DOCSLIB.ORG

Modeling & Simulation 2019 Lecture 8. Bond Graphs

Total Page：16

File Type：pdf, Size：1020Kb

Download full-text PDF Read full-text
Modeling & Simulation 2019 Lecture 8. Bond Graphs Modeling & Simulation 2019 Lecture 8. Bond graphs Claudio Altafini Automatic Control, ISY Linköping University, Sweden 1 / 45 Summary of lecture 7 • General modeling principles • Physical modeling: dimension, dimensionless quantities, scaling • Models from physical laws across different domains • Analogies among physical domains 2 / 45 Lecture 8. Bond graphs Summary of today • Analogies among physical domains • Bond graphs • Causality In the book: Chapter 5 & 6 3 / 45 Basic physics laws: a survey Electrical circuits Hydraulics Mechanics – translational Thermal systems Mechanics – rotational 4 / 45 Electrical circuits Basic quantities: • Current i(t) (ampere) • Voltage u(t) (volt) • Power P (t) = u(t) · i(t) 5 / 45 Electrical circuits Basic laws relating i(t) and u(t) • inductance d 1 Z t L i(t) = u(t) () i(t) = u(s)ds dt L 0 • capacitance d 1 Z t C u(t) = i(t) () u(t) = i(s)ds dt C 0 • resistance (linear case) u(t) = Ri(t) 6 / 45 Electrical circuits Energy storage laws for i(t) and u(t) • electromagnetic energy 1 T (t) = Li2(t) 2 • electric field energy 1 T (t) = Cu2(t) 2 • energy loss in a resistance Z t Z t Z t 1 Z t T (t) = P (s)ds = u(s)i(s)ds = R i2(s)ds = u2(s)ds 0 0 0 R 0 7 / 45 Electrical circuits Interconnection laws for i(t) and u(t) • Kirchhoff law for voltages On a loop: ( X +1; σk aligned with loop direction σkuk(t) = 0; σk = −1; σ against loop direction k k • Kirchhoff law for currents On a node: ( X +1; σk inward σkik(t) = 0; σk = −1; σ outward k k 8 / 45 Electrical circuits Transformations laws for u(t) and i(t) • transformer u1 = ru2 1 i = i 1 r 2 u1i1 = u2i2 ) no power loss • gyrator u1 = ri2 1 i = u 1 r 2 u1i1 = u2i2 ) no power loss 9 / 45 Electrical circuits Example State space model: d 1 i = (u − Ri − u ) dt L s C d 1 u = i dt C C 10 / 45 Mechanical – translational Basic quantities: • Velocity v(t) (meters per second) • Force F (t) (newton) • Power P (t) = F (t) · v(t) 11 / 45 Mechanical – translational Basic laws relating F (t) and v(t) • Newton second law d 1 Z t m v(t) = F (t) () v(t) = F (s)ds dt m 0 • Hook’s law (elastic bodies, e.g. spring) 1 d Z t F (t) = v(t) () F (t) = k v(s)ds k dt 0 • viscosity (e.g. dry friction) F (t) = bv(t) 12 / 45 Mechanical – translational Energy storage laws for F (t) and v(t) • kinetic energy 1 T (t) = mv2(t) 2 • potential energy 1 T (t) = F 2(t) 2k • energy loss due to friction Z t Z t Z t 1 Z t T (t) = P (s)ds = F (s)v(s)ds = b v2(s)ds = F 2(s)ds 0 0 0 b 0 13 / 45 Mechanical – translational Interconnection laws for F (t) and v(t) • sum of forces; same velocity (series connection) F = F1 + F2 v1 = v2 • sum of velocities; same force (parallel connection) F1 = F2 v = v1 + v2 14 / 45 Mechanical – translational Transformations laws for F (t) and v(t) • levers `2 F1 = − F2 `1 `1 v1 = − v2 `2 • pulleys 1 F = F 1 2 2 1 v = − v 1 2 2 15 / 45 Mechanical – rotational Basic quantities: • Angular Velocity !(t) (radians per second) • Torque M(t) (newton · meter) • Power P (t) = M(t) · !(t) 16 / 45 Mechanical – rotational Basic laws relating M(t) and !(t) • Newton second law d 1 Z t J !(t) = M(t) () !(t) = M(s)ds dt J 0 • torsion of a body 1 d Z t M(t) = !(t) () M(t) = k !(s)ds k dt 0 • rotational friction (typically nonlinear) M(t) = h(!(t)) 17 / 45 Mechanical – rotational Energy storage laws for M(t) and !(t) • rotational energy 1 T (t) = J!2(t) 2 • torsional energy 1 T (t) = M 2(t) 2k • energy loss due to rotational friction Z t Z t T (t) = P (s)ds = M(s)!