Nonlinear Wheel Rail Research Articles

A model for vehicle–track random interactions on effects of crosswinds and track irregularities

ABSTRACTA stochastic mathematical model is developed to evaluate the dynamic behaviours and statistical responses of vehicle–track systems when random system excitations including crosswinds and track irregularities are imposed. In this model, the railway vehicle is regarded as a multi-rigid-body system, the track system is modelled by finite element theory. These two systems are spatially coupled by the nonlinear wheel–rail contact forces and unsteady aerodynamic forces. The high efficiency and accuracy of this stochastic model are validated by comparing to the robust Monte-Carlo method. Numerical studies show that crosswinds have a great influence on the dynamic performance of vehicle–track systems, especially on transverse vibrations. When the railway vehicle initially runs into the wind field, it will experience a severe vibration stage, and then stepping into a relatively steady state where the fluctuating winds and track irregularities will play deterministic roles in the deviations of system responses. Moreover, it is found that track irregularities should be properly considered in the safety assessment of the vehicle even in strong crosswinds.

Probabilistic assessment of railway vehicle-curved track systems considering track random irregularities

ABSTRACTThe randomness of track irregularities directly leads to the random vibration of the vehicle–track systems. To assess the dynamic performance of a railway system in more comprehensive and practical ways, a framework for probabilistic assessment of vehicle-curved track systems is developed by effectively integrating a vehicle–track coupled model (VTCM), a track irregularity probabilistic model (TIPM) with a probability density evolution method (PDEM). In VTCM, the railway vehicle and the curved track are coupled by the nonlinear wheel–rail interaction forces, and through TIPM, the ergodic properties of random track irregularities on amplitudes, wavelengths and probabilities can be properly considered in the dynamic calculations. Lastly, PDEM, a newly developed method for solving probabilistic transmissions between stochastic excitations and deterministic dynamic responses, is introduced to this probabilistic assessment model. Numerical examples validate the correctness and practicability of the proposed models. In this paper, the results of probabilistic assessment are presented to illustrate the dynamic behaviours of a high-speed railway vehicle subject to curved tracks with various radii, and to demonstrate the importance of considering the actual status of wheel–rail contacts and curve negotiation effects in vehicle-curved track interactions.

Global Sensitivity Analysis for Vehicle–Track Interactions: Special Attention on Track Irregularities

The dynamic vehicle–track interactions are complex processes due to the highly nonlinear terms and spatially varying excitations in vehicle design, track maintenance, dynamic prediction, etc. Therefore, it is of importance to clarify the key factors affecting the dynamic behaviors of system components. In this paper, a comprehensive model is presented, which is capable of analyzing the global sensitivity of vehicle–track interactions. In this model, the vehicle–track interactions considering the nonlinear wheel–rail contact geometries are depicted in three-dimensional (3D) space, and then the approaches for global sensitivity analysis (GSA) and time–frequency analysis are combined with the dynamic model. In comparison to the local sensitivity analysis, the proposed model has accounted for the coupling contributions of various factors. Thus, it is far more accurate and reliable to evaluate the critical factors dominating the vehicle–track interactions. Based on the methods developed in the present study, numerical examples have been conducted to draw the following marks: track irregularities possess the dominant role in guiding the dynamic performance of vehicle–track systems, besides, the vertical stiffness of primary suspension and rail pads also shows significant influence on vertical acceleration of the car body and the wheel–rail vertical force, respectively. Finally, a method is developed to precisely extract the characteristic wavelengths and amplitude limits of track irregularities.

Locomotive dynamic performance under traction/braking conditions considering effect of gear transmissions

