The vertical and the longitudinal dynamic responses of the vehicle–track system to squat-type short wavelength irregularity

The squat, a kind of rolling contact fatigue occurring on the rail top, can excite the high-frequency vehicle–track interaction effectively due to its geometric deviations with a typical wavelength of 20–40 mm, leading to the accelerated deterioration of a track. In this work, a validated 3D transient finite element model is employed to calculate in the time domain the vertical and the longitudinal dynamic contact forces between the wheel and the rail caused by squats. The vehicle–track structure and the wheel–rail continua are both considered in order to include all the important eigencharacteristics of the system related to squats. By introducing the rotational and translational movements of the wheel, the transient wheel–rail rolling contact is solved in detail by a 3D frictional contact model integrated. The contact filter effect is considered automatically in the simulations by the finite size of the contact patch. The present work focuses on the influences of the length, width and depth of a light squat on the resulted dynamic contact forces, for which idealised defect models are used. The growth of a squat is also modelled to a certain extent by a series of defects with different dimensions. The results show that the system is mainly excited at two frequencies separately in the vertical and the longitudinal dynamics. Their superposition explains the typical appearance of mature squats. As a squat grows up, the magnitude of the excited vibration at the lower frequency increases faster than the one at the higher frequency.     

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.     

A Theory of Wheelset Forces for Two Point Contact Between Wheel and Rail

This paper describes a quasistatic theory of wheelset forces for an important practical case of the wheelset rolling when one of the wheels touches the rail in two contact zones. One of these zones lies on the tread and the other on the wheel flange. For such contact the specific problem of finding the distribution of forces between the tread and flange arises. The simultaneous frictional rolling contact problems for both contact zones have been described with Kalker×apos;s non-linear theory and wheelset equilibrium equations.

The numerical results presented are for an individual wheelset on straight track, the distribution of forces being described for a wide range of loading conditions. The influence of steering on the distribution of forces has also been presented.

This theory can be easily extended for quasistatic curving of railway vehicles and may assist wear studies for vehicles with worn wheels.     

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.     

Stochastic analysis of dynamic interaction between train and railway turnout

The performance of a railway turnout (switch and crossing) is influenced by a large number of input parameters of the complex train–turnout system. To reach a robust design that performs well for different traffic situations, random distributions (scatter) of these inputs need to be accounted for in the design process. Stochastic analysis methods are integrated with a simulation model of the dynamic interaction between train and turnout. For a given nominal layout of the turnout, using design of experiments methodology and a two-level fractional factorial screening design, four parameters (axle load, wheel–rail friction coefficient, and wheel and rail profiles) are identified to be the most significant. These parameters are further investigated using a three-level full factorial design and stochastic analysis. The random distributions of transverse wheel profile and set of transverse rail profiles along the switch panel are accounted for by the Karhunen–Loève expansion technique. The influence of the random distributions of the input parameters on the statistical outputs of wheel–rail contact forces, wear and rolling contact fatigue is assessed using Latin hypercube sampling to generate a number of stochastic load realizations.     

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.     

钢板弹簧迟滞特性的有限元分析

利用ANSYS有限元软件提供的面－面接触单元，分析了钢板弹簧的迟滞特性，叶片间的正压力和摩擦力用这些接触单元的节点力来代替；给出了加载和卸载过程的载荷－变形特性图；并结合实例分析了不同摩擦系数对钢板弹簧迟滞特性和阻尼特性的影响。此外，还分析了钢板弹簧在受到不同频率和振幅的正弦激励时所产生的等效阻尼。     

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.     

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.     

Numerical analysis of the dynamic interaction between wheel set and turnout crossing using the explicit finite element method

A three-dimensional (3-D) explicit dynamic finite element (FE) model is developed to simulate the impact of the wheel on the crossing nose. The model consists of a wheel set moving over the turnout crossing. Realistic wheel, wing rail and crossing geometries have been used in the model. Using this model the dynamic responses of the system such as the contact forces between the wheel and the crossing, crossing nose displacements and accelerations, stresses in rail material as well as in sleepers and ballast can be obtained. Detailed analysis of the wheel set and crossing interaction using the local contact stress state in the rail is possible as well, which provides a good basis for prediction of the long-term behaviour of the crossing (fatigue analysis). In order to tune and validate the FE model field measurements conducted on several turnouts in the railway network in the Netherlands are used here. The parametric study including variations of the crossing nose geometries performed here demonstrates the capabilities of the developed model. The results of the validation and parametric study are presented and discussed.     

An inverse design method for rail grinding profiles

Inspired by the optimisation design method for restoration of worn wheel profiles, an inverse design method based on optimal rail grinding profiles is presented in this paper. To improve grinding quality, vehicle dynamic performance is chosen as the main criteria and rolling radii difference function is selected as the key factor (also main target function) determining dynamic performance. Grinding material to be removed is chosen as the auxiliary target aimed at extending rail service life. Besides that, wheel–rail contact distribution is also taken into consideration as an auxiliary target preventing stress concentration and fatigue growth. By introducing certain presuppositions, all the design targets will form an inverse design problem. This problem can be solved using hybrid discrete numerical methods. Considering different grinding requirements, two examples of grinding profile design for straight and curved track will be discussed. Results show that the presented method is efficient and effective. Practical implementation has been carried out at several grinding sites in China.     

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.     

