Wheel/rail interface management in heavy haul railway operations—applying science and technology

The primary objective of the paper is to review science and technologies that have been developed by various scientists and engineers over the years and that have made it possible to push the limits within the wheel/rail interface in the heavy haul railway environment. After describing the wheel/rail stress-state and its consequences, preventative and corrective measures that can assist in optimising wheel and rail life, and thus reduce costs, are reviewed. The significant contribution of measurement and monitoring technologies to quantify the stress-state of the wheel/rail system is highlighted. Finally, a brief review of the fundamentals of contact mechanics, vehicle dynamics and wheel/rail interface analysis software is given.     

Modelling of wear and fatigue defect formation in wheel–rail contact

The model for analysing wear and fatigue defect formation is developed based on the approaches of contact and fracture mechanics. The model includes the solution of the contact problem for the wheel and rail to find the shape, size and position of the contact zones and the contact stresses and calculation of the surface wear and the function of damage accumulation in the rail and wheel. The wear rate and the worn-profile evolution of the wheel surface are calculated using both statistic and deterministic approaches to modelling of vehicle dynamics (tribo-dynamic modelling). The influence of the evolution of the wheel–rail profiles due to wear on the damage accumulation process is analysed. It is shown that for some values of the wear rate coefficient, the wear process can prevent the crack initiation under the wheel surface.     

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.     

History of Stability of Railway and Road Vehicles

Stability of running of vehicles is one of the important design criteria of railway and road vehicles. Railway vehicle stability is based on kinematics as well as contact mechanics. It reaches back to the 19th century and had its first hey-day with the work of Carter and Rocard on stability of locomotives. A rediscovery of their knowledge, which seemed to have been forgotten, was inevitable due to increased vehicle speeds since the early Fifties. — Though investigations on road vehicle stability only began approximately in 1930 with the treatment of the shimmy phenomenon, realistic solutions were available at the same time as for railway vehicles. Besides considering historical aspects we discuss in the paper links which exist between both approaches; open questions are described.     

History of Stability of Railway and Road Vehicles

Stability of running of vehicles is one of the important design criteria of railway and road vehicles. Railway vehicle stability is based on kinematics as well as contact mechanics. It reaches back to the 19th century and had its first hey-day with the work of Carter and Rocard on stability of locomotives. A rediscovery of their knowledge, which seemed to have been forgotten, was inevitable due to increased vehicle speeds since the early Fifties. — Though investigations on road vehicle stability only began approximately in 1930 with the treatment of the shimmy phenomenon, realistic solutions were available at the same time as for railway vehicles. Besides considering historical aspects we discuss in the paper links which exist between both approaches; open questions are described.     

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.     

A survey of wheel–rail contact models for rail vehicles

Accurate and efficient contact models for wheel–rail interaction are essential for the study of the dynamic behaviour of a railway vehicle. Assessment of the contact forces and moments, as well as contact geometry provide a fundamental foundation for such tasks as design of braking and traction control systems, prediction of wheel and rail wear, and evaluation of ride safety and comfort. This paper discusses the evolution and the current state of the theories for solving the wheel–rail contact problem for rolling stock. The well-known theories for modelling both normal contact (Hertzian and non-Hertzian) and tangential contact (Kalker's linear theory, FASTSIM, CONTACT, Polach's theory, etc.) are reviewed. The paper discusses the simplifying assumptions for developing these models and compares their functionality. The experimental studies for evaluation of contact models are also reviewed. This paper concludes with discussing open areas in contact mechanics that require further research for developing better models to represent the wheel–rail interaction.     

Research into the problem of wheel tread spalling caused by wheelset longitudinal vibration

This study mainly focuses on the mechanism of wheel tread spalling through wheelset longitudinal vibration that has been often neglected. Analysis of two actual cases of the wheel tread spalling problem leads to the conclusion that the wheel tread spalling is closely related to the wheelset longitudinal vibration in some locomotives, and many of these problems can be reasonably explained if the wheelset longitudinal vibration is considered. For better understanding of some abnormal wheel spalling problems, the formations of the wheelset longitudinal vibration and the wheel/rail contact parameters were analysed in the initial wheel tread spalling. With the preliminary analytical results, the wheelset longitudinal dynamic behaviour, the characteristics of wheel/rail contact and the mechanics in the condition of the wheelset longitudinal vibration were further studied quantitatively. The results showed that the wheelset longitudinal vibration changed not only the limit of these parameters and the position of principal stress, but also the direction of the principal stress on the surface of wheel/rail contact patch. It is likely that the significant stress changes provoke too much stress on the surface of wheel/rail contact patch, cause fatigue in wheel/rail contact patch and eventually lead to wheel tread spalling. The results of these studies suggest that the suppression of the wheelset longitudinal vibration extends wheel/rail life and the addition of a vertical damper with an ahead angle provides a possible solution to the wheel spalling problem.     

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.     

Dynamic simulation of railway vehicles: wheel/rail contact analysis

The multibody simulation of railway vehicle dynamics needs a reliable and efficient method to evaluate the contact points between wheel and rail, because their positions have a considerable influence on the direction and intensity of the contact forces. In this work, an innovative semi-analytic procedure for the detection of the wheel/rail contact points (named the DIFF method) is presented. This method considers the wheel and the rail as two surfaces whose analytic expressions are known and is based on the idea that in the contact points the difference between the surfaces has local minima and is equivalent to solving an algebraic two-dimensional system. The original problem can be reduced analytically to a simple scalar equation that can be easily solved numerically (since the problem dimension is one, even elementary non-iterative algorithms can be efficient).     

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.     

