Bond Graph Research Articles

Transient Dynamic System Behavior of Pressure Actuated Cellular Structures in a Morphing Wing

High aspect ratio aircraft have a significantly reduced induced drag, but have only limited installation space for control surfaces near the wingtip. This paper describes a multidisciplinary design methodology for a morphing aileron that is based on pressure-actuated cellular structures (PACS). The focus of this work is on the transient dynamic system behavior of the multi-functional aileron. Decisive design aspects are the actuation speed, the resistance against external loads, and constraints preparing for a future wind tunnel test. The structural stiffness under varying aerodynamic loads is examined while using a reduced-order truss model and a high-fidelity finite element analysis. The simulations of the internal flow investigate the transient pressurization process that limits the dynamic actuator response. The authors present a reduced-order model based on the Pseudo Bond Graph methodology enabling time-efficient flow simulation and compare the results to computational fluid dynamic simulations. The findings of this work demonstrate high structural resistance against external forces and the feasibility of high actuation speeds over the entire operating envelope. Future research will incorporate the fluid–structure interaction and the assessment of load alleviation capability.

Hybrid condition monitoring of nonlinear mechatronic system using biogeography-based optimization particle filter and optimized extreme learning machine

This paper proposes a hybrid condition monitoring approach, which integrates bond graph model-based diagnostic technique and data-driven remaining useful life (RUL) prediction, for a nonlinear mechatronic system. In this approach, various degrading faults can be considered and the physical degradation model is not required for RUL prediction. Firstly, an integrated fault signature matrix is proposed by the causal path of bicausal-bond graph model to improve fault isolation performance. After that, a biogeography-based optimization (BBO)-particle filter is developed for fault identification. For prognosis, an optimized extreme learning machine (OELM) is proposed where the hidden layer biases and input weights are optimized by BBO. The fault identification results provide data set to train the OELM for prognosis. Finally, the effectiveness of the approach is verified by simulation and experiment results.

Parameterization, Modeling, and Validation in Real Conditions of an External Gear Pump

This article presents a methodology for predicting the fluid dynamic behavior of a gear pump over its operating range. Complete pump parameterization was carried out through standard tests, and these parameters were used to create a bond graph model to simulate the behavior of the unit. This model was experimentally validated under working conditions in field tests. To carry this out, the pump was used to drive the auxiliary movements of a drilling machine, and the experimental data were compared with a simulation of the volumetric behavior under the same conditions. This paper aims to describe a method for characterizing any hydrostatic pump as a “black box” model predicting its behavior in any operating condition. The novelty of this method is based on the correspondence between the variation of the parameters and the internal changes of the unit when working in real conditions, that is, outside a test bench.

Stability Analysis upon High-Pressure Common Rail Fuel Injection System under Multiple Injection Modes

Fuel injection stability of high-pressure common rail fuel injection system (HPCRFIS) under multiple injection modes is a recognized technical problem. To explain it essentially, a numerical model based on bond graph method, which provides a standardized series of symbol system to describe various components in different physical fields as well as interactive effect analysis tool for different energy categories, was used to investigate the problem. As HPCRFIS is a typical nonlinear system with multi-physical coupling, it is very difficult to analyze system stability directly. Therefore, the system was linearized at typical moments. The system matrix for each typical moment was obtained thereby. To investigate the influential mechanism of system stability deeply, the variations of rank and eigenvalues distributions of state matrices were analyzed. The results show that the rank of state matrices changes abruptly when the needle or control valve moves. In terms of system stability, the oscillation characteristics are subject to the movement of needle or control valve. The ending of the former injection causes the system to show damping oscillation characteristics before the latter injection starts. The motion of control valve makes more contribution to system stability than that of needle, which could be concluded by Lyapunov stability criterion.