(s)ds 0 0 18 / 45 Mechanical – rotational Interconnection laws for M(t) and !(t) • sum of torques; same angular velocity (series connection) M = M1 + M2 !1 = !2 • sum of velocities; same force (parallel connection) M1 = M2 ! = !1 + !2 19 / 45 Mechanical – rotational Transformations laws for M(t) and !(t) • gears M1 = rM2 1 ! = − ! 1 r 2 • “gyrator” My = r!z 1 ! = − M y r z 20 / 45 Flow system Basic quantities: • Flow Q(t) (cubic meters per second) • Pressure p(t) (newton per square meter) • Power P (t) = p(t) · Q(t) 21 / 45 Flow system Basic laws relating p(t) and Q(t) • Newton second law ρ` d 1 Z t Q(t) = p(t) () Q(t) = p(s)ds A dt Lf 0 |{z} Lf =inertance • pressure of a liquid column A d 1 Z t p(t) = Q(t) () p(t) = Q(s)ds ρg dt Cf 0 |{z} Cf =capacitance • flow resistance (laminar flow) p(t) = Rf Q(t) |{z} flow resistance 22 / 45 Flow system Energy storage laws for p(t) and Q(t) • kinetic energy (fluid in a tube) 1 T (t) = L Q2(t) 2 f • potential energy (fluid in a tank) 1 T (t) = C p2(t) 2 f • energy loss due to flow resistance Z t Z t T (t) = P (s)ds = p(s)Q(s)ds 0 0 23 / 45 Flow system Interconnection laws for p(t) and Q(t) • series connection p = p1 + p2 Q1 = Q2 • parallel connection p1 = p2 Q = Q1 + Q2 24 / 45 Flow system Transformations laws for p(t) and Q(t) • flow transformer p1 = rp2 1 Q = Q 1 r 2 where r = A2=A1 25 / 45 Analogies among physical domains Electrical Mechanical Mechanical Hydraulic Thermal translational rotational flow current velocity angular volume heat flow velocity flow effort voltage force torque pressure temperature power power power power power power · temperature inductive inductor inertia moment of inertia of −− element inertia fluid capacitive capacitor spring torsional tank heat element spring storage resistive resistor friction friction friction thermal element resistance transformer transformer lever gears transducer −− gyrator gyrator −− gyro −− −− 26 / 45 Conversions among domains • Mechanical (translational) – Hydraulics transformer: 1 p = F A Q = A v • Mechanical (rotational) – Electrical gyrator: M = k i 1 ! = u k 27 / 45 Analogies among physical domains • two "power" variables 1. flow f = i; v; !; Q; q 2. effort e = u; F; M; p; T • their product: power e · f = u · i; F · v; M · !; p · Q; T · q 28 / 45 Analogies, cont’d • three energy "exchange" relationships 1. inductance =) effort storage df 1 1 Z t = e =) f(t) = e(s)ds dt α α 0 2. capacitance =) flow storage de 1 1 Z t = f =) e(t) = f(s)ds dt β β 0 3. resistance =) loss of energy e = γf (possibly nonlinear: e = h(f)) 29 / 45 Bond graphs Bond graph theory: an exchange of energy is a bond −−−e* f • line = connection between parts of the system • above the line (harpoon side): effort • below the line: flow • direction of half arrow = direction of energy flow (i.e., direction in which power p = e · f is positive) −−u* −−−F* −−−M* −−−p* −−T* i v ! Q q 30 / 45 Bond graphs for energy exchanges • bond graph for effort storage: I-type element 1 Z t f(t) = e(s)ds () −−−e* I : α α 0 f • bond graph for flow storage: C-type element 1 Z t e(t) = f(s)ds () −−−e* C : β β 0 f • bond graph for resistive elements: R-type element e(t) = γ f(t) () −−−e* R : γ f 31 / 45 Bond graphs for sources • bond graph for effort source e Se −−−−* system ] f • bond graph for flow source e Sf −−−−* system ] f 32 / 45 Bond graphs for junctions bond graph for series connection: s - junction e2 f2 .... .... e1 ... ........... s f . 1 ... ..... en fn f1 = f2 = ::: = fn =) common flow e1 + e2 + ::: + en = 0 outgoing harpoon at ej: change sign to ej in the summation 33 / 45 Bond graphs for junctions bond graph for parallel connection: p - junction e2 f2 ..... .... e .. 