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2003 | Buch

Symbolic Modeling of Multibody Systems

verfasst von: Jean-Claude Samin, Paul Fisette

Verlag: Springer Netherlands

Buchreihe : Solid Mechanics and Its Applications

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SUCHEN

Über dieses Buch

Modeling and analysing multibody systems require a comprehensive understanding of the kinematics and dynamics of rigid bodies. In this volume, the relevant fundamental principles are first reviewed in detail and illustrated in conformity with the multibody formalisms that follow. Whatever the kind of system (tree-like structures, closed-loop mechanisms, systems containing flexible beams or involving tire/ground contact, wheel/rail contact, etc), these multibody formalisms have a common feature in the proposed approach, viz, the symbolic generation of most of the ingredients needed to set up the model.
The symbolic approach chosen, specially dedicated to multibody systems, affords various advantages: it leads to a simplification of the theoretical formulation of models, a considerable reduction in the size of generated equations and hence in resulting computing time, and also enhanced portability of the multibody models towards other specific environments. Moreover, the generation of multibody models as symbolic toolboxes proves to be an excellent pedagogical medium in teaching mechanics.

Inhaltsverzeichnis

Frontmatter

Theory

Frontmatter
Chapter 1. Fundamental Mechanics
Abstract
The aim of this section is to introduce the notations that will be used throughout this book for representing vectors, tensors as well as their time derivatives. It is assumed that the reader is familiar with elementary vector and matrix calculus. Basic properties of vectors and tensors will thus be recalled without proofs.
Jean-Claude Samin, Paul Fisette
Chapter 2. Dynamics of rigid bodies
Abstract
The aim of this chapter is to describe the motion of several bodies. The fundamental notions of generalized coordinates, constraints and degrees of freedom will be introduced and illustrated via simple examples. Then, we shall develop the Newton-Euler procedure which produces the equations of motion relating the motion of the bodies (i.e. the evolution of the generalized coordinates) to the forces/torques applied to the system. Illustrated via an example, this procedure will show its limitations if applied manually, when the number of bodies becomes large. Finally, we shall present a variational approach based on the virtual power principle and use this second approach to treat the same example.
Jean-Claude Samin, Paul Fisette
Chapter 3. Tree-like multibody structures
Abstract
A multibody system (mbs) is a set of N body rigid bodies interconnected by joints. As illustrated in figure 3.1, mechanisms, road and railway vehicles, industrial or space manipulators, etc... are typical examples of multibody systems.
Jean-Claude Samin, Paul Fisette
Chapter 4. Complex multibody structures
Abstract
The preceding chapter dealt with multibody systems having a tree-like structure. However, in many practical cases, physical systems are not tree-like. Road vehicle suspensions, anthropomorphic and parallel robots, railway bogies, etc. are multibody systems whose topology is not tree-like.
Jean-Claude Samin, Paul Fisette
Chapter 5. Symbolic generation
Abstract
Before the appearance of efficient computer architectures for scientific numerical computations, only analytical methods were available for modeling systems. The analyses often used rather restrictive hypotheses (truncated and/or linearized models, for instance). The emergence of powerful processors and reliable and user-friendly languages and software led the scientific community to develop numerical programs able to cover a wide range of applications in a given field (ex.: structural dynamics, multibody dynamics, fluid mechanics, electronic circuits, ...). In particular, numerous multibody programs were developed all over the world as from the seventies [80], each of them being described as a general purpose multibody code, although, in reality, they all imposed some restrictions on both modeling and analysis.
Jean-Claude Samin, Paul Fisette