Short wavelength rail corrugation and non-steady-state contact mechanics

J. J. Kalker has been the first to consider non-steady-state or transient contact mechanics. Based on Kalker the second author developed a linear contact model for the non-steady-state rolling contact of a wheel running over slightly corrugated rails. The theoretical investigations are concentrated on linear, non-steady-state contact mechanics superimposed to a nonlinear reference state. The reference state is given by the running behaviour of a wheelset due to traction, curving or hunting. For the linear, non-steady-state analysis Kalker's theory has to be modified to predict wear rates in dependency of the corrugation wavelengths. As a result corrugations are only amplified in the range between 2 and 10 cm. Therefore, non-steady-state contact mechanics and wear are responsible for a wavelength fixing mechanism. Structural mechanics of the rail indicate that wavelength in this range is predominantly amplified.     

A linear complementarity method for the solution of vertical vehicle–track interaction

A new method is proposed for the solution of the vertical vehicle–track interaction including a separation between wheel and rail. The vehicle is modelled as a multi-body system using rigid bodies, and the track is treated as a three-layer beam model in which the rail is considered as an Euler-Bernoulli beam and both the sleepers and the ballast are represented by lumped masses. A linear complementarity formulation is directly established using a combination of the wheel–rail normal contact condition and the generalised-α method. This linear complementarity problem is solved using the Lemke algorithm, and the wheel–rail contact force can be obtained. Then the dynamic responses of the vehicle and the track are solved without iteration based on the generalised-α method. The same equations of motion for the vehicle and track are adopted at the different wheel–rail contact situations. This method can remove some restrictions, that is, time-dependent mass, damping and stiffness matrices of the coupled system, multiple equations of motion for the different contact situations and the effect of the contact stiffness. Numerical results demonstrate that the proposed method is effective for simulating the vehicle–track interaction including a separation between wheel and rail.     

A new method for determining wheel–rail multi-point contact

A new method for wheel–rail multi-point contact is presented in this paper. In this method, the first- and the second-order derivatives of the wheel–rail interpolation distance function and the elastic wheel–rail virtual penetration are used to determine multiple contact points. The method takes account of the yaw angle of the wheelset and allows the identification of all possible points of contact between wheel and rail surfaces with an arbitrary geometry. Static contact geometry calculations are first carried out using the developed method for both new and worn wheel profiles and with a new rail profile. The validity of the method is then verified by simulations of a coupled vehicle and track system dynamics over a small radius curve. The simulation results show that the developed method for multi-point contact is efficient and reliable enough to be implemented online for simulations of vehicle–track system dynamics.     

Influence of wheel–rail contact modelling on vehicle dynamic simulation

This paper presents a comparison of four models of rolling contact used for online contact force evaluation in rail vehicle dynamics. Until now only a few wheel–rail contact models have been used for online simulation in multibody software (MBS). Many more models exist and their behaviour has been studied offline, but a comparative study of the mutual influence between the calculation of the creep forces and the simulated vehicle dynamics seems to be missing. Such a comparison would help researchers with the assessment of accuracy and calculation time. The contact methods investigated in this paper are FASTSIM, Linder, Kik–Piotrowski and Stripes. They are compared through a coupling between an MBS for the vehicle simulation and Matlab for the contact models. This way the influence of the creep force calculation on the vehicle simulation is investigated. More specifically this study focuses on the influence of the contact model on the simulation of the hunting motion and on the curving behaviour.     

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.     

Modification of the semi-Hertz wheel–rail contact method based on recalculating the virtual penetration value

ABSTRACT

Wheel–rail contact calculation is of vital importance in vehicle system dynamics. In the existing methods of wheel–rail contact calculation, the finite element method and Kalker’s CONTACT program, which are based on the complementary energy principle, are the two methods with accuracy recognised. However, because of its very slow calculation speed, it cannot meet the requirement of online calculation, so a variety of fast non-elliptic algorithms have been proposed. The semi-Hertz method, which is recognised for its great contributions to the fast wheel–rail contact calculation, is based on the concept of virtual penetration. The calculation of virtual penetration is crucial to evaluate the shape and normal pressure distribution of the contact patch. In practice, the virtual penetration is related to the curvature of the whole contact patch; however, the range of the contact patch is determined by the value of penetration. Such an interaction leads the calculation into a dead loop. In the semi-Hertz method, the penetration is calculated by the Hertz parameters of the initial contact point. Thus, the practical range of the method is limited. In this paper, a fast-iterative method for solving virtual penetration is proposed, and a reliable value of virtual penetration can be obtained under any lateral wheel–rail relative curvature variation with good stability and speed. The normal and tangential solutions are analysed with different methods in this paper.     

A study on high-speed rolling contact between a wheel and a contaminated rail

A 3-D explicit finite element model is developed to investigate the transient wheel–rail rolling contact in the presence of rail contamination or short low adhesion zones (LAZs). A transient analysis is required because the wheel passes by a short LAZ very quickly, especially at high speeds. A surface-to-surface contact algorithm (by the penalty method) is employed to solve the frictional rolling contact between the wheel and the rail meshed by solid elements. The LAZ is simulated by a varying coefficient of friction along the rail. Different traction efforts and action of the traction control system triggered by the LAZ are simulated by applying a time-dependent driving torque to the wheel axle. Structural flexibilities of the vehicle–track system are considered properly. Analysis focuses on the contact forces, creepage, contact stresses and the derived frictional work and plastic deformation. It is found that the longitudinal contact force and the maximum surface shear stress in the contact patch become obviously lower in the LAZ and much higher as the wheel re-enters the dry rail section. Consequently, a higher wear rate and larger plastic flow are expected at the location where the dry contact starts to be rebuilt. In other words, contact surface damages such as wheel flats and rail burns may come into being because of the LAZ. Length of the LAZ, the traction level, etc. are varied. The results also show that local contact surface damages may still occur as the traction control system acts.     

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.