1 ... ........... p f . 1 ... ...... en fn e1 = e2 = ::: = en =) common effort f1 + f2 + ::: + fn = 0 outgoing harpoon at fj: change sign to fj in the summation 34 / 45 Bond graphs for transformer and gyrators • bond graph for transformer: TF - junction −−−−e1 * TF −−−−e2 * f1 f2 1 e = ne ; f = f 2 1 2 n 1 • bond graph for gyrator: GY - junction −−−−e1 * GY −−−−e2 * f1 f2 1 e = rf ; f = e 2 1 2 r 1 Both conserve power 35 / 45 Bond graphs and ports Edges (bonds) of the bond graph are connecting points (or ports) of the system. The number of ports can be • one port: Se, Sf , C, I, R • two ports: TF , GY • multiport: s-junction, p-junction 36 / 45 Example: electrical circuit = hydraulic system 37 / 45 Example: electrical circuit 37 / 45 Example: electrical circuit 38 / 45 Example: an hydraulic system 38 / 45 Example: an hydraulic system 39 / 45 State space description Is it possible to obtain a state space description out of a bond graph? Information flow in a state space model x_ = f(x; u) • for given x och u it is possible to compute x_? • in a bond graph: causality marking 40 / 45 Information flow Information flow for bond graphs of C , I, and Se, Sf types: | {z } integral causality 41 / 45 Causality Causal strokes • “A sets e and B sets f” (i.e., A is of C and Se types) • “B sets e and A sets f” (i.e., A is of I and Sf types) 42 / 45 Causality, cont’d • Bond graphs with fixed causality strokes: 1.
Load more

Recommended publications
  • Chapter 3: Bond Graph Synthesis & Equation
    9/4/2019 CHAPTER 3: BOND GRAPH Samantha SYNTHESIS Ramirez & EQUATION DERIVATION What type of mathematical equations are needed? How are these equations systematically derived? How are the individual constitutive relations of the components connected to generate a mathematical model? 1 9/4/2019 Objectives: To effectively use bond To understand the flow To be able to graphs to formulate of information within a systematically derive models that facilitate system dynamics mathematical deriving mathematical model and its relation representations using representations of to mathematical bond graphs, and dynamic systems, representations. OBJECTIVES & OUTCOMES Outcomes: Upon completion, you should be able to derive mathematical synthesize bond graph annotate bond graphs models in the form of models of mechanical, to indicate appropriate differential and electrical, and power flow and algebraic equations hydraulic systems, causality, and using bond graph representations. e e ▪ Power bond labels e f e f f f ▪ R-Elements ▪ Dissipate Energy e e ▪ Direct algebraic relationship between e & f f f ▪ C-Elements ▪ Store Potential Energy ▪ Derivative Causality ▪ I-Elements ▪ Store Kinetic Energy ▪ Derivative Causality 2 9/4/2019 ▪ Sources ▪ Supply energy ▪ Transformers ▪ Convert energy ▪ Power through ▪ Gyrators ▪ Convert energy 푒 = 푛푒 푒 = 푟푓 ▪ Power through 1 2 1 2 푛푓1 = 푓2 푟푓1 = 푒2 ▪ 1-Junction ▪ Common flow ▪ Summation of efforts ▪ 0-Junction ▪ Common effort ▪ Summation of flows 3 9/4/2019 • Power goes from the system to R-, C-, and I-elements • Sources generally assumed to supply power to the system • Effort sources specify effort into the system • Flow sources specify flow into the system • 2-ports have a power through convention Adjacent junctions of Junctions with two the same type are bonds (power in, power actually the same out) can be simplified junction and can be into a single bond collapsed What if power is not showing a power in, power out convention? 4 9/4/2019 BOND GRAPH 1.
