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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 practical three-dimensional wheel-rail interaction element for dynamic response analysis of vehicle-track systemsPublication . Liu, Yongdou; Montenegro, Pedro Aires; Gu, Quan; Guo, Wei; Calçada, Rui; Pombo, JoãoA novel practical three-dimensional (3D) wheel-rail interaction (WRI) element is developed to simulate the interaction between a fast-moving wheel node and nodes of the rail. Different from most previous methods of wheel-rail contact in multibody dynamics, the wheel-rail relationship in this paper is simulated by the WRI element. The WRI element is implemented into a general finite element software framework (i.e., OpenSees), which allows us study not only the vehicle behavior as the multibody models allow, but also the structure behavior with any degree of complexity. Implemented in a FEM framework with strong nonlinear capabilities, it also allows us to study scenarios with important nonlinearities. Compared to most existing models, the WRI element has a better compatible property and can be easily added to the vast majority of finite element platforms. The wheel-rail contact geometry is calculated efficiently with wheel/rail profiles fitted through linear curves and contact locations solved through algorithms with a higher efficiency. Local curvatures around contact points are calculated differently to avoid discontinuities of the contact force. Movements of a wheelset and of a train are studied to verify the accuracy and capability of the WRI element in the dynamic simulation of vehicle-track systems.
- 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.
- Wheel-rail contact models in the presence of switches and crossingsPublication . Magalhães, H.; Marques, F.; Antunes, P.; Flores, P.; Pombo, João; Ambrósio, J.; Qazi, A.; Sebes, M.; Yin, H.; Bezin, Y.The development and implementation of wheel-rail contact models in multibody codes are two active research topics, aiming at improving the accuracy of numerical results and computational efficiency of the dynamics analysis. However, the realism of numerical results is challenged when considering switches and crossings (S&C), where the most adverse wheel-rail contact conditions occur. This paper presents a benchmark study where the performance of the multibody codes MUBODyn, VOCO and VI-Rail are assessed using three case scenarios that involve typical contact conditions observed in S&C. A focused description of the relevant methods to determine the wheel-rail contact forces is presented for each software. The three scenarios considered in this work have been designed to represent typical challenging contact conditions observed in S&C, i.e. conformal contact, contact with a sharp edge, and impact loads. The scenarios proposed in this work are fully described, making them easily reproducible. The agreement between results is discussed in the framework of the methods implemented in each code. This work highlights the impact of wheel-rail contact methods on the results as well as on the computational efficiency of the multibody codes.
- 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 methodology to study the pantograph-catenary dynamics in curved railway tracksPublication . Antunes, Pedro; Ambrosio, Jorge; Pombo, João; Facchinetti, AlanThe pantograph-catenary system is responsible to provide an uninterrupted energy supply to power electric traction railway vehicles. The analysis of the dynamic behaviour of the catenary and pantograph, as well as its interaction, has been the objective of active research to improve energy collection quality. This work proposes an approach for the fully three-dimensional dynamic analysis of pantograph-catenary interaction in general railway tracks including curves. The catenary model and the trajectory of the pantograph base are defined with respect to the track geometry considering the conventional definition used by the rail industry, i.e. the track curvature, cross-level and vertical position. The pantograph is modelled using a multibody formulation being its base motion constrained to follow the generalised trajectory from the railway vehicle roof. The finite element method is used to model the catenary. A co-simulation procedure is set to establish the coupled dynamics of the two systems. In order to demonstrate the methodology, setup models for curved catenaries, analyse modelling implications and highlight applicability, realistic case studies of pantograph-catenary interaction in high-speed rail operations are presented and discussed. In the process, significant differences are found in the dynamic response of the catenary in curved and straight tracks.