ABSTRACTTraction or braking operations are usually applied to trains or locomotives for acceleration, speed adjustment, and stopping. During these operations, gear transmission equipment plays a very significant role in the delivery of traction or electrical braking power. Failures of the gear transmissions are likely to cause power loses and even threaten the operation safety of the train. Its dynamic performance is closely related to the normal operation and service safety of the entire train, especially under some emergency braking conditions. In this paper, a locomotive–track coupled vertical–longitudinal dynamics model is employed with considering the dynamic action from the gear transmissions. This dynamics model enables the detailed analysis and more practical simulation on the characteristics of power transmission path, namely motor–gear transmission–wheelset–longitudinal motion of locomotive, especially for traction or braking conditions. Multi-excitation sources, such as time-varying mesh stiffness and nonlinear wheel–rail contact excitations, are considered in this study. This dynamics model is then validated by comparing the simulated results with the experimental test results under braking conditions. The calculated results indicate that involvement of gear transmission could reveal the load reduction of the wheelset due to transmitted forces. Vibrations of the wheelset and the motor are dominated by variation of the gear dynamic mesh forces in the low speed range and by rail geometric irregularity in the higher speed range. Rail vertical geometric irregularity could also cause wheelset longitudinal vibrations, and do modulations to the gear dynamic mesh forces. Besides, the hauling weight has little effect on the locomotive vibrations and the dynamic mesh forces of the gear transmissions for both traction and braking conditions under the same running speed.

On the overriding issue of train front end collision in rail vehicle dynamics

ABSTRACTA three-dimensional dynamic model of crashed vehicles coupled with moving tracks is developed to research the dynamic behaviour of the train front end collision on tangent tracks. The three-dimensional dynamic model consists of a crashed vehicle model, moving track models, a simple wheel–rail contact model, a velocity-based coupler model and the model of energy absorption and anti-climbing devices. The vector method dealing with the nonlinear wheel–rail geometry is put forward in the paper. The developed model is applicable in the scope that central collisions occur on tangent tracks at low speeds. The examples of the vehicle impacting with a rigid wall and the train front end collision are carried out to obtain the dynamic responses of vehicles. The overriding issue is studied on the basis of the wheel rise in train collisions. The results show that the second bogie of the first colliding vehicle possesses the maximal wheel rise. The wheel rise increases with the increase of vehicles. However, the number of vehicles has tiny influence on the overriding in train collisions at low speeds. On the contrary, the impact speed has significant influence on the overriding in train collisions. The wheel rise increases rapidly if the impact speed is close to the critical speed of overriding. The large wheel rise is principally generated by the great coupler force related to the rigid impact in the axial direction.

An iterative method for solving the dynamic response of railway vehicle-track coupled systems based on prediction of wheel-rail forces

An iterative method based on prediction of wheel-rail forces is presented to determine the dynamic response of railway vehicle-track coupled systems. The key idea of the present method lies in the modification of the starting value of each step during the iteration by prediction. The conventional iterative method begins iteration of the current step at the previously converged value of the wheel-rail forces. However, in the present method, the predicted wheel-rail forces by the Weighted Least-Squares Error (WLSE) predictor are used as the starting value for the current step. The equations of motion of the vehicle and the track subsystems are established separately and solved iteratively. According to the response of the wheelsets and the rails, and considering the track irregularity, the predicted wheel-rail forces are corrected by the wheel-rail interaction model in which detailed wheel rail contact geometry relations and nonlinear wheel rail creep forces are taken into account. The relaxation technique is adopted to solve the problem of numerical diffusion in the iterative process.A moving vehicle travelling on a two layer flexible track is considered in this study. The accuracy of the proposed method is verified by comparing the results obtained from the present method with the results from the commercial software NUCARS and the efficiency are verified by comparing with the conventional iterative method. Numerical results show that the present method not only gives results comparable to those using the NUCARS software in terms of accuracy, but also saves at least 25% computational cost compared with the conventional iterative method. With the nonlinear wheel-rail contact relation fully considered, the present method can get more detailed results of the vehicle-track coupled model. Meanwhile, the efficiency of the present method is enhanced by means of prediction of wheel-rail forces with the WLSE predictor.