    [Show full text]
  • Hybrid Machine Modelling and Control
    HYBRID MACHINE MODELLING AND CONTROL by Lale Canan Tokuz This thesis is submitted in partial fulfilment of the requirements for the degree of Doctor of Philosophy of the Council for Xational Academic A wards. Mechanisms and Machines Group Liverpool Polytechnic February 1992 CONTENTS Acknowledgements ............................................................................................................. (5i) Abstract ............................................................................................................................. {6i) In trod uction Non- Uniform mechanism motion .................................................................................. 1 Two degrees of freedom mechanisms ............................................................................. 7 Thesis Structure .......................................................................................................... 10 Chapter 1 The Hybrid Arrangement 1.1. Introduction ................................................................................................................. 13 1.~. The General Description of the Experimental Set-Up .................................................... 13 1.2.1. The Drive Motors .............................................................................................. 15 1.2.2. The Differential Gear-Unit ................................................................................ 15 1.2.3. The Design of Slider-Crank Mechanism ............................................................. 16 1.3.
    [Show full text]
  • Pneumatic Test Bed
    Pneumatic Test Bed A Major Qualifying Project Report Submitted to the faculty of WORCESTER POLYTECHNIC INSTITUTE In partial fulfillment of the requirements for the Degree of Bachelor of Science By __________________ Richard MacKendrick [email protected] ___________________ Syed Kazim Naqvi [email protected] ___________________ Brendan White [email protected] Date of Submission: 22nd April 2010 Approved: Professor Eben C. Cobb [email protected] Abstract To enhance the learning experience of students in WPI’s mechatronics class, a pneumatic piston-spring assembly was designed and fabricated. Mathematical and bond graph analysis was performed to obtain theoretical metrics for the device’s operation. These theoretical metrics were compared with experimental results using sensors and data acquisition methods. The theoretical and experimental values were determined to have an acceptable deviation and can be reproduced by future students for the purpose of demonstrating the limits of theoretical metrics. ii Table of Contents ABSTRACT ......................................................................................................................................................................II TABLE OF CONTENTS ....................................................................................................................................................III TABLE OF TABLES ...................................................................................................................................................... VIII EXECUTIVE SUMMARY
    [Show full text]
  • The Stripline Circulator Theory and Practice
    The Stripline Circulator Theory and Practice By J. HELSZAJN The Stripline Circulator The Stripline Circulator Theory and Practice By J. HELSZAJN Copyright # 2008 by John Wiley & Sons, Inc. All rights reserved Published by John Wiley & Sons, Inc. Published simultaneously in Canada No part of this publication may be reproduced, stored in a retrieval system, or transmitted in any form or by any means, electronic, mechanical, photocopying, recording, scanning, or otherwise, except as permitted under Section 107 or 108 of the 1976 United States Copyright Act, without either the prior written permission of the Publisher, or authorization through payment of the appropriate per-copy fee to the Copyright Clearance Center, Inc., 222 Rosewood Drive, Danvers, MA 01923, (978) 750-8400, fax (978) 750-4470, or on the web at www.copyright.com. Requests to the Publisher for permission should be addressed to the Permissions Department, John Wiley & Sons, Inc., 111 River Street, Hoboken, NJ 07030, (201) 748-6011, fax (201) 748-6008, or online at http:// www.wiley.com/go/permission. Limit of Liability/Disclaimer of Warranty: While the publisher and author have used their best efforts in preparing this book, they make no representations or warranties with respect to the accuracy or completeness of the contents of this book and specifically disclaim any implied warranties of merchantability or fitness for a particular purpose. No warranty may be created or extended by sales representatives or written sales materials. The advice and strategies contained herein may not be suitable for your situation. You should consult with a professional where appropriate. Neither the publisher nor author shall be liable for any loss of profit or any other commercial damages, including but not limited to special, incidental, consequential, or other damages.
