Non-elliptical Contact Research Articles

A modified Hertzian-based wheel-rail contact model for vehicle system dynamics simulation

This paper develops a modified Hertzian-based wheel-rail contact model (MHM) to improve the robustness and accuracy of the traditional Hertzian contact model in vehicle-track coupling dynamics simulation. First, the wheel-rail non-Hertzian contact area is estimated based on the virtual penetration (VP) area, and an equivalent ellipse of the non-Hertzian contact area is calculated. Then, taking the equivalent elliptical contact patch as the input, the wheel-rail normal problem is solved by using Hertzian contact theory. Finally, considering the effect of the non-elliptical contact patch on Kalker’s linear coefficient, a modified Shen–Hedrick–Elkins model is proposed. The computation accuracy, robustness, and efficiency of the developed MHM are assessed by comparing it with a robust Kalker variational method (RKVM), a VP-based non-Hertzian contact model RNHM, and two traditional Hertzian-based models. The comparison results show that the MHM improves the computational robustness and accuracy of the traditional Hertzian-based contact models. MHM achieves almost the same computational accuracy as the RNHM, but its computational efficiency is 2.4 times faster than RNHM. The developed MHM is an ideal model for vehicle-track coupling dynamics simulation.

Application of the extended FASTSIM for non-Hertzian contacts towards the prediction of wear and rolling contact fatigue of wheel/rail systems

In this paper, the extension of the FASTSIM algorithm to a SDEC region is implemented and a strategy is proposed to generalise this algorithm to any general non-elliptic contact patch. The extended FASTSIM is applied to the prediction of wheel wear and rolling contact fatigue under typical non-Hertzian wheel/rail contact conditions, using CONTACT as a reference and showing that the extended version of FASTSIM proposed in this work provides more accurate solutions for non-Hertzian contact conditions, compared to other widely used formulations of FASTISM.

A novel local ellipse method for ellipse-based tangential contact model applied to wheel-rail contact

ABSTRACT In order to simplify wheel-rail rolling contact for engineering computation, it usually applies an ellipse-based tangential contact model to non-elliptical contact patch. This paper proposes a novel local ellipse method to reach this transition due to contact stiffness difference in elliptic and non-elliptical contact. The method is similar to STRIPES that regards the contact patch as some strips along the rolling direction and locating at the center of their respective virtual ellipses. However, it provides an alternative way for the determination of the local virtual ellipse using elliptic integral, normal contact pressure and longitudinal contact boundary. One novel aspect is the lateral curvature at each strip is solely determined and needs no additional modification. This method is combined with FaStrip and evaluated by CONTACT. It thus provides an efficient pre-process of simplified tangential contact model to be applied to non-elliptical contact in vehicle-track dynamics modelling and wheel-rail damage prediction.

Study of rail-wheel contact problem by analytical and numerical approaches

This study presents the rail wheel contact problems under normal and tangential categories. Both analytical and numerical approaches were used for modelling, where the analytical approach assumed elliptical contact patches based on the Hertz theory. In the numerical approach, 3D finite element models were used to investigate non-elliptical contact patches. The only elastic material model was considered in the case of Hertz theory. However, in the case of finite element analysis, both elastic and elastoplastic material models were used to simulate the material's behavior under the applied load. The elastoplastic material model was used to determine the amount of stress at which the plastic deformation starts, which enables determining the rail wheel's critical load. The commercial software ABAQUS was employed for 3D modeling and contact stress analysis. The study shows maximum stress at 3 mm from the rail wheel contact surface when the maximum load of 85 kN is applied. This initiates the cracks in the subsurface and causes the portion of the rail wheel to break off in the form of spalling after a certain time.

Comparison of wheel–rail contact models in the context of multibody system simulation: Hertzian versus non-Hertzian

The calculation of the wheel–rail contact forces is one of the most difficult yet time-consuming processes in multibody system (MBS) simulations for a vehicle-track interaction system. The classical combination of the Hertzian model with the FASTSIM algorithm is the most widely used model in MBS code for railway application and the ‘exact’ solver CONTACT is seldom used due to its high computational cost. A trade-off solution between accuracy and computational efficiency is the simplified and approximate non-Hertzian approach. This paper attempts to compare the influence on MBS simulation for rail vehicle system dynamics of the varied combinations of the classical contact models (i.e. Hertz model and FASTSIM), well-known simplified non-Hertzian model (Kik–Piotrowski model) recently developed improved simplified non-Hertzian models i.e. Extended Kik–Piotrowski and Kalker Book of Tables for Non-Hertzian contact (KBTNH), and the CONTACT algorithm. The results show that all non-Hertzian approaches deviate from the classical Hertzian solutions in both local contact and global dynamics and the KBTNH model provides better agreement with CONTACT than the FASTSIM algorithm for non-elliptic contact conditions considered in this study. A detailed analysis of the causes and influences of the difference due to varied contact models is presented.

