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CZECH TECHNICAL UNIVERSITY IN PRAGUE
STUDY PLANS
2019/2020

Multibody Modelling for Vehicle Systems

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Code Completion Credits Range Language
E311066 Z,ZK 5 3P+1C
Lecturer:
Michael Valášek (guarantor), Václav Bauma, Petr Beneš, Zdeněk Neusser, Zbyněk Šika, Jan Zavřel
Tutor:
Michael Valášek (guarantor), Václav Bauma, Petr Beneš, Zdeněk Neusser, Zbyněk Šika, Jan Zavřel
Supervisor:
Department of Mechanics, Biomechanics and Mechatronics
Synopsis:

Development Process of Simulation, Matrix Formulation of Kinematics, Different Coordinates for Description of Multibody Systems, Solution of Kinematical Loops, Numerical Methods for Solution of Multibody Kinematics, Kinematical Synthesis of Multibody Systems, Dynamics of Multibody Systems by Lagrange Equations of Mixed Type, Numerical Methods of DAE Solution, Advanced formulation of equations of motion of multibody systems

Practice of multibody modelling

Requirements:

1) Development Process of Simulation

2) Matrix Formulation of Kinematics

3) Different Coordinates for Description of Multibody Systems

4) Solution of Kinematical Loops

5) Numerical Methods for Solution of Multibody Kinematics

6) Kinematical Synthesis of Multibody Systems

7) Dynamics of Multibody Systems by Lagrange Equations of Mixed Type

8) Numerical Methods of DAE Solution

9) Advanced formulation of equations of motion of multibody systems

10) Practice of multibody modelling

Syllabus of lectures:

1 - Development Process of Simulation Model

Ideal objects of engineering sciences. Conceptual model, physical model, simulation model

2 - Matrix Formulation of Kinematics

Matrix of directional cosines, transformation, velocity and acceleration matrices. Basic motions, basic transformation matrices. Method of basic matrices

3 - Different Coordinates for Description of Multibody Systems

Independent and dependent, relative, Cartesian and physical coordinates. Euler angles, Cardan angles, Euler parameters. Kinematical description of open kinematic chain

4 - Solution of Kinematical Loops

Kinematical solution of kinematical loops by method of closed loop, method of disconnected loop, method of removed body, method of natural coordinates, method of compartments (physical coordinates)

5 - Numerical Methods for Solution of Multibody Kinematics

Position, velocity and acceleration problems. Solution of over- and under-constrained system of linear and nonlinear algebraic equations. Special and singular cases of multibody systems

6 - Kinematical Synthesis of Multibody Systems

Engineering design process, formulation of kinematical synthesis, solving procedures, optimization. Synthesis of vehicle suspensions

7 - Dynamics of Multibody Systems by Lagrange Equations of Mixed Type

Lagrange equations of mixed type, assembly of particular expressions. Multibody dynamic formalism by physical coordinates. Interpretation of Lagrange multipliers. Force elements for vehicle modelling

8 - Numerical Methods of DAE Solution

Numerical problems of solution of differential-algebraic equations (DAE). Solution in indepenedent and dependent coordinates, Baumgarte stabilization, coordinate partitioning, projection into independent coordinates

9 - Advanced formulation of equations of motion of multibody systems

Equivalence of Newton-Euler and Lagrange equations. Equations of motion of small vibrations. Dynamics of flexible multibody systems.

10 - Practice of multibody modelling

Multibody modelling for different multibody dynamic formalisms. Example of modelling in Simpack. Modelling of vehicle suspension, modelling of vehicle dynamics

Syllabus of tutorials:
Study Objective:
Study materials:

1. Lecturing material and hand-outs

2. Stejskal, V., Valasek, M.: Kinematics and Dynamics of Machinery, Marcel Dekker, New York 1996 (basis textbook)

Note:
Time-table for winter semester 2019/2020:
06:00–08:0008:00–10:0010:00–12:0012:00–14:0014:00–16:0016:00–18:0018:00–20:0020:00–22:0022:00–24:00
Mon
Tue
Fri
Thu
Fri
roomT4:D1-366
Valášek M.
09:00–11:30
(lecture parallel1)
Dejvice
Posluchárna 366
roomT4:D1-366
Valášek M.
11:30–12:15
(lecture parallel1
parallel nr.101)

Dejvice
Posluchárna 366
Time-table for summer semester 2019/2020:
Time-table is not available yet
The course is a part of the following study plans:
Data valid to 2019-10-14
For updated information see http://bilakniha.cvut.cz/en/predmet1520606.html