Ideal physical element representation from reduced bond graphs

2002 ◽  
Vol 216 (1) ◽  
pp. 73-83 ◽  
Author(s):  
L. S. Louca ◽  
J. L. Stein
Keyword(s):  
Graph Model ◽  
Bond Graph ◽  
The Body ◽  
System Model ◽  
Bond Graphs ◽  
State Equations ◽  
Rigorous Approach ◽  
Reduction Techniques ◽  
Relative Value ◽  
Element Removal

Previous research has demonstrated that bond graphs are a natural and convenient representation to implement energy-based metrics that evaluate the relative ‘value’ of energy elements in a dynamic system model. Bond graphs also provide a framework for systematically reformulating a reduced bond graph model (and thus the state equations) of the system that results from eliminating the ‘unimportant’ elements. This paper shows that bond graphs also provide a natural and convenient representation for developing a rigorous approach for interpreting the removal of ideal energy elements from the system model. For example, when a generalized inductance in the mechanical domain is eliminated from a model, the bond graph shows whether the coordinate representing the motion of the body becomes free to move (zero inertia) or fixed to ground (infinite inertia). This systematic interpretation of element removal makes bond graphs an attractive modelling language for automated model reduction techniques. An illustrative example is provided to demonstrate how the developed approach can be applied to provide the physical interpretation of energy element removal from a mechanical system.

scholarly journals BOND GRAPH METHODOLOGY IN THE RLC CIRCUIT ANALYSIS

2019 ◽  
pp. 261-270
Author(s):  
Darina Hroncová
Keyword(s):  
General Class ◽  
Bond Graph ◽  
Operating Conditions ◽  
Coupled Systems ◽  
System Model ◽  
Electrical System ◽  
Bond Graphs ◽  
State Equations ◽  
Mechatronic Systems ◽  
Physical Systems

Urgency of the research. The bond graphs theory aim for to formulate general class physical systems over power interactions. The factors of power are effort and flow. They have different interpretations in different physical domains. Yet, power can always be used as a generalized resource to model coupled systems residing in several energy domains. Target setting. Formalism of power graphs enables to describe different physical systems and their interactions in a uniform, algorithmizable way and transform them into state space description. This is useful when analyzing mechatronic systems transforming various forms of energy (electrical, fluid, mechanical) by means of information signals to the resulting mechanical energy. Actual scientific researches and issues analysis. Over the past two decades the theory of Bond Graphs has been paying attention to universities around the world, and bond graphs have been part of study programs at an ever-increasing number of universities. In the last decade, their industrial use is becoming increasingly important. The Bond Graphs method was introduced by Henry M. Paynter (1923-2002), a professor at MIT & UT Austin, who started publishing his works since 1959 and gradually worked out the terminology and formalism known today as Bond Graphs translated as binding graphs or performance graphs. Uninvestigated parts of general matters defining. The electrical system model is solved with the help of the above mentioned bond graphs formalism. Gradually, the theory of power graphs in the above example is explained up to the construction of state equations of the electrical system. The state equations are then solved in Matlab / Simulink. The statement of basic materials. Using bond graphs theory to simulate electrical system and verify its suitability for simulating electrical models. In various versions of the parameters of model we can monitor its behavior under different operating conditions. The language of bond graphs aspires to express general class physical systems through power interactions. The factors of power i.e., effort and flow, have different interpretations in different physical domains. Yet, power can always be used as a generalized coordinate to model coupled systems residing in several energy domains. Conclusions. We introduced a method of systematically constructing a bond graph of an electrical system model using Bond graphs. A practical example of an electrical model is given as an application of this methodology. Causal analysis also provides information about the correctness of the model. Differential equations describing the dynamics of the system in terms of system states were derived from a simple electrical system coupling graph. The results correspond to the equations obtained by the classical manual method, where first the equations for individual components are created and then a simulation scheme is derived based on them. The presented methodology uses the reverse procedure. However, manually deriving equations for more complex systems is not so simple. Bond charts prove to be a suitable means of analysis, among other systems and electrical systems.

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.

Bond Graph Model of a Squirrel Cage Induction Motor With Direct Physical Correspondence

2000 ◽  
Vol 122 (3) ◽  
pp. 461-469 ◽  
Author(s):  
Jongbaeg Kim ◽  
Michael D. Bryant
Keyword(s):  
Induction Motor ◽  
Mechanical Energy ◽  
Graph Model ◽  
Bond Graph ◽  
Graph State ◽  
State Equations ◽  
Squirrel Cage ◽  
Squirrel Cage Induction Motor ◽  
Cage Induction Motor ◽  
Cage Rotor

An existing bond graph of a squirrel cage induction motor was modified to make the bond graph physically more representative. The intent was to form a one-to-one correspondence between motor components and bond graph elements. Components explicitly represented include the stator coils, the squirrel cage rotor bars, and the magnetic flux routing section. The final bond graph spans electrical, magnetic, and mechanical energy domains, and contains common motor faults. From this bond graph. state equations were extracted and simulations performed. Simulated were the response of healthy motors, and motors with shorted stator coils and broken rotor bars. [S0022-0434(00)01203-X]

