Bond Graph Method Research Articles

Comparison performance study of singly-fed and doubly-fed induction generators-based bond-graph wind turbines model

This paper consecrates to a comparative performance study of singly-fed and doubly-fed of induction generators thrusted by wind power turbine of similar generation capacity of 2.5 kW, and constant or variably wind speed. The singly-fed induction generator model could be represented using natural reference frame and doubly-fed induction generator model is described using a Park reference frame. Because of several physical domains existing in both induction generators like mechanical and electrical, modeling of generators is difficult, therefore the modeling based on physical methods takes a high credibility under these conditions. Among the procedures is Bond-graph method that models the systems based on law of mass conservation and/or law of energy conservation containing in the systems. Modeling the parts of both singly-fed and double-fed induction generators are based on Bond-graph method. We found that the impact of stator coil winding for on the current is in the form of changes of its value and steady state intervals; increasing the number of stator coil windings may also lead to increased stator current and the longer their steady state interval. Our study demonstrates also that doubly-fed induction generator possesses advantages compared to singly-fed induction generator, namely better current quality output and an adaptation to fluctuating wind speeds. The performance study is done in constant and variably wind speeds using simulated results of 20-Sim software.

Bond-Graph-Based Approach to Teach PID and Sliding Mode Control in Mechatronics

The main contribution of this article is creating synergy between subjects; this means that students use the same graphical tool in several subjects. So far, the bond graph has not been used in control theory, but it is the “native language” of mechatronics engineers, so we would like to introduce it into the teaching of control theory. The bond graph method is proposed as a novel teaching method to teach mechatronics subjects in the paper. The bond graph is a graphical alternative to ordinary differential equations from a mathematical standpoint. Traditionally, control theory employs ordinary differential equations, as they are familiar to control theorists. However, mathematically, both approaches are equivalent but require a slightly different approach in their application. This article highlights the mathematical similarities between the two approaches while emphasizing the distinctions in graphical representation. Another contribution is that the PID and sliding mode controller are represented using the bond graph method. In the meantime, through the use of practical examples, we effectively illustrate how the same problem can be solved using either approach. In the training materials, the PID controller and an adaptive robust sliding mode controller (ARSMC) with the bond graph are utilized as examples to demonstrate synergy in mechatronics. Finally, we present proof that mechatronic engineers achieve superior outcomes when utilizing the bond graph approach, based on test results from undergraduate students.

Design and development of an autonomous unmanned aerial vehicle for surface coalmines surveillance

This paper presents a detailed investigation into the development of a specialized unmanned aerial vehicle (UAV) for practical applications in coal mining. The main focus is on enhancing surveillance capabilities, identifying potential hazards, and supporting various coal mine activities. This study initiates with the careful design of a quadcopter, taking into account essential parameters such as VTOL, maneuverability, and hover efficiency. The quadcopter model is meticulously developed to ensure smooth operation under ideal conditions. The design process involves utilizing SolidWorks software to create a robust and optimized quadcopter model. Additionally, the static deformation simulation of the quadcopter is conducted using Ansys software, providing valuable insights into its structural integrity and performance. Dynamic modelling using the Bond Graph Method enables a thorough understanding of the quadcopter’s behavior and informs propulsion system selection. The chosen propulsion system prioritizes maximizing thrust-to-weight ratio to about 2:1, achieving the factor of safety of approximately 4, and ensuring maneuverability. The use of eCalc, an online open-source software, assists in identifying the ideal motor-propeller combination for optimal thrust characteristics. Surveillance and mapping techniques are explored in detail. A step-by-step methodology is proposed for image identification, while mapping is achieved through image stitching and path planning using waypoints. Additionally, volume estimation and vulnerability assessment methods specific to coal mining are discussed.

The Dynamic Equations of a Mechanical System Using the Bond-Graph Method and the Kinetic Energy

Abstract Based on the bond-graph model of a system dynamics, the differential equations that represent the mathematical model can be determined. In case of a system with storing energy elements in derivative causality and with more degrees of freedom, the computational effort is an important one. The present work proposes an easier method for finding the differential equations, based on the derivative of kinetic energy.

Dynamic characteristics of single-loop gear system based on bond graph method

The complexity of single-loop gear system transmission structure makes it difficult for traditional modeling methods to establish precise dynamic model, which greatly affects the accuracy of its dynamic characteristics research. Firstly, a structure diagram is established by adopting modularization idea according to the structural properties of single-loop gear system. On this basis, a precise bond graph model of the single-loop gear system is obtained combining the modeling principle of bond graph method and the advantages of rich graphics library. Secondly, the dynamic state equation of single-loop gear system is obtained from bond graph model. The simulation model of gear system is established by numerical simulation method. Eventually, the dynamic characteristics of a single-loop gear system are acquired by calculating two dynamic indexes of the system under linear and weakly nonlinear states. The simulation results show that the bond graph method can accurately describe the mathematical model of single-loop gear train and master the dynamic characteristics of complex gear train. This will provide a reference for the structural design and dynamic characteristics of the transmission system.

