Paul Fisette

Symbolic generation of large multibody system dynamic equations using a new semi-explicit Newton Euler recursive scheme

SummaryThe aim of this paper is to show that multibody systems with a large number of degrees of freedom can be efficiently modelled, taking conjointly advantage of a recursive formulation of the equations of motion and of the symbolic generation capabilities.Recursive schemes are widely used in the field of multibody dynamics since they avoid the “explosion” of the number of arithmetical operations in case of large multibody models. Within the context of our field of applications (railway dynamics simulation), explicit integration schemes are still prefered and thus oblige us to compute the generalized accelerations at each time step. To achieve this, we propose a new formulation of the well-known Newton/Euler recursive method, whose efficiency will be compared with a so-called “O(N)” formulation.A regards the symbolic generation, often decried due to the size of the equations in case of large systems, we have recently implemented recursive multibody formalisms in the symbolic programme ROBOTRAN [1]. As we shall explain, the recursive nature of these formalisms is particularly well-suited to symbolic manipulation.All these developments have been successfully applied in the field of railway dynamics, and in particular allowed us to analyse the dynamic behaviour of several railway vehicles. Some typical results related to a completely non-conventional bogie will be presented before concluding.

A new wheel/rail contact model for independent wheels

SummaryThe classical multibody approach in railway vehicle dynamics considers as rolling element a rigid wheelset, for which the geometrical problem associated with the wheel/rail contact and the formulation of the dynamic equations are well known at the present time. New designs of non-conventional bogies led us to develop a new model for independent wheels in which each wheel/rail contact must be treated separately due to the absence of an axle between left and right wheels. This model constitutes an additional feature of the multibody approach for this type of application. The classical multibody formalism is first briefly reviewed and the wheel/rail contact model is then developed in the case of a straight track. The way the model has been extended to curved track is also explained. Finally, numerical results related to classical and non-conventional bogies will be presented before concluding.ÜbersichtDie klassische Mehrkörper-Annäherung in der Dynamik der Eisenbahnfahrzeuge betrachtet als Rollelement das steife Achse-Räder-System, dessen geometrisches Problem des Kontaktes zwischen Rad und Gleis sowie dessen Formulierung der dynamischen Gleichungen heutzutage allbekannt sind. Neue Konzepte von unkonventionellen Drehgestellen führte die Autoren zur Entwicklung eines neuen Modells für unabhängige Räder, in welchem aufgrund des Fehlens einer gemeinsamen Achse zwischen linkem und rechtem Rad jeder Rad-Gleis-Kontakt getrennt betrachtet werden soll. Dieses Modell bildet einen zusätzlichen Gesichtspunkt der Mehrkörper-Methode für die Lösung solcher Probleme. Nach kurzer Betrachtung des klassischen Mehrkörper-Formalismus wird ein Modell des Rad-Gleis-Kontaktes für eine gerade Strecke entwickelt. Weiter folgt die Ausweitung des Modells auf ein gekrümmtes Gleis und schließlich werden die numerischen Ergebnisse für klassische und nicht-konventionelle Drehgestelle vorgelegt.

A fully symbolic generation of the equations of motion of multibody systems containing flexible beams

The modelling of flexible elements in mechanical systems has been investigated via several methods issuing from both the field of multibody dynamics and the area of structural mechanics and vibration theory. A multibody approach using a recursive formalism in relative coordinates is adopted here. While leading to a highly non-linear system with a dense mass matrix, relative coordinates allow the setting up of the minimal set of equations of motion for open-loop systems. As for the recursive technique, the latter was proved to be a very good candidate for an optimized symbolic generation in the case of rigid multibody systems. These two assertions have led us to generalize such a formalism for a general multibody system containing flexible beams, in order to make its fully symbolic generation possible within the stand-alone program ROBOTRAN [1]. Several validation examples are presented to illustrate the method and to highlight the efficiency and the user-friendliness of this fully symbolic model, even when dealing with beams undergoing large motions.

Lateral Dynamics of a Light Railway Vehicle With Independent Wheels

This paper presents a multibody model developed for railway applications and, in particular, for the study of the lateral dynamics of a non-conventional articulated bogie with independent wheels. The classical multibody formalism is first briefly reviewed and the generation of the equations in symbolic form is also presented. Moreover, a new wheel/rail contact model compatible with the symbolic output of the MBS software ROBOTRAN has been developed. The validation with results available in the literature and some results concerning the articulated bogie are finally presented.

A fully symbolic model of multibody systems containing flexible plates

The modelling of flexible elements in mechanical systems has been investigated via several methods issuing from both the field of multi-body dynamics and the area of structural mechanics and vibration theory. As regards the multibody approach, recursive formulations in relative coordinates are quite suitable and efficient for a large variety of applications. Such a formalism is developed here for a general multibody system containing flexible plates and in such a way that its full symbolic generation is possible within the ROBOTRAN program [1].