Mechatronics by Bond Graphs (eBook)

Vjekoslav Damic was born on 27. February 1941 in Sarajevo, Bosnia and Herzegovina. He graduated at faculty of Mechanical Engineering University of Sarajevo in 1963. The PhD in Engineering he received from University of Sarajevo in 1985. During his professional career he was employed by different industry research institution and universities where he was engaged as lecturer and researcher in field of engineering mechanics, process control, automatic control, robotics, modeling and simulation. From 1992 he was with University of Dubrovnik as professor of Engineering mechanics and Vice Rector. He retired in 2010 as emeritus professor of the University of Dubrovnik. He was also the full member of Croatian Academy of Engineering. After retirement he is in the status of emeritus of the Academy. He published two books and more scientific papers in leading international journals and conferences. His main field of scientific interest is modeling and simulations of engineering system with emphasis on applications of Bond Graphs and 3D visualization. He is creator of BondSim and BondSimVisual programs for simulation and visualization of mechatronic systems.John Montgomery was born on the 1st of July 1936 in Kilmarnock Scotland. He graduated from the Faculty of Engineering, University of Glasgow with the degree of BSc in 1959. He was awarded the degree of PhD by the University of Nottingham in 1970. He worked for  Glenfield and Kennedy, Ruston and Hornsby as a research engineer in the fields of hydraulics and Diesel engines and as a part time lecturer at what is now NottinghamTrent University . He was employed as a full time  lecturer there during the period 1964 until 1998. He is co-author of two books He is now retired

Preface to the Second Edition 7
Preface to the First Edition 8
Contents 12
Part I Fundamentals 17
1 Basic Forms of Model Representation 18
1.1 Objectives 18
1.2 The General Modelling Approach 20
1.3 Physical Modelling, Analogies, and Bond Graphs 21
1.4 Block Diagrams 25
1.5 Symbolic Model Solving 26
1.6 The Object-Oriented Approach 27
1.7 Computer Aided Modelling 30
1.8 The Book Summary 34
References 36
2 Bond Graph Modelling Overview 38
2.1 Introduction 38
2.2 Word Models 38
2.3 Ports, Bonds, and Power Variables 39
2.4 Component Model Development 41
2.5 Modelling Basic Physical Processes 43
2.5.1 Elementary Components 43
2.5.2 The Inertial Components 44
2.5.3 The Capacitive Components 45
2.5.4 The Resistive Components 46
2.5.5 The Sources 47
2.5.5.1 Source Efforts SE 47
2.5.5.2 Source Flows SF 47
2.5.6 The Transformers and Gyrators 48
2.5.6.1 Transformer TF 48
2.5.6.2 Gyrators GY 49
2.5.7 The Effort and Flow Junctions 49
2.5.7.1 Effort Junctions 50
2.5.7.2 Flow Junctions 50
2.5.8 Controlled Components 50
2.6 Block Diagram Components 52
2.6.1 Introduction 52
2.6.2 Continuous-Time Components 53
2.6.2.1 Input Components 53
2.6.2.2 Output Components 53
2.6.2.3 Function Component 54
2.6.2.4 Integrator 54
2.6.2.5 Differentiator 54
2.6.2.6 Summator 55
2.6.2.7 Node 55
2.6.3 Discrete-Time Components 55
2.7 Modelling Simple Engineering Systems 58
2.7.1 Simple Body Spring Damper System 58
2.7.2 The Simple Electrical Circuit 63
2.7.3 A See-Saw Problem 68
2.8 Causality of Bond Graphs 78
