Pneumatic Drives: System Design, Modelling and Control

324 Pages·2007·4.55 MB·English

by  Prof. Dr.-Ing. Peter Beater (auth.)

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 2
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
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Preface
The idea to use air for transmitting power is very old. Ctesibius in an-
cient Greece described a catapult using pneumatic cylinders to first store
energy and then rapidly accelerate an arrow. Heron of Alexandria devel-
oped 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: (cid:652)(cid:542)(cid:304)(cid:547)µ(cid:302)(cid:306)(cid:538)(cid:539)(cid:553)(cid:546) -
pneumatics.
Pneumatic components and systems have become an important topic for
textbooks. Most have their focus on the description of the steady-state be-
haviour, practical problems like troubleshooting or Boolean algebra to help
designing control algorithms. Only a few textbooks covering the theoreti-
cal analysis and design of pneumatic systems have been published (Zal-
manzon et al. 1965; Andersen 1967; Andersson et al. 1975). But they were
written at a time when digital computers were not easily available to engi-
neers 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 steady-
state behaviour, the wish of a design engineer to test his design before ac-
tually 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 sys-
tems 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 ap-
proaches 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 under-
stand 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 re-
search 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 the-
sises or their work as laboratory assistant. They built test-rigs, made the
3D drawings or took time-consuming measurements and are listed in al-
phabetical 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 Mon-
tealegre 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 proof-
reading the whole manuscript.
I am indebted to several people at the Campus Soest of the Fach-
hochschule Südwestfalen for their support. First of all, to my laboratory
engineer Hans-Joachim Ratajczak, who solved every electrical or meas-
urement problem, and to Andreas Hülsbeck, who did the same on the me-
chanical side.
I am grateful to Dr. M. Göttert, Festo AG Esslingen, and Prof. G. Bel-
forte, 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
1 Introduction.............................................................................................1
2 Properties of Compressed Air...............................................................5
2.1 Mathematical Model of Air..............................................................6
2.2 Atmospheric Air...............................................................................8
2.3 Definitions Related to Compressed Air............................................9
3 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
4 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
5 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
6 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
7 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
8 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
9 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
Content s 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
Content s 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