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Index

actuatorbellows 133–137muscle 140–141piezoelectric 94rack and pinion 145–146Scotch yoke 147–148semi-rotatory 145–149spring-and-diaphragm 271vane 148–149

airatmospheric 8free 2, 10fuse 218motor 151–168properties 8, 10standard conditions 8turbine 168–170

ANR 10area

effectivebellows 134ISO 6358 51

effective cross-sectional 52armature 81artificial muscle 140–141atmospheric pressure 9

bar 10bellows 133–137bend 62–64bimorph bender 94–95Blasius 38bleed nozzle 195buckling of cylinder rod 101brake chamber 139–140

capillary 36, 37causality 287chamber stiffness 20change of state

isentropic 18isobaric 13isothermal 18polytropic 20

choked flow 31circuit

meter-in 241–242meter-out 239–241

closed system 12, 22coefficient of compressibility 51coil 82–84Colebrook’s formula 38compressed air 5

mathematical model 6compressibility factor 8compressible flow 34–35condensation 8conductance

line 58–59sonic 41

connectorlosses 62–63push-in 62push-on 62

continuity equation 27control

gain-scheduling 264hybrid 264position 247–265pressure 202speed 164–168state space 256–264stroke-time 235–237

process control valve 271

320 Index

critical pressure ratio 31cushion seal 99, 102–104cylinder

duplex 127efficiency 119friction 116–122heat transfer 123–126impact 142–143knocking 142–143leakage 122modelling 112–116multi-position 127–130rodless 130–133

cable 132magnetic 132–133split-seal 130–132

rolling diaphragm 137–139single rod 99stroke cushioning 102–112tandem 129triplex 127

density 5, 10dead volume 115design

air turbine 170bellows 134brake chamber 139cylinder

knocking 143multi-position 128rod 99rodless 130–133rolling diaphragm 138

directional control valve 173–174muscle actuator 140–141non-return valve 186oil cushioning 246pressure control valve

diaphragm 197piston 198

proportional solenoid 85rack-and-pinion 146relief valve 213vane actuator 149vane motor 154, 155

dew point 8diaphragm

charging valve 212–213pressure regulator 196–197process valve 269, 271–273rolling 137–139

digital simulation 281–296directional control valve 171–183

operation 175–181piloted 174poppet 173simulation model 181–183switching time 176–178

discharge coefficient 32dither 87droop 194duty cylce 86dwell time 118Dymola 289, 293–295

efficiencycylinder 119piezo-electric actuation 95–97vane motor 151

elbow 63electro-mechanical converter 81–97energy saving 243–244enthalpy 16equation

balance 284constitutive 284of state 7, 8, 25

expansion ratio 158

flowchoked 31coefficient 53force 228frictional 36function 30gain 224, 227laminar 33, 37orifice 32–35subsonic 31turbulent 33

flow control valve 215–219

Index 321

flow ratecalculation 41

restrictions 48simplified 49–50

mass 10nominal 52specification for valves 50–54volume 10

fluid 25fluid mechanics 25fluid power 1fluidics 1force balance

in positioner 275in regulator 196–198

forward flow characteristic 193free air 10free discharge 28frequency response

direct control valve 225, 226line 76–79vane motor 167

frictioncylinder 116–122

dynamic 118static 117steady-state 118

factor 37–39FRL unit 193full pressure motor 158

gaindynamic of positioner 274scheduling 264static of positioner 274

gasconstant 8ideal 6law 6

gauge pressure 9

Hagen 37handpiece 169heat transfer 123–126humidity 8hydraulics 1

hysteresis 211

ideal gas 6equation of state 7properties 6

impact energyimpact cylinder 142stroke cushioning 106

incompressible flow 32internal energy 16isobaric process 13isochoric process 11isothermal process 18isotropic process 18

laminar flow 33, 37Laval 31leakage

cylinder 122energy savings 243

linesteady-state loss 55–61frequency response 76–79mathematical model

discretized 65–69frequency domain 76–79resonance peak 79temperature 56–57

linearity 211

Mach number 23mass flow rate 10mathematical analogy 282mathematical model 282McKibben artifical muscle 140–141meter-in 241–242meter-out 239–241microfluidics 5Modelica 288–290modelling

causal 287object-oriented 287

motorcharacteristics 151–153process 160vane 153–168

322 Index

movingcoil 93magnet 93

nominaldiameter 52flow rate 52

nozzleideal 28–32model 41

nozzel-flapper 272–273

object oriented modelling 286–288observer 248, 263oil cushioning 245open system 22orifice

discharge coefficient 32flow 32–35

compressible 34incompressible 32

overlap 174

Pa 10packing 269–270parallel connection 50piezoelectric

bender 94–95effect 94stack 94

plunger 81pneumatics 1pneumatic timer 217Poiseuille 37polytropic process 20positioner 270–279

analogue electro-pneumatic 276digital 277pneumatic 275

pressure 9absolute 9atmospheric 9critical ratio 31dynamic 9effective 9gain 224, 228

gauge 9ratio 41regulator 193–212static 9total 9

process valve 269pulse-width modulation 86–88PV diagram

constant pressure 15reversible 19vane motor 160

ratiocritical pressure 31of specific heat capacities 19

relative humidity 5relief valve 212–213repeatability 212Reynolds number 38

critical 38

Sanville 41seal

cushioning 102–104viton 101

sensitivity 212series connection 49–50shading coil 82soft start valve 213–214solenoid 81–85

design 81–82dynamics 92proportional 85

sonicconductance 41velocity 23

specific heat capacityconstant pressure 16–17constant volume 11, 13

speedcontrol

cylinders 237–242vane motors 164–168

of sound in air 23spool 174

Index 323

standard reference atmospheremeteorological 10technical 5, 8

starting torque 152state reconstruction 263state-space model 256–258stiffness of chamber 20stroke cushioning 102–112St. Venant 30subsonic flow 31sucking coil 93Sutherland’s formula 26–27

thermal time constant 125thermodynamic process 11

constant pressure 13constant temperature 18constant volume 11general 22polytropic 20reversible 18

throttlingcylinder speed 239–241vane motor 164–166

turbomachine 168turbulent flow 33

underlap 189, 191

valveanalogue 222automatic shut-off 218charging 212check 185delay 217directional control 171non-return 185–187non-return override 188normally closed NC 171normally open NO 171one-way flow control 216pilot 172poppet 173port numbering 171pressure regulator 193–212

dome-loaded 199

pressure relief 212–213process control 269proportional directional 221–233quick exhaust 191relief 212shut-off 185–192shuttle 189–190soft-start 213–214switching time 176–178symbols 171–172throttling 215twin pressure 190–191

vane actuator 148–149vane motor

air consumption 165design 155design schemes 154efficiency 151mathematical model 156-164speed control 166–168starting torque 152throttling 164–166

variableacross 284through 284

VDR 84velocity of sound 23viscosity

dynamic 26kinematic 27Sutherland’s formula 26–27temperature dependency 26

voice coil 93volume flow rate 10

Wantzel 30