Reduction of freight car wheel wear of 1520 mm gauge railways

A brief description is given of the comprehensive modernization of standard freight car trucks through the use of devices of American companies adapted for railways with a 1520 mm gauge and wheels with ITM-73 specially developed wear-resistant profile, which allows several times to increase the resource of problematic running gears. An approximate method is proposed for solving the wheel–rail interaction problem with determining the position and size of non-elliptic contact patches, including with conformal contact. Using this method, new profiles have been developed for turning worn wheels (ITM-73-01), as well as new wheels for cars with an axial load on rails of 23.5 tf (ITM-73-02) and 25 tf (ITM-73-03). The data of experimental studies showed that the average wear rate of the wheel flanges of freight cars with complex modernized trucks equipped with wheels with ITM-73-01 profile is 3.5-5 times lower than that of a standard car with a standard wheel profile. According to forecast estimates, the use of wheels with profiles ITM-73-02, ITM-73-03 will allow to achieve even greater increase in the resource indicators of wheelsets for wear of the flanges.

Applying Two Simplified Ellipse-Based Tangential Models to Wheel-Rail Contact Using Three Alternative Nonelliptic Adaptation Approaches: A Comparative Study

In the modeling of railway vehicle-track dynamics and wheel-rail damage, simplified tangential contact models based on ellipse assumption are usually used due to strict limitation of computational cost. Since most wheel-rail contact cases appear to be nonelliptic shapes, a fast and accurate tangential model for nonelliptic contact case is in demand. In this paper, two ellipse-based simplified tangential models (i.e., FASTSIM and FaStrip) using three alternative nonelliptic adaptation approaches, together with Kalker’s NORM algorithm, are applied to wheel-rail rolling contact cases. It aims at finding the best approach for dealing with nonelliptic rolling contact. Compared to previous studies, the nonelliptic normal contact solution in the present work is accurately solved rather than simplification. Therefore, it can avoid tangential modeling evaluation affected by inaccurate normal contact solution. By comparing with Kalker’s CONTACT code, it shows both FASTSIM-based and FaStrip-based models can provide accurate global creep force. With regard to local rolling contact solution, only the accuracy of FaStrip-based models is satisfactory. Moreover, Ayasse-Chollet’s local ellipse approach appears to be the best choice for nonelliptic adaptation.

The Kalker book of tables for non-Hertzian contact of wheel and rail

ABSTRACTA new regularisation of non-elliptical contact patches has been introduced, which enables building the look-up table called by us the Kalker book of tables for non-Hertzian contact (KBTNH), which is a fast creep force generator that can be used by multibody dynamics system simulation programs. The non-elliptical contact patch is regularised by a simple double-elliptical contact region (SDEC). The SDEC region is especially suitable for regularisation of contact patches obtained with approximate non-Hertzian methods for solving the normal contact problem of wheel and rail. The new regularisation is suitable for wheels and rails with any profiles, including worn profiles.The paper describes the new procedure of regularisation of the non-elliptical contact patch, the structure of the Kalker book of tables, and parameterisation of the independent variables of the tables and creep forces.A moderate volume Kalker book of tables for SDEC region suitable for simulation of modern running gears has been computed in co-simulation of Matlab and program CONTACT.To access the creep forces of the Kalker book of tables, the linear interpolation has been applied.The creep forces obtained from KBTNH have been compared to those obtained by program CONTACT and FASTSIM algorithm. FASTSIM has been applied on both the contact ellipse and the SDEC contact patch. The comparison shows that KBTNH is in good agreement with CONTACT for a wide range of creepage condition and shapes of the contact patch, whereas the use of FASTSIM on the elliptical patch and SDEC may lead to significant deviations from the reference CONTACT solutions.The computational cost of calling creep forces from KBTNH has been estimated by comparing CPU time of FASTSIM and KBTNH. The KBTNH is 7.8–51 times faster than FASTSIM working on 36–256 discretisation elements, respectively.In the example of application, the KBTNH has been applied for curving simulations and results compared with those obtained with the creep force generator employing the elliptical regularisation. The results significantly differ, especially in predicted creepages, because the elliptical regularisation neglects generation of the longitudinal creep force by spin creepage.