Dynamic investigation of a locomotive with effect of gear transmissions under tractive conditions

Locomotive is used to drag trailers to move or supply the braking forces to slow the running speed of a train. The electromagnetic torque of the motor is always transmitted by the gear transmission system to the wheelset for generation of the tractive or braking forces at the wheel–rail contact interface. Consequently, gear transmission system is significant for power delivery of a locomotive. This paper develops a comprehensive locomotive–track vertical-longitudinal coupled dynamics model with dynamic effect of gear transmissions. This dynamics model enables considering the coupling interactions between the gear transmission motion, the vertical and the longitudinal motions of the vehicle, and the vertical vibration of the track structure. In this study, some complicated dynamic excitations, such as the gear time-varying mesh stiffness, nonlinear gear tooth backlash, the nonlinear wheel–rail normal contact force and creep force, and the rail vertical geometrical irregularity, are considered. Then, the dynamic responses of the locomotive under the tractive conditions are demonstrated by numerical simulations based on the established dynamics model and by experimental test. The developed dynamics model is validated by the good agreement between the experimental and the theoretical results. The calculated results reveal that the gear transmission system has strong dynamic interactions with the wheel–rail contact interface including both the vertical and the longitudinal motions, and it has negligible effect on the vibrations of the bogie frame and carbody.

Effect of vertical ground motion on earthquake-induced derailment of railway vehicles over simply-supported bridges

The running safety of railway vehicles on bridges can be negatively affected by earthquake events. This phenomenon has traditionally been investigated with only the lateral ground excitation component considered. This paper presented results from a numerical investigation on the contribution of vertical ground motion component to the derailment of vehicles on simply-supported bridges. A full nonlinear wheel–rail contact model was used in the investigation together with the Hertzian contact theory and nonlinear creepage theory, which allows the wheel to jump vertically and separate from the rail. The wheel–rail relative displacement was used as the criterion for derailment events. A total of 18 ground motion records were used in the analysis to account for the uncertainty of ground motions. The results showed that inclusion of vertical ground motion will likely increase the chance of derailment. It is recommended to include vertical ground motion component in earthquake induced derailment analysis to ensure conservative estimations. The derailment event on bridges was found to be more closely related to the deck acceleration rather than the ground acceleration.

On the investigation of wheel flange climb derailment mechanism and methods to control it

In this research, investigations are focused on the study of railway vehicle wheel flange climb derailment. A three dimensional nonlinear dynamic model of the wheel-set and suspension system is developed. Having validated the model through field tests, the effect of friction coefficient, wheel-set AOA, vehicle suspension system and running speed on the wheel flange climb derailment are investigated. In addition, different rail lubrication methods are studied and their effects on the wheel flange climb derailment are compared in the case of two point contact for nonlinear wheel-rail profiles. The results are debated and recommendations proposed to improve running safety against derailment.

Fault Detection and Isolation for a Railway Vehicle by Evaluating Estimation Residuals

The capacity of transport as well as the number of passengers is growing in the railway industry. At the same time, the pressure to reduce service costs rises. Reliability and dependability in complex mechanical systems can be improved by fault detection and isolation methods (FDI). These techniques are key elements for maintenance on demand, which could decrease service cost and time significantly. This work addresses FDI for a railway vehicle: The mechanical model is described as a multibody system, which is excited randomly due to track irregularities. The aim of this work is to detect faults in the suspension system of the vehicle. A Kalman filter is used to estimate the states. In order to detect and isolate faults, the detection error is minimized with multiple Kalman filters. A full scale train model with nonlinear wheel rail contact and nonlinear suspension forces serves as an example for the described techniques. Numerical results for different test cases are presented. For the analysed system it is possible not only to detect a failure of the suspension system from the system's dynamic response, but also to distinguish clearly between different possible causes for the changes in the dynamical behavior.

Numerical analysis of ship–bridge collision's influences on the running safety of moving rail train

This paper investigates the ship–bridge collision process and its influences on the running safety of the moving light rail train. Taking a long span cable-stayed bridge across the Huangpu River as example, the 3-D dynamic model of train-bridge coupled system subjected to ship impact was studied with the aid of the finite element analysis (FEA) code LS-DYNA 971. The bridge model and the coupled rigid–flexible multi-body train model were coupled through non-linear wheel–rail interface, and the coupled dynamic model was solved using mixed time explicit integration approach. By studying the effects of train speed and the momentum of impacting ship on the running safety of the rail train, the relationship between the maximum safety speed of the train and the momentum of the impacting ship is predicted, that is, the maximum allowable train speed decreases with the increase of the momentum of the impacting ship. The mixed time integration method could speed up the calculation process for crashworthiness analysis with great differences in element sizes at different parts of model.