Modelling of wind turbine gear stages for Digital Twin and real-time virtual sensing using bond graphs

In this paper a wind turbine high-speed gear stage model is developed for the purpose of real-time virtual sensing of gear and bearing loads in a Digital Twin framework. The model requirements are: accurate representation of gear meshing and shaft dynamics, high computational efficiency and compatibility with other Digital Twin components, such as physical sensors signals and virtual sensing methods. State equations are derived analytically using the Bond Graph method and implemented in the software 20sim for simulation. As opposed to standard multi-body simulation (MBS) software, 20sim allows for higher flexibility in implementing interfaces to other Digital Twin components. The model fidelity is close to state-of-the-art MBS models considering 6 DOF body motion, however a simplified gear contact formulation is used, which assumes ideal kinematic meshing. Nonetheless, the Bond Graph model is able to accurately reproduce the inhomogeneous load distribution over the tooth flank, as well as the cyclic compression and decompression for each meshing period. The results suggest that the presented model is capable of monitoring fatigue loads in gear contacts and bearings in a Digital Twin framework.

New approach in solving derivative causality problems in the bond-graph method

From the bond-graph model of a dynamic system, the state equations can be obtained. When the system contains only energy storing elements in integral causality, the system of state equations is immediately and directly determined. When the model contains at least one energy storing element in derivative causality, the resulted system of differential-algebraic equations arises some difficulties in finding the final form of the system of state equations. The work presents a new method of deducing the state equations in case of bond-graph models with one, or several energy storing elements in derivative causality. This method is based on the kinetic energy of the system and offers the possibility to avoid a difficult mathematical calculus for the transition from a system of differential algebraic equations to the system of state equations.

A Comparative Analysis of Brake-by-Wire Smart Actuators Using Optimization Strategies

Since the automotive industry is shifting towards electrification, brake-by-wire technologies are becoming more prevalent. However, there has been little research comparing and optimizing brake-by-wire actuators in terms of their energy expenditure and response time. This paper investigates the comparison of three different smart brake-by-wire actuators, Electro-Hydraulic Brakes (EHB), Electro-Mechanical Brakes (EMB), and Electronic Wedge Brakes (EWB), first by defining an objective metric and then using both linear and nonlinear optimization techniques. Modeling of the actuators is performed using the bond graph method. Then, the controllers are designed using a robust control strategy, Youla parameterization. After designing the controllers, two types of optimization are performed on the actuators. Optimizations are performed in two ways: 1. by linearizing the plants and optimizing using their transfer functions and 2. by nonlinear optimization of the plants in the closed-loop following a specific clamp force target. The objective metrics or the cost functions for these optimizations are chosen to be the energy usage of the plants during the closed-loop operation, maximum power requirement, and their dynamic responsiveness. Using this optimization framework, we can show a significant improvement in the energy usage of the actuators and slight improvements in their responsiveness. In the end, the actuators are compared in terms of their energy usage for sets of initial and optimized physical parameters.

Dynamics analysis and energy consumption modelling based on bond graph: Taking the spindle system as an example

The spindle system of a Computer Numerical Control (CNC) machine tool is essential for improving the machining efficiency and accuracy. Although there are many studies on the energy consumption of machine tool spindle, few comprehensively consider the energy consumption and dynamics characteristics of the mechanical transmission of the spindle system. Therefore, a new bond graph method for modelling the dynamics characteristics and energy consumption of the spindle system of a CNC machine tool is proposed to solve this problem. The bond graph model of the spindle system is established based on the structure and energy flow characteristics of the spindle system. The bond graph model is converted into a dynamic simulation model that can be run in the MATLAB-Simulink environment. The dynamics and energy consumption characteristics of the spindle system are analyzed by observing the response of different input torques in the dynamic simulation model. Finally, the feasibility and practicability of the model are verified by experiments. The predictive accuracy of the proposed model is above 95%, which offers a viable approach for optimizing the design of the spindle system.

Research on dynamic characteristic of planetary gear system based on bond graph method

The dynamic characteristics of planetary system directly affect the stable state of the whole transmission system. Firstly, an accurate dynamic model of planetary gear system is established by using bond graph method. Formerly, the state equation of the gear train dynamics is obtained based on the bond graph model. On this basis, the simulation model of the gear system was acquired by using the numerical simulation method, and four dynamic indexes including zero-pole diagram, Bode diagram, Nyquist diagram and Nichols diagram of the gear dynamics system were gained. Finally, the analysis results show that the accurate mathematical model is described by the bond graph method and the dynamic characteristics is comprehended of planetary gear system, while will provide a basis for the stability research of the transmission system.

Contribution to the systemic modeling of a photovoltaic devices

The modelling of systems using systemic tools has been for a few years, a subject which has attracted the attention of scientists and especially researchers to allow designers to acquire a rigorous approach to problem solving using the capabilities of already existing methods and tools. This document presents a contribution in the field of modelling, where a methodology based on two methods has been proposed. The first concerns the functional analysis to extract the use functions and the constraint parameters from the system. In this methodology, the static functional study is carried out using the SADT method. On the other hand, the dynamic behavioral analysis is carried out by the SA-RT method. Then, we used a behavioral and parametric analysis, the Bond Graph method, to observe the evolution of representative quantities of a photovoltaic system.

