Singularly Perturbed Bond Graph Models for Simulation of Multibody Systems

1995 ◽  
Vol 117 (3) ◽  
pp. 401-410 ◽  
Author(s):  
A. A. Zeid ◽  
J. L. Overholt
Keyword(s):  
Time Scale ◽  
Multibody Systems ◽  
Graph Model ◽  
Bond Graph ◽  
Rigid Bodies ◽  
Singularly Perturbed ◽  
Bond Graphs ◽  
Graph Models ◽  
Multibody Modeling ◽  
Nonlinear Properties

This paper develops a bond graph-based formalism for modeling multibody systems in a singularly perturbed formulation. As opposed to classical multibody modeling methods, the singularly perturbed formulation is explicit, which makes it suitable for modular simulation. Kinematic joints that couple rigid bodies are described by a set of differential equations with an order of magnitude smaller time scale than that of the system. Singularly perturbed models of joints can be used to investigate nonlinear properties of joints, such as clearance and friction. The main restriction of this approach is that the simulation may need to be computed using 64 bits precision because of the two-time scale nature of the solution. The formalism is based on developing bond graph models of an elementary set of graphical velocity-based constraint functions. This set can be used to construct bond graphs of any type of mechanical joint. Here, this set is used to develop bond graphs of several joints used in multibody systems and spatial mechanisms. Complex models of multibody systems may now be built by graphically concatenating bond graphs of rigid bodies and bond graphs of joints. The dynamic equations of the system are automatically generated from the resulting bond graph model. The dynamic equation derived from the bond graph are in explicit state space form, ready for numerical integration, and exclude the computationally intensive terms that arise from acceleration analysis.

scholarly journals Simulation methods of rigid holonomic multibody systems with bond graphs

2019 ◽  
Vol 11 (3) ◽  
pp. 168781401983415 ◽  
Author(s):  
Benjamin Boudon ◽  
Thu Thuy Dang ◽  
Rebecca Margetts ◽  
Wolfgang Borutzky ◽  
François Malburet
Keyword(s):  
Software Package ◽  
Multibody Systems ◽  
Three Dimensional ◽  
Bond Graph ◽  
Compact Model ◽  
Simulation Methods ◽  
Bond Graphs ◽  
Graph Models ◽  
The Past ◽  
Practical Guidance

Bond graph software can simulate bond graph models without the user needing to manually derive equations. This offers the power to model larger and more complex systems than in the past. Multibond graphs (those with vector bonds) offer a compact model which further eases handling multibody systems. Although multibond graphs can be simulated successfully, the use of vector bonds can present difficulties. In addition, most qualitative, bond graph–based exploitation relies on the use of scalar bonds. This article discusses the main methods for simulating bond graphs of multibody systems, using a graphical software platform. The transformation between models with vector and scalar bonds is presented. The methods are then compared with respect to both time and accuracy, through simulation of two benchmark models. This article is a tutorial on the existing methods for simulating three-dimensional rigid and holonomic multibody systems using bond graphs and discusses the difficulties encountered. It then proposes and adapts methods for simulating this type of system directly from its bond graph within a software package. The value of this study is in giving practical guidance to modellers, so that they can implement the adapted method in software.

Bond Graph Sign Conventions

1975 ◽  
Vol 97 (2) ◽  
pp. 184-188 ◽  
Author(s):  
A. S. Perelson
Keyword(s):  
Graph Model ◽  
Bond Graph ◽  
Equivalence Classes ◽  
Parameter System ◽  
Bond Graphs ◽  
Lumped Parameter ◽  
Oriented Object

The lack of arbitrariness in the choice of bond graph sign conventions is established. It is shown that an unoriented bond graph may have no unique meaning and that with certain choices of orientation a bond graph may not correspond to any lumped parameter system constructed from the same set of elements. Network interpretations of these two facts are given. Defining a bond graph as an oriented object leads to the consideration of equivalence classes of oriented bond graphs which represent the same system. It is also shown that only changes in the orientation of bonds connecting 0-junctions and 1-junctions can lead to changes in the observable properties of a bond graph model.

scholarly journals Analysing and simulating energy-based models in biology using BondGraphTools

