Antonio M. Recuero

Finite-element analysis of unsupported sleepers using three-dimensional wheel–rail contact formulation

Owing to repeated traffic loads, the ballast of a railroad track can become unevenly distributed, resulting in different settlements of adjacent sleepers and possibly to a sleeper–ballast loss of contact. The sleeper–ballast loss of contact can significantly change the stiffness properties and modes of deformation of the track. This in turn can cause damage to the structure and can lead to undesirable dynamic behaviour of the vehicles that negotiate this damaged track. The focus of this investigation is on developing a more comprehensive procedure that can be used to examine the effect produced by unsupported sleepers of a flexible track on the dynamics of railroad vehicle systems. The procedure used in this study is based on a validated non-linear multi-body railroad vehicle system formulation that takes into account the coupling between the elastic deformations of the track, the sleeper movements, and the three-dimensional contact parameters. The method used in this article allows for developing a detailed finite-element track model that accounts for non-periodic and asymmetrical mechanical defects. The finite-element equations of motion of the track that includes unsupported sleepers are integrated with the non-linear constrained dynamic equations of the multi-body railroad vehicle system. Component mode synthesis methods are used to reduce the number of the governing equations of motion and eliminate high-frequency modes. The dynamic coupling between the track modal co-ordinates and the wheel–rail contact parameters is considered in this investigation by using creepage and creep force expressions that depend on the track deformations and sleeper movements. In order to demonstrate the use of the procedure described in this article, a track model which has rails and sleepers modelled as beams rigidly connected at the intersection points is used. The effect of the ballast is considered using an elastic foundation. The results obtained in this investigation are used to compare between the responses of two tracks; one with no sleeper–ballast loss of support and the other with unsupported sleepers. The results are reported for different values of the forward velocities in order to have a better understanding of the effect of the sleeper loss of support on the system dynamics. The creepages that depend on the track deformations as well as the system frequencies are analysed. The results obtained in this investigation are found to be in good agreement with the results reported in the literature on unsupported sleepers.

Dynamics of the coupled railway vehicle–flexible track system with irregularities using a multibody approach with moving modes

In this work, we assessed the capabilities of a method that uses a multibody system description of railway vehicles based on a moving coordinate system in combination with moving modes of deformation to include track elastic displacements. Because this approach suppresses the influence of the boundary conditions of track models, track length ceases to be an issue for simulations. This existing procedure is briefly described and extended to a wide range of applications that require accounting for track frequency contents. A variety of phenomena long surveyed in the railway literature can thus be addressed. Several examples of a wheelset and a subway vehicle running on corrugated rails along varying-parameter tracks were simulated. Based on the results, the proposed method can efficiently capture the dynamic phenomena behind low-to-mid track frequency vehicle–track interactions, contact patch elasticity and vehicle dynamics.

Use of Finite Element and Finite Segment Methods in Modeling Rail Flexibility: A Comparative Study

Safety requirements and optimal performance of railroad vehicle systems require the use of multibody system (MBS) dynamics formulations that allow for modeling flexible bodies. This investigation will present three methods suited for the study of flexible track models while conclusions about their implementations and features are made. The first method is based on the floating frame of reference (FFR) formulation which allows for the use of a detailed finite element mesh with the component mode synthesis technique in order to obtain a reduced order model. In the second method, the flexible body is modeled as a finite number of rigid elements that are connected by springs and dampers. This method, called finite segment method (FSM) or rigid finite element method, requires the use of rigid MBS formulations only. In the third method, the FFR formulation is used to obtain a model that is equivalent to the FSM model by assuming that the rail segments are very stiff, thereby allowing the exclusion of the high frequency modes associated with the rail deformations. This FFR/FS model demonstrates that some rail movement scenarios such as gauge widening can be captured using the finite element FFR formulation. The three procedures FFR, FSM, and FFR/FS will be compared in order to establish differences among them and analyze the specific application of the FSM to modeling track flexibility. Convergence of the methods is analyzed. The three methods proposed in this investigation for modeling the movement of three-dimensional tracks are used with a three-dimensional elastic wheel/rail contact formulation that predicts contact points online and allows for updating the creepages to account for the rail deformations. Several conclusions will be drawn in view of the results obtained in this investigation.

