High Speed Stability for Rail Vehicles Considering Varying Conicity and Creep Coefficients

The critical or hunting speed of solid axle rail vehicles is known to be a strong function of primary suspension stiffness, wheel/rail profile geometry (conicity and gravitational stiffness), wheel/rail friction forces (creep coefficients), bogie/carbody inertia properties, and secondary suspension design. This paper deals with the problem of maximizing the critical speed through design of the primary and secondary suspension but with control only over the range of wheel/rail geometry and friction characteristics. For example, the conicity may varie from .05 to .3 and the linear creep coefficients from 25% to 100% of the predicted Kalker values.

It is shown that the maximum critical speed is greatly limited by the wheel/rail geometry and friction variations. It is also shown that, when lateral curving and ride quality are considered, the best design approach is to select an intermediate primary longitudinal stiffness, to limit the lowest value of conicity (e.g. to .1 or .2) by wheel profile redesign, increasing the secondary yaw damping value (yaw relaxation) and optimizing the primary and secondary lateral stiffness.     

Effect of System Nonlinearities on Locomotive Bogie Hunting Stability

This paper presents the effect of system parameters on hunting of a rail vehicle with nonlinear yaw dampers and wheel-rail interface. This study is intended to complement earlier studies by True et al. where they investigated the effect of nonlinearities stemming from creep-creep force saturation and wheel/rail contact forces. The rail vehicle is represented by a two-axle truck (bogie) that includes the dynamics of the wheelsets and the truck frame. The numerical simulation results show that yaw damping can have a mixed effect on the hunting critical speed. In some ranges, increasing damping can actually lower the critical speed, unlike the results commonly obtained from a linear model. Flange contact nonlinearities can also have a significant effect on the hunting behavior. Large lateral stiffness of the rail can increase lateral force to vertical force (L/V) ratio during hunting. Increasing the gauge clearance, however, can have an opposite effect. The effect of a variety of other parameters, such as the primary suspension yaw and lateral stiffness, primary suspension lateral damping, wheelset mass, and truck frame mass, are summarized in a table.     

Study on flange climb derailment criteria of a railway wheelset

The wheel flange climb derailment, which can be usually considered as a quasi-static process, is one of the main types of derailment, and often occurs on curved tracks due to large wheel lateral force and reduced vertical force. The general formula for the wheel critical derailment coefficient Q/P, the ratio of wheel lateral force to vertical force, is derived through analysing the forces exerted on the flange climb wheel. Based on the Coulomb's friction law and the creep force laws, the Friction Formula and Creep Formula for the evaluation of derailment are derived, respectively. The analysis shows that the derailment coefficients of Friction Formula and Creep Formula required for derailment are increased considerably for smaller and negative yaw angles, and tend to the value of Nadal's Formula at larger wheelset yaw angles. The Creep Formula is more reasonable for the assessment of derailment. The effect of some parameters on flange climb derailment, such as wheel/rail friction coefficient, yaw angle, flange contact angle, wheel vertical load and curve radius, are investigated. Finally, a simplified formula for wheel climb derailment based on the Creep Formula is proposed.     

Study on flange climb derailment criteria of a railway wheelset

The wheel flange climb derailment, which can be usually considered as a quasi-static process, is one of the main types of derailment, and often occurs on curved tracks due to large wheel lateral force and reduced vertical force. The general formula for the wheel critical derailment coefficient Q/P, the ratio of wheel lateral force to vertical force, is derived through analysing the forces exerted on the flange climb wheel. Based on the Coulomb's friction law and the creep force laws, the Friction Formula and Creep Formula for the evaluation of derailment are derived, respectively. The analysis shows that the derailment coefficients of Friction Formula and Creep Formula required for derailment are increased considerably for smaller and negative yaw angles, and tend to the value of Nadal's Formula at larger wheelset yaw angles. The Creep Formula is more reasonable for the assessment of derailment. The effect of some parameters on flange climb derailment, such as wheel/rail friction coefficient, yaw angle, flange contact angle, wheel vertical load and curve radius, are investigated. Finally, a simplified formula for wheel climb derailment based on the Creep Formula is proposed.     

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.     

