Systems-on-chip approach for real-time simulation of wheel–rail contact laws

This paper presents the development of a systems-on-chip approach to speed up the simulation of wheel–rail contact laws, which can be used to reduce the requirement for high-performance computers and enable simulation in real time for the use of hardware-in-loop for experimental studies of the latest vehicle dynamic and control technologies. The wheel–rail contact laws are implemented using a field programmable gate array (FPGA) device with a design that substantially outperforms modern general-purpose PC platforms or fixed architecture digital signal processor devices in terms of processing time, configuration flexibility and cost. In order to utilise the FPGA's parallel-processing capability, the operations in the contact laws algorithms are arranged in a parallel manner and multi-contact patches are tackled simultaneously in the design. The interface between the FPGA device and the host PC is achieved by using a high-throughput and low-latency Ethernet link. The development is based on FASTSIM algorithms, although the design can be adapted and expanded for even more computationally demanding tasks.     

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.     

Modelling of wheels and rail discontinuities in dynamic wheel–rail contact analysis

A classification of wheel–rail contact is given. Difference is made between modelling of a running wheel with continuous single-point-contact, as is common practice in wheel–rail contact analysis, and a wheel with transient double- or multi-point-contact, which may occur for rail irregularities with curvatures larger than that of the wheel circumference. It is shown that application of the first model for these irregularities will strongly underestimate the contact forces as it does not describe occurring mechanisms correctly. Further, it is shown that in principle it is not possible to describe the second type of contact fully correct with a lumped wheel model. Both wheel models are formulated mathematically for some basic contact cases. Afterwards, results are applied to a linear track model. Analytical closed-form solutions are found in the frequency domain for arbitrary type of contact and numerically transformed to the time domain. Finally, the necessity is shown to avoid situations where transient multiple-point-contact may occur (like rail joints) in practice.     

An alternative to FASTSIM for tangential solution of the wheel–rail contact

In most rail vehicle dynamics simulation packages, tangential solution of the wheel–rail contact is gained by means of Kalker's FASTSIM algorithm. While 5–25% error is expected for creep force estimation, the errors of shear stress distribution, needed for wheel–rail damage analysis, may rise above 30% due to the parabolic traction bound. Therefore, a novel algorithm named FaStrip is proposed as an alternative to FASTSIM. It is based on the strip theory which extends the two-dimensional rolling contact solution to three-dimensional contacts. To form FaStrip, the original strip theory is amended to obtain accurate estimations for any contact ellipse size and it is combined by a numerical algorithm to handle spin. The comparison between the two algorithms shows that using FaStrip improves the accuracy of the estimated shear stress distribution and the creep force estimation in all studied cases. In combined lateral creepage and spin cases, for instance, the error in force estimation reduces from 18% to less than 2%. The estimation of the slip velocities in the slip zone, needed for wear analysis, is also studied. Since FaStrip is as fast as FASTSIM, it can be an alternative for tangential solution of the wheel–rail contact in simulation packages.     

Assessment of a semi-Hertzian method for determination of wheel–rail contact patch

Wheel–rail contact calculations are essential for simulating railway vehicle dynamic behavior. Currently, these simulations usually use the Hertz contact theory to calculate normal forces and Kalker's ‘FASTSIM’ program to evaluate tangential stresses. Since 1996, new methods called semi-Hertzian have appeared: 5 Kik, W. and Piotrowski, J. A fast approximate method to calculate normal load at contact between wheel and rail and creep forces during rolling. Paper presented at the 2nd Mini-conference on Contact Mechanics and Wear of Rail/Wheel Systems. July29–31, Budapest.  [Google Scholar] 7 Ayasse, J. B., Chollet, H. and Maupu, J. L. 2000. Paramètres caractéristiques du contact roue-rail. Rapport de Recherche INRETS n225, ISSN 0768–9756 (in French) [Google Scholar] (STRIPES). These methods attempt to estimate the non-elliptical contact patches with a discrete extension of the Hertz theory. As a continuation of 2 Ayasse, J. B and Chollet, H. 2005. Determination of the wheel–rail contact patch in semi-Hertzian conditions. Vehicle System Dynamics, 43(3) [Google Scholar], a validation of the STRIPES method for normal problem computing on three test cases is proposed in this article. The test cases do not fulfill the hypothesis required for the Hertz theory. Then, the Kalker's FASTSIM algorithm is adapted to STRIPES patch calculus to perform tangential forces computation. This adaptation is assessed using Kalker's CONTACT algorithm.     