Control and modelling evaluation of a piezoelectric harvester system

The predominant role of a piezoelectric harvester system in Vibration Energy Harvesting (VEH) is to gather vibrations energy caused by road profile disturbances. In this paper, a new piezoelectric harvester model with two degrees of freedom is modelled by the Bond Graph technics and simulated in a 20-Sim environment connected to MATLAB/Simulink software. The proposed modelling techniques have the ability to extend the ride comfort of the driver when the electric vehicle is moving upon different types of road profiles such as random road surfaces. The proposed harvester system is used to examine and ensure the health criterion and ride comfort of drives. Further, simulation results in the time domain and electrical power spectrum density analysis are carried out for the EV and proposed modelling techniques. The simulation results confirm that the proposed piezoelectric harvester system is more efficient in all different dimensions, and significantly improves the ride comfort, and increases the power quantity for the three different road classes. Finally, the results are illustrated and discussed graphically for various particular cases.

Modeling and dynamic analysis of the dynamic stabilization unit based on bond graph

This paper, respectively, considers the nonlinear contact and Coulomb friction between rollers and rails, the characteristics of a hydraulic cylinder, and the contact characteristics between sleepers and ballast. The models of hydraulic cylinders are employed to realize the characteristics of hydraulic circuits and clamping forces. And the effects of the Coulomb friction between the track roller and the rail are simulated by calling the Boolean operation in the bond graph simulation software 20-sim. Based on the above analyses, this paper explores deeply which effect the pressures in the hydraulic cylinders and the hydraulic resistances of the flow passes at the inlets and outlets of the hydraulic cylinders will have on roller–rail contacts and working effects. As a result, the increase in pressure of the hydraulic cylinder will stabilize the roller–rail contact and improve the energy transmission efficiency. The increase in the hydraulic resistance value can enhance the working effect to some extent. With regard to the friction, there are four forms of frictional contact between the roller and the rail.

Linear electromagnetic energy harvester system embedded on a vehicle suspension: From modeling to performance analysis

Although linear electromagnetic energy harvester (LEH) is a promising technique for converting energy in a vehicle suspension, due to the large displacements, one of the main drawbacks of the solutions inside the vehicle is still their size and complexity. To address this issue, this paper focuses on the design and fabrication of a fully embedded LEH without any modification of the suspension initial structure. After a determination of the electrical, mechanical and electromechanical parameters using a Finite Element analysis, the dynamic efficiency is highlighted with a global Bond Graph model. This formalism is well adapted to simulate energy transfers inside multiphysic systems and to reduce the computational time, whereas the finite element model is not exploitable for a complete suspension simulation. In order to validate the Bond Graph simulation results, an embedded prototype has been built and tested in a laboratory environment. The embedded LEH system delivers around 10 W for a solicitation of linear velocity of 1 m/s which is sufficient to power a classical electronic circuit which is in good correlation with the measured ones and significant power has been obtained.

Dynamics of a rotor shaft driven by a non-ideal source through a universal joint

A rigid rotor system which is driven through a Universal joint (U-joint) and is mounted on weakly-damped flexible supports exhibits principal and combination type parametric instabilities at certain torque-speed combinations. In this article, the transient dynamics of such a non-linear system driven by a non-ideal source (a DC motor) is studied through numerical simulation of the bond graph model of the system. It is shown that the dynamic coupling between the DC motor and the whirling rotor in the non-ideal system can stabilize the system in the speed ranges where the corresponding ideal system is unstable. This stabilization depends upon the motor characteristic constant or the torque/speed constant; i.e. if two motors with different motor characteristic constants produce the same torque at the same operating speed (where the ideal system is unstable) then the motor with higher motor characteristic constant tends to better stabilize the system. This bounded-input bounded-output stabilization is shown to occur through repeated transitions between stable and unstable speed regions. Several simulation results for the system driven by ideal and non-ideal sources at different operating speeds are presented to derive motor sizing specifications.