Special topics

Frontmatter
Chapter 6. Road vehicles: wheel/ground model
Abstract
Road vehicles represent an important class of multibody systems, all the more interesting since recent developments in this field rely on dynamical properties (stability, riding comfort, etc.). From the mechanical point of view, a vehicle is intrinsically of a multibody nature. Depending on the application, the model refinement can vary noticeably, while being rigorous with respect to the envisaged analysis. For instance, one could wish to check for vehicle stability, or to improve the under/over steering behavior in a curve: for such analyses, the model (including data) must be sufficiently refined as regards all the suspension elements, wheel/ground properties etc... yet can disregard, partially or even totally, the engine and transmission internal motions. Reciprocally, the latter would be at the heart of the model if vibration and noise were the main issues of the study.
Jean-Claude Samin, Paul Fisette
Chapter 7. Railway vehicles: wheel/rail model
Abstract
Vehicles — on road or on track — certainly represent one of the most important types of application of the multibody approach. In the case of railway vehicles, an arduous aspect of the modeling phase results from the contact between the wheels and the track. Indeed, from a purely geometrical point of view, locating the contact point between a wheel and a rail becomes complicated since both are profiled, and from a dynamical point of view, the large number of parameters (shape of the profiles in contact, contact pressure, relative contact velocity, physical properties of the materials, ...) leads to complex theories such as those developed by Kalker [45].
Jean-Claude Samin, Paul Fisette
Chapter 8. Mechanisms: cam/follower model
Abstract
Cam/follower devices are used in a wide spectrum of applications, especially in automatic machines and instruments, textile machinery, printing presses, food-processing equipment, internal combustion engines, control systems, ... They constitute a simple and economic device with few movable parts. It is possible to design a cam such that the follower has a specific motion type. In particular, cam optimization [34] refers to determining the cam surface producing a given follower displacement that minimizes a certain cost (such as material volume or inertia of moving parts, ...) or maximizes a certain profit (force transmission, life span, ...).
Jean-Claude Samin, Paul Fisette
Chapter 9. Multibody systems with flexible beams
Abstract
Flexibility effects in multibody dynamics certainly represent one of the most arduous aspects of the modeling of mechanical systems. There are several reasons for this. First of all, contrary to the rigid case, flexible bodies require both physical and geometrical hypotheses (e.g.: elastic linear behavior, small flexible motion, ...) whose validity must be questioned a posteriori as regards the accuracy or even the meaningfulness of the simulation results.
Jean-Claude Samin, Paul Fisette
Chapter 10. Time integration of flexible MBS
Abstract
From an examination of system {4.1, 4.2, 4.3}, it readily appears that the equations of motion of constrained multibody systems are not only differential but differential-algebraic equations, abbreviated as DAEs [65], [40]. Time integration of DAEs has already been approached within the field of multibody dynamics using constraint stabilization [2], coordinate partitioning [92] or direct methods [66], [26].
Jean-Claude Samin, Paul Fisette

Tutorial

Frontmatter
Chapter 11. Introduction
Abstract
The present tutorial mainly focuses on the modeling process (from system hypotheses to simulation results), rather than on program capabilities, which is more the subject of a user’s manual. MBSOFT [23] to which this tutorial refers is the numerical complement of the ROBOTRAN program (see chapter 5) in the MATLAB environment. The objective of these softwares is the modeling (ROBOTRAN) and analysis (MBSOFT) of multibody systems, defined as being any mechanical system made up of articulated bodies. As can be seen from figure 11.1, the fields of application are numerous and varied: they range from robotics to biomechanics, and encompass the analysis of road and track vehicles. One should keep in mind that one of the main advantages of the approach is its capacity to generate equations of motion in symbolic form. This symbolic form is both compact and user-friendly, thereby allowing the user to easily understand and set up his model. The symbolic equations are then implemented in the numerical study which makes up the second processing stage, viz. the MBsim module (see figure 11.2).
Jean-Claude Samin, Paul Fisette
Chapter 12. Problems
Abstract
The objective is to determine the equilibrium configuration as well as I the eigenfrequencies of a double spring-mass system where both masses are constrained to move in a vertical plane.
Jean-Claude Samin, Paul Fisette
Backmatter
Metadaten
Titel
Symbolic Modeling of Multibody Systems
verfasst von
Jean-Claude Samin
Paul Fisette
Copyright-Jahr
2003
Verlag
Springer Netherlands
Electronic ISBN
978-94-017-0287-4
Print ISBN
978-90-481-6425-7
DOI
https://doi.org/10.1007/978-94-017-0287-4