Simulation of dynamic interaction between train and railway turnout

Dynamic train–track interaction is more complex in railway turnouts (switches and crossings) than that in ordinary tangent or curved tracks. Multiple contacts between wheel and rail are common, and severe impact loads with broad frequency contents are induced, when nominal wheel–rail contact conditions are disturbed because of the continuous variation in rail profiles and the discontinuities in the crossing panel. The absence of transition curves at the entry and exit of the turnout, and the cant deficiency, leads to large wheel–rail contact forces and passenger discomfort when the train is switching into the turnout track. Two alternative multibody system (MBS) models of dynamic interaction between train and a standard turnout design are developed. The first model is derived using a commercial MBS software. The second model is based on a multibody dynamics formulation, which may account for the structural flexibility of train and track components (based on finite element models and coordinate reduction methods). The variation in rail profile is accounted for by sampling the cross-section of each rail at several positions along the turnout. Contact between the back of the wheel flange and the check rail, when the wheelset is steered through the crossing, is considered. Good agreement in results from the two models is observed when the track model is taken as rigid.     

A method to determine the two-point contact zone and transfer of wheel–rail forces in a turnout

A practical method to determine the zone of two contact points and the transfer of wheel–rail forces between two rails in a turnout is presented in this paper. The method is based on a wheel–rail elastic penetration assumption and used to study a turnout system for a 200 km/h high-speed railway in China. Rail profiles in a number of key sections in the turnout are identified first, and profiles in other sections are then obtained by interpolation between key sections. The track is modelled as flexible with rails and sleepers represented by beams and the interaction between the vehicle and turnout is simulated for cases of the vehicle passing the turnout. Results are mainly presented for two-point contact positions and the characteristics of the wheel–rail forces transference. It is found that the heights of the switch and crossing rail top have significant effects on the wheel–rail contact forces. Finally, the optimised top height for the crossing rails is proposed to reduce the system dynamic force in the turnout system.     

Mathematical modelling of train–turnout interaction

The paper proposes a mathematical model of train–turnout interaction in the mid-frequency range (0–500 Hz). The model accounts for the effects of rail profile variation along the track and of local variation of track flexibility. The proposed approach is able to represent the condition of one wheel being simultaneously in contact with more than one rail, allowing the accurate prediction of the effect of wheels being transferred from one rail to another when passing over the switch toe and the crossing nose. Comprehensive results of train–turnout interaction during the negotiation of the main and the branch lines are presented, including the effect of wear of wheel/rail profiles and presence of track misalignment. In the final part of the paper, comparisons are performed between the results of numerical simulations and line measurements performed on two different turnouts for urban railway lines, showing a good agreement between experimental and numerical results.     

Numerical investigation on effect of the relative motion of stock/switch rails on the load transfer distribution along the switch panel in high-speed railway turnout

In railway turnout, the stock rail and switch rail are separated to enable the vehicle changing among the tracks, and they are provided with different rail resilience level on the baseplate. Therefore, there will be vertical relative motion between stock/switch rails under the wheel loads, and the relative motion will affect consequentially the wheel–rail contact conditions. A method is developed to investigate the effect of the relative motion of stock/switch rails on the load transfer distribution along the switch panel in high-speed railway turnout. First, the rigid wheel–rail contact points of stock/switch rails are calculated based on the trace line method, and then the contact status is determined by the presented equations, finally, the distribution of wheel–rail contact forces of stock/switch rails is obtained based on the continuity of interface displacements and forces which using an approximate surface deformation method. Some parametric studies have been performed, such as the lateral displacement of wheel set, the vertical contact forces, the wheel profiles and the vertical stiffness of rail pad. The results of the parametric study are presented and discussed.     

