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 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 and coordinate selection different methodologies can be used. 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. 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. This paper shows different methods for the eigenvalue analysis of steady motions of railroad vehicles. These methods correspond to: (1) Linear models of the lateral dynamics of railroad vehicles. (2) Nonlinear multibody models of the 3D dynamics of railroad vehicles based on global reference coordinates. (3) Nonlinear multibody models of the 3D dynamics of railroad vehicles based on trajectory coordinates. For the linear models the steady motion calculation is simply the solution of a system of linear equations and the eigenvalue analysis does not require linearization for obvious reasons. Nonlinear multibody models based on global coordinates show periodic orbits associated with the vehicle steady motions. In order to simplify the stability analysis, coordinate transformations can be used to get the steady motions in terms of a constant set of coordinates. In this case the calculation of the steady motion requires the solution of non-linear algebraic equations. If the DAE equations of motion are used in these calculations, a non-standard direct eigenvalue analysis can be used to obtain the system dynamics. If the ODE form of the equations of motion written in terms of independent coordinates is used, the eigenvalue analysis is the standard for ODE systems, however this method requires further computations. Nonlinear multibody models based on trajectory coordinates are more convenient for the eigenvalue analysis than those based on global coordinates. The reason in that the vehicle steady motions are directly obtained as a set of constant coordinates. After this point the calculation of the steady motions and the eigenvalue analysis is completely equivalent. The use of the trajectory coordinate system allows the description of the track deformation with the moving shape functions method. This method can be used to study the coupled vehicle-track dynamics including the eigenvalue analysis for stability calculations. Two numerical examples are presented in this paper. The first one shows the continuation diagram of the eigenvalues of a commercial vehicle as a function of the forward velocity. Results are obtained for the lineal model and for the nonlinear multibody model with global coordinates. The nonlinear multibody model accurately predicts the critical velocity when compared to previous results however the linear model predicts a much lower critical velocity. The second example is an academic model of an unsuspended wheelset travelling on a curved deformable track. The problem is solved with the nonlinear multibody formulation with trajectory coordinates and the moving shape function method. Results show the influence of track flexibility on the steady motion of the wheelset and its stability. This influence is only significant when flange contact occurs during the steady curving.
Eigenvalue analysis of railroad vehicles including track flexibility
2012
20 Seiten, 9 Bilder, 1 Tabelle, 29 Quellen
Conference paper
Storage medium
English
Entry of railroad vehicles into curved track section
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