A Simple Procedure for the Solution of Three-Dimensional Wheel/Rail Conformal Contact Problem

This paper describes a simple and efficient procedure for the treatment of conformal contact conditions with special emphasis on railroad wheel/rail contacts. The general three-dimensional nonconformal contact conditions are briefly reviewed. These nonconformal contact conditions, which are widely used in many applications because of their generality, allow for predicting online one point of contact, provided that the two surfaces in contact satisfy certain geometric requirements. These nonconformal contact conditions fail when the solution is not unique as the result of using conformal surface profiles or surface flatness, situations often encountered in many applications including railroad wheel/rail contacts. In these cases, the Jacobian matrix obtained from the differentiation of the nonconformal contact conditions with respect to the surface parameters suffer from singularity that causes interruption of the computer simulations. The singularities and the fundamental issues that arise in the case of conformal contact are discussed, and a simple and computationally efficient procedure for avoiding such singularities in general multibody systems (MBS) algorithms is proposed. In order to demonstrate the use of the proposed procedure, the wheel climb of a wheelset as the result of an external lateral force is considered as an example. In this example, the wheel and rail profiles lead to conformal contact scenarios that could not be simulated using the nonconformal contact conditions.

Analytical and Numerical Validation of a Moving Modes Method for Traveling Interaction on Long Structures

This work is devoted to the validation of a computational dynamics approach previously developed by the authors for the simulation of moving loads interacting with flexible bodies through arbitrary contact modeling. The method has been applied to the modeling and simulation of the coupled dynamics of railroad vehicles moving on deformable tracks with arbitrary undeformed geometry. The procedure presented makes use of a fully arbitrary Lagrangian–Eulerian (ALE) description of the long flexible solid (track) whose mechanical properties may be captured using a dynamics-preserving selection of modes, e.g., via a Pade approximation of a transfer function. The modes accompany the contact interaction rather than being referred to a fixed frame, as it occurs in the finite-element floating frame of reference formulation. In the method discussed in this paper, the mesh, which moves through the long flexible solid, is defined in the trajectory coordinate system (TCS) used to describe the dynamics of the set of bodies (vehicle) that interact with the long flexible structure. For this reason, the selection of modes can be focused on the preservation of the dynamics of the structure instead of having to ensure the structures static displacement convergence due to the motion of the load. In this paper, the validation of the so-called trajectory coordinate system/moving modes (TCS/MM) method is performed in four different aspects: (a) the analytical mechanics approach is used to obtain the equations of motion in a nonmaterial volume, (b) the resulting equations of motion are compared to the classical discretization procedures of partial differential equations (PDE), (c) the suitability of the moving modes (MM) to describe deformation due to variable-velocity moving loads, and (d) the capability of the finite nonmaterial volume to describe the dynamics of an infinitely long flexible body. Validation (a) is completely general. However, the particular example of a moving load applied to a straight beam resting on a Winkler foundation, with known semi-analytical solution, is used to perform validations (b), (c), and (d).

Use of ANCF finite elements in MBS textile applications

The objective of this investigation is to present a new flexible multibody system (MBS) approach for modeling textile roll-drafting sets used in chemical textile industry. The proposed approach can be used in the analysis of textile materials which have un-common material properties best described by specialized continuum mechanics constitutive models, for instance, the lubricated polyester filament bundles (PFB) presented in this paper. In this investigation, PFB is modeled as a hyper-elastic transversely isotropic material using absolute nodal coordinate formulation (ANCF). The PFB strain energy density function is decomposed into a fully isotropic component and an orthotropic, transversely isotropic component expressed in terms of five invariants of the right Cauchy-Green deformation tensor. Using this energy decomposition, the second Piola-Kirchhoff stress and the elasticity tensors can also be split into isotropic and transversely isotropic parts. Constitutive equations are used to evaluate the generalized material forces associated with the coordinates of three-dimensional fully-parameterized ANCF finite elements. The proposed model allows for modeling the dynamic interaction between the rollers and PFB and allows for using spline functions to specify the PFB forward velocity. The paper demonstrates that the textile material constitutive equations and the MBS algorithms can be used effectively to obtain numerical solutions that define the state of strain of the textile material and the relative slip between rollers and PFB and therefore provide a good method to study the roll-drafting process in the chemical textile industry.Copyright

