Bond Graph Structure Research Articles

Inverse Kinematics of a Spatial Mechanism using Multibond Graph

Various methods are available to compute kinematics and dynamics in the case of spatial mechanisms. These methods are cumbersome and laborious for large and multibody spatial mechanisms. The bond graph technique is a powerful alternative tool for modeling. A four-link closed-chain 3R2S (3Revolute 2Spherical) spatial mechanism stands out among the other four-link closed-chain spatial mechanisms due to its ability to be used in a number of applications. The main aim of this paper is to compute the inverse kinematics of the mechanism using the bond graph structure of the system. In this paper, modeling of a four-link closed-chain 3R2S spatial mechanism has been conducted using a multibond graph approach. Inverse kinematics of the spatial mechanism, under various applications, has been directly obtained from the bond graph modeling. MATLAB coding for simulation has been done directly from the multibond graph without explicitly deriving system equations. The simulation results have been analyzed and discussed using various plots.

Modeling and Simulation of Hydraulic Hammer for Sleeve Valve

Hydraulic hammer is commonly used hydraulic equipment in engineering work. The characteristics, high acceleration, high frequency and inertial working pressure, make it greatly different from the working conditions of conventional hydraulic equipment, while hydraulic hammer for sleeve type is also not the same as other hydraulic hammers in structure, efficiency and working performance. Based on the principle of hydraulic hammer for sleeve type, the mathematical model of hydraulic hammer for sleeve type was set with various conditions in the reciprocating movement of piston. In addition, more detailed sketch model can be easily built with the mathematical model in multi-domain system analysis software, AMESim. The simulation system of breaker built based on the principle of power bond graph structures in AMESim system is considered comprehensively to achieve its functions and characteristics, which can quickly realize the calculation of main simulation parameters for impactor. The calculated parameters can be proved to be biased with the test prototype. So these parameters must be optimized by Design Exploration to find the appropriate parameters.

Generalized controlled switched bond graph junctions

This article presents two dual-controlled switched bond graph structures called generalized switched junction structures. These structures can represent all the interconnections enforced by commutations involving bond graph elements around standard 0- and 1-junctions. Moreover, pre-existing multiport switched bond graph formalisms like controlled junctions and switched power junctions can be represented as particular configurations of generalized switched junction structures. The generalized switched junction structures incorporate some algebraic constraints into their equation sets, which in the bond graph domain can be represented with residual sinks, in order to make them able to keep fixed the causality assignment even under ideal switching (zero transition time switching), as a convenient tool for simulation purposes. However, just performing some minor modifications on their internal implementation using basic bond graph components, the generalized switched junction structure can also be used to model commutations relaxing the ideal switching hypothesis in favor of the approximate one which introduces some parasitic components, which is frequently used as a means to avoid possibly appearing causality changes. The generalized switched junction structure can be implemented in a compact way at high level using the equation sets defining their behavior, or in detailed way using elements out of the standard set of bond graph components.

Bond graph modeling of dynamics of soft contact interaction of a non-circular rigid body rolling on a soft material

The bond graph model for soft contact interaction between a circular rigid body and a soft material has already been developed and validated experimentally in a previous work. The present work further extends the approach to soft contact interaction for non-circular rigid bodies rolling on soft material which is difficult to model otherwise. An elliptical disc is taken as the non-circular rigid body as an example. An algorithm is developed to detect nodes of the soft material which contact the disc at any time. The contact interface between the two surfaces is assumed to be viscoelastic which is the penalty approach with additional dissipation. The model is applicable for all geometries of the rigid body. The contact model also takes normal force and tangential frictional force into account. The model dynamically determines the number of contact nodes, and hence the contact area at any time as the contact interface changes. Results of simulation of the model, based on code generated algorithmically from the bond graph structure, provide better understanding of the soft contact interaction issues involved.

Bond graph representations of hydraulic pipelines using normal modes with dissipative friction

The one-dimensional (1-D) unsteady-pressure-flow equations of hydraulic pipeline can be approximated and solved numerically using a finite-mode approach. This paper deals with constructing bond graph representations for the hydraulic pipelines with laminar flow by using the previously established 1-D linear-friction bond graph structures and modal approximation techniques when 2-D frequency-dependent friction is taken into account. To model hydraulic pipelines as components in different systems using bond graphs, there are four possible input–output causalities: pressure inputs at both ends, flow rate input at both ends and the two cases of mixed inputs. In this paper, all four configurations are considered. The developed bond graph structures together with their corresponding modal parameters are presented. A comparison is made for three models, namely lossless, 1-D linear fluid friction and 2-D fluid friction. Simulation results show that the modified bond graph models studied in this work can give more satisfactory results.

Fault Detection in a Cracked Pipeline Embedded with Piezoelectric Sensors/Actuators Employing Bond Graph Approach

The main scope of this article is to simulate a cracked pipeline embedded with piezoelectric sensors and actuators utilizing bond graph approach. Piezoelectric sensors/actuators are becoming very popular in various applications such as health monitoring, active vibration control or noise reduction, and as a part of the systems called smart structures. The proposed bond graph structure in this study, graphically illustrates the power flow between the electrical and mechanical frameworks included in the system. In addition, the proposed framework makes it possible to utilize a modular structure for separately representing the electrical polarization of the material and its macroscopic electrical and mechanical effects. Simulation results illustrate that at the location of the crack the equivalent impedance is increased and the capacitance is decreased in comparison with the intact region.