    [Show full text]
  • Dynamics of Multibody Systems with Bond Graphs
    Ogeâpkec"Eqorwvcekqpcn"Xqn"ZZXK."rr02943-2958 Ugtikq"C0"Gncumct."Gnxkq"C0"Rknqvvc."Igtoâp"C0"Vqttgu"*Gfu0+ Eôtfqdc."Ctigpvkpc."Qevwdtg"4229 DYNAMICS OF MULTIBODY SYSTEMS WITH BOND GRAPHS Germán Filippini, Diego Delarmelina, Jorge Pagano, Juan Pablo Alianak, Sergio Junco and Norberto Nigro Facultad de Ciencias Exactas, Ingeniería y Agrimensura Universidad Nacional de Rosario, Av. Pellegrini 250, S2000EKE Rosario, Argentina. Keywords : Bond Graphs, Multibody systems. Abstract . In this work a general multibody system theory is implemented within a bond graph modeling framework. In classical mechanics several procedures exist by which differential equations can be derived of a system of rigid bodies. In the case of large systems these procedures are labor-intensive and consequently error-prone, unless they are computerized. The bond graphs formalism allows for a unified modeling of multidisciplinary physical systems. It is well-suited for a modular modeling approach based on physical principles. The theory of multibody system dynamics in terms of bond graphs modeling is revisited with the purpose of designing a multibond graph library for such systems. Several mechanical systems undergoing large 3-dimensional rotations are numerically solved in order to validate this software library written in 20-sim software. Eqr{tkijv"B"4229"Cuqekcekôp"Ctigpvkpc"fg"Ogeâpkec"Eqorwvcekqpcn" jvvr<11yyy0coecqpnkpg0qti0ct 2943 1 INTRODUCTION Modeling and simulation has an increasing importance in the development of complex, large mechanical systems. In areas like road vehicles (Bos (1986); Filippini (2004); Filippini et al. (2007)), rail vehicles, high speed mechanisms, industrial robots and machine tools (Ersal (2004)), simulation is an inexpensive way to experiment with the system and to design an appropriate control system.
    [Show full text]
  • Using Bond-Graph Technique for Modelling and Simulating Railway Drive Systems
    2010 12th International Conference on Computer Modelling and Simulation Using Bond-Graph technique for modelling and simulating railway drive systems. J. Lozano, J. Felez, J:M. Mera, J.D. Sanz ETSI Engineering, Universidad Politecnica de Madrid Madrid, Spain e-mail: [email protected], [email protected], [email protected], [email protected] Abstract— This work presents the application of Bond- a) Resistances to the rolling of the wheels on the rails. Graph Technique to modelling and simulating the behaviour b) Passive resistances due to the relative movement of railway transport as a tool for studying its dynamic between the mechanical elements in contact with one another behaviour, consumption and energy efficiency, and used to make the train function. environmental impact. The basic aim of this study is to make a c) Aerodynamic resistances, due to the movement of contribution to the research and innovation into new the train within the air surrounding it. technologies that will lead to the discovery of ever more d) Resistances to the train’s forward motion on efficient environmentally-friendly transport. gradients and curves. We begin with an introduction to the study of longitudinal train dynamics as well as a description of the most currently used railway drive systems. Bond-Graph technique enables this modelling to be done systematically taking into account all the fields of science and technology involved while bringing together all the mechanical, electrical, electromagnetic, thermal, dynamic and regulatory aspects. Once the models have been developed, the behaviour of the drive systems is Figure 1. Longitudinal train dynamics.
    [Show full text]
  • Doppler-Based Acoustic Gyrator
    applied sciences Article Doppler-Based Acoustic Gyrator Farzad Zangeneh-Nejad and Romain Fleury * ID Laboratory of Wave Engineering, École Polytechnique Fédérale de Lausanne (EPFL), 1015 Lausanne, Switzerland; farzad.zangenehnejad@epfl.ch * Correspondence: romain.fleury@epfl.ch; Tel.: +41-412-1693-5688 Received: 30 May 2018; Accepted: 2 July 2018; Published: 3 July 2018 Abstract: Non-reciprocal phase shifters have been attracting a great deal of attention due to their important applications in filtering, isolation, modulation, and mode locking. Here, we demonstrate a non-reciprocal acoustic phase shifter using a simple acoustic waveguide. We show, both analytically and numerically, that when the fluid within the waveguide is biased by a time-independent velocity, the sound waves travelling in forward and backward directions experience different amounts of phase shifts. We further show that the differential phase shift between the forward and backward waves can be conveniently adjusted by changing the imparted bias velocity. Setting the corresponding differential phase shift to 180 degrees, we then realize an acoustic gyrator, which is of paramount importance not only for the network realization of two port components, but also as the building block for the construction of different non-reciprocal devices like isolators and circulators. Keywords: non-reciprocal acoustics; gyrators; phase shifters; Doppler effect 1. Introduction Microwave phase shifters are two-port components that provide an arbitrary and variable transmission phase angle with low insertion loss [1–3]. Since their discovery in the 19th century, such phase shifters have found important applications in devices such as phased array antennas and receivers [4,5], beam forming and steering networks [6,7], measurement and testing systems [8,9], filters [10,11], modulators [12,13], frequency up-convertors [14], power flow controllers [15], interferometers [16], and mode lockers [17].
