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

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 Graphsand its Application in 3D-Mechanics

Author:

Dirk Zimmer

Prof. François E. Cellier

Responsible:

Prof. Walter Gander

• Motivation

• Introduction to bond graphs

• Presentation of multibond graphs

• 3D-mechanical models

• Conclusions

• 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.

• 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.

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.

• 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 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.

• 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.

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

• Various other approaches to this subject are insufficient and/or outdated.

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.

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vx

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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

• 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 graph of a planar pendulum

• 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

Model of a free crane crab:

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.

• 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.

• Basic elements:

• Joints:

• Force elements:

• Ideal rolling objects:

Model of an uncontrolled bicycle

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 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

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

• 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.

• 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.

• Modeling of mutual gravitational attraction

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

• Modeling of mutual collisions

• Modeling of hard 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.

• 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.

• 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.