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- Implementation of a non-Hertzian contact model for railway dynamic applicationPublication . Magalhães, Hugo; Marques, Filipe; Liu, Binbin; Antunes, Pedro; Pombo, João; Flores, Paulo; Ambrosio, Jorge; Piotrowski, Jerzy; Bruni, StefanoThe development of wheel–rail contact models is an active topic of railway research with the dual objective of improving the accuracy of multibody simulations and reducing its computational effort. This paper extends the online Hertzian contact model, proposed by Pombo et al. (Veh. Syst. Dyn. 45: 165–189, 2007) to propose a non-Hertzian contact model. The new methodology presented here includes the following steps: (i) search of the points of contact; (ii) identification of the undeformed distance function; (iii) evaluation of the contact patch; (iv) calculation of the normal and tangential contact forces; (v) application of the contact forces in the multibody vehicle model. Among several contact models available in the literature, this non-Hertzian contact approach uses the Kik–Piotrowski model for the normal contact force, while the tangential forces are obtained from the interpolation of the available Kalker Book of Tables for non-Hertzian (KBTNH) contact. With the purpose to demonstrate the proper implementation and selection of parameters that define this new model, several contact analysis and dynamic simulations are performed in which the wheel S1002 and the rail UIC50 are considered. First, the contact analyses that determine the contact condition of different wheel–rail interactions serve to assess the accuracy of the Hertzian and non-Hertzian models with respect to the software of reference CONTACT. Second, the Hertzian and non-Hertzian models are utilised to perform dynamic simulations of a wheelset, a bogie and a vehicle running in tangent and curved tracks. In short, this work provides, not only a complete description of the implementation of a non-Hertzian contact model in a multibody code, but also suggests for the proper selection of the parameters that promote better accuracy and optimal computational efficiency.
- A three-dimensional approach for contact detection between realistic wheel and rail surfaces for improved railway dynamic analysisPublication . Marques, Filipe; Magalhães, Hugo; Pombo, João; Ambrosio, Jorge; Flores, PauloThe wheel-rail contact modeling problem assumes a preponderant role on the dynamic analysis of railway systems using multibody systems formulations. The accurate and efficient evaluation of both location and magnitude of the wheel-rail contact forces is fundamental for the development of reliable computational tools. The wheel concave zone might be a source of numerical difficulties when searching the contact points, which has been neglected in several works. Here, it is demonstrated that the minimum distance method does not always converge when the wheel surface is not fully convex, being an alternative methodology proposed to perform the contact detection. This approach examines independently the contact between each wheel strip and the rail, where the maximum virtual penetration is determined and associated with the location of the contact point. Then, an Hertzian-based force model is considered for both normal and tangential forces. The results obtained from dynamic simulations show that the minimum distance method and the proposed methodology provide a similar response for simplified wheel profiles. However, the new approach described here is reliable in the identification of the contact point when realistic wheel profiles are considered, which is not the case with the minimum distance method.
- A co-simulation approach to the wheel–rail contact with flexible railway trackPublication . Antunes, Pedro; Magalhães, Hugo; Ambrosio, Jorge; Pombo, João; Neves Costa, JoãoThe standard approach to railway vehicle dynamic analysis includes running the vehicle multibody models in rigid railway tracks. The wheel–rail contact, independently of the rolling contact model used, is either handled online or via lookup tables. This traditional approach disregards the coupling effects between the railway vehicle dynamics and the railway track flexibility. In this work the assumption of rigidity of the railway track is relaxed and a finite element model of the complete track, i.e. rails, pads, sleepers, ballast and infrastructure, is used to represent the track geometry and flexibility. A rail–wheel contact model that evaluates the contact conditions and forces is used online. The dynamics of the railway vehicle is described using a multibody methodology while the track structure is described using a finite element approach. Due to the fact that not only the multibody and the finite element dynamic analysis use different integration algorithms but also because the vehicle and track models are simulated in different, codes a co-simulation procedure is proposed and demonstrated to address the coupled dynamics of the system. This approach allows us to analyze the vehicle dynamics in a flexible track with a general geometry modeled with finite elements, i.e. including curvature, cant, vertical slopes and irregularities, which is another novel contribution. The methodology proposed in this work is demonstrated in an application, in which the railway vehicle–track interaction shows the influence of the vehicle dynamics on the track dynamics and vice versa.