    [Show full text]
  • Bond Graph for Modelling, Analysis, Control Design, Fault Diagnosis
    Bond Graph for Modelling, Analysis, Control Design, Fault Diagnosis Geneviève Dauphin-Tanguy Christophe Sueur Laboratoire d’Automatique et d’Informatique Industrielle de Lille Bond Graph Research Group Laboratoire d’Automatique et d’Informatique Industrielle de Lille Ecole Centrale de Lille • 6 academics (2 Profs, 2 associate profs, 2 assistant profs) • 10 PhD students Application areas : power systems (electrical machines, photovoltaic systems, fuel cells), thermofluid process, car industry Studies performed in collaboration with Peugeot -Citroën • Mechatronic design of an automatic gear box • Clutch management and drive comfort • Mechatronic design of an active hydraulic suspension • Thermal comfort regulation in a car interior • Modelling and simulation of a fuel cell system • Analysis of structural properties of bond graph models • Robustness of control laws for systems with parametric uncertainties • ….. Rosario - 22/11/02 LAIL - Ecole Centrale de Lille 3 Why a bond graph approach ? • Multidisciplinary systems à need for a communication language between people from different physical domains • Need for models with physical insight (virtual testing facility) • Unified modelling methodology for knowledge storage in model libraries • Integrated (« mechatronic ») design of controlled systems Rosario - 22/11/02 LAIL - Ecole Centrale de Lille 4 Mechatronic design Objectives Identification Simplification Analysis Modelling Control Actuators Validation Sensors Simulation Maintaining Faulty mode Diagnosis Fault Detection and Isolation Rosario
    [Show full text]
  • Snippe Msc Report
    On the Application of Extreme Interaction Torque with an Underactuated UAV M.J.W. (Max) Snippe Sc Report M Committee: Prof.dr.ir. S. Stramigioli Dr.ir. J.B.C. Engelen H. Wopereis, MSc Dr.ir. R.G.K.M. Aarts Dr.ir. A. Yenehun Mersha August 2018 033RAM2018 Robotics and Mechatronics EE-Math-CS University of Twente P.O. Box 217 7500 AE Enschede The Netherlands 1 On the Application of Extreme Interaction Torque with an Underactuated UAV Marcus J.W. Snippe Abstract—This paper aims at setting the initial steps towards as opening doors, pick-and-placing, and even building rope the application of extreme interaction torque using an underac- bridge-like structures [1]–[4]. tuated Unmanned Aerial Vehicle (UAV). Extreme torques are Although aerial manipulation has been a subject of research considered torques significantly larger than what UAVs can intrinsically generate. for several years, the manner of manipulation is limited to An optimization algorithm is designed that uses predetermined fairly low interaction wrenches. The main reason for this constraints, a desired application torque, and UAV parameters to is the fact that UAVs are free floating bodies, contrary to derive an optimal manipulator and input force and torques for for example a stationary robotic arm with a fixed base. the UAV. The optimization minimizes a nonlinearly constrained Therefore they are unable to close the force cycle with the cost function and returns an optimal homogeneous transforma- tion matrix and input covector. During optimization, the resulting environment and thus must intrinsically deliver the reaction torques and forces are scaled using a weighting function, which forces, which considerably limits the maximum interaction allows to assign priority to certain force or torque elements in forces and torques for UAVs.
    [Show full text]
  • 3. Synthesis of Mechanism Systems 3.1 Synthesis Methods for Mechanism Design
    Abstract The aim of this thesis is to provide a basis for efficient modelling and software use in simulation driven product development. The capabilities of modern commercial computer software for design are analysed experimentally and qualitatively. An integrated simulation model for design of mechanical systems, based on four different ”simulation views” is proposed: An integrated CAE (Computer Aided Engineering) model using Solid Geometry (CAD), Finite Element Modelling (FEM), Multi Body Systems Modelling (MBS) and Dynamic System Simulation utilising Block System Modelling tools is presented. A theoretical design process model for simulation driven design based on the theory of product chromosome is introduced. This thesis comprises a summary and six papers. Paper A presents the general framework and a distributed model for simulation based on CAD, FEM, MBS and Block Systems modelling. Paper B outlines a framework to integrate all these models into MBS simulation for performance prediction and optimisation of mechanical systems, using a modular approach. This methodology has been applied to design of industrial robots of parallel robot type. During the development process, from concept design to detail design, models have been refined from kinematic to dynamic and to elastodynamic models, finally including joint backlash. A method for analysing the kinematic Jacobian by using MBS simulation is presented. Motor torque requirements are studied by varying major robot geometry parameters, in dimensionless form for generality. The robot TCP (Tool Center Point) path in time space, predicted from elastodynamic model simulations, has been transformed to the frequency space by Fourier analysis. By comparison of this result with linear (modal) eigen frequency analysis from the elastodynamic MBS model, internal model validation is obtained.
