Multi-physics Modeling of Technological Systems

The development of mechatronic and multidomain technological systems requires the dynamic behavior to be simulated before detailed CAD geometry is available. This book presents the fundamental concepts of multiphysics modeling with lumped parameters. The approach adopted in this book, based on examples, is to start from the physical concepts, move on to the models and their numerical implementation, and finish with their analysis. With this practical problem-solving approach, the reader will gain a deep understanding of multiphysics modeling of mechatronic or technological systems – mixing mechanical power transmissions, electrical circuits, heat transfer devices and electromechanical or fluid power actuators. Most of the book's examples are made using Modelica platforms, but they can easily be implemented in other 0D/1D multidomain physical system simulation environments such as Amesim, Simulink/Simscape, VHDL-AMS and so on.

Table of Contents:
Foreword xi Chapter 1. Role of Simulation in the Design Cycle of Complex Technological Systems 1 1.1. Approach to the design of complex systems 2 1.1.1. Engineering activities in the design cycle 3 1.1.2. Modeling and simulation roles in the design cycle 4 1.1.3. Validation and verification 13 1.2. Book objectives and content 14 1.2.1. Modeling principles 14 1.2.2. Approaches and analysis tools 16 1.2.3. Multi-physics or multidisciplinary knowledge 17 1.2.4. Problem-based approach 17 Chapter 2. Fundamental Concepts of Lumped Parameter-Based Multi-Physics Modeling 19 2.1. Definition and modeling levels of mechatronic systems 20 2.1.1. From mechanical systems to mechatronic systems 20 2.1.2. Modeling levels in the design of mechatronic systems 22 2.2. Modeling of mechatronic systems with lumped parameters 23 2.2.1. Lumped parameters 23 2.2.2. Port and causality notions 24 2.2.3. Kirchhoff’s laws and network approach 27 2.2.4. Representation of energy flows 30 2.2.5. Types of generic elements 30 2.3. Multi-physics modeling of a power window system 34 2.3.1. Description of the system and of modeled domains 34 2.3.2. Domains and elements used for modeling 35 2.3.3. Incremental modeling 37 2.3.4. Graphic or text modeling 39 2.3.5. Transient control and simulations 39 2.4. Revision exercises and multiple-choice questions 40 2.4.1. Revision of Kirchhoff’s laws in multi-domain modeling 40 2.4.2. Questions related to the power window system example 42 2.4.3. Multiple-choice questions related to the modelling of technological components 44 2.5. Problems 46 2.5.1. Analysis of the conditioning electronics of a pressure sensor 46 2.5.2. Modeling the power transmission of an electric scooter 49 2.5.3. Modeling a hydraulic actuation system for launcher thrust vector control 53 2.5.4. Electromagnetic interferences 58 Chapter 3. Setting Up a Lumped Parameter Model 65 3.1. Introduction to the notion of adapted model 66 3.1.1. Chapter objectives and approach 66 3.1.2. Problem under study 67 3.1.3. Importance of the type of excitation 68 3.2. Identifying the main effects 69 3.2.1. Systematic setup of domains and effects 69 3.2.2. From geometry to network 70 3.3. Modeling approaches and selection of adapted models 73 3.3.1. Incremental modeling by increasing complexity 73 3.3.2. Model reduction by activity index analysis 77 3.3.3. Model reduction by design of the experiment or by comparison of effects 80 3.4. Introductory exercises related to setting up models with lumped parameters 83 3.4.1. Building up analytical skills 84 3.4.2. Geometry/network link: power steering analysis 88 3.4.3. Systematic analysis of effects: analysis of a direct injection system by common rail 91 3.5. Problems related to the choice of modeling level 93 3.5.1. Thermal response of a TGV motor – deductive approach 93 3.5.2. Modeling of a power steering torque sensor – geometry analysis 95 3.5.3. Calculation of the short-circuit torque of a submarine propulsion motor – model reduction 99 Chapter 4. Numerical Simulation of Multi-Physics Systems 103 4.1. From mathematical model to numerical model 104 4.1.1. Mathematical models – various systems of equations 104 4.1.2. Advantages of integration 107 4.1.3. Various representations of a system of equations 110 4.2. From numerical model to computer simulated model 112 4.2.1. Causality 112 4.2.2. Reaching consistency 113 4.2.3. Bond graph modeling 117 4.3. Simulation: numerical resolution of ODEs 124 4.3.1. Review and definitions 124 4.3.2. Separate steps methods 125 4.3.3. Linked steps methods 129 4.3.4. Stability domain of a method for solving ODE 131 4.4. The main sources of error in modeling and simulation 131 4.4.1. Model representativity 131 4.4.2. Validity of parameters 133 4.4.3. System initialization 