Numerical analysis of the effect of track parameters on the wear of turnout rails in high-speed railways

In this study, a numerical procedure is developed to predict the wear of turnout rails, and the effect of track parameters is investigated. The procedure includes simulation of the dynamic interaction between the train and the turnout, the rolling contact analysis, and the wear model. The dynamic interaction is simulated with the validated commercial software Simpack that uses a space-dependent model of a railway turnout. To reproduce the actual operating conditions of a railway turnout, stochastic variations in the input parameters are considered in the simulation of the dynamic interaction. The rolling contact is analyzed with the semi-Hertzian method and improved FASTSIM algorithm, which enable the contact model to deal with situations of multipoint contact and nonelliptic contact. Based on the Archard’s wear law, the wear model requires the calculation of normal/tangential stresses and a relative slide on the contact patches. The numerical procedure is performed for the selected sections of the vehicle, which runs through the railway turnout in the diverging route. By using the numerical procedure, the effect of track parameters (track gage, rail inclination, and friction coefficient) on the wear of turnout rails is analyzed. The results show that the wear of the front wheelset is more serious than the wear of the rear wheelset for a single vehicle. The degree of wear of switch rails is more severe than that of the stock rails and the difference is more obvious for the front wheelset of the switch rails. The wear of switch rails is mainly concentrated on the rail gage corner, while the wear of stock rails is mainly concentrated on the rail crown. For the analysed CN60-1100-1:18 turnout and the high-speed vehicle CRH2 in China, the rail wear rate could be slowed down by increasing the track gage and decreasing the rail inclination. Alternatively, the rail wear rate could be slowed by decreasing the friction coefficient; however, the variation of wear depth is quite small for friction coefficients that are larger than 0.3.

Effects of wheel–rail contact modelling on wheel wear simulation

Three non-elliptic contact models, namely Kik–Piotrowski method, STRIPES and ANALYN, are first compared to the Hertz theory and the CONTACT code in terms of the normal contact solution. Further, for the contact models except for CONTACT, the tangential contact solutions are calculated by a modified simplified theory of Kalker (FASTSIM) based on the normal ones to compare with that of CONTACT. Afterwards, a wheel wear prediction model, consisting of a multi-body dynamic model of the railway vehicle, a wheel–rail contact model and a wear function developed by the University of Sheffield, is developed. The influences of the five contact models mentioned above on the wheel wear prediction are investigated from viewpoints of calculation efficiency and accuracy. The results indicate that using Hertz theory and FASTSIM to solve the normal and tangential contact problem, respectively, in the wheel wear simulation is a good choice in order to consider a compromise between the calculation efficiency and accuracy.

Wheel/Rail Tangential Contact Stress Evaluation by Means Of the Modified Strip Method

The article deals with the way of calculating tangential stresses over non-elliptical contact patch where Kalker's simplified method FASTSIM can be used advantageously. This method named FASTSTRIP is adapted for non-elliptical contact area calculated by means of the Strip method. This method is almost as quick as FASTSIM and the results are similar to the CONTACT results. This method may be useful for rail vehicles in track dynamics computation.

A novel method to model wheel–rail normal contact in vehicle dynamics simulation

An approximate analytical method is proposed for calculating the contact patch and pressure distribution in the wheel–rail interface. The deformation of the surfaces in contact is approximated using the separation between them. This makes it possible to estimate the contact patch analytically. The contact pressure distribution in the rolling direction is assumed to be elliptic with its maximum calculated by applying Hertz' solution locally. The results are identical to Hertz's for elliptic cases. In non-elliptic cases good agreement is achieved in comparison to the more accurate but computationally expensive Kalker's variational method (CONTACT code). Compared to simplified non-elliptic contact methods based on virtual penetration, the calculated contact patch and pressure distribution are markedly improved. The computational cost of the proposed method is significantly lower than the more detailed methods, making it worthwhile to be applied to rolling contact in rail vehicle dynamics simulation. Such fast and accurate estimation of contact patch and pressure paves the way for on-line modelling of damage phenomena in dynamics simulation packages.

A 3D dynamic model to investigate wheel–rail contact under high and low adhesion

In this article the finite element elastic-plastic code ANSYS/LS-DYNA was utilised to investigate the stress states and material response of wheel/rail under three contact situations, which included high and low adhesion, and full slip. Canted and non-canted rails were considered to measure how the cant angle affected the contact stress levels. Furthermore, the effects of the contact curvatures on the contact zone and contact pressure were also examined. The simulation of wheel flange contact was conducted to compare the stress state of the rail head and rail gauge. The results showed that a higher level of adhesion would enlarge the slip region in the stick/slip contact patch and widen the surface damage to a larger area. Moreover, the worn wheel/rail profiles would result in a non-elliptical contact patch and an increase of the contact pressure. Based on the shakedown map, it was anticipated that the rail would be damaged from the ratchetting response of the material. • New and worn profiles of wheel and rail were introduced in the contact analysis. • Canted and non-canted rails were applied to evaluate its influence on the contact stresses. • The stress states were determined under high and low adhesion, and full slip contact conditions. • The material response of rail to contact loading was predicted by the shakedown map.