    [Show full text]
  • Bond Graph Methodology
    Bond Graph Methodology • An abstract representation of a system where a collection of components interact with each other through energy ports and are placed in a system where energy is exchanged. • A domain-independent graphical description of dynamic behavior o physical systems • System models will be constructed using a uniform notations for al types of physical system based on energy flow • Powerful tool for modeling engineering systems, especially when different physical domains are involved • A form of object-oriented physical system modeling Bond Graphs Use analogous power and energy variables in all domains, but allow the special features of the separate fields to be represented. The only physical variables required to represent all energetic systems are power variables [effort (e) & flow (f)] and energy variables [momentum p (t) and displacement q (t)]. Dynamics of physical systems are derived by the application of instant-by-instant energy conservation. Actual inputs are exposed. Linear and non-linear elements are represented with the same symbols; non-linear kinematics equations can also be shown. Provision for active bonds . Physical information involving information transfer, accompanied by negligible amounts of energy transfer are modeled as active bonds . A Bond Graph’s Reach Mechanical Rotation Mechanical Hydraulic/Pneumatic Translation Thermal Chemical/Process Electrical Engineering Magnetic Figure 2. Multi-Energy Systems Modeling using Bond Graphs • Introductory Examples • Electrical Domain Power Variables : Electrical Voltage (u) & Electrical Current (i) Power in the system: P = u * i Fig 3. A series RLC circuit Constitutive Laws: uR = i * R uC = 1/C * ( ∫i dt) uL = L * (d i/dt); or i = 1/L * ( ∫uL dt) Represent different elements with visible ports (figure 4 ) To these ports, connect power bonds denoting energy exchange The voltage over the elements are different The current through the elements is the same Fig.
    [Show full text]
  • Bond Graph Modeling and Simulation of a Vibration Absorber System in Helicopters Benjamin Boudon, François Malburet, Jean-Claude Carmona
    Bond Graph Modeling and Simulation of a Vibration Absorber System in Helicopters Benjamin Boudon, François Malburet, Jean-Claude Carmona To cite this version: Benjamin Boudon, François Malburet, Jean-Claude Carmona. Bond Graph Modeling and Simulation of a Vibration Absorber System in Helicopters. Wolfgang Borutzky. Bond Graphs for Modelling, Con- trol and Fault Diagnosis of Engineering Systems, 332 (1), Springer International Publishing, pp.387- 429, 2017, 978-3-319-47434-2. 10.1007/978-3-319-47434-2_11. hal-01430124 HAL Id: hal-01430124 https://hal.archives-ouvertes.fr/hal-01430124 Submitted on 29 Sep 2017 HAL is a multi-disciplinary open access L’archive ouverte pluridisciplinaire HAL, est archive for the deposit and dissemination of sci- destinée au dépôt et à la diffusion de documents entific research documents, whether they are pub- scientifiques de niveau recherche, publiés ou non, lished or not. The documents may come from émanant des établissements d’enseignement et de teaching and research institutions in France or recherche français ou étrangers, des laboratoires abroad, or from public or private research centers. publics ou privés. Chapter 11 Bond Graph Modeling and Simulation of a Vibration Absorber System in Helicopters Benjamin Boudon, François Malburet, and Jean-Claude Carmona Notation Subscripts i Relative to the i loop (i D 1 :::4) j Relative to the body j (j D MGB, SBi,MBi, F) MGB Relative to the body MGB SBi Relative to the body SARIB bar i MBi Relative to the body MGB bar i F Relative to the body fuselage Mechanical Notation Generality !h MN Vector associated with the bipoint (MN) expressed in the Rh frame ! 0 P pes!j Weight vector of body j expressed in the inertial reference frame R0 B.
    [Show full text]