Consideration of nonlinear wheel–rail contact forces for dynamic vehicle–bridge interaction in high-speed railways

In this work models with nonlinear wheel–rail contact forces are considered for analysing the dynamic interaction between high speed trains and bridges, in order to study dynamic effects both in the bridge and in the vehicles resulting from the coupling. Nonlinear contact models may be necessary for evaluating the stability and the safety of running traffic in situations such as vehicle overturn when the train is crossing a bridge under strong lateral winds or when an earthquake occurs. For studying the coupled dynamic response of trains and bridges, models of multibody dynamics are used for vehicles and the finite element method for structures. Special relevance is given here to the consideration of contact interaction forces between railway vehicles and the track. Four different interaction models are compared in this work: (1) a model where the vehicle wheelset is considered to be rigidly coupled to the track; (2) a staggered uncoupled method in which vehicle and structure are analysed separately; (3) a linear contact model in which lateral relative displacements between rails and train wheels are allowed, assuming biconic wheel and rail profiles and linear Kalker theory for tangential contact; (4) a nonlinear model in which realistic wheel and rail profiles, Hertz's nonlinear theory for normal contact and Kalker's nonlinear theory for tangential contact are used. The different models are applied and compared to experimental measurements for a test case of a high-speed train in China.

Symmetric/asymmetric bifurcation behaviours of a bogie system

Based on the bifurcation and stability theory of dynamical systems, the symmetric/asymmetric bifurcation behaviours and chaotic motions of a railway bogie system under a complex nonlinear wheel–rail contact relation are investigated in detail by the ‘resultant bifurcation diagram’ method with slowly increasing and decreasing speed. It is found that the stationary equilibrium solution and the periodic motions coexist due to the sub-critical Hopf bifurcation in the railway bogie system. It is also found that multiple solutions coexist in many speed ranges. The coexistence of multiple solutions may result in a jump and hysteresis of the oscillating amplitude for different kinds of disturbances. It should be avoided in the normal operation. Furthermore, it is found that symmetry-breaking of the system through a pitchfork bifurcation leads to asymmetric chaotic motions in the railway bogie system. The speed ranges of asymmetric chaotic motions are, however, small.

A precise integration method for solving coupled vehicle–track dynamics with nonlinear wheel–rail contact

A new method is proposed as a solution for the large-scale coupled vehicle–track dynamic model with nonlinear wheel–rail contact. The vehicle is simplified as a multi-rigid-body model, and the track is treated as a three-layer beam model. In the track model, the rail is assumed to be an Euler-Bernoulli beam supported by discrete sleepers. The vehicle model and the track model are coupled using Hertzian nonlinear contact theory, and the contact forces of the vehicle subsystem and the track subsystem are approximated by the Lagrange interpolation polynomial. The response of the large-scale coupled vehicle–track model is calculated using the precise integration method. A more efficient algorithm based on the periodic property of the track is applied to calculate the exponential matrix and certain matrices related to the solution of the track subsystem. Numerical examples demonstrate the computational accuracy and efficiency of the proposed method.

Effect on vehicle and track interaction of installation faults in the concrete bearing surface of a direct-fixation track

Various installation faults can occur in fasteners in the construction of a direct-fixation track using the top-down method. In extreme cases, these faults may cause excessive interaction between the train and track, compromise the running safety of the train, and cause damage to the track components. Therefore, these faults need to be kept within the allowable level through an investigation of their effects on the interactions between the train and track. In this study, the vertical dynamic stiffness of fasteners in installation faults was measured based on a dynamic stiffness test by means of an experimental apparatus that was devised to feasibly reproduce installation faults with an arbitrary shape. This study proposes an effective analytical model for a train–track interaction system in which most elements, except the nonlinear wheel–rail contact and some components that behave bilinearly, exhibit linear behavior. To investigate the effect of the behavior of fasteners in installation faults in a direct-fixation track on the vehicle and track, vehicle–track interaction analyses were carried out, targeting key review parameters such as the wheel load reduction factor, vertical rail displacement, wheel load, and mean stress of the elastomer. From the results, it was noted that it is more important for the installation faults in the concrete bearing surface of a direct-fixation track to be limited for the sake of the long-term durability of the elastomer rather than for the running safety of the train or the structural safety of the track.

