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Fluid Power Systems: A Lecture Note in Modelling, Analysis and Control
ISBN-13: 9783031150883 / Angielski / Twarda / 2023 / 340 str.
Fluid Power Systems: A Lecture Note in Modelling, Analysis and Control
ISBN-13: 9783031150883 / Angielski / Twarda / 2023 / 340 str.
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Kategorie:
Kategorie BISAC:
Wydawca:
Springer International Publishing AG
Seria wydawnicza:
Język:
Angielski
ISBN-13:
9783031150883
Rok wydania:
2023
Ilość stron:
340
Wymiary:
23.5 x 15.5
Oprawa:
Twarda
1 Introduction 1
1.1 Hydro-statics and hydro-dynamics . . . . . . . . . . . . . . . . 1
1.1.1 Pascals law . . . . . . . . . . . . . . . . . . . . . . . . . 1
I Physics of Fluid 3
2 Fluid parameters 5
2.1 Viscosity . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5
2.1.1 Force due to shear velocity field . . . . . . . . . . . . . . 6
2.1.2 ViscosityModels . . . . . . . . . . . . . . . . . . . . . . 8
2.2 Fluid Compressibility and Density . . . . . . . . . . . . . . . . 11
2.2.1 Equation of State for a Fluid . . . . . . . . . . . . . . . 11
2.2.2 Pressure dependent density and stiffness of Fluid-air mixture
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12
3 Fluids Mechanics 19
3.1 Conservation ofMass . . . . . . . . . . . . . . . . . . . . . . . . 19
3.1.1 Control Volume Approach . . . . . . . . . . . . . . . . . 19
3.1.2 Continuity Equation - Differential form . . . . . . . . . 22
3.2 Momentum of Fluids - Newton II. Law . . . . . . . . . . . . . . 25
3.2.1 Differential Form- Cartesian Coordinates . . . . . . . . 25
3.2.2 MomentumEquation of a Fluid . . . . . . . . . . . . . . 29
3.2.3 Conservation of Momentum - Control Volume Form . . 30
3.3 Inviscid Flow . . . . . . . . . . . . . . . . . . . . . . . . . . . . 32
3.4 Viscous Flow . . . . . . . . . . . . . . . . . . . . . . . . . . . . 32
3.4.1 Incompressible fluid . . . . . . . . . . . . . . . . . . . . 33
4 Flow Through Restriction 37
4.1 Reynolds Number . . . . . . . . . . . . . . . . . . . . . . . . . . 37
4.2 Flow in a tube . . . . . . . . . . . . . . . . . . . . . . . . . . . 37
v
vi CONTENTS
4.2.1 FromNaiver-Stokes equation . . . . . . . . . . . . . . . 38
4.2.2 Fromforce balance . . . . . . . . . . . . . . . . . . . . . 40
4.2.3 Turbulent Flow in Pipes . . . . . . . . . . . . . . . . . . 424.2.4 Summary on Flow in Tubes . . . . . . . . . . . . . . . . 43
4.3 Flow in Gaps . . . . . . . . . . . . . . . . . . . . . . . . . . . . 44
4.3.1 FromForce Balance . . . . . . . . . . . . . . . . . . . . 44
4.3.2 Velocity Profile fromNaiver-Stokes Equation . . . . . . 46
4.3.3 Summary on flow between parallel plates . . . . . . . . 48
4.4 The Orifice Equation . . . . . . . . . . . . . . . . . . . . . . . . 50
4.4.1 Laminar versus turbulent orifice flow . . . . . . . . . . . 52
II Fluid Power Components 55
5 Fluid Power Pumps 57
5.1 Displacement Pumps . . . . . . . . . . . . . . . . . . . . . . . . 57
5.1.1 Data Sheet Units . . . . . . . . . . . . . . . . . . . . . . 57
5.1.2 Single Piston Pump . . . . . . . . . . . . . . . . . . . . 58
5.2 The General PumpModel - steady state . . . . . . . . . . . . . 58
5.2.1 Ideal PumpModel . . . . . . . . . . . . . . . . . . . . . 59
5.2.2 Non-ideal PumpModel . . . . . . . . . . . . . . . . . . 60
5.2.3 Summary on General PumpModel . . . . . . . . . . . . 62
5.3 Pump Types . . . . . . . . . . . . . . . . . . . . . . . . . . . . 64
5.3.1 Gear pumps . . . . . . . . . . . . . . . . . . . . . . . . . 64