- A new simplified approach to deal with conformal contact in railway dynamicsPublication . Marques, Filipe; Magalhães, Hugo; Liu, Binbin; Pombo, João; Flores, Paulo; Ambrosio, Jorge; Bruni, StefanoThe contact between a wheel and a rail in the context of railway dynamics is mostly the result of the interaction of two convex surfaces. However, when negotiating sharp curves and due to worn profiles, the conformal contact tends to occur. In this type of interaction, the contact zone cannot be contained in a single plane as opposed to the non-conformal case. Hence, a new methodology to deal with conformal contact in the framework of railway dynamics is proposed in this work. A curved axis in the lateral direction is considered, and it is used to measure the separation between profiles. Moreover, the contact patch is divided into strips in which it is locally planar, and the pressure distribution is estimated based on Kik-Piotrowski model. The interaction between a wheel and rail has been tested for four static cases. The preliminary results show that this methodology can be a reliable alternative to the use of more computationally intensive approaches as the boundary or finite element methods.
- Utilization of non-conformal wheel surfaces for railway dynamicsPublication . Marques, Filipe; Magalhães, Hugo; Pombo, João; Ambrosio, Jorge; Flores, PauloThe dynamic analysis of railway systems using multibody systems formulation is nowadays a reliable tool for several studies, in which the wheelrail contact interaction has significant importance. The definition of contacting geometries affects directly the dynamic response of the system. For sake of simplicity and computational efficiency, some authors simplify the wheel profile to avoid its concave part. This work intends to study the impact of utilizing a simplified non-conformal profile instead of a real wheel profile. For this purpose, an Hertzian-based contact force model is used to compute either the normal and creep forces. A wheelset rolling over a straight track is used as demonstration case. The results show that although the location of the contact points is similar, the use of simplified wheel profile may have an extensive impact on the dynamic response of the system.
- A dedicated control design methodology for improved tilting train performancePublication . Magalhães, Hugo; Antunes, Pedro; Pombo, João; Ambrosio, JorgeThe development of detailed multibody models of railway vehicles is essential to address industrial problems through computational tools. The assessment of vehicle dynamic performance is one of the studies that can be performed with a multibody software. But when tilting trains are considered, which comprise active suspension elements, control engineering theories are required to estimate the forces developed by the actuators. Despite its importance, in general the details about the tilting control algorithm are unknown. In this work, a dedicated control design methodology is proposed to estimate the control algorithm of a tilting system in order to assure a proper vehicle performance. For this purpose, a detailed multibody model of a tilting train is used to perform a batch of simulations in order to develop an accurate linear model of the tilting system and to study its performance in realistic operation conditions. Thus, the traditional control techniques can be used to assess the tilting system dynamics and to design the control algorithm so that proper tilting performance is ensured. The control algorithm and the tilting performance are tested on a curved and tangent track with track irregularities. The comfort indexes PCT and RMS are used here to assess the tilting system.
- A novel methodology to automatically include general track flexibility in railway vehicle dynamic analysesPublication . Neves Costa, João; Antunes, Pedro; Magalhães, Hugo; Pombo, João; Ambrosio, JorgeThe interaction between the rolling stock and the infrastructure plays a crucial role in railway vehicle dynamics. The standard approach consists of using a multibody formulation to model the railway vehicles running on simplified tracks. The track model can be rigid, if it comprises only a geometric description of the rail; semi-rigid, if it considers an elastic foundation underneath the rail; or a moving track model, if it comprises a track section underneath each wheelset traveling with the same speed of the vehicle. Despite their computational inexpensiveness, these approaches do not provide a complete representation of track flexibility and disregard coupling effects with the vehicle and among the track components. This work proposes a methodology to automatically generate finite element models of railway tracks comprising its relevant flexible components, i.e., rails, pads, fastening systems, sleepers, and ballast or slab. The finite element mesh is generated based on a parametric description of the track that allows an accurate description of its geometry, including curvature, cross-level, grade, and irregularities. The methodology is demonstrated with a case study in which a track with a complex geometry is loaded with two different approaches. The first approach prescribes moving loads, which is a typical approach used to design or analyze the infrastructure. The second approach applies loads retrieved from the dynamic analysis of a complete vehicle. The results show the benefits of this method and reveal that prescribed loading underestimates the forces resulting from the vehicle dynamics, which is an important issue on curved sections.