A Method to Find the Differential Equations from the Bond Graph Containing Inertial Elements in Derivative Causality

Abstract The bond-graph method is used for finding the equations which describe the systems dynamics, by analysing the way of power transmission from the source to the working elements. When the energy storage elements I and C are in integral causality, the number of state equations equals the number of these elements. If there are also energy storage elements in derivative causality, the system contains a number of differential equations equal to the number of energy storage elements in integral causality and a number of algebraic equations equal to the number of energy storage elements in derivative causality. The work presents a new method for finding the system of differential equations for mechanical systems with one degree of freedom, starting from the original system which contains both algebraic and differential equations.

Dynamic Modeling and Simulation of Double-Planetary Gearbox Based on Bond Graph

New generations of powertrains are using gearboxes with multiple speed-shift designs to improve fuel efficiency. However, transmission controls and calibration are substantially time consuming, specifically during shift processes. To study the dynamic characteristics of a gearbox with a double-planetary gear train and analyze the influence of external excitation and internal parameters on the dynamic response of a system, dynamic modeling and simulation of the transmission system are conducted. Some physical processes are complex and difficult to express via lumped mass modeling. The dynamic model of a double-planetary gearbox is obtained by adopting the bond graph method based on the working principle analysis of the transmission, as well as the kinematic characteristics of the double-planetary gear train. Subsequently, state equations are deduced from the dynamic model of the power transmission system for simplified calculations, which can effectively facilitate the shift process simulation. The basic case of different shift plans and times is originally analyzed, followed by an analysis of the influence of damping, stiffness, and moment of inertia on transmission systems. The analysis results provide references for the structural design, control strategy optimization, and failure diagnostics of this gearbox type.

Research on the torsional vibration performance of a CVT powertrain with a dual-mass flywheel damper system

Continuously variable transmissions (CVTs) can achieve continuous changes in speed ratio and can better improve the ride comfort of the car. However, the torque fluctuation of the engine will reduce its transmission efficiency, and the torsional damper is usually matched to improve transmission efficiency and reduce vibration noise. In this paper, the model of a complete vehicle power transmission system was established by using the bond graph method. The relationships between each state variable were obtained according to the system causality and the direction of the power flow, based on which the dynamic model of the entire vehicle power transmission system was derived. A simulation of the powertrain with dual-mass flywheel-continuously variable transmission (DMF-CVT) was carried out, and the torsional stiffness of the dual-mass flywheel (DMF) was optimized. Taking a certain sport-utility vehicle (SUV) as the test bench, the vehicle road testing of the DMF before and after improvement was carried out, and the test results before and after the improvement were compared to verify the correctness of the optimization direction, which provided a reference for the matching and optimization design of the DMF-CVT power transmission system.

A new method for extracting the state equations from bond graph of dynamical systems (SEBG method)

The bond graph (BG) method is an appropriate tool to model hybrid systems. The automated extraction of state equations from BG is the main drawback of this method. In this paper, a new method has been presented to simply extract the state equations from BG (SEBG method). Initially, SEBG has converted the BG model to the bond-element table (BE-table) to gain all the information of BG in a systematic representation. It has then formed a set of algebraic equations using elements’ functions (E-functions) and found the power variables by solving them. Finally, the system’s state equations are established using BE table, power variables, state vector, and states’ functions, based on the fact that only the relations of inertial and capacity elements contain the first-order differential equations. Moreover, the simplicity and practicality of SEBG have been examined for finding the state equations of two systems.

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.

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.

Importing the Human Factor into Safe Human–Robot Interaction Function Using the Bond Graph Method

SUMMARYThe variable stiffness actuator (VSA) is helpful to realize the post-collision safety strategies for safe human–robot interaction.1 The stiffness of the robot will be reduced to protect the user from injury when the collision between the robot and human occurs. However, The VSA has a mechanism limit constraint that can cause harm to users even if the stiffness is minimized. Accordingly, in this article, a concept combining danger index and robust fault detection and isolation is presented and applied to active–passive variable stiffness elastic actuator (APVSEA). APVSEA can actively change joint stiffness with the change of danger index. Experimental results show that this concept can effectively confirm the fault mode and provide additional protection measures to ensure the safety of users when the joint stiffness has been adjusted to the minimum.

Power Transformer Model in Railway Applications Based on Bond Graph and Parameter Identification

Validation and verification are the most important issues in railway applications due to cost and security reasons. Therefore, having a model of the system would be necessary in this case. Due to nonideal test conditions in industrial applications, an accurate parameter identification process has to be defined. In this article, the bond graph method is used to model energy exchanges within the components of a traction chain. More precisely, the nonlinear transformer model and its parameter identification are studied. In the case of nonideal test conditions, the usual Jiles–Atherton (JA) parameter identification procedure cannot be performed. Regarding the state of the art, the JA parameter identification is discussed. It is highlighted that an incomplete hysteresis cycle, including the extremum point and coercive field, is mandatory for accurate parameter identification. The proposed identification process is applied to a real-application case. The obtained parameters are then inserted into the overall system model. The consecutive simulations are compared with experimental data obtained through the traction chain test bench.