Multibody Modelling for Vehicle Systems (E311066)

Departments: | ústav mechaniky, biomech.a mechatr. (12105) | ||

Abbreviation: | Approved: | 04.06.2010 | |

Valid until: | ?? | Range: | 3P+1C |

Semestr: | * | Credits: | 5 |

Completion: | Z,ZK | Language: | EN |

Annotation

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

Practice of multibody modelling

Teacher's

prof. Ing. Michael Valášek DrSc.

Zimní 2023/2024

prof. Ing. Michael Valášek DrSc.

Zimní 2022/2023

prof. Ing. Michael Valášek DrSc.

Zimní 2021/2022

Structure

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

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

Literarture

1. Lecturing material and hand-outs

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

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

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

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

Keywords

Kinematics, Dynamics, Multibody Systems, Lagrange Equations of Mixed Type, Modelling