Simulation model for predicting reciprocating internal combustion engine wear

The article presents the results of software development, using the Modelica language, designed to create and use simulation models as part of reciprocating internal combustion engines digital twins. The software was created on the basis of component, system and declarative approaches, the theory of a casual bond graphs. The software includes submodels for determining the main engine parts wear rate and allows to predict engine parts life time, to simulate normal and accelerated engine reliability and durability tests. In the course of the study, the well-known model for determining mechanical frictional losses SLM (Shayler, Leong, Murphy, 2005) was adapted to calculate the relative change in the wear rate of engine parts. Universal equations are obtained to determine the friction forces as applied to rotationally and reciprocally moving engine parts. A method is proposed for calculating the relative change in the wear rate of parts and the time of failure due to wear, taking into account the physical properties (hardness), geometric dimensions and the speed of the relative movement of parts in the conjunction.

Optimized fault detection using bond graph in linear fractional transformation form

This article deals with the optimal robust fault detection problem using the bond graph in its linear fractional transformation form. Generally, this form of the bond graph allows the generation of two perfectly separate analytical redundancy relations, that are used as residual and threshold. However, the uncertainty calculation method gives overestimated thresholds. This may, for instance, lead to undetectable faults. Therefore, enhancing the robustness of fault detection and isolation algorithms is of utmost importance in designing a bond graph–based fault detection system. The main idea of this article is to develop optimized thresholds to ensure an optimal detection, otherwise this article proposes a method to detect tiny magnitude faults concerning parameter’s uncertainties. This work considers the issue of optimal fault detection as an optimization problem of the gap between the residuals and its threshold. New uncertainty values will be calculated in a way that these estimated parameters ensure the desired optimized gap between residuals and thresholds. These estimated uncertainty values will be used to generate optimized adaptive thresholds. Through these thresholds, we increase the sensitivity of the residuals to tiny magnitude faults, and we ensure an optimal and early detection.

Real-time thermal modelling approach of a machine tool spindle based on bond graph method

The thermal characteristics of spindles have a significant influence on the workpiece quality. This paper proposes a novel real-time thermal characteristic modelling approach for spindles based on the bond graph method, with simplified thermal structure and brief estimation and calibration of thermal parameters. First, the thermal characteristics of this spindle are analysed and simply divided into different thermal components. Then, a network of thermal capacitances and thermal resistances is established based on the mechanism analysis of heat generation and heat transfer, and consequently, a thermal characteristics model is developed based on the bond graph method. Parameters of thermal conditions of the spindle are briefly estimated using theoretical analysis and empirical formulas. An experiment is designed to calibrate these thermal parameters of the model, followed by verification experiments of accuracy and robustness, the results of which indicate stable good prediction performance, with the maximum error of 0.7355 °C and the average error of 0.1989 °C. Finally, this model is applied in the quantitative investigation of the influence of working conditions on the thermal characteristics of the spindle and the real-time prediction of spindle’s thermal deformation with 5.26 μm maximum error and 1.45 μm average error. The results indicate that this approach has considerable advantages in the real-time prediction of thermal behaviours of spindles and can be used in industrial applications.

Design and Validation of Energy Management Strategy for Extended-Range Fuel Cell Electric Vehicle Using Bond Graph Method

In view of the aggravation of global pollution and greenhouse effects, fuel cell electric vehicles (FCEVs) have attracted increasing attention, owing to their ability to release zero emissions. Extended-range fuel cell vehicles (E-RFCEVs) are the most widely used type of fuel cell vehicles. The powertrain system of E-RFCEV is relatively complex. Bond graph theory was used to model the important parts of the E-RFCEV powertrain system: Battery, motor, fuel cell, DC/DC, vehicle, and driver. In order to verify the control effect of energy management strategy (EMS) in a real-time state, bond graph theory was applied to hardware-in-the-loop (HiL) development. An HiL simulation test-bed based on the bond graph model was built, and the HiL simulation verification of the energy management strategy was completed. Based on the comparison to a power-following EMS, it was found that fuzzy logic EMS is more adaptive to vehicle driving conditions. This study aimed to apply bond graph theory to HiL simulations to verify that bond graph modeling is applicable to complex systems.

