HYDRAULIC CONTROL SYSTEMS Noah D. Manring Mechanical and Aerospace Engineering Department University of Missouri-Columbia WILEY John Wiley & Sons, Inc.
vii Preface Introduction xiii XV FUNDAMENTALS 1 Fluid Properties 1.1 1.2 1.3 1.4 1.5 1.6 1.7 1.8 1.9 Introduction / 3 Fluid Mass Density / 3 1.2.1 Equation of State / 3 1.2.2 Density-Volume Relationship / 5 Fluid Bulk Modulus / 5 1.3.1 Definitions / 5 1.3.2 Effective Bulk Modulus / 8 1.3.3 Measuring the Fluid Bulk Modulus / 21 Thermal Fluid Properties / 25 1.4.1 1.4.2 1.4.3 Fluid 1.5.1 1.5.2 1.5.3 Vapor Coefficient of Thermal Expansion / 25 Thermal Conductivity / 30 Specific Heat / 31 Viscosity / 32 Definitions / 32 Viscous Drag Coefficient / 35 Viscosity Charts and Models / 35 Pressure / 37 Chemical Properties / 38 Fluid 1.8.1 1.8.2 1.8.3 1.8.4 1.8.5 Types and Selection / 39 Petroleum Based Fluids / 39 Synthetic Fluids / 39 Biodegradable Fluids / 39 Water / 40 Fluid Selection / 40 Conclusion / 41 1 3
viii 1.10 References / 41 1.11 Homework Problems / 41 2 Fluid Mechanics 2.1 Introduction / 44 2.2 Governing Equations / 44 2.2.1 Navier-Stokes (N-S) Equations / 44 2.2.2 High-Reynolds-Number Flow / 45 2.2.3 Low-Reynolds-Number Flow / 48 2.2.4 Turbulent versus Laminar Flow / 52 2.2.5 Control-Volume Analysis / 53 2.3 Fluid Flow / 60 2.3.1 The Reynolds Number / 60 2.3.2 Bernoulli Flow and the Orifice Equation / 61 2.3.3 Poiseuille Flow and the Annular Leakage Equation / 64 2.3.4 Pipe Flow / 70 2.4 Pressure Losses / 75 2.4.1 Major Losses / 75 2.4.2 Minor Losses / 76 2.5 Pressure Transients / 82 2.5.1 Hydraulic Conduits / 82 2.5.2 Water Hammer / 86 2.5.3 Pressure Rise Rates within a Varying Control Volume / 88 2.6 Hydraulic Energy and Power / 91 2.6.1 Fluid Power / 91 2.6.2 Heat Generation in Hydraulic Systems / 92 2.7 Lubrication Theory / 93 2.8 Conclusion / 98 2.9 References / 98 2.10 Homework Problems / 99 3 Dynamic Systems and Controls 3.1 Introduction / 102 3.2 Modeling / 103 3.2.1 General / 103 3.2.2 Mechanical Systems / 103 3.2.3 Hydromechanical Systems / 104 3.2.4 Electromechanical Systems / 105 3.2.5 Summary / 107 44 102
ix 3.3 3.4 3.5 3.6 3.7 3.8 3.9 3.10 3.11 Linearization / 107 3.3.1 General / 107 3.3.2 The Taylor Series Expansion / 108 3.3.3 Examples of Linearization / 109 Dynamic Behavior / 111 3.4.1 3.4.2 3.4.3 First-Order Response / 111 Second-Order Response / 116 Higher-Order Response / 129 State-Space Analysis / 129 3.5.1 3.5.2 3.5.3 Block 3.6.1 3.6.2 3.6.3 3.6.4 General / 129 State-Space Equations / 130 Characteristic Equation / 131 Diagrams and the Laplace Transform / 131 General / 131 Laplace Transform / 132 Partial Fraction Expansion / 135 Block Diagrams / 139 Stability / 150 3.7.1 3.7.2 3.7.3 General / 150 Stability Criterion / 150 Summary / 154 Compensation / 154 3.8.1 3.8.2 3.8.3 3.8.4 3.8.5 3.8.6 3.8.7 General / 154 Controller Design / 155 P Control / 156 PI Control / 157 PID Control / 159 Control Gain Selection / 160 Summary / 162 Conclusion / 162 References / 162 Homework Problems / 163 II HYDRAULIC COMPONENTS 167 4 Hydraulic Control Valves 169 4.1 4.2 Introduction / 169 Valve Flow Coefficients / 170 4.2.1 Overview / 170 4.2.2 Linearized Flow Equation / 172
