Rosario Chamorro

A multi-body system approach for finite-element modelling of rail flexibility in railroad vehicle applications

In this investigation, a non-linear finite-element formulation for modelling the rail structural flexibility in multi-body railroad vehicle systems is presented. Two different types of interpolations are used in the kinematic equations developed in this study; the geometry interpolation and the deformation interpolation. In the proposed formulation, the rails can have arbitrary geometry, which is described using the isoparametric geometric interpolation. The coordinates of the polynomials used in this interpolation represent constant position and gradient coordinates, which can be used to describe accurately the rail geometry. On the other hand, the rail deflections are described using the deformation interpolation and the non-linear finite-element floating frame of reference formulation. In the formulation proposed in this investigation, the rail tangent and normal vectors as well as other geometric parameters such as the curvature and torsion at the wheel/rail contact points are expressed in terms of the rail deformation coordinates. The non-linear dynamic coupling between the rail geometry and the vehicle dynamics is also considered in the formulation proposed in this paper. In particular, the coupling between the rail deformation and geometry, contact coordinates, and the non-linear vehicle dynamics is taken into consideration. Furthermore, the longitudinal, lateral, and spin creepages are expressed in terms of the rail deformations, which are the result of the wheel/rail contact forces. This non-linear coupled analysis allows for more accurate prediction of the railroad vehicle dynamics. The main outcome of this study is the development of a new procedure that allows building a complex track model that includes significant details using a finite-element preprocessor computer program. The detailed track model can be used as an input to a general purpose flexible multi-body computer program for a non-linear analysis that accounts for the dynamic coupling between the track flexibility and the vehicle coordinates. Numerical results are presented in order to demonstrate the use of the formulation proposed in this study.

Validation of three-dimensional multi-body system approach for modelling track flexibility

Abstract The objective of this investigation is to examine the results and demonstrate the validity of a proposed multi-body railroad vehicle system formulation that accounts for the dynamic coupling between three-dimensional (3D) contact parameters and the rail structural flexibility. This formulation allows building complex track models that include significant details at a finite-element preprocessing stage. The data of the detailed track model can be used as an input to a general purpose flexible multi-body computer program for a non-linear analysis that accounts for the dynamic coupling between the track flexibility, 3D wheel—rail contact, and the vehicle dynamics. The simulations are performed using the methods of multi-body system dynamics that employ 3D wheel—rail contact methodology capable of finding the wheel—rail contact points online. The effect of the structural flexibility of the rails is included in the equations of motion using the finite-element floating frame of reference formulation. While this formulation allows for an arbitrary reference displacement for the track, this reference displacement is constrained in order to be able to compare the results with those results obtained using simplified approaches. The results obtained by applying the proposed multi-body system/finite-element formulation to a simple railroad vehicle travelling on a deformable tangent track are compared with the results of a moving load on a Winkler foundation. In addition to the simple moving load model used, a second model that accounts for the effect of the vehicle inertia is also used in this study. The comparative study presented in this article shows a good agreement between the results obtained using the two different methods. Furthermore, the results obtained in the case of a flexible track are compared with the results obtained using a rigid track in order to examine the effect of the track structural flexibility on the non-linear dynamics of the rail system.

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.

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

Modelling a Flexible Track in Multibody Railroad Dynamic Simulations

In this investigation a new formulation that can be used to model the track flexibility in railroad dynamic simulations is presented. In contrast to the regular frame of reference formulation used in flexible multibody dynamics, the proposed formulation introduces shape functions for the description of deformation which are defined in a trajectory frame of reference instead of in the body frame of reference. This trajectory frame of reference moves along the track with the same speed as the vehicle does. The selected moving shape functions are those that show a beam on Winkler foundation when a moving load is applied on it. The fact that these functions are not fixed with respect to the body frame introduces new terms for the description of the inertia forces that appear in the track. Results are obtained for an unsuspended wheelset moving on a tangent track for different stiffness foundation. Results are also compared with those obtained on a rigid track.Copyright

Analysis of Steady Motions on Curved Tracks Using Multibody Models

In this paper a systematic procedure for evaluating the steady curving of railroad vehicles is developed. The equations of motion obtained using multibody dynamics and the elastic contact method are used to this end. The method proposed can deal with flange contact of the wheels. Two coordinate transformations are needed to evaluate the steady curving as an equilibrium position of the system instead of a periodic orbit. The stability of the motions is also evaluated by using a special eigenvalue analysis of the equations of motion. The procedure developed simplifies significantly the analysis of the curving performance of railroad vehicles without loosing accuracy or generality. The paper includes as a numerical example the steady motion of an unsuspended wheelset. The comparison of the numerical results with classical theories shows the accuracy of the method proposed.Copyright