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The Modelica Multi-Bond Graph Library

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

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The Modelica Multi-Bond Graph Library

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

  2. Abstract • 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.

  3. Overview • Introduction to bond graphs • Presentation of multi-bond graphs • 2D- and 3D-mechanical models • Conclusions

  4. 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 being distributed along specified paths. • These concepts suggest a general modeling approach for physical systems: bond graphs.

  5. Introduction to Bond Graphs 2 e f • 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.

  6. 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:

  7. Bond Graphs: Example

  8. Bond Graphs: Example

  9. Bond Graphs: Example

  10. 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.

  11. The BondLib • The BondLib was presented at the Modelica Conference 2005. • 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

  12. MultiBond Graphs fx vx } f3 v fy vy t  • 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. Composition of a multi-bond for planar mechanics

  13. 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.

  14. MultiBondLib: Example Multi-bond graph of a planar pendulum

  15. Wrapping: Example The process of wrapping is illustrated by means of a free crane crab:

  16. Wrapping: Example

  17. Wrapping: Example Mass 1 Mass 2 Wall Prismatic Joint Revolute Joint Rod

  18. Wrapping: Example Mass 1 Mass 2 Wall Prismatic Joint Revolute Joint Rod

  19. Wrapping: Example 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.

  20. Mechanical sub-libraries • 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.

  21. 3D Mechanics: Components • Basic elements: • Joints:

  22. 3D Mechanics: Components • Force elements: • Ideal rolling objects:

  23. 3D Mechanics: Components Model of an uncontrolled bicycle

  24. 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:

  25. 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

  26. 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 Plot Window: Lean Angle

  27. 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:

  28. Further Achievements • 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.

  29. Conclusions • 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.

  30. The End

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