Design optimisation of switch rails in railway turnouts

Inspired by a manufacturing process of switch rails for railway turnouts, a method for the optimisation of switch rail profile geometry is presented. The switch rail profile geometry is parameterised with four design variables to define a B-spline curve for the milling tool profile, and two design variables to prescribe the deviation from the nominal vertical path of the milling tool. The optimisation problem is formulated as a multi-objective minimisation problem with objective functions based on the contact pressure and the energy dissipation in the wheel–rail contact. The front of Pareto optimal solutions is determined by applying a genetic type optimisation algorithm. The switch rail profile designs are evaluated by simulations of dynamic train–turnout interaction. It is concluded that the obtained set of Pareto optimal solutions corresponds to a rather small variation in design variables where increased profile height and increased profile shoulder protuberance are preferred for both objectives. The improvement in the objectives comes at the cost of an earlier wheel transition to the switch rail and thus increased vertical loading at a thinner rail cross-section. The performance of the optimised geometry is evaluated using a set of 120 measured wheel profiles, and it is shown that the optimised geometry reduces damage also for this large load collective. It is concluded that accurate limits on switch rail loading need to be established to determine the feasible design space for switch rail geometry optimisation.     

Simulation of dynamic interaction between train and railway turnout

Dynamic train-track interaction is more complex in railway turnouts (switches and crossings) than that in ordinary tangent or curved tracks. Multiple contacts between wheel and rail are common, and severe impact loads with broad frequency contents are induced, when nominal wheel-rail contact conditions are disturbed because of the continuous variation in rail profiles and the discontinuities in the crossing panel. The absence of transition curves at the entry and exit of the turnout, and the cant deficiency, leads to large wheel-rail contact forces and passenger discomfort when the train is switching into the turnout track. Two alternative multibody system (MBS) models of dynamic interaction between train and a standard turnout design are developed. The first model is derived using a commercial MBS software. The second model is based on a multibody dynamics formulation, which may account for the structural flexibility of train and track components (based on finite element models and coordinate reduction methods). The variation in rail profile is accounted for by sampling the cross-section of each rail at several positions along the turnout. Contact between the back of the wheel flange and the check rail, when the wheelset is steered through the crossing, is considered. Good agreement in results from the two models is observed when the track model is taken as rigid.     

Sensitivity of the wheel–rail contact interactions and Dang Van Fatigue Index in the rail with respect to irregularities of the track geometry

This paper investigates the effects of the track geometry irregularities on the wheel–rail dynamic interactions and the rail fatigue initiation through the application of the Dang Van criterion, that supposes an elastic shakedown of the structure. The irregularities are modelled, using experimental data, as a stochastic field which is representative of the considered railway network. The tracks thus generated are introduced as the input of a railway dynamics software to characterise the stochastic contact patch and the parameters on which it depends: contact forces and wheelset–rail relative position. A variance-based global sensitivity analysis is performed on quantities of interest representative of the dynamic behaviour of the system, with respect to the stochastic geometry irregularities and for different curve radius classes and operating conditions. The estimation of the internal stresses and the fatigue index being more time-consuming than the dynamical simulations, the sensitivity analysis is performed through a metamodel, whose input parameters are the wheel–rail relative position and velocity. The coefficient of variation of the number of fatigue cycles, when the simulations are performed with random geometry irregularities, varies between 0.13 and 0.28. In a large radius curve, the most influent irregularity is the horizontal curvature, while, in a tight curve, the gauge becomes more important.     

重载75kg/m钢轨12号道岔曲尖轨加强设计方案研究

为提高尖轨承载能力,减小轮轨接触应力,增加尖轨薄弱段的耐磨性能,延长道岔使用寿命,对曲尖轨截面在横向荷载下的接触应力进行了研究;通过建立基本轨和曲尖轨的实体模型,应用有限元法,对曲尖轨各截面应力、曲尖轨均匀加宽后各截面应力以及曲尖轨缩短后各截面应力进行了分析。结果表明,尖轨截面应力随轨顶宽度的增加呈现非线性减小趋势,均匀加宽曲尖轨和缩短曲尖轨有利于尖轨的受力。结合对曲尖轨截面应力的研究,提出了尖轨加强的方案。     