Simulation of Hydraulic Cylinder Cushioning

The internal cushioning systems of hydraulic linear actuators avoid mechanical shocks at the end of their stroke. The design where the piston with perimeter grooves regulates the flow by standing in front of the outlet port has been investigated. First, a bond graph dynamic model has been developed, including the flow throughout the internal cushion design, characterized in detail by computational fluid-dynamic simulation. Following this, the radial movement of the piston and the fluid-dynamic coefficients, experimentally validated, are integrated into the dynamic model. The registered radial movement is in coherence with the significant drag force estimated in the CFD simulation, generated by the flow through the grooves, where the laminar flow regime predominates. Ultimately, the model aims to predict the behavior of the cushioning during the movement of the arm of an excavator. The analytical model developed predicts the performance of the cushioning system, in coherence with empirical results. There is an optimal behavior, highly influenced by the mechanical stress conditions of the system, subject to a compromise between an increasing section of the grooves and an optimization of the radial gap.

Three-Dimensional Dynamic Modelling and Validation for Vibration of a Beam-Cable System

ABSTRACT In order to understand and to predict cable effects on structures, three-dimensional numerical models for a stranded cable and a beam–cable system consisting of a cantilever beam and two connected cables are presented. The multibond graph formalism is used to model the coupled cable–beam system, with the cable and beam substructures using 3D rigid lumped segments. The stranded cables are modelled considering the bending stiffness, tension and sag due to self-weight. The generally applicable cable-structure modelling approach in this paper is applied to vibration-based non-destructive evaluation of electrical utility poles, where simulated modal testing of the pole-conductor system is required. Experimental parametrization of a stranded cable is carried out using specially designed apparatus to accurately measure the bending stiffness at different tensions, and to measure the axial stiffness and axial damping. A reduced-scale lab set-up and finite element models are developed for verification of the numerical models. Experimental free and forced vibration testing is performed on individual cantilever beam and stranded cable subsystems, and on the coupled cable–beam system to verify the numerical models in the frequency and time domains. It is concluded that the 3D bond graph models can be used to understand the interaction between cable and structure, allowing prediction of the in-plane and out-of-plane natural frequencies and time response of the connected pole. It is also concluded that by adding the cable to the pole structure, some modes emerge in the eigenvalue solution of the system which may be categorized as cable-dominated modes, pole-dominated or hybrid modes.

Dynamic bond graph modelling of a two-phase cooling system with experimental analysis

The power electronics components are a significant source of heat energy which must be managed in spite of conventional cooling systems' limitations. In order to surpass these restrictions, an innovative heat transfer system is here investigated: two-phase loop mechanically pump (TLMP). An instrumented test rig is built with temperature, pressure and mass flow rate sensors to analyse the flow response in both steady and transient state. In this work, we focus on the pump-pipes subsystem. The results confirm the system's ability to manage heat power dissipation by maintaining stable power electronics temperature. In addition, the experiment results validate a thermo-hydraulic model based on 'bond graph' theory. The variables used to simulate phase-change phenomena are: mass enthalpy, temperature and pressure. This modelling allows estimating the influence of external conditions on loop operation. Moreover, it offers sizing prospects for this kind of loop development on-board future missiles.

Dynamic bond graph modelling of a two-phase cooling system with experimental analysis

The power electronics components are a significant source of heat energy which must be managed in spite of conventional cooling systems' limitations. In order to surpass these restrictions, an innovative heat transfer system is here investigated: two-phase loop mechanically pump (TLMP). An instrumented test rig is built with temperature, pressure and mass flow rate sensors to analyse the flow response in both steady and transient state. In this work, we focus on the pump-pipes subsystem. The results confirm the system's ability to manage heat power dissipation by maintaining stable power electronics temperature. In addition, the experiment results validate a thermo-hydraulic model based on 'bond graph' theory. The variables used to simulate phase-change phenomena are: mass enthalpy, temperature and pressure. This modelling allows estimating the influence of external conditions on loop operation. Moreover, it offers sizing prospects for this kind of loop development on-board future missiles.