Computation of wheel–rail contact force for non-mapping wheel–rail profile of Translohr tram

Translohr tram has steel wheels, in V-like arrangements, as guide wheels. These operate over the guide rails in inverted-V arrangements. However, the horizontal and vertical coordinates of the guide wheels and guide rails are not always mapped one-to-one. In this study, a simplified elastic method is proposed in order to calculate the contact points between the wheels and the rails. By transforming the coordinates, the non-mapping geometric relationship between wheel and rail is converted into a mapping relationship. Considering the Translohr tram’s multi-point contact between the guide wheel and the guide rail, the elastic-contact hypothesis take into account the existence of contact patches between the bodies, and the location of the contact points is calculated using a simplified elastic method. In order to speed up the calculation, a multi-dimensional contact table is generated, enabling the use of simulation for Translohr tram running on curvatures with different radii.     

An efficient approach to the analysis of rail surface irregularities accounting for dynamic train–track interaction and inelastic deformations

A two-dimensional computational model for assessment of rolling contact fatigue induced by discrete rail surface irregularities, especially in the context of so-called squats, is presented. Dynamic excitation in a wide frequency range is considered in computationally efficient time-domain simulations of high-frequency dynamic vehicle–track interaction accounting for transient non-Hertzian wheel–rail contact. Results from dynamic simulations are mapped onto a finite element model to resolve the cyclic, elastoplastic stress response in the rail. Ratcheting under multiple wheel passages is quantified. In addition, low cycle fatigue impact is quantified using the Jiang–Sehitoglu fatigue parameter. The functionality of the model is demonstrated by numerical examples.     

Simulation of curving at low speed under high traction for passive steering hauling locomotives

The traction control in modern electric and diesel electric locomotives has allowed rail operators to utilise high traction adhesion levels without undue risk of damage from uncontrolled wheel spin. At the same time, some locomotive manufacturers have developed passive steering locomotive bogies to reduce wheel rail wear and further improve locomotive adhesion performance on curves. High locomotive traction loads in curving are known to cause the loss of steering performance in passive steering bogies. At present there are few publications on the curving performance of locomotive steering with linkage bogies. The most extreme traction curving cases of low speed and high adhesion for hauling locomotives have not been fully investigated, with effects of coupler forces and cant excess being generally ignored. This paper presents a simulation study for three axle bogie locomotives in pusher and pulling train positions on tight curves. The simulation study uses moderate and high traction adhesion levels of 16.6% and 37% for various rail friction conditions. Curving performance is assessed, showing forced steering bogies to have considerable advantages over self steering bogies. Likewise it is shown that self steering bogies are significantly better than yaw relaxation bogies at improving steering under traction. As the required traction adhesion approaches the rail friction coefficient, steering performance of all bogies degrades and yaw of the bogie frame relative to the track increases. Operation with excess cant and tensile coupler forces are both found to be detrimental to the wear performance of all locomotive bogies, increasing the bogie frame yaw angles. Bogie frame pitching is also found to have significant effect on steering, causing increased performance differences between bogie designs.     

The Elastic Cross-Influence between Two Quasi-Hertzian Contact Zones

In this paper a type of contact between two bodies is considered, which leads to the formation of two separate contact zones. The contact zones considered are Hertzian ellipses if the distance between them is large. When the distance between the zones is finite it is necessary to take into account the elastic cross-influence of the two zones. In this paper an approximate method is proposed which allows the determination of the actual contact zones as Hertz's ellipses but without disregarding the cross-influence. Numerical results are presented for two, two-humped bodies pressed against each other and for steady state rolling of a flanged wheel along a steel rail.

It is shown that neglecting the cross influence for a flanged wheel leads to a negligible error in the contact forces but the forces are transmitted between wheel and rail through contact patches which are generally more slender than with the cross-influence neglected.     

Behaviour of the Normal Contact Force Under Multiple Wheel/Rail Interaction

The wheel/rail contact forces are calculated in the frequency domain using a track model with multiple wheels on the rail. The effects of the wave reflections between the wheels on the contact force are studied. Different pad stiffnesses are used in the calculations to investigate the influence on the contact force. It is shown that the contact force can have up to four main peaks in the frequency region 550-1200?Hz due to the wave reflections between the wheels, so that the wavelengths of short pitch corrugation can be expected to be associated with multiple frequencies. As a conclusion, it is recommended that in a model for predicting short pitch corrugation the effects of multiple wheel/rail interactions need to be included.     

Inverse identification of wheel–rail contact forces based on observation of wheel disc strains: an evaluation of three numerical algorithms

In this paper, three numerical algorithms for the identification of wheel–rail contact forces based on measured wheel disc strains on an instrumented railway wheelset are discussed and compared. The three algorithms include one approach resting on static calibration, one that is applying a Kalman filter and the third is exploiting an inverse identification scheme. To demonstrate and evaluate the alternative methods, two load cases including periodic excitation by sinusoidal wheel–rail irregularities and transient excitation by an insulated rail joint are considered. Based on a previously presented vehicle–track interaction model in the time domain, load scenarios are defined by taking the calculated vertical wheel–rail contact forces as the reference force to be re-identified by the proposed algorithms. The reference contact forces are applied on a finite element model of the wheel to generate synthetic observation data, that is, radial strains at the positions of the strain gauges, serving as input to the identification procedures. It is concluded that the inverse identification scheme leads to superior accuracy at higher computational cost. If on-line implementation and evaluation is required, the Kalman filter generates better accuracy than the static calibration approach.