Switch Panel wear loading – a parametric study regarding governing train operational factors

The acting forces and resulting material degradation at the running surfaces of wheels and rail are determined by vehicle, track, interface and operational characteristics. To effectively manage the experienced wear, plastic deformation and crack development at wheels and rail, the interaction between vehicle and track demands a system approach both in maintenance and in design. This requires insight into the impact of train operational parameters on rail- and wheel degradation, in particular at switches and crossings due to the complex dynamic behaviour of a railway vehicle at a turnout. A parametric study was carried out by means of vehicle-track simulations within the VAMPIRE® multibody simulation software, performing a sensitivity analysis regarding operational factors and their impact on expected switch panel wear loading. Additionally, theoretical concepts were cross-checked with operational practices by means of a case study in response to a dramatic change in lateral rail wear development at specific switches in Dutch track. Data from train operation, track maintenance and track inspection were analysed, providing further insight into the operational dependencies. From the simulations performed in this study, it was found that switch rail lateral wear loading at the diverging route of a 1:9 type turnout is significantly influenced by the level of wheel–rail friction and to a lesser extent by the direction of travel (facing or trailing). The influence of other investigated parameters, being vehicle speed, traction, gauge widening and track layout is found to be small. Findings from the case study further confirm the simulation outcome. This research clearly demonstrates the contribution flange lubrication can have in preventing abnormal lateral wear at locations where the wheel–rail interface is heavily loaded.     

Further study on the wheel–rail impact response induced by a single wheel flat: the coupling effect of strain rate and thermal stress

A comprehensive dynamic finite-element simulation method was proposed to study the wheel–rail impact response induced by a single wheel flat based on a 3-D rolling contact model, where the influences of the structural inertia, strain rate effect of wheel–rail materials and thermal stress due to the wheel–rail sliding friction were considered. Four different initial conditions (i.e. pure mechanical loading plus rate-independent, pure mechanical loading plus rate-dependent, thermo-mechanical loading plus rate-independent, and thermo-mechanical loading plus rate-dependent) were involved into explore the corresponding impact responses in term of the vertical impact force, von-Mises equivalent stress, equivalent plastic strain and shear stress. Influences of train speed, flat length and axle load on the flat-induced wheel–rail impact response were discussed, respectively. The results indicate that the maximum thermal stresses are occurred on the tread of the wheel and on the top surface of the middle rail; the strain rate hardening effect contributes to elevate the von-Mises equivalent stress and restrain the plastic deformation; and the initial thermal stress due to the sliding friction will aggravate the plastic deformation of wheel and rail. Besides, the wheel–rail impact responses (i.e. impact force, von-Mises equivalent stress, equivalent plastic strain, and XY shear stress) induced by a flat are sensitive to the train speed, flat length and axle load.     

High-speed trains subject to abrupt braking

The dynamic response of high-speed train subject to braking is investigated using the moving element method. Possible sliding of wheels over the rails is accounted for. The train is modelled as a 15-DOF system comprising of a car body, two bogies and four wheels interconnected by spring-damping units. The rail is modelled as a Euler–Bernoulli beam resting on a two-parameter elastic damped foundation. The interaction between the moving train and track-foundation is accounted for through the normal and tangential wheel–rail contact forces. The effects of braking torque, wheel–rail contact condition, initial train speed and severity of railhead roughness on the dynamic response of the high-speed train are investigated. For a given initial train speed and track irregularity, the study revealed that there is an optimal braking torque that would result in the smallest braking distance with no occurrence of wheel sliding, representing a good compromise between train instability and safety.     

