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.     

Carbody elastic vibrations of high-speed vehicles caused by bogie hunting instability

In particular locations of the high-speed track, the worn wheel profile matched up with the worn rail profile will lead to an extremely high-conicity wheel–rail contact. Consequently, the bogie hunting instability arises, which further results in the so-called carbody shaking phenomenon. In this paper, the carbody elastic vibrations of a high-speed vehicle in service are firstly introduced. Modal tests are conducted to identity the elastic modes of the carbody. The ride comfort and running safety indices for the tested vehicle are evaluated. The rigid–flexible coupling dynamic model for the high-speed passenger car is then developed by using the FE and MBS coupling approach. The rail profiles in those particular locations are measured and further integrated into the simulation model to reproduce the bogie hunting and carbody elastic vibrations. The effects of wheel and rail wear on the vehicle system response, e.g. wheelset bifurcation graph and carbody vibrations, are studied. Two improvement measures, including the wheel profile modification and rail grinding, are proposed to provide possible solutions. It is found that the wheel–rail contact conicity can be lowered by decreasing wheel flange thickness or grinding rail corner, which is expected to improve the bogie hunting stability under worn rail and worn wheel conditions. The carbody elastic vibrations caused by bogie hunting instability can be further restrained.     

Long-term wear and rolling contact fatigue behaviour of a conformal wheel profile designed for large radius curves

There are many reasons to optimise the wheel–rail interface through redesign or maintenance. Minimising wear and rolling contact fatigue (RCF) initiation on wheels and/or rails is often at the forefront of such considerations. This paper covers the design of a conformal wheel profile and its long-term wear and RCF performance to optimise the wheel–rail interface and subsequently reduce the occurrence of surface-initiated RCF on South Africa’s iron ore export line. A comparative study is performed using multibody dynamics simulation together with numerical wheel wear and RCF predictions. The advantages of a conformal wheel profile design are illustrated by evaluating the worn shape and resulting contact conditions of the conformal design. The conformal design has a steadier equivalent conicity progression and a smaller conicity range compared with the current wheel profile design over the wheel’s wear life. The combination of a conformal wheel profile design with 2?mm hollow wear and inadequate adherence to grinding tolerances often result in two-point contact, thereby increasing the probability of RCF initiation. The conformal wheel profile design proved to have wear and potential RCF benefits compared with the current wheel profile design. However, implementation of such a conformal wheel profile must be accompanied by improved rail grinding practices to ensure rail profile compliance.     

Optimisation of railway crossing geometry considering a representative set of wheel profiles

A numerical method for robust geometry optimisation of railway crossings is presented. The robustness is achieved by optimising the crossing geometry for a representative set of wheel profiles. As a basis for the optimisation, a crossing geometry is created where rail cross-sectional profiles and longitudinal height profiles of both wing rails and crossing nose are parameterised. Based on the approximation that the two problems are decoupled, separate optimisations are performed for the cross-sectional rail profiles and the longitudinal height profiles. The rail cross sections are optimised to minimise the maximum Hertzian wheel–rail contact pressure. The longitudinal height profiles are optimised to minimise the accumulated damage in the wing rail to crossing nose transition zone. The accumulated damage is approximated using an objective criterion that accounts for the angle of the wheel trajectory reversal during the transition from the wing rail to the crossing nose as well as the distribution of transition points for the utilised wheel profile set. It is found that small nonlinear height deviations from a linear longitudinal wing rail profile in the transition zone can reduce the objective compared to the nominal design. It is further demonstrated that the variation in wheel profile shapes, lateral wheel displacements and the feasible transition zone length of the crossing will determine the longitudinal height profiles of the wing rail and crossing nose if all wheel profiles are to make their transition within the transition zone.     

Design and optimisation of wheel–rail profiles for adhesion improvement

This paper describes a study for the optimisation of the wheel profile in the wheel–rail system to increase the overall level of adhesion available at the contact interface, in particular to investigate how the wheel and rail profile combination may be designed to ensure the improved delivery of tractive/braking forces even in poor contact conditions. The research focuses on the geometric combination of both wheel and rail profiles to establish how the contact interface may be optimised to increase the adhesion level, but also to investigate how the change in the property of the contact mechanics at the wheel–rail interface may also lead to changes in the vehicle dynamic behaviour.     

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.     