5.3.2 Vane Pumps . . . . . . . . . . . . . . . . . . . . . . . . 65
5.3.3 Piston Pumps . . . . . . . . . . . . . . . . . . . . . . . . 67
5.3.4 Discrete Displacement pumps . . . . . . . . . . . . . . . 68
6 Rotary Actuator* 71
6.1 MotorModels . . . . . . . . . . . . . . . . . . . . . . . . . . . . 71
6.1.1 IdealMotorModel . . . . . . . . . . . . . . . . . . . . . 71
6.1.2 Non-idealMotorModel . . . . . . . . . . . . . . . . . . 72
7 Linear Actuators
- Fluid Power Cylinders 75
7.1 Differential Cylinder . . . . . . . . . . . . . . . . . . . . . . . . 76
7.1.1 Modelling . . . . . . . . . . . . . . . . . . . . . . . . . . 76
7.1.2 Steady StateModel . . . . . . . . . . . . . . . . . . . . 79
7.1.3 Summery . . . . . . . . . . . . . . . . . . . . . . . . . . 81
7.2 Multi-Chamber Cylinder . . . . . . . . . . . . . . . . . . . . . . 82
CONTENTS vii
8 Control Elements - Valves 83
8.1 General ValveModels . . . . . . . . . . . . . . . . . . . . . . . 83
8.2 Directional Valves . . . . . . . . . . . . . . . . . . . . . . . . . 84
8.2.1 Check Valve . . . . . . . . . . . . . . . . . . . . . . . . . 84
8.2.2 On-Off Valves . . . . . . . . . . . . . . . . . . . . . . . . 85
8.2.3 Directional Spool Valve . . . . . . . . . . . . . . . . . . 85
8.2.4 Flow Force on Spool Valve . . . . . . . . . . . . . . . . 89
8.2.5 Servo valves . . . . . . . . . . . . . . . . . . . . . . . . . 91
8.2.6 Direct Drive Servo Valves -Moog D633 . . . . . . . . . 92
8.3 Pressure control Valves . . . . . . . . . . . . . . . . . . . . . . . 95
8.3.1 Pressure relief . . . . . . . . . . . . . . . . . . . . . . . . 95
8.3.2 Pressure Reduction . . . . . . . . . . . . . . . . . . . . . 98
8.3.3 Pressure Control . . . . . . . . . . . . . . . . . . . . . . 100
8.4 Flow Control Valves . . . . . . . . . . . . . . . . . . . . . . . . 1028.4.1 Throttle Valve . . . . . . . . . . . . . . . . . . . . . . . 102
8.4.2 Pressure Compensated Flow Control Valve . . . . . . . 105
8.4.3 Pressure Compensated Flow Control Valve - By Pass . . 108
8.5 Pressure Compensated Proportional Valves . . . . . . . . . . . 112
9 Accumulators 115
9.1 Piston Accumulator . . . . . . . . . . . . . . . . . . . . . . . . 115
9.1.1 Mass Loaded Piston Accumulators . . . . . . . . . . . . 116
9.1.2 Spring Loaded Piston Accumulators . . . . . . . . . . . 117
9.1.3 Gas loaded piston Accumulators . . . . . . . . . . . . . 117
9.2 Bladder Accumulator . . . . . . . . . . . . . . . . . . . . . . . . 118
9.3 DiaphragmAccumulator . . . . . . . . . . . . . . . . . . . . . . 119
10 Pipes and Hoses 121
10.1 Fluid Power Pipes . . . . . . . . . . . . . . . . . . . . . . . . . 122
10.2 Fluid Power Hoses . . . . . . . . . . . . . . . . . . . . . . . . . 122
10.2.1 Construction . . . . . . . . . . . . . . . . . . . . . . . . 123
10.3 Steady State Transmission LineModel . . . . . . . . . . . . . . 123
10.4 Dynamic Transmission LineModel . . . . . . . . . . . . . . . . 123
10.4.1 Lumped ParameterModel . . . . . . . . . . . . . . . . . 123
III Fluid Power Systems 127
11 System Design 129
11.1 Synthesis of Fluid Power Systems . . . . . . . . . . . . . . . . . 129
11.1.1 System Operation . . . . . . . . . . . . . . . . . . . . . 130
11.1.2 Operation of Sub Function . . . . . . . . . . . . . . . . 130
11.1.3 System Architecture - Diagram . . . . . . . . . . . . . . 131
viii CONTENTS
11.1.4 System Pressure Level . . . . . . . . . . . . . . . . . . . 131
11.1.5 Actuator sizing . . . . . . . . . . . . . . . . . . . . . . . 132
11.1.6 Pump and PrimaryMover Sizing . . . . . . . . . . . . . 132