Dynamic comparison of different types of slab track and ballasted track using a flexible track model

The dynamic performance of a ballasted track and three types of slab track is analysed and compared by means of a comprehensive dynamic model of the train–track system, generated using two commercial analysis software packages: the commercial multibody system (MBS) analysis software SIMPACK and the finite element method (FEM) analysis software NASTRAN. The use of a commercial MBS software makes it possible to include, in a reliable way, models of advanced non-linear wheel–rail contact as well as complex elements or joints in the vehicle model, while the FEM the flexibility of the rail and the slab to be taken into account. As a result, a combined MBS–FEM representation of the vehicle–track model is integrated into the MBS software, which allows for the study of dynamic phenomena in a wide frequency range. In this study, other simpler approaches for modelling the dynamic vehicle–track interaction are also considered, such as pure multibody or FE representations of the whole vehicle–track system. The quality of the results obtained with the different types of models used is analysed, and some conclusions are put forth regarding the possible validity of rather simple train–track interaction model types under certain conditions as well as the most suitable configuration of the most complex models.

An investigation of sleeper voids using a flexible track model integrated with railway multi-body dynamics

This article describes a flexible track system model (FTSM) that represents the track structure for a typical ballasted track, taking into account the flexibility of the rails, the sleeper mass and the resilience of the pad/fastening elements, as well as the ballast support stiffness condition. The detailed track model is integrated into a commercial railway vehicle dynamics software, thus allowing for any vehicle to be simulated onto the flexible track while at the same time taking into account the detailed calculation of the non-linear wheel—rail contact interaction. As an example, the application of the FTSM to the study of hanging sleepers, with respect to the UK Railway Group Standard limits, is presented. This example shows the impact of forces because of hanging sleepers on the vehicle and on the track, and attempts at quantifying the damage made to the track components for the specific conditions simulated.

The effect of dynamic rail roll on the wheel–rail contact conditions

Simulation tools are now widely used to predict the dynamic behaviour of railway vehicles and they have been developed to include highly complex vehicle models which can represent non-linear wheel–rail contact and suspension characteristics. Less emphasis has so far been placed on the track models used in these simulations which have tended to be fairly simple linear representations of the track and subgrade although these can also contain significant discrete non-linearities. This paper first reviews the track models used in current railway vehicle dynamic software and identifies their main limitations. The particular focus of the work reported here is the rail roll degree of freedom (DOF) and its influence on the wheel–rail contact condition. The rigid body track model in the software tool VI-Rail powered by MSC Adams is modified to fully take into account rail roll in combination with the non-linear on-line contact algorithm. Various static and dynamic track cases are designed to test the hypothesis that rail roll may affect the contact condition. Results show the influence of the dynamic rail roll on the location of the contact between the wheel and rail and some analysis is made into the implications this may have on wear and rolling contact fatigue calculations among other applications.

Fatigue Life Prediction of a Railway Bogie under Dynamic Loads through Simulation

SUMMARY For dynamically loaded lightweight structures fatigue strength is an important design criteria. In this paper a new method to predict fatigue lifetime is shown. This is based on the combination of frequency domain and time domain calculations, which allows lifetime prediction with reduced computational effort. The method is implemented to work in a concurrent engineering software environment together with a computer aided design (CAD), a finite-element-method (FEM) and a multibody system (MBS) program. The benefits of the new approach are demonstrated by application to the bogie of a freight locomotive. The dynamic loads acting on the bogie are computed by multibody simulation. The bogie frame is considered as an elastic body of the MBS and the highly nonlinear wheel rail contact is modeled quasi-elastically. For the ride on a straight track the equations of motion can be linearized and the covariance matrix of the loads is calculated. The ride through a ramp is simulated by using the nonlinear differential equations. FEM yields the stresses in the most stressed locations of the bogie depending on the loads calculated by multibody simulation. Based on these stresses the fatigue life prediction is carried out in the MBS post-processing program FATIGUE.

Design of a Limit Cycle Controller for the Nonlinear Wheel Rail System

Design of a Limit Cycle Controller for the Nonlinear Wheel Rail System