2021 ◽  
Author(s):  
Peter Cudmore ◽  
Michael Pan ◽  
Peter J. Gawthrop ◽  
Edmund J. Crampin
Keyword(s):  
Systems Biology ◽  
Mathematical Models ◽  
Bond Graph ◽  
Experimental Measurements ◽  
Bond Graphs ◽  
Graph Models ◽  
Conservation Of Energy ◽  
Conservation Of Mass ◽  
Physical Systems ◽  
Complex Interactions

AbstractLike all physical systems, biological systems are constrained by the laws of physics. However, mathematical models of biochemistry frequently neglect the conservation of energy, leading to unrealistic behaviour. Energy-based models that are consistent with conservation of mass, charge and energy have the potential to aid the understanding of complex interactions between biological components, and are becoming easier to develop with recent advances in experimental measurements and databases. In this paper, we motivate the use of bond graphs (a modelling tool from engineering) for energy-based modelling and introduce, BondGraphTools, a Python library for constructing and analysing bond graph models. We use examples from biochemistry to illustrate how BondGraphTools can be used to automate model construction in systems biology while maintaining consistency with the laws of physics.

A Vector Bond Graph Method of Kineto-Static Analysis for Spatial Multibody Systems

2013 ◽  
Vol 321-324 ◽  
pp. 1725-1729 ◽  
Author(s):  
Zhong Shuang Wang ◽  
Yang Yang Tao ◽  
Quan Yi Wen
Keyword(s):  
Static Analysis ◽  
Multibody Systems ◽  
Degrees Of Freedom ◽  
Multibody System ◽  
Graph Model ◽  
Bond Graph ◽  
Constraint Forces ◽  
Decoupling Method ◽  
Complete Form ◽  
Three Degrees Of Freedom

In order to increase the reliability and efficiency of the kineto-static analysis of complex multibody systems, the corresponding vector bond graph procedure is proposed. By the kinematic constraint condition, spatial multibody systems can be modeled by vector bond graph. For the algebraic difficulties brought by differential causality in system automatic kineto-static analysis, the effective decoupling method is proposed, thus the differential causalities in system vector bond graph model can be eliminated. In the case of considering EJS, the unified formulae of driving moment and constraint forces at joints are derived based on vector bond graph, which are easily derived on a computer in a complete form and very suitable for spatial multibody systems. As a result, the automatic kineto-static analysis of spatial multibody system on a computer is realized, its validity is illustrated by the spatial multibody system with three degrees of freedom.

Multiport Models in Mechanics

1972 ◽  
Vol 94 (3) ◽  
pp. 206-212 ◽  
Author(s):  
R. C. Rosenberg
Keyword(s):  
State Space ◽  
Large Scale ◽  
Force Fields ◽  
Digital Simulation ◽  
Bond Graph ◽  
Rigid Bodies ◽  
System Structure ◽  
Graph Models ◽  
Geometric Variables ◽  
Scale Motion

Problems in mechanics involving rigid bodies in large-scale motion in force fields of both conservative and nonconservative types are approached from a multiport viewpoint. A procedure for constructing bond graph models based on key geometric variables and the velocity transformations relating them is described. Contributions of such models to improving the representation and communication of system structure, the formulation of governing state-space equations, and the direct digital simulation of complicated mechanics problems are suggested.

Application of Vector Bond Graphs to the Modeling of a Class of Hand Prostheses

Volume 3 ◽  
2004 ◽  
Author(s):  
Anand Vaz ◽  
Shinichi Hirai
Keyword(s):  
Three Dimensional ◽  
Graph Model ◽  
Systems Design ◽  
Bond Graph ◽  
Bond Graphs ◽  
Prosthetic Joints ◽  
Angular Velocities ◽  
Control Systems Design ◽  
And Control ◽  
Systematic Derivation

Vector bond graphs have been systematically applied to the modeling of prosthesis for a partially impaired hand. The partial impairment considered covers a category of the hand that has lost one or more fingers but retains the ability of its remaining natural fingers. The fingers and their prosthetic extensions are considered as rigid links. Rotation matrices which specify orientation of finger links are obtained from respective angular velocities. String-tube mechanism used to actuate prosthetic joints is modeled with the connection to joint variables of the mechanism. The vector bond graph approach enables the modeling of three dimensional movement of the hand mechanism. An example of a two joint string-tube actuated prosthetic mechanism is presented to describe the construction of the vector bond graph model. Systematic derivation of dynamics from the vector bond graphs is shown. The approach based on vector bond graphs presented here is useful for simulations and control systems design of such biomechanical systems.