Critical Speed and Limit Speed in Phenomena of Lateral Instability on Railway Vehicles

A comparison between theoretical calculations on dynamic lateral behaviour of railway vehicles and experimental results shows quite a sizeable difference between the calculated critical speed and the actual speed at which side impact phenomena will repeatedly occur between wheel flange and rail (running speed limit), such impact speed being remarkably lower than calculated.

Another typical experimental aspect is that the running speed limit will considerably vary for the same vehicle depending on the test track conditions. Such difference is usually attributed to alterations of the wheel-rail contact surfaces, only.

This paper will discuss some concurrent causes which may prove far from negligible, such as the effects of track defects, an amplification of the dynamic lateral displacement between wheel and rail on approaching the critical speed, the track mechanical properties, and in particular the track lateral rigidity.

The influence of some geometrical factors typical of the wheel-rail contact, such as side clearance and linearized conicity, will also be discussed. The approach is based on the application of statistical methods to dynamic linear systems.     

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.     

The stability mechanism and its application to heavy-haul couplers with arc surface contact

To investigate the stability mechanism of a type of heavy-haul coupler with arc surface contact, the force states of coupler were analysed at different yaw angles according to the friction circle theory and the structural characteristics of this coupler were summarised. A multi-body dynamics model with four heavy-haul locomotives and three detailed couplers was established to simulate the process of emergency braking. In addition, the coupler yaw instability was tested in order to investigate the effect of relevant parameters on the coupler stability. The results show that this coupler exhibits the self-stabilisation and less lateral force at a small yaw angle. The yaw angle of force line is less than the actual coupler yaw angle which reduces the lateral force and the critical instability. An increase in the friction coefficient of the arc contact surfaces can improve the stability of couplers. The friction coefficient needs to be increased with the increase in the maximum coupler longitudinal compressive force. The stability of couplers is significantly enhanced by increasing the secondary suspension stiffness and reducing the clearance of the lateral stopper of the locomotives. When the maximum coupler compressive force reaches 2500 kN, the required friction coefficient reduces from 0.6 to 0.35, which notably lowers the derailment risk caused by the coupler. The critical instability angle of the coupler mainly depends on the arc contact friction coefficient. When the friction coefficient is 0.3, the critical instability angle was 4–4.5°. The simulation results are consistent with the locomotive line tests. These studies establish meaningful improvements for the stability of couplers and match the heavy-haul locomotive with its suspension parameters.     

Critical Speed and Limit Speed in Phenomena of Lateral Instability on Railway Vehicles

SUMMARY

A comparison between theoretical calculations on dynamic lateral behaviour of railway vehicles and experimental results shows quite a sizeable difference between the calculated critical speed and the actual speed at which side impact phenomena will repeatedly occur between wheel flange and rail (running speed limit), such impact speed being remarkably lower than calculated.

Another typical experimental aspect is that the running speed limit will considerably vary for the same vehicle depending on the test track conditions. Such difference is usually attributed to alterations of the wheel-rail contact surfaces, only.

This paper will discuss some concurrent causes which may prove far from negligible, such as the effects of track defects, an amplification of the dynamic lateral displacement between wheel and rail on approaching the critical speed, the track mechanical properties, and in particular the track lateral rigidity.

The influence of some geometrical factors typical of the wheel-rail contact, such as side clearance and linearized conicity, will also be discussed. The approach is based on the application of statistical methods to dynamic linear systems.     

Re-adhesion control for a railway single wheelset test rig based on the behaviour of the traction motor

A method for detecting wheel slip/slide and re-adhesion control of AC traction motors in railway applications is presented in this paper. This enables a better utilisation of available adhesion and could also reduce wheel wear by reducing high creep values. With this method, the wheel–rail (roller) creepage, creep force and friction coefficient can be indirectly detected and estimated by measuring the voltage, current and speed of the AC traction motor and using an extended Kalman filter. The re-adhesion controller is designed to regulate the motor torque command according to the maximum available adhesion based on the estimated results. Simulations under different friction coefficients are carried out to test the proposed method.     

Nonlinear PI front and rear steering control in four wheel steering vehicles

Vehicle steering dynamics show resonances, which depend on the longitudinal speed, unstable equilibrium points and limited stability regions depending on the constant steering wheel angle, longitudinal speed and car parameters.