Stability Analysis of Multibody Systems With Long Flexible Bodies Using the Moving Modes Method and Its Application to Railroad Dynamics

In order to model a long flexible body subjected to a moving load within multibody systems, the flexibility can be considered by using a special floating frame of reference approach. In this approach the body deformations are described using shape functions defined in a frame of reference that follows the load. The definition of the deformation shape functions in the load-following frame of reference leads to additional terms of the inertia forces of the flexible body. This method was recently presented by the authors and named the moving modes method. The selected shape functions used in this work are the steady deformation shown by a flexible straight body subjected to a moving load. In this investigation the new formulation is applied to the steady motion and stability analysis of railroad vehicles moving on curved tracks.

Modeling Infinitely Long Flexible Railroad Tracks Using Moving Modes and Krylov Subspaces Techniques

This paper presents a method to model the flexibility of railroad tracks for the dynamic analysis of vehicle-track interaction. In addition to being a complex structure, the flexible track is infinitely long and shows small areas of deformation whose position moves with time. Due to these properties, the efficient modeling of the track as a flexible body in a multibody system formalism is a challenging problem. In this work the model is developed using the moving modes method in combination with Krylov subspaces techniques. The moving modes method that was previously presented by the authors defines the deformation modes in a trajectory frame whose position changes with respect to the flexible track. In this paper the moving modes are selected from a detailed finite element model of the track and a model order reduction technique based on Krylov subspaces. These modes of deformation are adequate to be selected as moving modes since they affect a small area of the flexible body and they are obtained by assuming the load distribution that actually takes place during the dynamic interaction. However, the most interesting property of the Krylov subspace modes is that they can be selected such that the frequency response function of the reduced order model matches that of the full model with the desired degree of accuracy. In this paper a multibody formulation of railroad vehicles and flexible tracks based on the trajectory frame is presented and applied to the numerical simulation of a full railroad car on a track with geometric irregularities.Copyright

Modeling Rail Flexibility Using Finite Element and Finite Segment Methods

Safety requirements and optimal performance of railroad systems require the utilization of multibody System (MBS) formulations that allow for modeling flexible bodies. This investigation will present three methods suited for the study of flexible track models while conclusions about their implementations and features are made. A validated method combining Floating Frame of Reference (FFR) and Finite Element (FE) to model flexible rails is utilized for comparison. In this procedure, component mode synthesis is used to extract a number of low-frequency modes of vibration which describe the deformation of the rail. Likewise, a method that discretizes the flexible body as a finite number of rigid elements that are linked by springs and dampers is applied for railroad simulations. This method, called Finite Segment or Rigid Finite Element (FS), can in turn be combined with FFR through the extraction of mode shapes of the FS model. Convergence of the methods is analyzed. A comparison will be made between these three procedures establishing differences among them and analyzing the specific application of FS to modeling track flexibility. The three aforementioned procedures may be applied to three-dimensional track models and will be used together with three-dimensional wheel/rail contact formulation that predicts contact points online and allows for updating the creepages to account for the rail movements and deformations. Several comparisons and conclusions will be drawn in view of the results obtained in this investigation.Copyright

Eigenvalue Analysis of Multibody Models of Railroad Vehicles Including Track Flexibility

The stability analysis of railroad vehicles using eigenvalue analysis can provide essential information about the stability of the motion, ride quality or passengers comfort. The system eigenvalues are not in general a vehicle property but a property of a vehicle travelling steadily on a periodic track. Therefore the eigenvalue analysis follows three steps: calculation of steady motion, linearization of the equations of motion and eigenvalue calculation. This paper deals with different numerical methods that can be used for the eigenvalue analysis of multibody models of railroad vehicles that can include deformable tracks. Depending on the degree of nonlinearity of the model, coordinate selection or the coordinate system used for the description of the motion, different methodologies are used in the eigenvalue analysis. A direct eigenvalue analysis is used to analyse the vehicle dynamics from the differential-algebraic equations of motion written in terms of a set of constrained coordinates. In this case not all the obtained eigenvalues are related to the dynamics of the system. As an alternative the equations of motion can be obtained in terms of independent coordinates taking the form of ordinary differential equations. This procedure requires more computations but the interpretation of the results is straightforward.Copyright