A Distributed Parameter Pseudo Bond Graph for Heat Conduction Modelling: Notion of Cellular Bond Graph

2003 ◽  
Author(s):  
Aziz Nakrachi ◽  
Genevieve Dauphin-Tanguy
Keyword(s):  
Heat Conduction ◽  
Heat Flow ◽  
Finite Difference ◽  
Heat Conduction Equation ◽  
Graph Model ◽  
Bond Graph ◽  
Distributed Parameter ◽  
Heat Flow Rate ◽  
Finite Volume Schemes ◽  
Bond Graphs

The paper presents a new procedure for building a pseudo bond graph model representing 1D and 2D heat conduction phenomena, in their distributed parameter form. The heat conduction equation is written in such a way that conjugate variables, temperature T(t,x,y) and heat flow rate Q⃗˙(t,x,y), and their space derivatives appear explicitly in the equation. New conjugations between variables are introduced as (T,div(Q⃗˙)) and (gradT,Q⃗˙). We define new bond graph elements named “distributed C- and R-elements”, and we build a “Distributed Parameter Bond Graph” (DPBG), with a form slightly different from the classical one. The approximation of the space derivatives leads to submodels we call “cellular bond graphs”, new notion which could be compared to the cellular automata. Moreover, we show how this representation enables to easily build classical finite difference or finite volume schemes.

Structural Simplification of Modular Bond-Graph Models Based on Junction Inactivity

2006 ◽  
Author(s):  
Tulga Ersal ◽  
Hosam K. Fathy ◽  
Jeffrey L. Stein
Keyword(s):  
Graph Model ◽  
Bond Graph ◽  
General Purpose ◽  
Graph Models ◽  
Modular Modeling ◽  
System Models ◽  
Modeling Paradigm ◽  
Component Models ◽  
Domain Independent ◽  
Structural Simplification

The modular modeling paradigm facilitates the efficient building, verification and handling of complex system models by assembling them from general-purpose component models. A drawback of this paradigm, however, is that the assembled system models may have excessively complex structures for certain purposes due to the amount of detail of the component models, which is introduced to promote modularity. This work presents a domain-independent structural simplification technique that can detect such unnecessary complexities in a modular bond-graph model and eliminate them from the model without compromising accuracy. To this end, the activity concept in the literature is extended to define "inactivity" for junction elements, and simplification is obtained by detecting and eliminating inactive junction elements and by propagating the implications. It is shown that this simple idea can result in models that are conceptually and computationally more efficient. Some subtleties associated with this approach are highlighted.

scholarly journals Bond graphs and object-oriented modelling—a comparison

2002 ◽  
Vol 216 (1) ◽  
pp. 21-33 ◽  
Author(s):  
W Borutzky
Keyword(s):  
Hydraulic Drive ◽  
Object Oriented ◽  
Bond Graph ◽  
Massachusetts Institute Of Technology ◽  
Bond Graphs ◽  
Graph Models ◽  
Electrical Systems ◽  
Generalized Networks ◽  
Institute Of Technology ◽  
Object Oriented Modelling

Bond graph modelling was devised by Professor Paynter at the Massachusetts Institute of Technology in 1959 and subsequently developed into a methodology for modelling multidisciplinary systems at a time when nobody was speaking of object-oriented modelling. On the other hand, so-called object-oriented modelling has become increasingly popular during the last few years. By relating the characteristics of both approaches, it is shown that bond graph modelling, although much older, may be viewed as a special form of object-oriented modelling. For that purpose the new object-oriented modelling language Modelica is used as a working language which aims at supporting multiple formalisms. Although it turns out that bond graph models can be described rather easily, it is obvious that Modelica started from generalized networks and was not designed to support bond graphs. The description of bond graph models in Modelica is illustrated by means of a hydraulic drive. Since VHDL-AMS as an important language standardized and supported by IEEE has been extended to support also modelling of non-electrical systems, it is briefly investigated as to whether it can be used for description of bond graphs. It turns out that currently it does not seem to be suitable.

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