- On the generation of enhanced lookup tables for wheel-rail contact modelsPublication . Marques, Filipe; Magalhães, Hugo; Liu, Binbin; Pombo, João; Flores, Paulo; Ambrosio, Jorge; Piotrowski, Jerzy; Bruni, StefanoIn railway dynamics, the interpolation of lookup tables (LUTs) is a procedure utilized to reduce the computational effort when computing the wheel-rail contact forces. However, the generation of LUTs with multiple inputs and multiple outputs is a challenging task for which aspects such as their minimal size and uniform accuracy over the LUT domain have not been systematically addressed in the literature. Thus, this work presents a comprehensive methodology for a detailed analysis of general LUTs, and identifies ways to improve them. For that, an analysis of the variation of the input parameters is made and the interpolation error is assessed on the cells and edges of the original table, then, based on this analysis, two enhanced LUTs are proposed. The first one is approximately 5 times smaller than the original but holds similar accuracy. The second table exhibits half of the maximum interpolation error of the original LUT but holds an identical size. The methodology is demonstrated here using the recently published Kalker Book of Tables for Non-Hertzian contact (KBTNH) but it can be used by any other LUT approach in order to improve accuracy and/or to reduce size.
- Implementation of a non-Hertzian Contact Model for Railway DynamicsPublication . Magalhães, Hugo; Marques, Filipe; Liu, Binbin; Pombo, João; Flores, Paulo; Ambrosio, Jorge; Bruni, StefanoThe development of wheel-rail contact models is an active topic of research, in which more accurate and reliable methodologies are required to improve the realism of multibody simulations while reducing the computational effort. However, their implementation in a multibody software consists of a challenging task for itself. This paper presents a generalized strategy for the implementation of non-Hertzian contact models. This new methodology is split into the following steps: determination of points of contact; identification of the undeformed distance function; determination of the contact patch; and calculation of the normal and tangential forces which are computed according to the contact conditions and the theories used. Here, the normal force is determined with the Kik-Piotrowski model, while the tangential forces are obtained from the interpolation of the Kalker Book of Tables for Non-Hertzian contact patches. To demonstrate the proper implementation of the new methodology, static and dynamic simulations have been performed. First, a static wheel-rail interaction at different slip conditions is simulated being observed a good agreement with respect to the results obtained from CONTACT. Secondly, a dynamic simulation of a bogie running in a tangent track is considered, in which the contact developed respect the Hertzian conditions. Thus, a comparison between the Hertzian approach and the proposed methodology is possible, being discussed the slight differences between the results obtained from both simulations. Besides the proposed implementation is 4.5 times slower than the Hertzian method considered in this work, for the case study presented in this work, the proposed methodology allows to deal with non-Hertzian contact.
- A finite element methodology to model flexible tracks with arbitrary geometry for railway dynamics applicationsPublication . Costa, J. N.; Antunes, Pedro; Magalhães, Hugo; Pombo, João; Ambrósio, J.The dynamic analysis of railway vehicles requires an accurate representation of the vehicle, the track geometry and structure, and their interaction. Generally, flexible track models with curved geometries represent the rails with straight beam elements, which results in a piecewise linear representation of the rails. Consequently, the wheel-rail contact mechanics are not properly captured, and the wheel-rail contact forces present spurious high-frequency oscillations. This work proposes a novel approach to model flexible railway tracks with arbitrary geometries, in which the correct geometry in the wheel-rail contact mechanics is assured by modeling the rails as Timoshenko curved beam elements. This approach improves both the geometric representation of the rails and the accuracy of the wheel-rail contact forces calculation. A realistic operation scenario in which a multibody model of a railway vehicle runs on a flexible track with a curved geometry is used here to demonstrate the novel aspects of this work and then discuss the improvements over the conventional approaches. The results show that the proposed methodology greatly improves the computation of the wheel-rail interaction forces and prevents spurious oscillations from propagating to the vehicle.