2.8.1 The Concept of Causality 78
2.8.2 Causalities of Elementary Components 79
2.8.3 The Procedure for Assigning Causality 82
2.9 The Formulation of the System Equations 84
2.10 The Causality Conflicts and Their Resolution 87
References 90
3 An Object-Oriented Approach to Modelling 92
3.1 Introduction 92
3.2 The Component Model 92
3.2.1 The Component Class 93
3.2.2 The Document Class 94
3.3 The Component Class Hierarchy 98
3.4 Port and Bond Classes 100
3.5 Description of the Element Constitutive Relations 104
3.6 Modelling Vector and Higher-Dimensional Quantities 105
3.7 Port Connection Rules 107
3.8 The Component Set Classes 110
3.9 Systematic Top/Down Model Development 112
3.10 Component Libraries and Model Reuse 115
References 117
4 Object Oriented Modelling in a Visual Environment 119
4.1 Introduction 119
4.2 The Visual Environment 120
4.3 The Component Hierarchy 124
4.4 The Port and Bond Classes Hierarchy 126
4.5 The Document Architecture 126
4.6 Editing Models 132
4.6.1 The Editing Box 132
4.6.2 Developing Bond Graph Models 135
4.6.3 Developing Block Diagram Models 140
4.6.4 Modelling Discrete-Time Processes 143
4.7 Generating Electrical and Mechanical Schemas 145
4.7.1 Developing Electrical Circuits 145
4.7.2 Developing Mechanical Circuits 148
4.8 Editing Elementary Components Constitutive Relations 149
4.8.1 Component Port Dialogues 149
4.8.2 Defining the Parameters 152
4.9 Library Operations 155
4.9.1 Library Projects 156
4.9.2 Library Components 157
4.10 Important Operations at the Document Level 160
4.10.1 Open, Close and Save Commands 161
4.10.2 Page Layout and Print Commands 162
4.10.3 The Delete, Copy, Cut, and Insert Operations 163
4.11 Inter-process Communications 165
References 169
5 Generation of the Model Equations and Their Solution 170
5.1 Introduction 170
5.2 General Forms of the Model Equations 171
5.2.1 Generating the System Variables 171
5.2.2 Generation of the Equations 175
5.2.3 The Characteristics of the Model 179
5.3 Numerical Solution Using BDF Methods 186
5.3.1 The Implementation of the BDF Method 186
5.3.2 The Generation of the Partial Derivative Matrix 190
5.3.3 The Error Control Strategy 190
5.4 Decompiling the Model Equations 193
5.5 The Problem of Starting Values 195
5.6 The Treatment of Discontinuities 198
5.7 A Stack Based Approach to Function Evaluation 199
References 202
Part II Applications 204
6 Mechanical Systems 205
6.1 Introduction 205
6.2 The Body Spring Damper Problem 206
6.2.1 The Problem 206
6.2.2 The Bond Graph Model 206
6.2.2.1 System Level Model 206
6.2.2.2 The Components Models 213
6.2.2.3 The Use of Mechanical Components 218
6.2.3 Analysis of the System Behaviour by Simulation 220
6.2.3.1 Building the Model 221
6.2.3.2 Running Simulations 223
6.2.3.3 Response to Harmonic Excitation 226
6.3 Effect of Dry Friction 234
6.3.1 The Model of Dry Friction 234
6.3.2 Free Vibration of a Body with Dry Friction 241
6.3.3 Stick-Slip Motion 243
6.3.4 The Stick-Slip Oscillator 246
6.4 Bouncing Ball Problems 249
6.4.1 Simple Model of Impact 249
6.4.2 A Ball Bouncing on a Table 253
6.4.3 A Ball Bouncing on a Vibrating Table 255
6.5 The Pendulum Problem 257
References 263
7 Electrical Systems 264
7.1 Introduction 264
7.2 Electrical Circuits 265
7.2.1 The Problem 265
7.2.2 The Bond Graph Model 266