The Stationary Motion of a One-Axle Vehicle Along a Circular Curve with Real Rail and Wheel Profiles

In this paper, we present a theory on the stationary motion of a one-axle railway vehicle along a circular curve in the presence of single- or double-point contact. The rail and the wheel profiles may be either stylized or real and as an example we take the profile combination UIC60 1:40 S1002. The mathematical model of the system is based on De Pater's first-order theory [1]. The geometrical contact problem between wheel and rail is solved by using a modified Newton-Raphson procedure. Both the cases with and without friction are considered. When friction is present, the non-linear Kalker creep law [6, 7] is used to describe the physical contact. For various values of the friction coefficient, the cant angle and the curvature of the track, the contact forces are presented as functions of the velocity parameter C v = V 2 / V 2 eq , where V is the velocity of the vehicle and V eq is the equilibrium velocity of the frictionless case. For the case of stylized profiles in which both the wheel treads and the wheel flanges are conical, and the rail cross sections are circular, we have determined the velocity range with single point contact in dependence on the friction coefficient, the conicity of the tread, the curvature of the track and the cant angle.     

Modelling,validation and analysis of a three-dimensional railway vehicle–track system model with linear and nonlinear track properties in the presence of wheel flats

This paper presents dynamic contact loads at wheel–rail contact point in a three-dimensional railway vehicle–track model as well as dynamic response at vehicle–track component levels in the presence of wheel flats. The 17-degrees of freedom lumped mass vehicle is modelled as a full car body, two bogies and four wheelsets, whereas the railway track is modelled as two parallel Timoshenko beams periodically supported by lumped masses representing the sleepers. The rail beam is also supported by nonlinear spring and damper elements representing the railpad and ballast. In order to ensure the interactions between the railpads, a shear parameter beneath the rail beams has also been considered into the model. The wheel–rail contact is modelled using nonlinear Hertzian contact theory. In order to solve the coupled partial and ordinary differential equations of the vehicle–track system, modal analysis method is employed. Idealised Haversine wheel flats with the rounded corner are included in the wheel–rail contact model. The developed model is validated with the existing measured and analytical data available in the literature. The nonlinear model is then employed to investigate the wheel–rail impact forces that arise in the wheel–rail interface due to the presence of wheel flats. The validated model is further employed to investigate the dynamic responses of vehicle and track components in terms of displacement, velocity, and acceleration in the presence of single wheel flat.     

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

The 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.     

Tangential force variation due to the bogie direction reversal procedure

A range of tangential forces is generated within the contact patch when a wheelset moves on the rail. These forces are intensified when incorporating curved tracks and motored axle rail vehicles [Arrus, P., de Pater, A.D. and Meyers, P., 2002, The stationary motion of a one-axle vehicle along a circular curve with real rail and wheel profiles. Vehicle System Dynamics, 37(1), 29–58]. The wheelset is subject to flange contact if an unbalanced force remains in a curve towards the high rail gauge face. The resultant force in the transverse direction includes the lateral force, the radial force, and the creep forces in addition to the effect of the frequent wheelset displacement due to the kinematic oscillation [Iwnicki, S., 2003, Simulation of wheel–rail contact forces. Fatigue Fracture Engineering Material Structure, 26, 887–900]. This article has focused on a potential variation in some of the forces cited when the wheelset is subject to backward and forward movements. A severe wear rate observed within the wheel flange region in Iranian Railways was investigated by operating a test bogie on a curvaceous track. An obvious improvement in the wear rate and wear pattern of the wheels was attained when the second test bogie encountered a bogie direction reversal procedure. This enhancement is considered in this article from the force analysis standpoint.     

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 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.     

Robust optimisation of railway crossing geometry

This paper presents a methodology for improving the crossing (frog) geometry through the robust optimisation approach, wherein the variability of the design parameters within a prescribed tolerance is included in the optimisation problem. Here, the crossing geometry is defined by parameterising the B-spline represented cross-sectional shape and the longitudinal height profile of the nose rail. The dynamic performance of the crossing is evaluated considering the variation of wheel profiles and track alignment. A multipoint approximation method (MAM) is applied in solving the optimisation problem of minimising the contact pressure during the wheel–rail contact and constraining the location of wheel transition at the crossing. To clarify the difference between the robust optimisation and the normal deterministic optimisation approaches, the optimisation problems are solved in both approaches. The results show that the deterministic optimum fails under slight change of the design variables; the robust optimum, however, has improved and robust performance.     