Comparison of non-elliptic contact models: Towards fast and accurate modelling of wheel–rail contact

The demand to investigate and predict the surface deterioration phenomena in the wheel–rail interface necessitates fast and accurate contact modelling. During the past 20 years, there have been attempts to determine more realistic contact patch and stress distributions using fast simplified methods. The main aim of the present work is to compare some of these state-of-the-art, non-elliptic contact models available in the literature. This is considered as the first step to develop a fast and accurate non-elliptic contact model that can be used on-line with vehicle dynamics analysis. Three contact models, namely STRIPES, Kik-Piotrowski and Linder are implemented and compared in terms of contact patch prediction, as well as contact pressure and traction distributions. The evaluation of these models using CONTACT software indicate the need for improvement of contact patch and pressure estimation in certain contact cases.

A Modified Strip Method to Speed up the Tangential Stress between Wheel and Rail Calculation

The articles deals with the way of calculation of tangential stresses over non-elliptical contact patch, where is possible to utilize with advantage the Kalkers simplified method FASTSIM. This method named FASTSTRIP is adapted for non-elliptical contact area calculated by means of the Strip method. This method is almost quick as FASTSIM and the results are similar to the CONTACT results. This method may be useful for rail vehicles in track dynamics computation.

The FASTSIM Method Modification to Speed up the Calculation of Tangential Contact Stresses between Wheel and Rail

The articles deals with the way of calculation of tangential stresses over non-elliptical contact patch, where is possible to utilize with advantage the Kalker's simplified method FASTSIM. This method named FASTSTRIP is adapted for non-elliptical contact area calculated by means of the Strip method. This method is almost quick as FASTSIM and the results are similar to the CONTACT results. This method may be useful for rail vehicles in track dynamics computation.

Refining the modelling of vehicle–track interaction

An enhanced model of a passenger coach running on a straight track is developed. This model includes wheelsets modelled as rotating flexible bodies, a track consisting of flexible rails supported on discrete sleepers and wheel–rail contact modules, which can describe non-elliptic contact patches based on a boundary element method (BEM). For the scenarios of undisturbed centred running and permanent hunting, the impact of the structural deformations of the wheelsets and the rails on the stress distribution in the wheel–rail contact is investigated.

Impact of non-elliptic contact modelling in wheel wear simulation

Advances in simulation of railway wheel wear in the sense of material removal have drawn the attention to the importance of wheel–rail contact modelling. As a further step of enhancing the used simulation procedure in direction of increased generality and reduced need for application-dependent calibration, the focus of this investigation is the influence of non-elliptic contact models on the wheel wear rate and profile shape. To facilitate evaluation the semi-Hertzian contact procedure Stripes, developed by INRETS in France, has been implemented. To investigate the capabilities of Stripes to assess the contact area and pressure, shape comparisons have been made with other numerical methods for a set of wheel–rail contact situations. The referenced results are based on the linear elastic half-space assumption, elastic finite element analysis, and elastic–plastic finite element analysis. For reference also the elliptic contact area according to Hertz is shown as given by the contact data table of the multi-body simulation code. After exploring the properties of the Stripes procedure with respect to contact area estimation and pressure distribution, the focus is moved to the influence on wear rate, being the principal objective of this investigation. First the wear distribution over the contact patch is studied and compared to results using the elliptic model from the MBS code Gensys and the non-elliptic approach with Kalker's code Contact. Finally the evolution of the wheel profile is simulated for a few typical cases. This investigation of wear distributions over non-elliptic patches under different operating conditions indicates significant differences compared to both Contact and the applied Hertzian approach. The expansion from single contact occasions to complete simulations indicates comparable material removal rates but relocation towards the flange side. This tendency is apparent in all of the cases shown, however limited to initial wear in tangent run or reasonably mild curve negotiation.

A simplified model of wheel/rail contact mechanics for non-Hertzian problems and its application in rail vehicle dynamic simulations

The presented model assumes semi-elliptical normal pressure distribution in the direction of rolling. The contact area is found by virtual penetration of wheel and rail. The normal pressure is calculated by satisfying contact conditions at the geometrical point of contact. The calculation is non-iterative, fast and completely reliable. It may be carried out on-line in MultiBody Systems (MBS) computer codes. The tests using the programme CONTACT by Kalker and experience from application in MBS codes show that the model is suitable for technical applications. The creep forces have been calculated with the FASTSIM algorithm, adapted for a non-elliptical contact area. Some applications in rail vehicle dynamics and wear simulation have been outlined.

Tangential problem solution for non-elliptical contact areas with the FastSim algorithm

This article deals with the application of the FastSim algorithm to the solution of the tangential contact problem for non-elliptical contact areas. At first, the causes creating problems for the solution of non-hertzian contact areas with this algorithm shall be analyzed. Then, different currently existing methods shall be studied, analyzing their accuracy characteristics and computational cost to determine whether or not they are appropriate to use in dynamic simulations. Finally, a new strategy shall be proposed that, in the opinion of the authors, offers good characteristics of precision and computational cost.