Hydraulic Control Systems

Preface to the Second Edition xv Preface to the First Edition xvii Introduction xix I Fundamentals 1 1 Fluid Properties 3 1.1 Introduction 3 1.2 Fluid Mass Density 3 1.2.1 Equation of State 3 1.2.2 Density-Volume Relationship 4 1.3 Fluid Bulk Modulus 5 1.3.1 Definitions 5 1.3.2 Effective Bulk Modulus 7 1.3.3 Measuring the Fluid Bulk Modulus 16 1.4 Thermal Fluid Properties 19 1.4.1 Coefficient of Thermal Expansion 19 1.4.2 Thermal Conductivity 23 1.4.3 Specific Heat 24 1.5 Fluid Viscosity 25 1.5.1 Definitions 25 1.5.2 Viscous Drag Coefficient 27 1.5.3 Viscosity Charts and Models 27 1.6 Vapor Pressure 29 1.7 Chemical Properties 29 1.8 Fluid Types and Selection 30 1.8.1 Petroleum-Based Fluids 30 1.8.2 Synthetic Fluids 30 1.8.3 Biodegradable Fluids 30 1.8.4 Water 31 1.8.5 Fluid Selection 31 1.9 Conclusion 32 1.10 References 32 1.11 Homework Problems 32 1.11.1 Fluid Mass Density 32 1.11.2 Fluid Bulk Modulus 33 1.11.3 Thermal Fluid Properties 33 1.11.4 Fluid Viscosity 34 2 Fluid Mechanics 35 2.1 Introduction 35 2.2 Governing Equations 35 2.2.1 Navier-Stokes Equations 35 2.2.2 High Reynolds Number Flow 36 2.2.3 Low Reynolds Number Flow 38 2.2.4 Turbulent versus Laminar Flow 41 2.2.5 Control Volume Analysis 42 2.3 Fluid Flow 47 2.3.1 The Reynolds Number 47 2.3.2 Bernoulli Flow and the Orifice Equation 48 2.3.3 Poiseuille Flow and the Annular Leakage Equation 50 2.3.4 Pipe Flow 56 2.4 Pressure Losses 60 2.4.1 Major Losses 60 2.4.2 Minor Losses 60 2.5 Pressure Transients 66 2.5.1 Hydraulic Conduits 66 2.5.2 Water Hammer 68 2.5.3 Pressure Rise Rates within a Varying Control Volume 70 2.6 Hydraulic Energy and Power 72 2.6.1 Fluid Power 72 2.6.2 Heat Generation in Hydraulic Systems 73 2.7 Lubrication Theory 74 2.8 Conclusion 77 2.9 References 78 2.10 Homework Problems 78 2.10.1 Governing Equations 78 2.10.2 Fluid Flow 78 2.10.3 Fluid Pressure 79 2.10.4 Fluid Power 79 3 Dynamic Systems and Control 81 3.1 Introduction 81 3.2 Modeling 81 3.2.1 General 81 3.2.2 Mechanical Systems 82 3.2.3 Hydromechanical Systems 83 3.2.4 Electromechanical Systems 84 3.2.5 Summary 85 3.3 Linearization 85 3.3.1 General 85 3.3.2 The Taylor Series Expansion 86 3.3.3 Examples of Linearization 87 3.4 Dynamic Behavior 88 3.4.1 First-Order Response 88 3.4.2 Second-Order Response 92 3.4.3 Higher-Order Response 102 3.5 State Space Analysis 103 3.5.1 General 103 3.5.2 State Space Equations 103 3.5.3 Characteristic Equation 104 3.6 Block Diagrams and the Laplace Transform 104 3.6.1 General 104 3.6.2 Laplace Transform 104 3.6.3 Partial Fraction Expansion 107 3.6.4 Block Diagrams 110 3.7 Stability 119 3.7.1 General 119 3.7.2 Stability Criterion 119 3.7.3 Summary 123 3.8 Feedback Control 123 3.8.1 General 123 3.8.2 PID Controller Design in the Time Domain 125 3.8.3 Control Design in the Frequency Domain 130 3.8.4 Digital Control 138 3.8.5 Controllability and State Feedback Controller Design 148 3.8.6 Observability and State Estimation 150 3.8.7 Summary 152 3.9 Conclusion 152 3.10 References 152 3.11 Homework Problems 153 3.11.1 Modeling 153 3.11.2 Linearization 153 3.11.3 Dynamic Behavior 153 3.11.4 Block Diagrams and the Laplace Transform 154 3.11.5 Feedback Control 154 II Hydraulic Components 155 4 Hydraulic Valves 157 4.1 Introduction 157 4.2 Valve Flow Coefficients 158 4.2.1 Overview 158 4.2.2 Linearized Flow Equation 159 4.2.3 Valve Porting Geometry 160 4.2.4 Summary 163 4.3 Two-Way Spool Valves 163 4.3.1 Overview 163 4.3.2 Efficiency 164 4.3.3 Flow Forces 165 4.3.4 Pressure Relief Valves 172 4.3.5 Summary 176 4.4 Three-Way Spool Valves 176 4.4.1 Overview 176 4.4.2 Efficiency 180 4.4.3 Flow Forces 181 4.4.4 Hydromechanical Valves 182 4.4.5 Summary 185 4.5 Four-Way Spool Valves 185 4.5.1 Overview 185 4.5.2 Efficiency 188 4.5.3 Flow Forces 190 4.5.4 Two-Stage Electrohydraulic Valves 191 4.5.5 Summary 199 4.6 Poppet Valves 200 4.6.1 Overview 200 4.6.2 