11.1.7 Fluid . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 133
11.1.8 Fluid Lines . . . . . . . . . . . . . . . . . . . . . . . . . 134
11.1.9 Control Elements . . . . . . . . . . . . . . . . . . . . . . 136
11.1.10Steady state analysis - overall efficiency . . . . . . . . . 136
11.1.11Tank and cooling . . . . . . . . . . . . . . . . . . . . . . 136
11.1.12 Filtration . . . . . . . . . . . . . . . . . . . . . . . . . . 137
11.2 Steady State Analysis . . . . . . . . . . . . . . . . . . . . . . . 14011.2.1 Simple differential cylinder system . . . . . . . . . . . . 140
11.2.2 Differential Cylinder System. . . . . . . . . . . . . . . . 145
12 Modelling and Analysis 149
12.1 Models . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 150
12.1.1 LinearModel . . . . . . . . . . . . . . . . . . . . . . . . 150
12.1.2 Frequency analysis . . . . . . . . . . . . . . . . . . . . . 152
12.2 Symmetric Cylinder Valve Drive . . . . . . . . . . . . . . . . . 154
12.2.1 Time DomainModel . . . . . . . . . . . . . . . . . . . . 154
12.2.2 Reduced OrderModel . . . . . . . . . . . . . . . . . . . 156
12.2.3 Linear Reduced OrderModel . . . . . . . . . . . . . . . 160
12.2.4 Linear model . . . . . . . . . . . . . . . . . . . . . . . . 162
12.2.5 Transfer Function for the Reduced Order Model . . . . 165
12.2.6 Results of Full System . . . . . . . . . . . . . . . . . . . 172
12.3 Fixed Displacement Motor Valve drive . . . . . . . . . . . . . . 173
12.3.1 Time DomainModel . . . . . . . . . . . . . . . . . . . . 174
12.3.2 Reduced OrderModel . . . . . . . . . . . . . . . . . . . 175
12.3.3 Reduced Order Linear and Laplace Domain Model . . . 17612.3.4 Linear model . . . . . . . . . . . . . . . . . . . . . . . . 176
IV Control
of Fluid Power Systems 179
13 Controller Design and System Manipulations 181
13.1 Pressure feedback . . . . . . . . . . . . . . . . . . . . . . . . . . 182
13.2 Flow Feed Forward . . . . . . . . . . . . . . . . . . . . . . . . . 183
13.2.1 Passive . . . . . . . . . . . . . . . . . . . . . . . . . . . 184
13.2.2 Active . . . . . . . . . . . . . . . . . . . . . . . . . . . . 185
13.3 Valve Compensator . . . . . . . . . . . . . . . . . . . . . . . . . 186
13.4 Valve Dynamics . . . . . . . . . . . . . . . . . . . . . . . . . . . 187
13.5 Multi-Input Systems . . . . . . . . . . . . . . . . . . . . . . . . 187
13.5.1 SMISMO - System . . . . . . . . . . . . . . . . . . . . . 188
CONTENTS ix
14 Reference generation 191
14.1 Power . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 191
14.1.1 Maximumpower transfer . . . . . . . . . . . . . . . . . 191
14.1.2 Power request . . . . . . . . . . . . . . . . . . . . . . . . 192
14.2 Input versus state requirement . . . . . . . . . . . . . . . . . . 192
14.3 Polynomial position reference . . . . . . . . . . . . . . . . . . . 193
V Exercises and Solutions 195
15 Problem Solving 197
15.1 FluidMechanics I . . . . . . . . . . . . . . . . . . . . . . . . . . 198
15.1.1 Fluid Compressibility . . . . . . . . . . . . . . . . . . . 198
15.1.2 Fluid Spring . . . . . . . . . . . . . . . . . . . . . . . . 198
15.1.3 Viscous force on rotating body . . . . . . . . . . . . . . 199
15.1.4 FluidMomentum . . . . . . . . . . . . . . . . . . . . . . 199
15.2 FluidMechanics II . . . . . . . . . . . . . . . . . . . . . . . . . 201
15.2.1 Orifice flow I . . . . . . . . . . . . . . . . . . . . . . . . 201
15.2.2 Orifice flow II . . . . . . . . . . . . . . . . . . . . . . . . 201
15.2.3 Pipe flow I . . . . . . . . . . . . . . . . . . . . . . . . . 202
