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).     

A rail roughness growth model for a wheelset with non-steady,non-Hertzian contact

This paper presents a model simulating rail roughness growth in which the interaction of a wheelset with the track is considered. The aim is to investigate any possible mechanism for roughness growth due to the coupling between the vertical dynamics, the torsional vibration across the axle of the wheelset and the non-steady contact mechanics. The time-domain simulations are carried out for a driven wheelset on tangent track. Both rigid and flexible are considered with parameter variations for moments of the wheelset, vehicle speeds and wavelengths of initial roughnesses. The 2D non-Hertzian and non-steady contact model used in simulations are based on influence coefficients obtained from a boundary element model. The nonlinear development of the rail roughnesses after millions of wheelset passages is also presented.     

High-speed wheel/rail contact determining method with rotating flexible wheelset and validation under wheel polygon excitation

A rotating flexible wheelset model is developed and integrated into a vehicle/track dynamic model. Flexible wheelset modes with natural frequencies less than 1000?Hz are considered in the wheelset modelling. An innovation of the paper is that wheel/rail rolling contact calculation considers the effect of the wheelset flexibility and the rotating effect. By introducing two half dummy rigid wheelsets the rolling contact between the flexible wheelset and the two rails can be transformed to that between a rigid wheelset and the rails. As an extension application, the wheel OOR (Out-Of-Round) wears with the 11th, 15th, and 17th orders are used to the vehicle system dynamic model with rigid, flexible and rotating-flexible wheelset model. The results of the three models are compared to study the influence of wheelset flexibility and rotation. The ‘online searching contact method’ developed in this paper is compared with the traditional contact method with considering the rotating flexible wheelset. And then a measured OOR is used to excite the rotating flexible wheelset, the response of which is analysed and verified.     

History of wheel/rail contact mechanics: from Redtenbacher to Kalker

The history of wheel/rail contact mechanics is an integrated part of contact mechanics. Problems of wheel/rail contact (damage phenomena and influence of contact mechanics on vehicle dynamics, especially on vehicle stability) have been investigated since the middle of the 19th Century. In 1855, Redtenbacher was the first to consider head checking. Stability investigations started with Boedecker (1887) and were continued by Carter (1916); however, they were not recognized at that time. Stability analysis was only considered to be an integrated step in vehicle design in about 1955 when stability problems started to occur in practice. The scientific foundations of our present investigations are based on Heinrich Hertz, Frederick William Carter and Hans Fromm. The key contributors to research in the last fifty years in the field of wheel/rail contact mechanics are Joost Kalker and Ken Johnson.     

A method for testing railway wheel sets on a full-scale roller rig

Full-scale roller rigs for tests on a single axle enable the investigation of several dynamics and durability problems related with the design and operation of the railway rolling stock. In order to exploit the best potential of this test equipment, appropriate test procedures need to be defined, particularly in terms of actuators’ references, to make sure that meaningful wheel –rail contact conditions can be reproduced. The aim of this paper is to propose a new methodology to define the forces to be generated by the actuators in the rig in order to best reproduce the behaviour of a wheel set and especially the wheel –rail contact forces in a running condition of interest as obtained either from multi-body system (MBS) simulation or from on-track measurements. The method is supported by the use of a mathematical model of the roller rig and uses an iterative correction scheme, comparing the time histories of the contact force components from the roller rig test as predicted by the mathematical model to a set of target contact force time histories. Two methods are introduced, the first one considering a standard arrangement of the roller rig, the second one assuming that a differential gear is introduced in the rig, allowing different rolling speeds of the two rollers. Results are presented showing that the deviation of the roller rig test results from the considered targets can be kept within low tolerances (1% approximately) as far as the vertical and lateral contact forces on both wheels are concerned. For the longitudinal forces, larger deviations are obtained except in the case where a differential gear is introduced.     

Development and validation of a wear model for the analysis of the wheel profile evolution in railway vehicles

The numerical wheel wear prediction in railway applications is of great importance for different aspects, such as the safety against vehicle instability and derailment, the planning of wheelset maintenance interventions and the design of an optimal wheel profile from the wear point of view. For these reasons, this paper presents a complete model aimed at the evaluation of the wheel wear and the wheel profile evolution by means of dynamic simulations, organised in two parts which interact with each other mutually: a vehicle's dynamic model and a model for the wear estimation. The first is a 3D multibody model of a railway vehicle implemented in SIMPACK?, a commercial software for the analysis of mechanical systems, where the wheel–rail interaction is entrusted to a C/C++user routine external to SIMPACK, in which the global contact model is implemented. In this regard, the research on the contact points between the wheel and the rail is based on an innovative algorithm developed by the authors in previous works, while normal and tangential forces in the contact patches are calculated according to Hertz's theory and Kalker's global theory, respectively. Due to the numerical efficiency of the global contact model, the multibody vehicle and the contact model interact directly online during the dynamic simulations.

The second is the wear model, written in the MATLAB® environment, mainly based on an experimental relationship between the frictional power developed at the wheel–rail interface and the amount of material removed by wear. Starting from a few outputs of the multibody simulations (position of contact points, contact forces and rigid creepages), it evaluates the local variables, such as the contact pressures and local creepages, using a local contact model (Kalker's FASTSIM algorithm). These data are then passed to another subsystem which evaluates, by means of the considered experimental relationship, both the material to be removed and its distribution along the wheel profile, obtaining the correspondent worn wheel geometry.

The wheel wear evolution is reproduced by dividing the overall chosen mileage to be simulated in discrete spatial steps: at each step, the dynamic simulations are performed by means of the 3D multibody model keeping the wheel profile constant, while the wheel geometry is updated through the wear model only at the end of the discrete step. Thus, the two parts of the whole model work alternately until the completion of the whole established mileage. Clearly, the choice of an appropriate step length is one of the most important aspects of the procedure and it directly affects the result accuracy and the required computational time to complete the analysis.

The whole model has been validated using experimental data relative to tests performed with the ALn 501 ‘Minuetto’ vehicle in service on the Aosta–Pre Saint Didier track; this work has been carried out thanks to a collaboration with Trenitalia S.p.A and Rete Ferroviaria Italiana, which have provided the necessary technical data and experimental results.     

A railway vehicle multibody model for real-time applications

Hardware in the loop (HIL) techniques are widely used for fast prototyping of control systems, electronic and mechatronic devices. In the railway field, several mechatronic on board subsystems are often tested and calibrated following the HIL approach. The accuracy of HIL tests depends on how the simulated virtual environment approximates the physical conditions. As the computational power available on real-time hardware grows, the demand for more complex and realistic models of railway vehicles for real-time application increases. In past research activities, the authors worked on the implementation of simplified real-time models for several applications and in particular for an HIL test rig devoted to the type approval of wheel slide protection systems. The activity has then been focused on the development of a three-dimensional model of the dynamics of a railway vehicle for more complex applications. The paper summarises the features and the results of the study.     

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.     

A contact-area model for rail-pads connections in 2-D simulations: sensitivity analysis of train-induced vibrations

A numerical model to predict train-induced vibrations is presented. The dynamic computation considers mutual interactions in vehicle/track coupled systems by means of a finite and discrete elements method. The rail defects and the case of out-of-round wheels are considered. The dynamic interaction between the wheel-sets and the rail is accomplished by using the non-linear Hertzian model with hysteresis damping. A sensitivity analysis is done to evaluate the variables affecting more the maintenance costs. The rail–sleeper contact is assumed extended to an area-defined contact zone, rather than a single-point assumption which fits better real case studies. Experimental validations show how prediction fits well experimental data.     

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.