Master thesis a modelica library for multibond graphs and its application in 3d mechanics
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Master Thesis: A Modelica Library for Multibond Graphs and its Application in 3D-Mechanics. Author: Dirk Zimmer. Adviser: Prof. François E. Cellier. Responsible: Prof. Walter Gander. Overview. Motivation Introduction to bond graphs Presentation of multibond graphs

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Master Thesis: A Modelica Library for Multibond Graphs and its Application in 3D-Mechanics

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Master thesis a modelica library for multibond graphs and its application in 3d mechanics

Master Thesis:A Modelica Library for Multibond Graphsand its Application in 3D-Mechanics

Author:

Dirk Zimmer

Adviser:

Prof. François E. Cellier

Responsible:

Prof. Walter Gander


Overview

Overview

  • Motivation

  • Introduction to bond graphs

  • Presentation of multibond graphs

  • 3D-mechanical models

  • Conclusions


Motivation

Motivation

  • First objective:Implementation of a general modeling tool for multidimensional physical processes: multibond graphs.

  • Second objective:The modeling of mechanical systems in terms of multibond graphs.


Introduction to bond graphs 1

Introduction to bond graphs 1

  • Elements of a physical system have a certain behavior with respect to power and energy.

    • A battery is a source of energy.

    • A thermal capacitance stores energy.

    • A mechanical damper dissipates energy.

    • Power is distributed along a junction.

  • This offers a general modeling approach for physical systems: bond graphs.


Introduction to bond graphs 2

e

f

Introduction to bond graphs 2

  • Bond graphs are a modeling tool for continuous physical systems.

  • The edges of the graph are the bonds themselves.

  • A bond carries an effort and a flow variable. The product of them is power.


Introduction to bond graphs 3

Introduction to bond graphs 3

  • The choice of effort and flow determines the modeling domain:

  • The vertex elements are denoted by a mnemonic code corresponding to their behavior with respect to energy and power:


Bond graphs example

Bond graphs: Example


Bond graphs example1

Bond graphs: Example


Bond graphs example2

Bond graphs: Example


Advantages of bond graphs

Advantages of bond graphs

  • Bond graphs offer a general modeling approach to a wide range of physical systems. They find the right balance between specificity and generality.

  • The concept of energy and power creates a semantic level for each bond graph.

  • Relations can more naturally be expressed in 2D-drawings than in 1D-code.


The modelica dymola bondlib

The Modelica/Dymola BondLib

  • Bond graphs can be composed on screen by drag and drop.

  • The resulting model can directly be simulated.

  • The library features domain specific solutions, e.g., a library for electric systems.


Bondgraphs for mechanics 1

Bondgraphs for mechanics 1

  • Unfortunately, the BondLib doesn’t feature mechanical applications.

  • Various other approaches to this subject are insufficient and/or outdated.


Bondgraphs for mechanics 2

Bondgraphs for mechanics 2

Problems of mechanical bond graphs:

  • Mechanical processes are multidimensional

    • Usage of MultiBond Graphs.

  • Holonomic constraints are non-physical

    • Need for extra modeling via signals.

  • Mechanical bond graphs become very large

    • Wrapping of the bondgraphic models.


Multibond graphs

fx

vx

}

f3

v

fy

vy

t

MultiBond Graphs

Multibonds are a vectorial extension of bond graphs.

A multibond covers an arbitrary number of single bonds of the same domain.

All vertex elements are extended accordingly.

Composition of a multibond for planar mechanics


The multibondlib

The MultiBondLib

  • A Modelica/Dymola Library for modeling Multibond graphs has been developed.

  • It is an adaptation of the BondLib.

  • Further possible applications of multibond graphs are:

    • multidimensional heat distribution

    • chemical reaction dynamics

    • general relativity.


Multibond graphs example

Multibond graphs: Example

Multibond graph of a planar pendulum


Multibond graphs sensors

Multibond graphs: Sensors

  • Sensor elements serve for different purposes. They can be used to...

    • ...measure bondgraphic variables.

    • ...convert bondgraphic variables to non-bondgraphic signals.

    • ...establish algebraic relationships between bondgraphic elements.

Application of a bondgraphic sensor element


Multibond graphs example 2

Multibond graphs: Example 2

Model of a free crane crab:


Multibond graphs example 21

Multibond graphs: Example 2


Multibond graphs example 22

Multibond graphs: Example 2


Multibond graphs example 23

Multibond graphs: Example 2


Wrapping

Wrapping

Wrapping combines the best of two worlds:

  • An easy-to-use model is provided at the top level.