15.2.4 Pipe flow II . . . . . . . . . . . . . . . . . . . . . . . . . 202
15.2.5 Pipe flow III . . . . . . . . . . . . . . . . . . . . . . . . 203
15.2.6 Velocity profile in an annular flow . . . . . . . . . . . . 203
15.3 Pumps,Motors and Cylinders . . . . . . . . . . . . . . . . . . . 204
15.3.1 Pump I . . . . . . . . . . . . . . . . . . . . . . . . . . . 20415.3.2 Pump II . . . . . . . . . . . . . . . . . . . . . . . . . . . 204
15.3.3 Motor I . . . . . . . . . . . . . . . . . . . . . . . . . . . 204
15.3.4 Cylinder I . . . . . . . . . . . . . . . . . . . . . . . . . . 204
15.3.5 Cylinder II . . . . . . . . . . . . . . . . . . . . . . . . . 205
15.3.6 Cylinder III . . . . . . . . . . . . . . . . . . . . . . . . . 206
15.3.7 Volumetric Pump Efficiency - VLE* . . . . . . . . . . . 207
15.3.8 Pump Efficiency map - VLE* . . . . . . . . . . . . . . . 207
15.3.9 Constant Pressure Pump - VLE* . . . . . . . . . . . . . 207
15.3.10Hydrostatic Transmission - VLE* . . . . . . . . . . . . . 207
15.3.11Valve cylinder drive - VLE* . . . . . . . . . . . . . . . . 208
15.4 Valves . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 209
15.4.1 Pressure relief valve I . . . . . . . . . . . . . . . . . . . 209
15.4.2 Valve flow . . . . . . . . . . . . . . . . . . . . . . . . . . 209
15.5 Steady State SystemAnalysis . . . . . . . . . . . . . . . . . . . 210
15.5.1 System 1, raising the piston . . . . . . . . . . . . . . . . 210
15.5.2 System 1, lowering the piston . . . . . . . . . . . . . . . 211
15.5.3 System 2 - with flow control valve . . . . . . . . . . . . 212
15.5.4 System 3 -Motor lifting the load . . . . . . . . . . . . . 213
x CONTENTS
15.5.5 System 3 -Motor lowering the load . . . . . . . . . . . . 213
15.5.6 System 4 . . . . . . . . . . . . . . . . . . . . . . . . . . 215
15.6 System Modelling . . . . . . . . . . . . . . . . . . . . . . . . . . 216
15.6.1 Workshop system flow control valves - Steady state . . . 216
15.6.2 Dynamic model of Workshop system - Servo valves . . . 217
15.7 System Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . 218
15.7.1 Pilot Chamber I . . . . . . . . . . . . . . . . . . . . . . 218
15.7.2 Pilot Chamber II . . . . . . . . . . . . . . . . . . . . . . 218
15.7.3 Pressure relief valve . . . . . . . . . . . . . . . . . . . . 219
15.7.4 System analysis - Differential cylinder and servo valve . 219
15.8 System Control . . . . . . . . . . . . . . . . . . . . . . . . . . . 220
15.8.1 Position and velocity control of differential cylinder . . . 220
15.8.2 System manipulation by pressure feedback . . . . . . . . 220
15.9 System Power Limits and Input Reference . . . . . . . . . . . . 221
15.9.1 Maximum load pressure, flow diagram . . . . . . . . . . 221
15.9.2 Position input trajectory . . . . . . . . . . . . . . . . . . 221
15.9.3 Simulation of position trajectory . . . . . . . . . . . . . 221
15.10System design . . . . . . . . . . . . . . . . . . . . . . . . . . . . 222
16 Solution 235
16.1 FluidMechanics I . . . . . . . . . . . . . . . . . . . . . . . . . . 236
16.1.1 Fluid Compressibility . . . . . . . . . . . . . . . . . . . 236
16.1.2 Fluid Spring . . . . . . . . . . . . . . . . . . . . . . . . 236
16.1.3 Viscous force on rotating body . . . . . . . . . . . . . . 238
16.1.4 FluidMomentum . . . . . . . . . . . . . . . . . . . . . . 238
16.2 FluidMechanics II . . . . . . . . . . . . . . . . . . . . . . . . . 240
16.2.1 Orifice Flow I . . . . . . . . . . . . . . . . . . . . . . . . 240
16.2.2 Orifice Flow II . . . . . . . . . . . . . . . . . . . . . . . 240
