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.     

A study on the stability of a motorcycle wheel–swingarm suspension with chain transmission

The present study describes a possible driving mechanism for a self-excited oscillation observed in motorcycle dynamics, often referred to as chatter. This phenomenon, affecting the performance of road racing motorcycles, has been simulated in straight running braking manoeuvres with multibody motorcycle models. It involves rear suspension bounce and driveline oscillation in the frequency range between 17 and 22?Hz. A simplified model of a motorcycle rear suspension with chain transmission is proposed and its stability in equilibrium configurations is studied via eigenvalue analysis. The sensitivity with respect to all its governing parameters is analysed by means of stability maps and the self-excitation mechanism is explained with the aid of energy balance analysis and phase diagrams. It is found that the key role for the instability onset is played by the gradient of the nonlinear characteristic slip function of the tyre.     

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.     

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 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.     

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.     

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.     

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.     

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 robust non-Hertzian contact method for wheel–rail normal contact analysis

A modified Kik–Piotrowski (MKP) model is proposed in this paper for an accurate and robust calculation of wheel–rail normal contact problem. The presented method is able to consider the relationship between the elastic deformation of a line and the normal pressure distribution within the contact patch. A novel shape correction method is put forward to correctly describe the elastic deformation of the contact patch. Taking the results estimated by Kalker’s variational method and Kik–Piotrowski method as references, the proposed method is validated by three contact cases, including the assumed standardised non-Hertzian contact and the two-point contact, as well as the contact behaviours based on three actual wheel–rail profiles. The simulation results indicate that, compared with Kik–Piotrowski method, the proposed MKP method achieves better agreement with Kalker’s variational method. Moreover, the MKP method can avoid the abrupt change of wheel–rail normal force due to the sudden transfer of the contact point, which contributes to a better computational stability.     

Strategies to simulate wheel–rail adhesion in degraded conditions using a roller-rig

Railway vehicles adopt mechatronic devices to maximize the traction/braking effort. These systems often use complex algorithms that require long experimental validation tests on track. The possibility to perform the same tests on a roller-rig gives the opportunity to simplify the validation activity, under safe conditions, and to reduce the costs. The main challenge is to be able to reproduce the same adhesion conditions on a roller-rig with respect to the track, especially in degraded conditions. First, the paper shows experiments performed to reproduce degraded adhesion on a conventional roller-rig for a single wheelset. Then, an innovative roller-rig is proposed in order to reproduce the effect of the passage of several wheelsets on the track.     

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.     

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.     

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.     

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.     

Facing the Challenge from WTO, Creating the Future of the Auto Industry

Editor's note: With a joint expectation of governments and common publics, China is speeding up to enter into the World Trade Organization and may be a member of WTO family soon. The concerns on the China's accession to WTO are what kinds of deep impacts will be brought on the China Auto Industry. Therefore, from now on, here's a series of articles collected to discuss that, covering whole auto industry, car industry, auto market, as well as after-market, etc. Meanwhile, I am grateful for any responses on this issue at your convenient time.     

Guidelines for the Development of the Auto Industry

Ⅰ. Cars The emphasis of this sector must be on developing economy cars which meet the demands of safety, energy conservation, emission regulations and individual use, and further raising the share in the total auto production. Environmentally-friendly cars for use as taxis should also be developed. By the end of the Tenth Five-Year-Plan period, gasoline