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MFM120 Multibody Dynamics Stand: 2009-06-07 22:25:23
Semester:1 (MFM1)
Sprache:EN
SWS:4 (2V 2U)
ECTS:5 CP
Turnus:WS,SS
Lernziele / Bezug
zum Studiengang:		Students will be able to derive the kinematical and dynamical equations of multibody systems (MBS) (a MBS is a system of rigid bodies connected by joints and force elements)
to understand the motion of multibody systems attached by mechatronic component
to setup small multibody models using Math programs and MBS program
to interpret the results of multibody dynamics simulations in mechatronic system
Inhalte:Part I -Rigid Body Dynamic
*
1 Introduction to Flexible Multibody Dynamic
Herein, the state of the art in MBS dynamics and their general purpose programs will be given. Applications in mechanical engineering, mechatronics and micro engineering will be presented.

2 The Multibody Program
Two important general MBS programs are presented to demonstrate the power of the method: SIMPACK and WorkingModel.
They demonstrate that the application users should have knowledge in kinematics and dynamics of MBS for an efficient usage, correct data import and interpretation of the simulation results.
The usage of the programs are shown by simple mechanical problems.

3 Kinematics of Rigid Multibody System
The most complex part of the lecture starts with the description of frames, transformation matrices and applications on position, velocity and acceleration of a rigid body.
Herein, a special MBS Notation used in SIMPACK is performed, in particularly, to describe the relative kinematics of joints and force elements.
Exercises and a project referring to the kinematics are included. Therefore, the Math tool Maple is preliminary proposed.

4 Dynamics of Rigid Multibody System
We start with the linear and angular momentum to setup the dynamical equations of motions of a rigid body. Alternative the Jourdain's principle is applied for a more efficient derivation of the equations of motion.
These equations have to be extended by constraint equations of joints. Both descriptions -implicit and explicit -are presented to perform a differential-algebraic equation system (DAE) or the ordinary differential equation system (ODE) of the MBS. The advantages of both derivations are discussed.
Exercises and an additional project referring to the dynamics are included. Herein, a Maple script for rigid MBS is used to see all derivations of the equations of motion.

Part II -Flexible Body Dynamic
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5 Introduction to Flexible Body Modeling and Finite Element Approximation
A brief description of flexible body modeling starts from the linearized equations of motion of a 3D-continuum model, next -it contains the Ritz approximation using modes shapes and generalized elastic coordinates and includes the FE-discretization. It will be demonstrated by a 2D-beam element where a specific Maple script is available.
The embedding of these flexible body descriptions in the equations of multibody systems is shown ruffly and their data import is discussed.
Literatur:
  1. Schwertassek,R. and Wallrapp,0., (1999) Mehrkörperdynamik, Vieweg
  2. Schabana, A. (1998) Dynamics of Multibody Systems, Cambridge Univ Press
Vorauss. nach SPO:Bachelor in Mechatronics or Mechanical Engineering
Vorauss. empfohlen:Mechanical Engineering, Mechanism Anaysis, Computer Algebra, Matrix Calculus, basics of Vibration Analysis, Structural Analysis
Ist selbst Vorauss. für:
Lehrmethoden:Seminaristischer Unterricht mit Übungen und Projekt
Arbeitsaufwand:150 h, davon:
30 h seminaristischer Unterricht
30 h Übung
33 h Class Project
57 h Eigenstudium (Vor- und Nachbearbeitung, Prüfungsvorbereitung)
Prüfung:50% KL: 90'; 50% PA: PA
Modulverantwortung:Prof. Dr. Wiedemann
Dozenten:Prof. Dr. Wiedemann

 

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