133 4.4.4. Numerical robustness 134 4.4.5. Observation errors 134 4.5. Revision exercises 135 4.5.1. Revision of various modeling methods 135 4.5.2. Causality studies and associated modifications 136 4.6. Problem 138 Chapter 5. Dynamic Performance Analysis Tools 141 5.1. Dynamic performance indicators 142 5.2. Laplace transform and transfer functions 148 5.3. Stability of linear dynamic systems 158 5.4. Analysis of first- and second-order systems. Model reduction 167 5.4.1. First-order systems 167 5.4.2. Second-order systems 176 5.4.3. Model reduction 185 5.5. Revision exercises 196 5.5.1. Dynamic performances 196 5.5.2. Transfer functions 200 5.5.3. Stability 202 5.5.4. Model reduction 205 5.5.5. First-order systems 211 5.5.6. Second-order systems 213 Chapter 6. Mechanical and Electromechanical Power Transmissions 217 6.1. Introduction 218 6.1.1. Objective 218 6.1.2. Case study 218 6.2. Variational approaches 220 6.2.1. Variational equivalents of network approaches in mechanics 220 6.2.2. Systems with several degrees of freedom 223 6.2.3. Multi-domain systems 226 6.3. Modeling by direct integration of local laws: bulk and multi-layer ceramics 228 6.3.1. Equations of piezoelectricity 228 6.3.2. Equivalent model of piezoelectric ceramics 231 6.3.3. Modelica implementation 233 6.4. Principle of virtual works: amplified actuators 235 6.4.1. Presentation of actuators and modeling hypotheses 235 6.4.2. Turns ratio 236 6.4.3. Modelica implementation 237 6.5. Energy and co-energy balances: bimetals 239 6.5.1. Presentation of actuators and modeling hypotheses 239 6.5.2. Modeling 239 6.6. Lagrange equations: Langevin transducers 242 6.6.1. Actuator presentation 242 6.6.2. Modeling 243 6.6.3. Modelica implementation 247 6.7. Introductory exercises 249 6.7.1. Principle of virtual works: scissor mechanism 249 6.7.2. Energies and co-energies: electromagnetic power-off brakes 250 6.7.3. Lagrange equation: modeling of a personal transporter 253 6.8. Modeling problems 255 6.8.1. Modeling of the mechanical efforts in a car steering system 255 6.8.2. High bandwidth fast steering mirror 257 Chapter 7. Power Transmission by Low-Compressibility Fluids 261 7.1. Fluid power 262 7.1.1. Context 262 7.1.2. Advantages of fluid power use 262 7.2. Presentation of a helicopter actuation system 263 7.3. Minimal fluid modeling according to the phenomena involved 265 7.3.1. Fluid model requirements 265 7.3.2. Mass density modeling 267 7.3.3. Modeling of dynamic viscosity 268 7.3.4. Modeling of the bulk modulus 268 7.3.5. Properties modeling by tables 268 7.4. Modeling of the various physical phenomena 269 7.4.1. R element 269 7.4.2. C element 270 7.4.3. I element 270 7.5. Modeling of the main hydraulic components 271 7.5.1. Modeling of hydraulic fluid storage 271 7.5.2. Modeling of hydraulic power generation 272 7.5.3. Modeling of the hydraulic power distribution 274 7.5.4. Modeling of hydraulic power modulation 275 7.5.5. Modeling of hydraulic power transformation 277 7.6. Simulation of a helicopter actuation system 278 7.6.1. Modelica model of an actuation system 278 7.6.2. Variation of performances depending on temperature 279 7.6.3. Variation of performances depending on antagonist load 281 7.7. Exercises and problems 282 7.7.1. Multiple-choice questions on the modelling of hydraulic components 282 7.7.2. Problem 1: simple modeling of a hydraulic servo valve 284 7.7.3. Problem 2: modeling of the pressure regulator 287 Chapter 8. Heat Power Transmission 293 8.1. Heat exchangers 293 8.1.1. Classification of heat exchangers 294 8.1.2. Objectives of the study 296 8.2. Effectiveness-based thermal modeling of heat exchangers. Constant effectiveness 298 8.3. Estimation of the heat exchanger effectiveness 302 8.4. Estimation of the global heat transfer coefficient of a heat exchanger 308 8.5. Estimation of the pressure drops (losses) in the heat exchangers 318 8.6. Revision exercises and problems 322 8.6.1. Sizing of a heat exchanger with concentric tubes 322 8.6.2. Sizing and modeling of a heat exchanger for the recovery of thermal energy in a double flow CMV 323 Chapter 9. Thermal Power Conversion 327 9.1. Several examples of heat engines 328 9.2. Behavior of compressible fluids 331 9.2.1. Fluid modeling 331 9.2.2. Modeling of thermodynamic processes 334 9.3. Thermodynamics review 335 9.3.1. First law of thermodynamics 335 9.3.2. Thermodynamic cycles 337 9.4. Modeling of the components of heat engines 341 9.4.1. Modeling of a turbine 342 9.4.2. Modeling of a compressor 345 9.5. Simulation of a thermal power plant 349 9.6. Revision exercises and problems 352 9.6.1. Modeling of fluids 352 9.6.2. Efficiency of a gas turbine 352 9.6.3. Optimization of a gas turbine 354 9.6.4. Simulation of a heat pump 354 References 357 Index 361