The main contribution of this paper is to show that a combined decentralized proportional active front steering control and proportional-integral active rear steering control from the yaw rate tracking error can assign the eigenvalues of the linearised single track steering dynamics, without lateral speed measurements, using a standard single track car model with nonlinear tire characteristics and a non-linear first-order reference model for the yaw rate dynamics driven by the driver steering wheel input. By choosing a suitable nonlinear reference model it is shown that the responses to driver step inputs tend to zero (or reduced) lateral speed for any value of longitudinal speed: in this case the resulting controlled vehicle static gain from driver input to yaw rate differs from the uncontrolled one at higher speed. The closed loop system shows the advantages of both active front and rear steering control: higher controllability, enlarged bandwidth for the yaw rate dynamics, suppressed resonances, new stable cornering manoeuvres, enlarged stability regions, reduced lateral speed and improved manoeuvrability; in addition comfort is improved since the phase lag between lateral acceleration and yaw rate is reduced.

For the designed control law a robustness analysis is presented with respect to system failures, driver step inputs and critical car parameters such as mass, moment of inertia and front and rear cornering stiffness coefficients. Several simulations are carried out on a higher order experimentally validated nonlinear dynamical model to confirm the analysis and to explore the robustness with respect to unmodelled dynamics.     

Effect of curved track support failure on vehicle derailment

In order to investigate the effect of curved track support failure on railway vehicle derailment, a coupled vehicle–track dynamic model is put forward. In the model, the vehicle and the structure under rails are, respectively, modelled as a multi-body system, and the rail is modelled with a Timoshenko beam rested on the discrete sleepers. The lateral, vertical, and torsional deformations of the beam are taken into account. The model also considers the effect of the discrete support by sleepers on the coupling dynamics of the vehicle and track. The sleepers are assumed to move backward at a constant speed to simulate the vehicle running along the track at the same speed. In the calculation of the coupled vehicle and track dynamics, the normal forces of the wheels/rails are calculated using the Hertzian contact theory and their creep forces are determined with the nonlinear creep theory by Shen et al [Z.Y. Shen, J.K. Hedrick, and J.A. Elkins, A comparison of alternative creep-force models for rail vehicle dynamic analysis, Proceedings of the 8th IAVSD Symposium, Cambridge, MA, 1984, pp. 591–605]. The motion equations of the vehicle/track are solved by means of an explicit integration method. The failure of the components of the curved track is simulated by changing the track stiffness and damping along the track. The cases where zero to six supports of the curved rails fail are considered. The transient derailment coefficients are calculated. They are, respectively, the ratio of the wheel/rail lateral force to the vertical force and the wheel load reduction. The contact points of the wheels/rails are in detail analysed and used to evaluate the risk of the vehicle derailment. Also, the present work investigates the effect of friction coefficient, axle load and vehicle speed on the derailments under the condition of track failure. The numerical results obtained indicate that the failure of track supports has a great influence on the whole vehicle running safety.     

Nonlinear PI front and rear steering control in four wheel steering vehicles

Vehicle steering dynamics show resonances, which depend on the longitudinal speed, unstable equilibrium points and limited stability regions depending on the constant steering wheel angle, longitudinal speed and car parameters.

The main contribution of this paper is to show that a combined decentralized proportional active front steering control and proportional-integral active rear steering control from the yaw rate tracking error can assign the eigenvalues of the linearised single track steering dynamics, without lateral speed measurements, using a standard single track car model with nonlinear tire characteristics and a non-linear first-order reference model for the yaw rate dynamics driven by the driver steering wheel input. By choosing a suitable nonlinear reference model it is shown that the responses to driver step inputs tend to zero (or reduced) lateral speed for any value of longitudinal speed: in this case the resulting controlled vehicle static gain from driver input to yaw rate differs from the uncontrolled one at higher speed. The closed loop system shows the advantages of both active front and rear steering control: higher controllability, enlarged bandwidth for the yaw rate dynamics, suppressed resonances, new stable cornering manoeuvres, enlarged stability regions, reduced lateral speed and improved manoeuvrability; in addition comfort is improved since the phase lag between lateral acceleration and yaw rate is reduced.