General Bond Graph model for piezoelectric actuators and methodology for experimental identification

Piezoelectric actuators are becoming very popular in applications such as nanopositioning, active vibration control or noise reduction, sometimes as part of so called smart structures. The possibility of accurately moving big loads on a micrometric scale and over a wide range of frequencies has resulted in an intense growth of this technology. This interest has prompted the development of a wide variety of mathematical models available for describing their behaviour, whose suitability depends on the specific application involved. This work overcomes this limitation by unifying the different modelization options for stack and stack-based actuators in a general Bond Graph model structure capable of handling the most important physical phenomena observed in these actuators, both linear, such as direct and indirect piezoelectric effects or rate dependence, and nonlinear, such as hysteresis. This model structure represents a basis for specific applications, and can be used for control or simulation purposes thanks to its high generality and adjustment capabilities. The proposed Bond Graph structure graphically shows the power flow between the electrical and mechanical frameworks of the piezoelectric actuator, and uses a modular structure for separately representing the electrical polarization of the material and its macroscopic electrical and mechanical effects. Finally, the model is successfully applied to describe the rate dependent behaviour of the Cedrat Groupe APA-120ML actuator. In this connection, an experimental identification method is described and adapted for implementing hysteresis descriptions based on simple operators or in differential equations in the model structure (O-based and DE-based models). These two typologies cover the majority of the models available, proving the generality of the proposed piezoelectric model for implementing less general or specific phenomenon descriptions into its structure. In consequence, the main contribution of this work is the development of a general framework for modelling piezoelectric actuators, comprising a graphical Bond Graph model and an adjustment procedure, which is flexible enough to embody different representations of the phenomena present in these actuators, and with a modular structure that admits different levels of complexity depending on the phenomena incorporated in the model.

Port based modelling of a multiscale adsorption column

A port-based distributed parameter model of an adsorption column under isothermal conditions is presented. This model is made using bond graph terminology and basic axioms of irreversible thermodynamics. The particularity of this model is to split each phenomenon in basic elements with particular energetic behaviour, such as accumulation or dissipation. These basic elements are interconnected using the port variables and some interconnection power conserving structures, named Dirac structures. These energetic elements are presented in terms of the geometry of the different scales of the adsorption column. Moreover it is shown that each scale of the model has the same bond graph structure. The different scales of the model are also connected by a power conserving structure.

A model for simulating a lead-acid battery using bond graphs

This paper presents a model of a lead-acid battery developed with bond graphs. The bond graph structure is used to reproduce the behavior of reversible electrochemical cells in charging conditions or in discharging conditions. The work presented here has been applied to the particular case of lead-acid battery, so widely used in the automotive industry as standard 12 V batteries and as traction batteries in electrical or hybrid vehicles. The model considers each half-cell independently. For each half-cell the main electrode reaction and the electrolysis reaction of water are considered, that will be the hydrogen evolution reaction in the negative electrode and the oxygen evolution reaction in the positive. Electrochemical principles are considered in order to consider the main phenomena that appear in the battery, like the equilibrium potential, and the overpotential, modeled by means of the activation or charge transfer and the diffusion mechanisms. Each one of this phenomena are modeled with their corresponding bond graph elements and structures, showing the correspondence between bond graph elements and its physical interpretation in this field. First, an isothermal model has been developed in order to show the behavior of the main phenomena. A more complex model has also been developed including thermal behavior. This model is very useful in the case of traction batteries in electrical and hybrid vehicles where high current intensities appear. Some simulation results are also presented in order to show the accuracy of the proposed models and the differences of behavior if thermal effects are considered.

A bond graph approach to the modeling of general multibody dynamic systems

A vector bond approach which effectively leads to a compact form of Hamiltonian bond graph structure and naturally to Hamilton’s equation of motion is proposed for the modeling of general multibody dynamic system. The methods for determining required bond graph elements are formulated in terms of kinematic influence coefficients. All moduli of transformers and their time rate of changes are found by pure vector (matrix) operations for the readiness for computer simulation of the resulting bond graph.

Using Bond Graphs to Model Production Systems with Machine Failure

Abstract During these last years, the problem of modelling production systems has received considerable attention. The standard tools generally used are queuing networks, Petri nets or Markov chains. The aim of this paper is to show that it is possible to use the bond graph formalism to model such systems, and especially machine failures which can occur during their functioning. This tool allows a clear graphical representation, a study of the properties of the system from the bond graph structure, and finally a dynamic description by a state equation.