Efficiency 202 4.6.3 Flow Forces 202 4.6.4 Pressure Relief Valves 203 4.6.5 Summary 207 4.7 Flapper Nozzle Valves 208 4.7.1 Overview 208 4.7.2 Efficiency 209 4.7.3 Flow Forces 210 4.7.4 Two-Stage Electrohydraulic Valves 213 4.7.5 Summary 222 4.8 Conclusion 222 4.9 References 222 4.10 Homework Problems 222 4.10.1 Valve Flow Coefficients 222 4.10.2 Spool Valves 223 4.10.3 Poppet Valves 223 4.10.4 Flapper Nozzle Valves 224 5 Hydraulic Pumps 225 5.1 Introduction 225 5.1.1 Overview 225 5.1.2 Hydrostatic Pump Types 226 5.1.3 Summary 232 5.2 Pump Efficiency 233 5.2.1 Overview 233 5.2.2 Efficiency Definitions 233 5.2.3 Modeling Pump Efficiency 234 5.2.4 Measuring Pump Efficiency 235 5.2.5 Summary 239 5.3 Gear Pumps 239 5.3.1 Overview 239 5.3.2 Pump Flow Characteristics 240 5.3.3 Pump Control 243 5.3.4 Summary 243 5.4 Axial-Piston Swash-Plate Pumps 243 5.4.1 Overview 243 5.4.2 Pump Flow Characteristics 244 5.4.3 Pressure-Controlled Pumps 246 5.4.4 Displacement-Controlled Pumps 254 5.4.5 Summary 258 5.5 Conclusion 259 5.6 References 259 5.7 Homework Problems 260 5.7.1 Pump Efficiency 260 5.7.2 Gear Pumps 260 5.7.3 Axial-Piston Swash-Plate Pumps 261 6 Hydraulic Actuators 263 6.1 Introduction 263 6.2 Actuator Types 263 6.2.1 Linear Actuators 263 6.2.2 Rotary Actuators 265 6.3 Linear Actuators 266 6.3.1 Overview 266 6.3.2 Efficiency 266 6.3.3 Actuator Function 267 6.3.4 Summary 270 6.4 Rotary Actuators 270 6.4.1 Overview 270 6.4.2 Efficiency 270 6.4.3 Actuator Function 272 6.4.4 Summary 273 6.5 Conclusion 273 6.6 References 274 6.7 Homework Problems 274 6.7.1 Linear Actuators 274 6.7.2 Rotary Actuators 274 7 Auxiliary Components 275 7.1 Introduction 275 7.2 Accumulators 275 7.2.1 Function of the Accumulator 275 7.2.2 Design of the Accumulator 277 7.3 Hydraulic Conduits 281 7.3.1 Function of Hydraulic Conduits 281 7.3.2 Specification of Hydraulic Conduits 281 7.4 Reservoirs 283 7.4.1 Functions of the Reservoir 283 7.4.2 Design of the Reservoir 283 7.5 Coolers 286 7.5.1 Function of the Cooler 286 7.5.2 Design of the Cooler 286 7.6 Filters 287 7.6.1 Function of the Filter 287 7.6.2 Placement of the Filter 287 7.7 Conclusion 289 7.8 References 290 7.9 Homework Problems 290 7.9.1 Accumulators 290 7.9.2 Hydraulic Conduits 290 7.9.3 Reservoirs 291 7.9.4 Coolers 291 7.9.5 Filters 292 III Hydraulic Control Systems 293 8 Valve-Controlled Hydraulic Systems 295 8.1 Introduction 295 8.2 Four-Way Valve Control of a Linear Actuator 297 8.2.1 Description 297 8.2.2 Analysis 298 8.2.3 Design 300 8.2.4 Control 306 8.2.5 Summary 311 8.3 Three-Way Valve Control of a Single-Rod Linear Actuator 312 8.3.1 Description 312 8.3.2 Analysis 313 8.3.3 Design 315 8.3.4 Control 320 8.3.5 Summary 325 8.4 Four-Way Valve Control of a Rotary Actuator 326 8.4.1 Description 326 8.4.2 Analysis 327 8.4.3 Design 329 8.4.4 Control 333 8.4.5 Summary 339 8.5 Conclusion 340 8.6 References 341 8.7 Homework Problems 341 8.7.1 Four-Way Valve Control of a Linear Actuator 341 8.7.2 Three-Way Valve Control of a Single Rod Linear Actuator 342 8.7.3 Four-Way Valve Control of a Rotary Actuator 342 9 Pump-Controlled Hydraulic Systems 345 9.1 Introduction 345 9.2 Fixed-displacement Pump Control of a Linear Actuator 346 9.2.1 Description 346 9.2.2 Analysis 348 9.2.3 Design 349 9.2.4 Control 352 9.2.5 Summary 357 9.3 Variable-displacement Pump Control of a Rotary Actuator 358 9.3.1 Description 358 9.3.2 Analysis 359 9.3.3 Design 361 9.3.4 Control 366 9.3.5 Summary 372 9.4 Conclusion 372 9.5 References 373 9.6 Homework Problems 373 9.6.1 Fixed-displacement Pump Control of a Linear Actuator 373 9.6.2 Variable-displacement Pump Control of a Rotary Actuator 374 Unit Conversions 375 Length 375 Area 375 Mass 375 Volume 375 Density 375 Temperature 375 Pressure 376 Flow 376 Torque 376 Angular Speed 376 Force 376 Linear Velocity 376 Power 376 Index 377

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