  • A look inside the model reveals a familiar bondgraphic model.


3d mechanics

3D Mechanics

  • A Modelica library for the object-oriented modeling of 3D-mechanical systems has been developed.Partial reimplementation of the MultiBody library.

  • All models consist of wrapped bondgraphic models.

  • 3D-specific problems had to be solved.

    • Handling of different coordinate systems.

    • Description of the orientation.


3d mechanics components

3D Mechanics: Components

  • Basic elements:

  • Joints:


3d mechanics components1

3D Mechanics: Components

  • Force elements:

  • Ideal rolling objects:


3d mechanics example 1

3D Mechanics: Example 1

Model of an uncontrolled bicycle


3d mechanics example 11

3D Mechanics: Example 1

Animation Window:

Translation:

  • FrontRevolute.phi

  • RearWheel.phi[1]

  • RearWheel.phi[2]

  • RearWheel.phi[3]

  • RearWheel.phi_d[1]

  • RearWheel.phi_d[2]

  • RearWheel.phi_d[3]

  • RearWheel.xA

  • RearWheel.xB

  • Steering.phi

    Systems of 3 and 17 linear equations

    1 non-linear equation

    Simulation

    20 sec, 2500 output points

    213 integration steps.

    0.7s CPU-Time


3d mechanics example 12

Animation Window:

3D Mechanics: Example 1

Translation:

  • FrontRevolute.phi

  • RearWheel.phi[1]

  • RearWheel.phi[2]

  • RearWheel.phi[3]

  • RearWheel.phi_d[1]

  • RearWheel.phi_d[2]

  • RearWheel.phi_d[3]

  • RearWheel.xA

  • RearWheel.xB

  • Steering.phi

    Systems of 3 and 17 linear equations

    1 non-linear equation

    Simulation

    20 sec, 2500 output points

    213 integration steps.

    0.7s CPU-Time


3d mechanics example 13

3D Mechanics: Example 1

Translation:

  • FrontRevolute.phi

  • RearWheel.phi[1]

  • RearWheel.phi[2]

  • RearWheel.phi[3]

  • RearWheel.phi_d[1]

  • RearWheel.phi_d[2]

  • RearWheel.phi_d[3]

  • RearWheel.xA

  • RearWheel.xB

  • Steering.phi

    Systems of 3 and 17 linear equations

    1 non-linear equation

    Simulation

    20seconds, 2500 output points

    213 integration steps.

    0.7s CPU-Time

Plot Window: Lean Angle


3d mechanics kinematic loops

3D Mechanics: Kinematic Loops

  • Redundant statements appear in kinematic loops and lead to a singularity of the model.

  • Automatic removal of the redundant statements.

  • Systems of non-linear equations have to be solved.


Efficiency of the simulation

Efficiency of the simulation

  • Same efficiency as the MultiBody library. The efficiency is not impaired by the bondgraphic methodology

  • The state selection is of major importance for the efficiency. Relative positions and motions of the joints do usually form a good set of state variables.

  • The automatic state selection is mostly meaningful

    and can be improved manually if necessary.

  • Kinematic loops could be closed more efficiently by special cut joints, that contain analytic solutions.


Additional work

Additional work

  • Modeling of mutual gravitational attraction

  • Alternative approach to the multibondgraphic modeling of 3D-Systems

  • Modeling of mutual collisions

  • Modeling of hard impacts…


Additional work impacts

Additional work: Impacts

  • Extension of the continuous models to hybrid models that allow a discrete change of motion.

  • The impulse equations were derived out of the continuous bondgraphic models.

  • Several impact models (elasticity, friction, shape).

  • Impacts can act on kinematic loops.

  • Solution is fine for small scale models.


Conclusions

Conclusions

  • A general solution for multibondgraphic modeling is provided.

  • Object-oriented modeling of 2D- and 3D-mechanical systems is supported.

  • Hybrid mechanical systems can be simulated.

  • The modeling is convenient and the simulation is done efficiently.


Outlook on future tasks

Outlook on future tasks

  • Modeling of structural changes:

    • Modeling of friction and the transition to adhesion.

    • Modeling of constrained joints.

  • Improvement of the hybrid models.

  • Bondgraphic modeling of deformable objects.


The end

The End


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