7.2.2.1 System Level Model 266
7.2.2.2 The Component Models 269
7.2.3 Analysis of the System Behaviour by Simulation 274
7.3 Models of Circuit Elements 277
7.3.1 Resistors 277
7.3.2 Capacitor 278
7.3.3 Inductors 280
7.3.3.1 Simple Inductor 280
7.3.3.2 Coupled Inductors 281
7.3.4 Sources 283
7.3.4.1 Voltage and Current Sources 283
7.3.4.2 Constitutive Relations 284
7.3.4.3 Dependent Sources 288
7.3.5 Switches 290
7.4 Modelling Semiconductor Components 293
7.4.1 Diodes 294
7.4.1.1 Static Model 294
7.4.1.2 Dynamical Model 300
7.4.1.3 Diode Self-heating 304
7.4.2 Transistors 309
7.4.2.1 Bipolar Junction Transistor 310
7.4.2.2 Junction Field Effects Transistor 316
7.4.2.3 Metal-Oxide Semiconductor Field Effect Transistors 322
7.4.3 Operational Amplifiers 328
7.5 Electromagnetic Systems 335
7.5.1 Electromagnetic Actuator Problem 335
7.5.2 System Bond Graph Model 336
7.5.3 Electromagnetic Flux and Force Expressions 337
7.5.4 Magnetic Actuator Component Model 339
7.5.5 Simulation of Magnetic Actuator Behaviour 341
References 343
8 Control Systems 344
8.1 Introduction 344
8.2 A Simple Control System 345
8.3 PID Control System Modelling 354
8.4 Permanent Magnet DC Servo System 358
References 366
9 Multibody Dynamics 368
9.1 Introduction 368
9.2 Modelling of Rigid Multibody Systems in Plane 369
9.2.1 The Component Model of a Rigid Body in Planar Motion 369
9.2.2 Joints 374
9.2.2.1 The Revolute Joint 375
9.2.2.2 The Prismatic Joint 376
9.2.3 Modelling and Simulation of a Planar Mechanism 379
9.3 Andrews' Squeezer Mechanism 384
9.4 Engine Torsional Vibrations 394
9.5 Motion of Constrained Rigid Bodies in Space 402
9.5.1 Basic Kinematics 402
9.5.2 Bond Graph Representation of a Body Moving in Space 407
9.5.3 Rigid Body Dynamics 412
9.5.4 Modelling of Body Interconnections in Space 415
9.5.4.1 Revolute Joints 416
9.5.4.2 Prismatic Joints 421
9.6 Dynamics of Puma 560 Robot 424
9.6.1 Problem Formulation 424
9.6.2 Model of the Robot 430
9.6.2.1 System Level Model 430
9.6.2.2 Model of PUMA 560 Manipulator 432
9.6.2.3 Model of Workspace 436
9.6.2.4 The Robot Controller 437
9.6.3 Simulation of PUMA 560 439
9.7 3D Visualization of Robots 445
9.7.1 Concept of 3D Visualization 445
9.7.2 Generating 3D Virtual Scene 447
9.7.3 Visualization of Robot Dynamics 456
References 458
10 Continuous Systems 460
10.1 Introduction 460
10.2 Spatial Discretisation of Continuous Systems 461
10.3 Model of Electric Transmission Line 463
10.4 Bond Graph Model of a Beam 470
10.5 A Packaging System Analysis 476
10.5.1 Description of the Problem 476
10.5.2 Bond Graph Model Development 477
10.5.2.1 Model of Beam Elements 478
10.5.2.2 Motion of the Device 480
10.5.2.3 Model of the System 482
10.5.3 Evaluation of Vibration Test Characteristics 485
10.6 Coriolis Mass Flowmeters 488
10.6.1 Problem Statement 488
10.6.2 Principle of Operations 489
10.6.3 Dynamics of Curved CMF Tubes 491
10.6.3.1 Out-of-Plane Vibrations of Circular Tubes 491
10.6.3.2 Vibration of the Curved Tube 496
10.6.3.3 Dynamics of the Perturbed Motion of CMF Tube 498
10.6.4 Bond Graph Model of CMF Transducer 501
10.6.5 Control of CMF Transducer 505
10.6.6 Simulation of CMF Control Loop 512
References 514
Appendix 516
A.1 Installation of BondSim 516
A.2 Launching and Using BondSim 516
A.3 Contact Addresses 517
Index 518