Robust Diagnosis of a Fuel Cell Pumping System by Bond Graph Modeling Approach

This article presents the obtained results by studying the efficiency of a developed diagnosis system dedicated for a PEM Fuel Cell pumping system. The studied system is composed of PEM fuel cell powering an electrical pumping system via an electronic adaptation stage which consists of a cascade-connected DC-DC boost converter and a voltage inverter. The diagnosis system is developed based on Bond Graph approach which allows to model the studied system graphically in order to facilitate to investigate its working performances by simulating the developed model under the 20-Sim software. Obtained results show an efficient fault detection for different simulation scenarios.

The problem of mathematical modeling of a vibration protected rod under kinematic exitations

In this paper, we consider the problem of mathematical modeling of nonlinear vibrations of a rod with distributed parameters and elastic-dissipative characteristics of the hysteresis type, and also having a liquid section dynamic absorber under kinematic excitations. The method of obtaining the differential equations of motion of the system protected from vibrations under consideration in the work using the structural method -the method of bond graph. An expression is obtained for the transfer function of a vibration-protective system for analyzing the dynamics and stability of the system and evaluating the effectiveness of a dynamic absorber.

Port-Hamiltonian Modeling of Thermofluid Systems and Object-Oriented Implementation With Modelica I: Thermodynamic Part

In this paper, we present the physical foundations and the development of the thermodynamic part of a Modelica library with the fundamental components for modeling thermofluid systems. We have chosen Modelica because it is an object-oriented modeling language that allows an elegant design of the library, with a top-down conception that starts from very general components where we model the thermodynamic properties common to all simple substances and descend by inheritance to model the properties of each particular substance. To model the behavior of each component, we have used: classical thermodynamics to define the equilibrium states, the local equilibrium hypothesis of Classical Irreversible Thermodynamics to model the changes of state, and the port-Hamiltonian approach to obtain the equations of the system dynamics. With this formulation, we implement the thermodynamic behavior of ideal gases (including monatomic gases as a particular case), the 2073 substances defined for the CEA (Chemical Equilibrium with Applications) NASA Glenn computer program, the IAPWS Formulation 1995 for the Thermodynamic Properties of Water Substance for General and Scientific Use, and the Syltherm 800 HTF (Heat Transfer Fluid). We also define graphical symbols for each library component that facilitate modeling complex systems with simple drag-and-drop manipulations, component connection, and parameter selection. These symbols are a slightly modified version of those used in bond graphs to facilitate their reading and the representation of the structure of complex systems. We also show the modeling, simulation, and comparison for accuracy, performance, and scalability of some thermodynamic systems implemented with the Modelica Standard Library (MSL) and the proposed library.

Analysis and Identification of a Dynamic Model for Proportional Solenoid

To solve the problem of difficult analysis and modeling of the strongly nonlinear characteristics of a proportional solenoid (PS) valve drive component, namely, the PS in engineering, a simplified mathematical model was established using a power bond graph, and the PS was numerically analyzed by Maxwell Simulation. After verifying the accuracy of the simulation model through experimental data, the static and dynamic output characteristics of the PS under different working conditions were analyzed in an auxiliary manner in the simulation model. Finally, the parameters of the mathematical model built were identified based on the principle of least squares (LSQ). The results show that the goodness of fit between the identified mathematical model and the static output characteristics of the PS reached 0.9866, and the relative error of the dynamic characteristics was 2%. The established model can provide engineers and technicians with a method to quickly analyze the dynamic characteristics of the PS and provide a basis for designing the control strategy of the PS’s current and force.