Modeling and Simulation for Dual-Drive Transmission System of TBM Based on Bond Graph

2010 ◽  
Vol 44-47 ◽  
pp. 1703-1707
Author(s):  
Chao Lin ◽  
Xin Hong Su ◽  
Da Tong Qin ◽  
Song Song Yu
Keyword(s):  
High Power ◽  
Dynamic Performance ◽  
Graph Model ◽  
Tunnel Boring Machine ◽  
Bond Graph ◽  
Transmission System ◽  
State Equations ◽  
Response Curves ◽  
Tunnel Boring ◽  
Planetary Transmission

The dual-drive system to be used in the tunnel boring machine (TBM) is a new kind of high-power planetary transmission system. On the basis of the system’s transmission theory and the bond graph principle, the bond graph model of the dual drive transmission system is established and then the state equations are deduced. Based on this model, dynamic performance of the system is simulated by means of MATLAB/Simulink and the dynamic response curves of the speed and torques are acquired. The simulation response illustrates that the bond graph model of dual drive transmission systems is accurate. In addition this system is suitable for three types of TBM and can satisfy the requirements of dramatic changes of load in the running of TBM.

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.

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 Bond Graph Model of Cerebral Circulation: Toward Clinically Feasible Systemic Blood Flow Simulations

2020 ◽  
Author(s):  
Shan Su ◽  
Pablo J. Blanco ◽  
Lucas O. Müller ◽  
Peter J. Hunter ◽  
Soroush Safaei
Keyword(s):  
Cerebral Circulation ◽  
Graph Model ◽  
Bond Graph ◽  
The Body ◽  
Lumped Parameter Model ◽  
Desktop Computer ◽  
Detailed Model ◽  
Simulation Speed ◽  
Lumped Parameter ◽  
Proposed Model

The primary paper Safaei et al. (2018) proposed an anatomically detailed model of the human cerebral circulation that runs faster than real-time on a desktop computer and is designed for use in clinical settings when the speed of response is important. Based on a one-dimensional formulation of the flow of an incompressible fluid in distensible vessels, a lumped parameter model was developed for 218 arterial segments. The proposed model improved simulation speed by approximately 200-fold while preserved accuracy. Bond graph formulation was used to ensure mass and energy conservation. The model predicted the pressure and flow signatures in the body.

Non-iterative evaluation of multiphase thermal compliances in bond graphs

2002 ◽  
Vol 216 (1) ◽  
pp. 13-19 ◽  
Author(s):  
F. T. Brown
Keyword(s):  
Bond Graph ◽  
The State ◽  
Refrigeration Cycle ◽  
State Variables ◽  
Unfinished Business ◽  
Bond Graphs ◽  
State Equations ◽  
Efficient Simulation ◽  
Multiple Phase ◽  
Iterative Evaluation

The practical use of bond graphs to organize the efficient simulation of multiple-phase thermodynamic systems is perhaps the most significant piece of unfinished business regarding the evolution of bond graphs. The most widely recognized form for these cases, called the pseudo bond graph, dictates particular causalities that require iteration, assuming the use of available state equations. This paper shows how the alternative convection bond graphs can direct non-iterative evaluation of state properties of multiphase thermal compliances. The state variables of a compliance become temperature, mass and volume. A refrigeration cycle is used as an example.

Bond Graph Models for Linear Motion Magnetostrictive Actuators

1996 ◽  
Vol 118 (1) ◽  
pp. 161-167 ◽  
Author(s):  
M. D. Bryant
Keyword(s):  
Transfer Functions ◽  
Mechanical Energy ◽  
Constitutive Relations ◽  
Graph Model ◽  
Bond Graph ◽  
Linear Motion ◽  
State Equations ◽  
Graph Models ◽  
Magnetostrictive Actuator ◽  
Audio Range

Bond graph models for the audio range response of a dynamically continuous, linear motion magnetostrictive actuator are formulated and presented. The actuator involves a continuous rod of magnetostrictive material that extends, contracts, and vibrates in modes when energized by magnetic flux produced by a coil. The left end is fixed, force is extracted from the right end. The bond graph model includes dynamics of the energizing coil, the flux routing circuit, magnetic to mechanical energy conversion, and mechanical elements. Constitutive relations for magnetostriction suggest use of a multipart capacitor with ports for magnetic and mechanical power flow; constraints imposed by modal dynamics require a separate mechanical port for each vibration mode. Values were assigned to bond graph parameters in a non-empirical manner: solely from theory and handbook data. State equations and transfer functions were extracted from the bond graph. For audio range operation, theory (the bond graph model) compared well with experiment (measurements taken on a magnetostrictive actuator designed and built by the author).

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