A new method for wheel–rail contact force continuous measurement using instrumented wheelset

With the aim of improving the continuous measurement of wheel–rail contact force by instrumented wheelset, instead of solving the non-linear equations, we proposed a new method based on state space theory. With this new method, the wheel–rail contact force can be calculated by the recurrence relation and the signals from strain gauge bridges on wheel web. The implementation of continuous instrumented wheelset is quite general and simplified, due to the specific bridging scheme is not necessary. It means that continuous measurement of the contact force could be realised with a simple bridging scheme, even as simple as discrete instrumented scheme. In this work, we first demonstrated and discussed the effectiveness and accuracy of this new method by estimation results with the numerical simulations, and we also applied this new method to two field tests, including one was conducted in a loop test line using a high-speed train and the other one was conducted in an urban line with a light rail vehicle. In a word, this new method is proved to be an effective way to monitor the wheel–rail contact force of rail vehicle track system.     

Physical processes in wheel–rail contact and its implications on vehicle–track interaction

Friction within the wheel–rail contact highly influences all aspects of vehicle–track interaction. Models describing this frictional behaviour are of high relevance, for example, for reliable predictions on drive train dynamics. It has been shown by experiments, that the friction at a certain position on rail is not describable by only one number for the coefficient of friction. Beside the contact conditions (existence of liquids, solid third bodies, etc.) the vehicle speed, normal loading and contact geometry are further influencing factors. State-of-the-art models are not able to account for this sufficiently. Thus, an Extended-Creep-Force-Model was developed taking into account effects from third body layers. This model is able to describe all considered effects. In this way, a significant improvement of the prediction quality with respect to all aspects of vehicle–track interaction is expected.     

Variation in predicting pantograph–catenary interaction contact forces,numerical simulations and field measurements

The contact force between the pantograph and the contact wire ensures energy transfer between the two. Too small of a force leads to arching and unstable energy transfer, while too large of a force leads to unnecessary wear on both parts. Thus, obtaining the correct contact force is important for both field measurements and estimates using numerical analysis. The field contact force time series is derived from measurements performed by a self-propelled diagnostic vehicle containing overhead line recording equipment. The measurements are not sampled at the actual contact surface of the interaction but by force transducers beneath the collector strips. Methods exist for obtaining more realistic measurements by adding inertia and aerodynamic effects to the measurements. The variation in predicting the pantograph–catenary interaction contact force is studied in this paper by evaluating the effect of the force sampling location and the effects of signal processing such as filtering. A numerical model validated by field measurements is used to study these effects. First, this paper shows that the numerical model can reproduce a train passage with high accuracy. Second, this study introduces three different options for contact force predictions from numerical simulations. Third, this paper demonstrates that the standard deviation and the maximum and minimum values of the contact force are sensitive to a low-pass filter. For a specific case, an 80?Hz cut-off frequency is compared to a 20?Hz cut-off frequency, as required by EN 50317:2012; the results show an 11% increase in standard deviation, a 36% increase in the maximum value and a 19% decrease in the minimum value.     

Comments on ‘the Kalker book of tables for non-Hertzian contact of wheel and rail’

The ‘simple double-elliptical contact’ (SDEC) approach by Piotrowski et al. [The Kalker book of tables for non-Hertzian contact of wheel and rail. Vehicle Syst Dyn. 2017;55:875–901] generates a-symmetrical contact patches in an elegant way. This allows to extend the table-based approach for the wheel–rail creep force calculation towards non-Hertzian contact geometry. This is an important line of research, because FASTSIM is intricate for non-Hertzian contacts, whereas CONTACT requires long calculation times.

Here, we comment on the further motivation that's provided for the approach. According to the authors, ‘the spin creepage generates longitudinal creep force in non-symmetric, non-elliptical contacts’, which is ‘completely lost’ when using elliptical regularisation. We demonstrate that this mainly depends on the choice of contact origin, and that the interaction is much reduced if different choices are made. This suggests that elliptical regularisation may be viable still, if the details are properly worked out. Furthermore, we introduce the spin center and the free-rolling position as means to extend the table-based approach towards more general non-Hertzian circumstances.     

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 non-Hertzian method for solving wheel–rail normal contact problem taking into account the effect of yaw

A novel approach is proposed in this paper to deal with non-Hertzian normal contact in wheel–rail interface, extending the widely used Kik–Piotrowski method. The new approach is able to consider the effect of the yaw angle of the wheelset against the rail on the shape of the contact patch and on pressure distribution. Furthermore, the method considers the variation of profile curvature across the contact patch, enhancing the correspondence to CONTACT for highly non-Hertzian contact conditions. The simulation results show that the proposed method can provide more accurate estimation than the original algorithm compared to Kalker’s CONTACT, and that the influence of yaw on the contact results is significant under certain circumstances.     

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.