Dynamic System Synthesis With a Bond Graph Approach: Part I—Synthesis of One-Port Impedances

This is the first part of a two-part paper developing a procedure for impedance synthesis and dynamic system conceptual design using a bond graph approach. The first part examines impedance synthesis with bond graphs and develops some useful properties of impedance related to bond graph structure. The second part of the paper uses the impedance synthesis approach as a tool in conceptual design for generating dynamic system solutions meeting frequency domain input-output specifications. In Part I, impedance and transfer functions are directly formulated from bond graphs. An invertible procedure is developed in order to allow for synthesis. Frequency domain properties of bond graphs are developed that will aid in impedance synthesis and the synthesis of bond graph structures from impedance specifications is formulated with a view toward conceptual design. The synthesis is not unique, a given impedance can be synthesized into multiple bond graph structures depending on its complexity. The work presented focuses on the synthesis of passive impedances but may be generalized for active systems.

BOND GRAPH SIMULATION OF A CURRENT SOURCE INVERTER DRIVEN INDUCTION MOTOR (CSI–IM) SYSTEM

ABSTRACT Based on the bond graph approach, the paper presents a developement of a dynamic model required for the simulation of a current–source–inverter (CSI) driven induction motor. The induction machine Is represented by the mutually perpendicular α–β model in a stationary reference frame, and is linked with the three phase current source inverter by a power conserving transformation which is taken as displacement modulated transformer structure In the bond graph model. A specific digital simulation program (COSMO–CAD) yields state space representation of the system from the bond graph structure with no reference to particular circuit configurations, representing various modes, during normal or abnormal operation. The acceptability of the simulation technique is shown by comparison of some results with those obtained from an available method of simulation.

Vector Bond Graph Analysis of Mechanical Systems

The utility of existing bond graph methods in the analysis of complex mechanical systems has been limited significantly by the absence of a tensor based vector modeling methodology. Topological simplifications are needed in order to recapture the efficiency of graphical model formulation work for complex mechanisms. The needed simplifications can be achieved by the introduction of new bond graph structures which express in coordinate free form the momentum and energy balance relations and kinematic constraints commonly encountered in mechanical system dynamics.

Bond graph modeling of automotive power trains

This paper starts with a development of a simple, basic bond graph model of automotive power trains. The model contains key components needed to reproduce the dominant (shuffle) mode oscillations that are often observed in manual transmission vehicles. The basic model is illustrated with an example and supported by experimental data. Various extensions of the basic model are also considered, including four wheel drive vehicles and power trains with automatic transmissions. The modeling extensions were facilitated by a generic bond graph structure for planetary gears, which are appropriately modified for the present tasks. The derived models are useful for preliminary assessment of the effects of power train system/component design changes, and for power train control system design.

Representation of Measured Ejector Characteristics by Simple Eulerian Bond Graph Models

Ejectors (or jet pumps) are highly reliable pure fluidic devices very commonly used in power plants, propulsion systems, petrochemical processes and other thermofluid systems. However, little off-design data has been available in a form suitable for dynamic simulation and control system design. Fortunately, concerns of the nuclear industry have recently led the Idaho National Engineering Laboratory (INEL) to obtain, from their LOFT Test Support facility, ejector test data sufficiently extensive to formulate a complete model accurately describing all flow conditions. Thus an elementary fixed-constant bond graph structure will approximate complete ejector characteristics, while a model only slightly more complex fits all INEL data within experimental scatter.

Modelling the dynamics and kinematics of mechanical systems with multibond graphs

A method to model mechanical systems with multibond graphs is described. The method is based on the description of the vector velocity relation of a moving point in a rotating system. This relation is incorporated in a bond graph. Since bond graphs are based on the power conserving concept, the force or momenta relations are then available too. By repeating the same bond graph structure for every point (which is of interest within a chosen coordinate frame), where each point has the same rotational velocity, a systematic way of modelling mechanical systems is achieved. It is explained how connected mechanical linkages have to be handled. Two simple examples are given.

Complementary formulations in vibrations: bond graph structures and modal transformations

Lumped parameter, undamped vibratory system models are studied starting from a vector bond graph representation which yields a symmetric set of equations of motion in terms of momenta and displacements. Four additional formulations are obtained depending upon the choices of displacement or impulse-momentum degrees of freedom including the classical formulation in terms of mass displacements. Differences in terms of forcing and response variables are found among the alternative formulations and differences in system order are explained. A new form of normal mode equations is developed using first order symmetric variables and a bond graph representation is given. Advantages in the use of the new model analysis for subsystem coupling are discussed.

Basis order for bond-graph junction structures

Junction structures are bond graph representations of the multiport topology of energy-based systems. The basis variable order is the number of independent effort variables and flow variables that must be specified for a particular topology. Two algebraic equations are developed that predict the effort-flow basis order for an arbitrary simple junction structure (SJS). These numbers are shown to be completely determined by the topological characteristics of the SJS. The results are extended to weighted junction structures.

Dynamic analysis of field energy systems using bond graphs

Notations and power-energy relationships are reviewed for the basic multiports used in bond graph analysis and extended to include two new multiports called the inductance and capacitance mutators respectively. With these multiports, the technique of bond graph analysis can be applied to electromagnetic and electrostatic field systems and illustrations of some of the bond graph structures appropriate to energy conversion devices such as transformers and machines are developed accordingly.