Dirk Zimmer François E. Cellier Institute of Computational Science Department of Computer Science ETH Zürich A bondgraphic modeling tool and its application in mechanics. The Modelica Multi-Bond Graph Library Conference 2006

© Dirk Zimmer, September 2006, Slide 2 ETH Zürich Departement of Computer Science Institute of Computational Science Multi-bond graphs are a general, graphical modeling tool for multi-dimensional physical processes. This presentation introduces their Modelica implementation: The MultiBondLib. Multi-bond graphs are especially well suited for modeling mechanical systems. The MultiBondLib offers a partial reimplementation of the standard MultiBody library. Abstract

© Dirk Zimmer, September 2006, Slide 3 ETH Zürich Departement of Computer Science Institute of Computational Science Introduction to bond graphs Presentation of multi-bond graphs 2D- and 3D-mechanical models Conclusions Overview

© Dirk Zimmer, September 2006, Slide 4 ETH Zürich Departement of Computer Science Institute of Computational Science 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 being distributed along specified paths. These concepts suggest a general modeling approach for physical systems: bond graphs. Introduction to Bond Graphs 1

© Dirk Zimmer, September 2006, Slide 5 ETH Zürich Departement of Computer Science Institute of Computational Science Bond graphs are a modeling tool for continuous physical systems. They form a directed graph where the vertices represent the physical elements. The edges of the graph are the bonds themselves. A bond represents a power flow. It carries two adjugate variables: the effort e and the flow f. The product of them is power. efef Introduction to Bond Graphs 2

© Dirk Zimmer, September 2006, Slide 6 ETH Zürich Departement of Computer Science Institute of Computational Science 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: SourcesSeSf DissipativeRG StorageCI Junctions01 domain effortflow electricui mechanicfv thermalTdS/dt Introduction to Bond Graphs 3

© Dirk Zimmer, September 2006, Slide 7 ETH Zürich Departement of Computer Science Institute of Computational Science Bond Graphs: Example

© Dirk Zimmer, September 2006, Slide 8 ETH Zürich Departement of Computer Science Institute of Computational Science Bond Graphs: Example

© Dirk Zimmer, September 2006, Slide 9 ETH Zürich Departement of Computer Science Institute of Computational Science Bond Graphs: Example

© Dirk Zimmer, September 2006, Slide 10 ETH Zürich Departement of Computer Science Institute of Computational Science Advantages of Bond Graphs Bond graphs offer a suitable balance between general usability and domain orientation. The concepts of energy and power flows define a helpful semantic framework for bond graphs of all physical systems. Relations can more naturally be expressed in two- dimensional drawings than in one-dimensional code.

© Dirk Zimmer, September 2006, Slide 11 ETH Zürich Departement of Computer Science Institute of Computational Science The BondLib was presented at the Modelica Conference Bond graphs can be composed on screen by drag and drop. The resulting models can be directly simulated. The library offers application- specific solutions for: – electrical systems – hydraulic components The BondLib

© Dirk Zimmer, September 2006, Slide 12 ETH Zürich Departement of Computer Science Institute of Computational Science Multi-bond graphs are a vectorial extension of the regular bond graphs. A multi-bond contains a freely selectable number of regular bonds of identical or similar domains. All bond graph component models are adjusted in a suitable fashion. } f3vf3v tt fyvyfyvy fxvxfxvx Composition of a multi-bond for planar mechanics MultiBond Graphs

© Dirk Zimmer, September 2006, Slide 13 ETH Zürich Departement of Computer Science Institute of Computational Science The MultiBondLib The library can be used for the modeling of multi- dimensional physical systems. Hence, possible fields of application are: –2D and 3D mechanical systems –multidimensional heat distribution –chemical reaction dynamics –general relativity The MultiBondLib is a free Modelica library that enables the convenient modeling of multi-bond graphs.