For the designed control law a robustness analysis is presented with respect to system failures, driver step inputs and critical car parameters such as mass, moment of inertia and front and rear cornering stiffness coefficients. Several simulations are carried out on a higher order experimentally validated nonlinear dynamical model to confirm the analysis and to explore the robustness with respect to unmodelled dynamics.     

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.     

Design of an optimised wheel profile for rail vehicles operating on two-track gauges

This article sets out an optimum synthesis methodology for wheel profiles of railway vehicles in order to secure good dynamic behaviour with different track configurations. Specifically, the optimisation process has been applied to the case of rail wheelsets mounted on double-gauge bogies that move over two different gauges, which also have different types of rail: the Iberian gauge (1668 mm) and the International Union of Railways (UIC) gauge (1435 mm). Optimisation is performed using Genetic Algorithms and traditional optimisation methods in a complementary way. The objective function used is based on an ideal equivalent conicity curve which ensures good stability on straight sections and also proper negotiation of curves. To this end, the curve is constructed in such a way that it is constant with a low value for small lateral wheelset displacements (with regard to stability), and increases as the displacements increase (to facilitate negotiation of curved sections). Using this kind of ideal conicity curve also enables a wheel profile to be secured where the contact points have a larger distribution over the active contact areas, making wear more homogeneous and reducing stresses. The result is a wheel profile with a conicity that is closer to the target conicity for both gauges studied, producing better curve negotiation while maintaining good stability on straight sections of track. The article shows the resultant wheel profile, the contact curves it produces, and a number of dynamic analyses demonstrating better dynamic behaviour of the synthesised wheel on curved sections with respect to the original wheel.     

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.     

A New Wheel/Rail Spatially Dynamic Coupling Model and its Verification

Based on the theory of vehicle-track coupling dynamics, a new wheel/rail spatially dynamic coupling model is established in this paper. In consideration of rail lateral, vertical and torsion vibrations and track irregularities, the wheel/rail contact geometry, the wheel/rail normal contact force and the wheel/rail tangential creep force are solved in detail. In the new wheel/rail model, the assumption that wheel contacts rail rigidly and wheel always contacts rail is eliminated. Finally, by numeric simulation comparison with international well-known software NUCARS, comparison with vehicle-track vertical coupling model, and comparison with running test results by China Academy of Railway Sciences, the new wheel/rail spatially dynamic coupling model is shown to be correct and effective.     

A New Wheel/Rail Spatially Dynamic Coupling Model and its Verification

Based on the theory of vehicle-track coupling dynamics, a new wheel/rail spatially dynamic coupling model is established in this paper. In consideration of rail lateral, vertical and torsion vibrations and track irregularities, the wheel/rail contact geometry, the wheel/rail normal contact force and the wheel/rail tangential creep force are solved in detail. In the new wheel/rail model, the assumption that wheel contacts rail rigidly and wheel always contacts rail is eliminated. Finally, by numeric simulation comparison with international well-known software NUCARS, comparison with vehicle-track vertical coupling model, and comparison with running test results by China Academy of Railway Sciences, the new wheel/rail spatially dynamic coupling model is shown to be correct and effective.     

Wheel/Rail Non-linear Interactions With Coupling Between Vertical and Lateral Directions

Summary A theoretical model is developed to explore the high frequency wheel/rail interaction with coupling between the vertical and lateral directions. This coupling is introduced through the track dynamics due to the offset of the wheel/rail contact point from the rail centre line. Equivalent models of the railway track in the time domain are developed according to the rail vibration receptances in the frequency domain. The wheel is represented by a mass in each direction with no vertical-lateral coupling. The vertical wheel/rail interaction is generated through a non-linear Hertzian contact stiffness, allowing for the possibility of loss of contact between the wheel and rail. The lateral interaction is represented by a contact spring and a creep force damper in series and their values depend on the vertical contact force. The vibration source is the roughness on the wheel and rail contact surfaces which forms a relative displacement excitation in the vertical direction. Using the combined interaction model with this relative displacement excitation, the wheel/rail interactions with coupling between the vertical and lateral vibrations are simulated. It is found that the lateral interaction force caused by the offset is usually less than thirty percent of the vertical dynamic force. The lateral vibration of the rail is significantly reduced due to the presence of the lateral coupling, whereas the vertical interaction is almost unaffected by the lateral force.     

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.