Tangential force variation due to the bogie direction reversal procedure

A range of tangential forces is generated within the contact patch when a wheelset moves on the rail. These forces are intensified when incorporating curved tracks and motored axle rail vehicles [Arrus, P., de Pater, A.D. and Meyers, P., 2002, The stationary motion of a one-axle vehicle along a circular curve with real rail and wheel profiles. Vehicle System Dynamics, 37(1), 29-58]. The wheelset is subject to flange contact if an unbalanced force remains in a curve towards the high rail gauge face. The resultant force in the transverse direction includes the lateral force, the radial force, and the creep forces in addition to the effect of the frequent wheelset displacement due to the kinematic oscillation [Iwnicki, S., 2003, Simulation of wheel-rail contact forces. Fatigue Fracture Engineering Material Structure, 26, 887-900]. This article has focused on a potential variation in some of the forces cited when the wheelset is subject to backward and forward movements. A severe wear rate observed within the wheel flange region in Iranian Railways was investigated by operating a test bogie on a curvaceous track. An obvious improvement in the wear rate and wear pattern of the wheels was attained when the second test bogie encountered a bogie direction reversal procedure. This enhancement is considered in this article from the force analysis standpoint.     

Energy Dissipation Due to Vehicle/Track Interaction

The effects of track irregularities and wheel profile on the amount of energy dissipated in railroad freight vehicles is examined. A nonlinear computational model is used to determine the average dissipation in the vehicle suspension and the wheel/rail contact patches. This dissipation is a component of the total resistance force acting on the vehicle. Parametric results are presented showing the effects of track geometry, wheel profile, suspension design, and hunting on train resistance. Track geometry studies consider the effects of track quality and curving. The AAR 1:20 wheel profile and the Heumann wheel profile are compared under various operating conditions. Compared with the Heumann profile, the AAR 1:20 profile is shown to have lower average resistance on good quality tangent track, but higher average resistance in steady curves. A trade-off exists between the two profiles when dynamic curve entry is considered.     

Influence of polygonal wear of railway wheels on the wheel set axle stress

The coupled vehicle/track dynamic model with the flexible wheel set was developed to investigate the effects of polygonal wear on the dynamic stresses of the wheel set axle. In the model, the railway vehicle was modelled by the rigid multibody dynamics. The wheel set was established by the finite element method to analyse the high-frequency oscillation and dynamic stress of wheel set axle induced by the polygonal wear based on the modal stress recovery method. The slab track model was taken into account in which the rail was described by the Timoshenko beam and the three-dimensional solid finite element was employed to establish the concrete slab. Furthermore, the modal superposition method was adopted to calculate the dynamic response of the track. The wheel/rail normal forces and the tangent forces were, respectively, determined by the Hertz nonlinear contact theory and the Shen–Hedrick–Elkins model. Using the coupled vehicle/track dynamic model, the dynamic stresses of wheel set axle with consideration of the ideal polygonal wear and measured polygonal wear were investigated. The results show that the amplitude of wheel/rail normal forces and the dynamic stress of wheel set axle increase as the vehicle speeds rise. Moreover, the impact loads induced by the polygonal wear could excite the resonance of wheel set axle. In the resonance region, the amplitude of the dynamic stress for the wheel set axle would increase considerably comparing with the normal conditions.     

Energy Dissipation Due to Vehicle/Track Interaction

SUMMARY

The effects of track irregularities and wheel profile on the amount of energy dissipated in railroad freight vehicles is examined. A nonlinear computational model is used to determine the average dissipation in the vehicle suspension and the wheel/rail contact patches. This dissipation is a component of the total resistance force acting on the vehicle. Parametric results are presented showing the effects of track geometry, wheel profile, suspension design, and hunting on train resistance. Track geometry studies consider the effects of track quality and curving. The AAR 1:20 wheel profile and the Heumann wheel profile are compared under various operating conditions. Compared with the Heumann profile, the AAR 1:20 profile is shown to have lower average resistance on good quality tangent track, but higher average resistance in steady curves. A trade-off exists between the two profiles when dynamic curve entry is considered.     

Influence of the track quality and of the properties of the wheel–rail rolling contact on vehicle dynamics

This work describes an analytical approach to determine what degree of accuracy is required in the definition of the rail vehicle models used for dynamic simulations. This way it would be possible to know in advance how the results of simulations may be altered due to the existence of errors in the creation of rolling stock models, whilst also identifying their critical parameters. This would make it possible to maximise the time available to enhance dynamic analysis and focus efforts on factors that are strictly necessary. In particular, the parameters related both to the track quality and to the rolling contact were considered in this study. With this aim, a sensitivity analysis was performed to assess their influence on the vehicle dynamic behaviour. To do this, 72 dynamic simulations were performed modifying, one at a time, the track quality, the wheel–rail friction coefficient and the equivalent conicity of both new and worn wheels. Three values were assigned to each parameter, and two wear states were considered for each type of wheel, one for new wheels and another one for reprofiled wheels. After processing the results of these simulations, it was concluded that all the parameters considered show very high influence, though the friction coefficient shows the highest influence. Therefore, it is recommended to undertake any future simulation job with measured track geometry and track irregularities, measured wheel profiles and normative values of the wheel–rail friction coefficient.