Pneumatic Drives Peter Beater Pneumatic Drives System Design, Modelling and Control With 244 Figures and 14 Tables 123 Prof Dr.-Ing Peter Beater Fachhochschule Südwestfalen Fachbereich Maschinenbau-Automatisierungstechnik Lübecker Ring 59494 Soest Germany Library of Congress Control Number: 2006939785 ISBN-10 3-540-69470-6 Springer Berlin Heidelberg New York ISBN-13 978-3-540-69470-0 Springer Berlin Heidelberg New York This work is subject to copyright All rights are reserved, whether the whole or part of the material is concerned, specifically the rights of translation, reprinting, reuse of illustrations, recitation, b roadcasting, reproduction on microfilm or in any other way, and storage in data banks Duplication of this of this publication or parts thereof is permitted only under the provisions of the German Copyright Law of September 9, 1965, in its current version, and permission for use must always be obtained from Springer Violations are liable for prosecution under the German Copyright Law Springer is a part of Springer Science+Business Media © Springer-Verlag Berlin Heidelberg 2007 springer.com The use of general descriptive names, trademarks, etc in this publication does not imply, even in the absence of a specific statement, that such names are exempt from the relevant protective laws and regulations and therefore free for general use Cover design: eStudio Calamar, Steinen Typesetting by author and SPi Printed on acid-free paper SPIN: 11745556 62/3100/SPi Preface The idea to use air for transmitting power is very old Ctesibius in ancient Greece described a catapult using pneumatic cylinders to first store energy and then rapidly accelerate an arrow Heron of Alexandria developed automatic temple doors which opened and closed by means of hot air And from the Greek word for breath he coined the term that was used as title for his book and today describes a whole industry: ʌȞİȣµĮIJȚțȩȢ pneumatics Pneumatic components and systems have become an important topic for textbooks Most have their focus on the description of the steady-state behaviour, practical problems like troubleshooting or Boolean algebra to help designing control algorithms Only a few textbooks covering the theoretical analysis and design of pneumatic systems have been published (Zalmanzon et al 1965; Andersen 1967; Andersson et al 1975) But they were written at a time when digital computers were not easily available to engineers and therefore contain few material about modelling and simulation This book tries to bridge the gap between scientific disciplines (fluid mechanics, thermodynamics, mathematics, control, etc.), the conventional approach to describe pneumatic components and systems by their steadystate behaviour, the wish of a design engineer to test his design before actually building hardware and the resulting need for mathematical models in order to use today’s powerful digital computers The book covers first the basic laws of nature and then the design and modes of operation of pneumatic components, including equations to model their static and dynamic response In the third part of the book systems are described: binary mode cylinder drives, position controlled drives and computer aided analysis of complex systems Whenever applicable, this book contains equations that can direct be used for the analysis and design of drives But in a number of cases the approaches of different manufacturers vary considerably such that no unique mathematical model can be given An example is the calculation of the permissible stroke length of a cylinder under axial compressive load This book will be useful to engineers and scientists who want to understand the dynamic effects occurring in a pneumatic circuit in order to de- VI Preface sign an optimum system The tool of choice is a digital computer with a package for time-domain simulation using the models presented This book contains a number of measurements to illustrate and validate the theory Most of them were carried out in the control lab in Soest with great care However, their quality should not be compared with those from specialised physics labs whose equipment is qualified for scientific research while in the Soest lab we use devices typically found in production machines This book is not the work of a single person, but many people helped me First of all, my students with the results of their diploma or master thesises or their work as laboratory assistant They built test-rigs, made the 3D drawings or took time-consuming measurements and are listed in alphabetical order: Ralf Bergmann, Eva Brückner, Yann Décaillet, Daniel Diers, Thomas Grosserüschkamp, Roland Henze, Kai Hansmeier, Ilona Huppert, Peter Iles, Oliver Jürgens, Joachim Lütticke, Norma Alicia Montealegre Agramont, Michael Otte, Ansgar Päschke, Cornelius Schaffranek, David Schlüter, Thomas Schulze-Rudolphi, Torsten Volmer and Michael Voß I am particularly thankful to Ilona Huppert for her help in proofreading the whole manuscript I am indebted to several people at the Campus Soest of the Fachhochschule Südwestfalen for their support First of all, to my laboratory engineer Hans-Joachim Ratajczak, who solved every electrical or measurement problem, and to Andreas Hülsbeck, who did the same on the mechanical side I am grateful to Dr M Göttert, Festo AG Esslingen, and Prof G Belforte, Politecnico Torino, for their feedback on an early draft of this book Last, but certainly not least, I want to thank my wife for her patience and