Study on the derailment behaviour of a railway wheelset with solid axles in a railway turnout

ABSTRACT

Dynamic wheel–rail interaction in railway turnouts is more complicated than on ordinary track. In order to evaluate the derailment behaviour of railway wheelsets in railway turnouts, this paper presents a study of dynamic wheel–rail interaction during a wheel flange climbs on the turnout rails, by applying the elasticity positioning wheelset model. A numerical model is established based on a coupled finite element method and multi-body dynamics, and applied to study the derailment behaviour of a railway wheelset in both the facing and trailing directions in a railway turnout, as well as dynamic wheel–turnout rail interaction during the wheel flange climbing on the turnout rails. The influence of the wheel–rail attack angle and the friction coefficient on the dynamic derailment behaviour is investigated through the proposed model. The results show that the derailment safety for a wheelset passing the railway turnout in facing direction is significantly lower than that for the trailing direction and the ordinary track. The possibility of derailment for the wheelset passing the railway turnout in facing and trailing directions at positive wheel–rail attack angles will increase with an increase in the attack angles, and the possibility of derailment can be reduced by decreasing the friction coefficient.     

Parametric study of wheel transitions at railway crossings

Vehicle–track interaction at railway crossings is complex due to the discontinuity of the crossings. In this study, the effect of the local crossing geometry, the track alignment, and the wheel profiles on the wheel transition behaviour is investigated using the multi-body system software package VI-Rail. The transition behaviour is evaluated based on the location of the transition point along the crossing (and the location of impact), the contact pressure and the energy dissipation during the wheel–rail contact. A detailed parametric study of the crossing geometry has been performed, through which the most effective parameters for defining the crossing geometry are identified. These parameters are the cross-sectional shape of the nose rail, which can be tuned by one variable, and the vertical distance between the top of the wing rail and the nose rail. Additionally, a parametric study on the interaction influence of the crossing geometry, the track alignment and the wheel profile is performed using the design of experiments method with a two-level full factorial design. The longitudinal height profile of the crossing and the wheel profile are the most significant factors.     

Dynamic vehicle–track interaction in switches and crossings and the influence of rail pad stiffness – field measurements and validation of a simulation model

A model for simulation of dynamic interaction between a railway vehicle and a turnout (switch and crossing, S&C) is validated versus field measurements. In particular, the implementation and accuracy of viscously damped track models with different complexities are assessed. The validation data come from full-scale field measurements of dynamic track stiffness and wheel–rail contact forces in a demonstrator turnout that was installed as part of the INNOTRACK project with funding from the European Union Sixth Framework Programme. Vertical track stiffness at nominal wheel loads, in the frequency range up to 20?Hz, was measured using a rolling stiffness measurement vehicle (RSMV). Vertical and lateral wheel–rail contact forces were measured by an instrumented wheel set mounted in a freight car featuring Y25 bogies. The measurements were performed for traffic in both the through and diverging routes, and in the facing and trailing moves. The full set of test runs was repeated with different types of rail pad to investigate the influence of rail pad stiffness on track stiffness and contact forces. It is concluded that impact loads on the crossing can be reduced by using more resilient rail pads. To allow for vehicle dynamics simulations at low computational cost, the track models are discretised space-variant mass–spring–damper models that are moving with each wheel set of the vehicle model. Acceptable agreement between simulated and measured vertical contact forces at the crossing can be obtained when the standard GENSYS track model is extended with one ballast/subgrade mass under each rail. This model can be tuned to capture the large phase delay in dynamic track stiffness at low frequencies, as measured by the RSMV, while remaining sufficiently resilient at higher frequencies.     

Extended applications of track irregularity probabilistic model and vehicle–slab track coupled model on dynamics of railway systems

Track irregularities are inevitably in a process of stochastic evolution due to the uncertainty and continuity of wheel–rail interactions. For depicting the dynamic behaviours of vehicle–track coupling system caused by track random irregularities thoroughly, it is a necessity to develop a track irregularity probabilistic model to simulate rail surface irregularities with ergodic properties on amplitudes, wavelengths and probabilities, and to build a three-dimensional vehicle–track coupled model by properly considering the wheel–rail nonlinear contact mechanisms. In the present study, the vehicle–track coupled model is programmed by combining finite element method with wheel–rail coupling model firstly. Then, in light of the capability of power spectral density (PSD) in characterising amplitudes and wavelengths of stationary random signals, a track irregularity probabilistic model is presented to reveal and simulate the whole characteristics of track irregularity PSD. Finally, extended applications from three aspects, that is, extreme analysis, reliability analysis and response relationships between dynamic indices, are conducted to the evaluation and application of the proposed models.     