- Prediction of mechanical properties of rail pads under in-service conditions through machine learning algorithmsPublication . Ferreño, Diego; Sainz-Aja, Jose Adolfo; Carrascal, Isidro; Cuartas, Miguel; Pombo, João; Casado, José A.; DIEGO, SORAYATrain operations generate high impact and fatigue loads that degrade the rail infrastructure and the vehicle components. Rail pads are installed between the rails and the sleepers in order to damp the transmission of vibrations and noise and to provide flexibility to the track. These components play a crucial role in maximizing the durability of the railway assets and minimizing maintenance costs. Rail pads can be fabricated with different polymeric materials that exhibit non-linear mechanical behaviours, which strongly depend on the service conditions. Therefore, it is extremely difficult to estimate their mechanical properties, in particular the dynamic stiffness. In this work, several machine learning methodologies (multilinear regression, K nearest neighbours, regression tree, random forest, gradient boosting, multi-layer perceptron and support vector machine) were used to determine the dynamic stiffness of rail pads depending on their in-service conditions (temperature, frequency, axle load and toe load). 720 experimental tests, under different realistic operating conditions, were performed to produce a dataset that was then used for the training and testing of the machine learning methods. The optimal algorithm was gradient boosting for EPDM (R2 of 0.995 and mean absolute percentage error of 5.08% in the test dataset), TPE (0.994 and 2.32%) and EVA (0.968 and 4.91%) pads. This model was implemented in an application, available for the readers of this journal, developed on the Microsoft .Net platform that allows the dynamic stiffness of the pads study to be estimated as a function of the temperature, frequency, axle load and toe load.
- 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.
- Three-dimensional modelling of slab-track systems based on dynamic experimental testsPublication . Thölken, D.; Abdalla Filho, João Elias; Pombo, João; Sainz-Aja, J.; Carrascal, I.; Polanco, J.; Esen, A.; Laghrouche, O.; Woodward, P.The accurate computational modelling of railway systems is crucial for analysis and design, which allows for excellent and enduring performance of such systems. It is capable of providing the industry with data for improving speed, comfort, load capacity and reliability. Further, as accurate solutions serve as an aid to improve railway systems, they contribute to quality services, social welfare, cost effectiveness and sustainability. An important component of a railway system is the track, which, in general, requires high investments for construction and maintenance. This work develops calibrated three-dimensional (3D) Finite Element (FE) models for slab track systems which can be employed for analysis and design with great level of reliability. These models are developed based on full-scale dynamic tests performed under the application of loads which simulate the passage of high-speed trains. The components considered are the rails, rail pads, slab track, grout, Hydraulicaly Bonded Layer (HBL), Frost Protection Layer (FPL) and subgrade. The FE models are built and calibrated in order to reproduce the measured displacement and acceleration test results. Due to the uncertainties in some material properties, a parametric analysis is also performed to establish to which material characteristics of the system the model is more sensitive to. It has been found that the Young’s moduli for the FPL layer and subgrade are the most important parameters. Further, the stiffness properties of rail pads play a paramount role in the accuracy of the model.
- The importance of sleepers spacing in railwaysPublication . Ortega, Roberto Sañudo; Pombo, João; Ricci, Stefano; Miranda, MarinaThe railway tracks are composed of steel rails that are supported by the infrastructure through sleepers, which are generally assembled with a fixed separation between them. Sleepers and fastenings are the most numerous elements of the superstructure. The global cost of these elements is directly proportional to their number along the track. Therefore, the reduction of the number of these components can generate relevant reductions of track construction costs. Nonetheless, very few studies focused on the optimal sleeper spacing and its consequences. Moreover, the railway industry uses fixed separation values based on past experience, rather than on scientific knowledge. In line with this reasoning, the objective of this work is to analyse the optimal sleeper spacing in order to contribute to the minimization of track costs. The work starts from an overview of the sleepers spacing used over the world and analyses how this can affect the track performance. This study is valuable for design and construction of new tracks, as well as for the maintenance and renewal of existing ones, helping to achieve cost savings for the rail industry, positive environmental results and consequent contributions to the competitiveness of rail transport.
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