encouragement during the long time this book took me to finish November 2006 Peter Beater Contents Introduction Properties of Compressed Air 2.1 Mathematical Model of Air 2.2 Atmospheric Air 2.3 Definitions Related to Compressed Air Thermodynamic Processes 11 3.1 Constant Volume Processes 11 3.2 Constant Pressure Processes 13 3.3 Constant Temperature Processes 18 3.4 Reversible Processes without Heat Transfer 18 3.5 Polytropic Processes 20 3.6 General Processes 22 3.7 Sonic Velocity 23 Some Results from Fluid Mechanics 25 4.1 Viscosity 26 4.2 Continuity Equation 27 4.3 Free Discharge from Nozzles 28 4.4 Orifice Flow 32 4.4.1 Incompressible Flow 32 4.3.2 Compressible Flow 34 4.5 Frictional Flow 36 Engineering Flow Rate Calculations 41 5.1 Mathematical Flow Rate Model 41 5.2 Flow Rate Characteristics of Restrictions 48 5.3 Simplified Flow Calculations 49 5.4 Flow Capacity Specifications in Data Sheets 50 VIII Contents Modelling of Long Lines 55 6.1 Steady-State Losses of Long Lines 55 6.1.1 Fluid Mechanics Model 57 6.1.2 Empirical Models 58 6.1.3 Test Results 59 6.2 Steady-State Losses of Fittings 62 6.3 Time Domain Models 65 6.3.1 Derivation of Time Domain Model 65 6.3.2 Test Results in the Time Domain 69 6.4 Frequency Domain Models 76 Electro-Mechanical Converters 81 7.1 Solenoids 81 7.1.1 Switching Solenoids 83 7.1.2 Proportional Solenoids 85 7.1.3 Pulse-Width Modulation 86 7.2 Voice Coil and Plunger Type Systems 93 7.3 Piezoelectric Actuators 94 7.3.1 Stack Translators 94 7.3.2 Benders 94 7.3.3 Piezoelectric Elements in Pneumatic Valves 95 Cylinders 99 8.1 Stroke Cushioning 102 8.2 Mathematical Model 112 8.3 Cylinder Parameters 116 8.3.1 Seal Friction 116 8.3.2 Cylinder Leakage 122 8.3.3 Coefficient of Heat Transfer 123 Non-Standard Linear Actuators 127 9.1 Multi-Position and Tandem Cylinders 127 9.2 Rodless Cylinders 130 9.2.1 Split-Seal or Slot Type 130 9.2.2 Cable Type 132 9.2.3 Magnetic Type 132 9.3 Bellows 133 9.4 Rolling-Diaphragm Cylinders 137 9.6 Brake Chambers 139 9.5 Muscle Actuators 140 9.6 Impact and Knocking Cylinders 142 Contents IX 10 Semi-Rotary Actuators 145 10.1 Cylinder Based Actuators 145 10.2 Vane Type Actuators 148 11 Air Motors and Air Turbines 151 11.1 Vane Motors 153 11.1.1 Principle of Operation of Vane Motors 154 11.1.2 Mathematical Model 156 11.1.3 Speed Control 164 11.2 Air Turbines 168 12 Directional Control Valves 171 12.1 Design of Directional Control Valves 173 12.2 Operation of Directional Control Valves 175 12.3 Simulation Model of Directional Control Valves 181 13 Shut-Off Valves 185 13.1 Non-Return Valves 185 13.2 Non-Return Valves with Override 188 13.3 Shuttle Valves 189 13.4 Twin Pressure Valves 190 13.5 Quick Exhaust Valves 191 14 Pressure Control Valves 193 14.1 Spring Controlled Pressure Regulators 193 14.1.1 Design of Direct Acting Valves 196 14.1.2 Simulation Model of a Pressure Reducing Valves 199 14.1.3 Linear model 202 14.1.4 Non-Linear Effects 203 14.1.5 Design of Pilot Operated Valves 205 14.2 Electrically Operated Pressure Regulators 207 14.3 Pressure Regulators with Closed-Loop Control 209 14.3.1 Reports about Commercial Valves 212 14.4 Pressure Relief Valves 212 14.5 Soft-Start Valves 213 15 Flow Control Valves 215 15.1 Throttling Valve 215 15.2 One-Way Flow Control Valve 216 15.3 Delay Valve 217 15.4 Automatic Shut-Off Valves 218 X Contents 16 Proportional Directional Control Valves 221 16.1 Design of Proportional Directional Control Valves 222 16.2 Operation of Proportional Directional Control Valves 224 16.3 Simulation Model of Proportional Control Valves 230 16.4 Reports about Experimental and Commercial Valves 232 17 Stroke-Time Control 235 17.1 Circuits using Quick Exhaust Valves 237 17.2 Meter-Out Control 239 17.3 Meter-In Control 241 17.4 Circuits using Two Pressures 242 17.5 Oil Cushioning 244 18 Position Control of Pneumatic Systems 247 18.1 Mathematical Model for Control System Design 249 18.2 Model of Control Valves 250 18.3 Pressure Dynamics 253 18.4 Equation of Motion 256 18.5 Control Laws 258 18.5.1 Single Loop Controllers 259 18.5.2 Additional Loops 260 18.5.3 State Feedback Control 260 18.5.4 Reconstruction of the Velocity and Acceleration Signal 263 18.5.5 Non-Linear Control Laws 263 18.6 Performance of a Commercial System 265 19 Control of Actuators for Process Valves 269 19.1 Characteristics of Process Control Systems 271 19.2 Positioners 273 19.2.1 Pneumatic Positioners 275 19.2.2 Analogue Electro-Pneumatic Positioners 276 19.2.3 Digital Positioners 277 Contents XI 20 Digital Simulation 281 20.1 Modelling Approaches 282 20.2 Principles of Object-Oriented Modelling 286 20.3 The Object-Oriented Modelling Language Modelica 288 20.4 Fluid Power Libraries in Modelica 289 20.4.1 Examples of Library Models 290 20.4.2 Complex Component Model of the Pneumatic Library 292 20.5 Library Solution for Example 293 20.6 Multi-Domain Models 294 References 297 Index 319 ... of pneumatic components, including equations to model their static and dynamic response In the third part of the book systems are described: binary mode cylinder drives, position controlled drives. .. Around 1900 the most often used pneumatic components were pneumatic hammers, e.g in ship yards As technology evolved, riveting has been replaced by welding and pneumatic hammers are now used mostly... control systems for electric drives that made them superior to formerly used fluid power actuators This technology can also enhance the performance of pneumatic drives Examples are open or closed-loop