16.2.3 Pipe Flow I . . . . . . . . . . . . . . . . . . . . . . . . . 242
16.2.4 Pipe Flow II . . . . . . . . . . . . . . . . . . . . . . . . 242
16.2.5 Pipe Flow III . . . . . . . . . . . . . . . . . . . . . . . . 242
16.2.6 Velocity profile in an annular flow . . . . . . . . . . . . 243
16.3 Pumps,Motors and Cylinders . . . . . . . . . . . . . . . . . . . 245
16.3.1 Pump I . . . . . . . . . . . . . . . . . . . . . . . . . . . 245
16.3.2 Pump II . . . . . . . . . . . . . . . . . . . . . . . . . . . 245
16.3.3 Motor I . . . . . . . . . . . . . . . . . . . . . . . . . . . 246
16.3.4 Cylinder I . . . . . . . . . . . . . . . . . . . . . . . . . . 246
16.3.5 Cylinder II . . . . . . . . . . . . . . . . . . . . . . . . . 247
16.3.6 Cylinder III . . . . . . . . . . . . . . . . . . . . . . . . . 248
16.4 Valves . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 251
16.4.1 Pressure relief valve I . . . . . . . . . . . . . . . . . . . 251
16.5 Steady State Analysis . . . . . . . . . . . . . . . . . . . . . . . 252
16.5.1 System 1, raising the piston . . . . . . . . . . . . . . . . 252
CONTENTS xi
16.5.2 System 1, lowering the piston . . . . . . . . . . . . . . . 252
16.5.3 System 2 - with flow control valve . . . . . . . . . . . . 253
16.5.4 System 3 -Motor lifting the load . . . . . . . . . . . . . 255
16.5.5 System 3 -Motor lowering the load . . . . . . . . . . . . 256
16.5.6 System 4 . . . . . . . . . . . . . . . . . . . . . . . . . . 256
16.6 Dynamic Modelling . . . . . . . . . . . . . . . . . . . . . . . . . 257
16.6.1 Steady State analysis ofWorkshop System. . . . . . . . 257
16.6.2 DynamicModel ofWorkshop System. . . . . . . . . . . 261
16.7 Frequency Analysis . . . . . . . . . . . . . . . . . . . . . . . . . 263
16.7.1 Pilot Chamber I . . . . . . . . . . . . . . . . . . . . . . 263
16.7.2 Pilot Chamber II . . . . . . . . . . . . . . . . . . . . . . 264
16.7.3 Pressure Relief Valve . . . . . . . . . . . . . . . . . . . . 265
16.7.4 System analysis -Workshop System . . . . . . . . . . . 265
Anders Hansen is an associate professor at Department of Energy Technology. He holds a master of science in Electro-Mechanical System Design 2010 (Mechanical Engineering) and a Ph.D. in Energy Engineering 2014 (Investigation and Optimisation of a Discrete Fluid Power PTO-system for Wave Energy Converters) from Aalborg University. Professor Hansen has taught the subject of fluid power systems since 2010. Next to teaching courses in fluid power systems, he supervises student semester projects concerning design, modeling, analysis, and control of fluid power and mechatronic systems. His research is in the field of energy efficient fluid power systems, especially in digital fluid power system.
This book covers some of the fundamental topics in fluid power technology, presenting detailed derivations of formulas that form the basis of the theory. It shows the reader how to properly (i) design basic fluid power systems, (ii) construct lumped parameter models of simple fluid power systems, (iii) perform frequency analysis of fluid power components and systems, and (iv) develop controllers for fluid power systems. The book mainly focusses on mathematical modelling and analysis of fluid power components and systems i.e. practical issues such as working principles and construction of components are not covered in depth. The text is organized in four main parts: I Physics of Fluid, II Fluid Power Components, III Fluid Power Systems and IV Learning by Doing.
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