The role of the contact geometry in wheel–rail impact due to wheel flats: Part II

A classification of wheel flats according to the different stages of their growth is given, along with the characteristic features of the dynamic wheel–rail interaction for each category. Mathematical expressions and frequency spectra of the corresponding wheel mass trajectories are derived. Difference is made between the subcritical and the transcritical speed regime. A criterion is derived for contact loss for worn flats. Simulations show that the dynamic wheel–rail interaction is governed by the track stiffness for low train speeds or long flat lengths; for high speeds and/or short flat lengths the interaction is governed by the inertial properties of the wheel and the rail. For a given flat geometry, nonlinearities in the relationship between the impact magnitude and the train speed occur in the stiffness-dominated speed domain, whereas this relationship is approximately linear in the inertia-governed domain. In the latter domain, the impact magnitude is found to be linearly dependent upon the maximum trajectorial curvature or inversely linearly dependent on the minimum circumferential wheel tread curvature. The above relationships are valid for the subcritical speed regime, in which no contact loss occurs. Different contributions from the literature are compared with respect to the established relationship between impact magnitude and speed. Significant differences are found, due to insufficiently defined parameters and conditions. Conditions are derived for a consistent application of the so-called equivalent rail indentation in experiments with wheel flats, and the indirect strain registration method for measuring dynamic wheel–rail contact forces is reviewed.     

Study on lateral dynamic characteristics of vehicle/turnout system

Based on Chinese No. 12 high speed, single-way swing nose rail concrete sleeper turnout, a comprehensive vehicle/turnout system coupling dynamic model has been established in this paper, and the lateral and vertical dynamic characteristics of vehicle/turnout systems have been simulated while the car passes through the turnout zone on divergence. These dynamic characteristics show that the lateral impact and vibration of the systems caused by the wheel/rail contact and irregularity are very intensive, especially at the switch zone and nose area of the turnout, and the lateral dynamics of the turnout system, such as lateral stability, vibrating responses, impacting and the allowable passing velocity force between the wheelsets and the switch rails are much more complicated than that of the vertical ones.     

Study on lateral dynamic characteristics of vehicle/turnout system

Based on Chinese No. 12 high speed, single-way swing nose rail concrete sleeper turnout, a comprehensive vehicle/turnout system coupling dynamic model has been established in this paper, and the lateral and vertical dynamic characteristics of vehicle/turnout systems have been simulated while the car passes through the turnout zone on divergence. These dynamic characteristics show that the lateral impact and vibration of the systems caused by the wheel/rail contact and irregularity are very intensive, especially at the switch zone and nose area of the turnout, and the lateral dynamics of the turnout system, such as lateral stability, vibrating responses, impacting and the allowable passing velocity force between the wheelsets and the switch rails are much more complicated than that of the vertical ones.     

A third-order approximation method for three-dimensional wheel–rail contact

Multibody train analysis is used increasingly by railway operators whenever a reliable and time-efficient method to evaluate the contact between wheel and rail is needed; particularly, the wheel–rail contact is one of the most important aspects that affects a reliable and time-efficient vehicle dynamics computation. The focus of the approach proposed here is to carry out such tasks by means of online wheel–rail elastic contact detection. In order to improve efficiency and save time, a main analytical approach is used for the definition of wheel and rail surfaces as well as for contact detection, then a final numerical evaluation is used to locate contact. The final numerical procedure consists in finding the zeros of a nonlinear function in a single variable. The overall method is based on the approximation of the wheel surface, which does not influence the contact location significantly, as shown in the paper.