corrugation is decomposed into five kinds with different wavelength components by filtering. The results show that the typical rail corrugation has a large impact on ground vibration response, which increases significantly in the range 8–16 Hz and 50–80 Hz, and the impact decreases with the distance from the vibration source. For typical subway rail corrugation with the significant wavelength of 125 mm and the secondary significant wavelength of 63 mm, the ground vibration response is sensitive to two wavelength components at 40–60 mm and 60–100 mm. Rail corrugation with the short wavelength of 60–100 mm significantly affects ground vibration levels.

Analysis of Vibration Reduction Effect of the Floating Slab Track with Different Base Forms in a Small Radius Curve of Subway Lines

This paper compares the vibration characteristics of the floating slab track with different base forms and proposes a method to comparatively improve the vibration reduction effect of the “integrated assembly” construction method. Firstly, the wheel-rail force of the train passing through the small radius curve section is obtained by the dynamic simulation, and steel spring floating slabs with the flat and inclined base, tunnel models with different superelevation are established by the finite element method. Next the fundamental frequencies of slab tracks are analysed and the reaction forces of the bottom of the steel spring and the 1/3 octave vibration level of tunnel wall nodes are calculated. The results show the vibration levels of nodes of the tunnel with inclined base is larger when the train speed and the superelevation are the same, which is due to the vertical forces being applied to the different base forms of the tunnel have different vibration effects, and the larger the superelevation is, the greater the difference becomes. In view of this, we could redistribute the superelevation between the floating slab track and tunnel base instead of being completely provided by the floating slab track or tunnel base as before.

Effect of CA mortar disengagement on Dynamic characteristics of Slab Ballastless Track on Subgrade

According to the improved model of the vehicle-ballastless slab track-subgrade coupling system, the effects of cement asphalt mortar (CA) disengagement on dynamic characteristics of vehicle and track are analysed. The results show that when the CA mortar longitudinal disengagement length exceeds 0.65m and the horizontal disengagement degree exceeds 0.5, the maximum and minimum of wheel-rail force, the maximum of the displacement of track system change obviously with the increase of CA mortar disengagement length. The effect of CA mortar disengagement on track system is larger than the vehicle system. The CA mortar disengagement should be repaired timely.

Wheel flat effect on wheel-rail dynamic interaction

In the present paper is investigated the influence of wheel flat on wheel-rail dynamic interaction, considering various parameters of the vehicle, track and wheel defect. The analysis shows that wheel-rail dynamic forces have very large magnitudes, even for low speeds. Over a certain speed, the maximum wheel-rail force is increasing with the vehicle speed. In the lower speed domain, it was noticed a maximum, depending on the flat length, corresponding to the natural frequency of the system. It is found that wheel-rail interaction maximum forces are higher for flats with larger ratio a/L. The maximum dynamic forces are also influenced by the track parameters especially by track stiffness while among the vehicle parameters only the wheelset mass have a perceivable influence.

Safety analysis of high speed trains under cross winds using indirect wheel-rail force measuring method

For several years the China railway has been investigating the safety risk of passenger cars subjected to cross winds in the LX railway lines. In this paper, an indirect method for wheel-rail force measurement is proposed. By analyzing the forces exerted on the wheelset, the wheel axle lateral force and wheel-rail vertical forces can be derived from the suspension forces and inertia forces. Since it is difficult to separate the wheel-rail lateral forces at two sides of the wheelset, the union safety domain based on the wheelset derailment coefficient and wheel unloading ratio is applied to assess the running safety of the train. The field test of a high speed train travelling in the wind area of the LX high speed railway line was carried out. The identified wheel-rail forces based on the indirect method were compared with that of the instrumented wheelset. The measured wheel-rail forces are analysed to evaluate the running safety of train under cross winds. The derailment evaluation based on union safety domain is compared with the traditional criterion. This indirect method is finally applied to the long-term safety monitoring of high speed trains in operations.

Measuring the wheel-rail forces of a roller coaster

Abstract. During a roller coaster ride, the vehicles and their passengers are exposed to multiple times the acceleration of earth's gravity. The corresponding forces must be transmitted by the wheels to the track and the support structure. To validate the load assumptions of static and fatigue analysis, it is necessary to measure these forces. Currently, it is deemed sufficient to measure only the accelerations, providing a limited view of the whole. This article presents a method to measure the actual forces and moments that act on a wheel. Since the diameters of roller coaster wheels are comparatively small (approx. 200 mm) and the loads high (approx. 30 kN), industrially available multi-axis transducers cannot be used. Therefore, a transducer design based on strain gauges was developed and successfully implemented in a roller coaster vehicle. Due to its scalability, its application is not limited to just roller coaster wheels: it can be used for all types of non-driven wheels as well.

Train running safety on non-ballasted bridges

ABSTRACTThe train running safety on non-ballasted bridges is studied based on safety indices from the vertical wheel–rail forces. A 2D train–track–bridge interaction model that allows for wheel–rail contact loss is adopted for a comprehensive parametric study on high-speed passenger trains. The relation between bridge response and vehicle response is studied for more than 200 theoretical bridges in 1–3 spans. The bridge’s influence on running safety and passenger comfort is differentiated from the influence of the track irregularities. The Eurocode bridge deck acceleration limit for non-ballasted bridges is 5 m/s2 based on the assumed derailment risk at 1 g from wheel–rail contact loss. This study shows that the running safety indices are not compromised for bridge accelerations up to 30 m/s2. Thus, accelerations at 1 g do not in itself lead to contact loss and there is potential to enhance the Eurocode safety limits for non-ballasted bridges.

A Novel Analytical Method to Calculate Wheel-Rail Tangential Forces and Validation on a Scaled Roller-Rig

The study of railway dynamic strongly depends on the estimation of the tangential forces acting between wheel and rail. Simulation of the dynamical behaviour of railway vehicles is often performed using multibody codes, and the calculation of the contact forces must be efficient and accurate, even if the contact problem is strongly nonlinear. Therefore, the contact problem is still of great interest for researchers. This work proposes an analytical and efficient algorithm to calculate wheel-rail tangential forces. The proposed method is compared with the most commonly used algorithms under different conditions. In addition, experimental tests are performed on a scaled prototype on roller-rig to demonstrate that the method can be easily adjusted using experimental results. The benefit of the proposed method is to provide an analytical and fast solution, able to obtain accurate results and to allow corrections based on empirical evidence.

Dynamic analysis of coupled train–track–bridge system subjected to debris flow impact

With the increasing popularity of high-speed railway, more and more bridges are being constructed in Western China where debris flows are very common. A debris flow with moderate intensity may endanger a high-speed train traveling on a bridge, since its direct impact leads to adverse dynamic responses of the bridge and the track structure. In order to address this issue, a dynamic analysis model is established for studying vibrations of coupled train–track–bridge system subjected to debris flow impact, in which a model of debris flow impact load in time domain is proposed and applied on bridge piers as external excitation. In addition, a six-span simply supported box girder bridge is considered as a case study. The dynamic responses of the bridge and the running safety indices such as derailment factor, offload factor, and lateral wheel–rail force of the train are investigated. Some influencing factors are then discussed based on parametric studies. The results show that both bridge responses and running safety indices are greatly amplified due to debris flow impact loads as compared with that without debris flow impact. With respect to the debris flow impact load, the boulder collision has a more negative impact on the dynamic responses of the bridge and train than the dynamic slurry pressure. Both the debris flow impact intensity and train speed determine the running safety indices, and the debris flow occurrence time should be also carefully considered to investigate the worst scenario.