© Dirk Zimmer, September 2006, Slide 14 ETH Zürich Departement of Computer Science Institute of Computational Science Multi-bond graph of a planar pendulum MultiBondLib: Example

© Dirk Zimmer, September 2006, Slide 15 ETH Zürich Departement of Computer Science Institute of Computational Science The process of wrapping is illustrated by means of a free crane crab: Wrapping: Example

© Dirk Zimmer, September 2006, Slide 16 ETH Zürich Departement of Computer Science Institute of Computational Science Wrapping: Example

© Dirk Zimmer, September 2006, Slide 17 ETH Zürich Departement of Computer Science Institute of Computational Science Wrapping: Example WallPrismatic Joint Mass 1 Revolute JointRod Mass 2

© Dirk Zimmer, September 2006, Slide 18 ETH Zürich Departement of Computer Science Institute of Computational Science Wrapping: Example WallPrismatic Joint Mass 1 Revolute JointRod Mass 2

© Dirk Zimmer, September 2006, Slide 19 ETH Zürich Departement of Computer Science Institute of Computational Science Wrapping combines the best of two worlds: On the upper mechanical layer, an intuitive and simply usable interface is being offered. The lower multi-bond graph layer offers a meaningful graphical interpretation. This reduces the semantic distance from the lowest graphical layer down to the equation layer. Wrapping: Example

© Dirk Zimmer, September 2006, Slide 20 ETH Zürich Departement of Computer Science Institute of Computational Science The MultiBondLib provides sub-libraries for planar and 3D mechanical systems. The elements are based on wrapped multi-bond graphs. All mechanical components are represented by meaningful icons. They can be configured by means of parameter menus and feature a suitable animation. Kinematic loops are handled automatically. State variables can be manually selected if the automatic selection appears to be inappropriate. Mechanical sub-libraries

© Dirk Zimmer, September 2006, Slide 21 ETH Zürich Departement of Computer Science Institute of Computational Science Basic elements: Joints: 3D Mechanics: Components

© Dirk Zimmer, September 2006, Slide 22 ETH Zürich Departement of Computer Science Institute of Computational Science Force elements: Ideal rolling objects: 3D Mechanics: Components

© Dirk Zimmer, September 2006, Slide 23 ETH Zürich Departement of Computer Science Institute of Computational Science 3D Mechanics: Components Model of an uncontrolled bicycle

© Dirk Zimmer, September 2006, Slide 24 ETH Zürich Departement of Computer Science Institute of Computational Science 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 Animation Window:

© Dirk Zimmer, September 2006, Slide 25 ETH Zürich Departement of Computer Science Institute of Computational Science 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 Animation Window:

© Dirk Zimmer, September 2006, Slide 26 ETH Zürich Departement of Computer Science Institute of Computational Science 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 Plot Window: Lean Angle 3D Mechanics: Example 1

© Dirk Zimmer, September 2006, Slide 27 ETH Zürich Departement of Computer Science Institute of Computational Science Efficiency of the simulation The efficiency is not impaired by the bondgraphic approach. Since the mechanical models of the MultiBondLib are very similar to the components of the standard MultiBody library, one can easily compare these two libraries:

© Dirk Zimmer, September 2006, Slide 28 ETH Zürich Departement of Computer Science Institute of Computational Science Another sub-library contains an extension of the continuous models to hybrid models. These models allow discrete changes of motion to happen as they occur in hard collisions. Various kinds of impacts can be modeled. Impacts can also act on kinematic loops. Further Achievements

© Dirk Zimmer, September 2006, Slide 29 ETH Zürich Departement of Computer Science Institute of Computational Science The MultiBondLib provides a general solution for the multi- bondgraphic modeling of physical systems. The wrapping technique enables us to handle larger bond graphs. The wrapped mechanical components enable a convenient object-oriented modeling of 2D- and 3D-mechanical systems including animation. Multi-bond graphs lead to an intuitive, yet efficient description of mechanical systems. Conclusions

The End