4.3 4.4 4.5 4.6 4.7 4.8 4.9 4.10 4.2.3 Valve Porting Geometry / 173 4.2.4 Summary / 177 Two-Way Spool Valves / 177 4.3.1 Overview / 177 4.3.2 Efficiency / 178 4.3.3 Flow Forces / 179 4.3.4 Pressure-Relief Valves / 187 4.3.5 Summary / 194 Three-Way Spool Valves / 194 4.4.1 4.4.2 4.4.3 4.4.4 4.4.5 Overview / 194 Efficiency / 197 Flow Forces / 199 Hydromechanical Valves / 201 Summary / 204 Four-Way Spool Valves / 205 4.5.1 4.5.2 4.5.3 4.5.4 4.5.5 Overview / 205 Efficiency / 209 Flow Forces / 211 Two-Stage Electrohydraulic Valves / 213 Summary / 223 Poppet Valves / 224 4.6.1 4.6.2 4.6.3 4.6.4 4.6.5 Overview / 224 Efficiency / 226 Flow Forces / 227 Pressure-Relief Valves / 228 Summary / 233 Flapper Nozzle Valves / 234 4.7.1 4.7.2 4.7.3 4.7.4 4.7.5 Overview / 234 Efficiency / 236 Flow Forces / 236 Two-Stage Electrohydraulic Valves / 240 Summary / 252 Conclusion / 252 References / 252 Homework Problems / 253 5 Hydraulic Pumps 5.1 Introduction / 256 5.1.1 Overview / 256 5.1.2 Hydrostatic Pump Types / 257 5.1.3 Summary / 265 5.2 Pump Efficiency / 265 5.2.1 Overview / 265 5.2.2 Efficiency Definitions / 265 256
XI 5.2.3 Modeling Pump Efficiency / 267 5.2.4 Measuring Pump Efficiency / 268 5.2.5 Summary / 273 5.3 Gear Pumps / 273 5.3.1 Overview / 273 5.3.2 Pump Flow Characteristics / 274 5.3.3 Pump Control / 278 5.3.4 Summary / 278 5.4 Axial-Piston Swash-Plate Pumps / 279 5.4.1 Overview / 279 5.4.2 Pump Flow Characteristics / 279 5.4.3 Pressure-Controlled Pumps / 283 5.4.4 Displacement-Controlled Pumps / 294 5.4.5 Summary / 300 5.5 Conclusion / 300 5.6 References / 301 5.7 Homework Problems / 302 6 Hydraulic Actuators 6.1 Introduction / 305 6.2 Actuator Types / 306 6.2.1 Linear Actuators / 306 6.2.2 Rotary Actuators / 307 6.3 Linear Actuators / 309 6.3.1 Overview / 309 6.3.2 Efficiency / 309 6.3.3 Actuator Function / 310 6.3.4 Summary / 313 6.4 Rotary Actuators / 313 6.4.1 Overview / 313 6.4.2 Efficiency / 314 6.4.3 Actuator Function / 316 6.4.4 Summary / 317 6.5 Conclusion / 318 6.6 References / 318 6.7 Homework Problems / 318 305 HYDRAULIC CONTROL SYSTEMS 7 Valve-Controlled Hydraulic Systems 7.1 Introduction / 323 321 323
XII 7.2 7.3 7.4 7.5 7.6 7.7 Four-Way Valve Control of a Linear Actuator / 325 7.2.1 Description / 325 7.2.2 Analysis / 327 7.2.3 Design / 330 7.2.4 Control / 337 7.2.5 Summary / 344 Three-Way Valve Control of a Linear Actuator / 345 7.3.1 Description / 345 7.3.2 Analysis / 347 7.3.3 Design / 350 7.3.4 Control / 355 7.3.5 Summary / 363 Four-Way Valve Control of a Rotary Actuator / 364 7.4.1 Description / 364 7.4.2 Analysis / 364 7.4.3 Design / 368 7.4.4 Control / 373 7.4.5 Summary / 381 Conclusion / 382 References / 383 Homework Problems / 384 8 Pump-Controlled Hydraulic Systems 8.1 Introduction / 387 8.2 Fixed-Displacement Pump Control of a Linear Actuator / 389 8.2.1 Description / 389 8.2.2 Analysis / 391 8.2.3 Design / 393 8.2.4 Control / 396 8.2.5 Summary / 404 8.3 Variable-Displacement Pump Control of a Rotary Actuator / 405 8.3.1 Description / 405 8.3.2 Analysis / 407 8.3.3 Design / 409 8.3.4 Control / 415 8.3.5 Summary / 423 8.4 Conclusion / 424 8.5 References / 425 8.6 Homework Problems / 425 387 INDEX 427