Preface xiii
Acknowledgements xvii
About the Companion Website xix
1 Introduction to Power Transmission 1
1.1 Transmission Ratio 1
1.1.1 Generalities 1
1.1.2 Definition 3
1.1.3 Classification 3
1.2 Mechanical Transmissions 4
1.2.1 Gear Trains 4
1.2.2 Gearboxes 6
1.2.3 Efficiency 8
1.2.4 Continuously and Infinitely Variable Transmissions 11
1.3 Hydraulic Transmissions 15
1.4 Hydrostatic Transmissions 19
1.4.1 Operational Principles 19
1.4.2 Formal Definition of Hydrostatic Transmissions 32
1.4.3 Classification of Hydrostatic Transmissions 34
1.4.4 Efficiency Considerations 40
1.5 Hydromechanical Power-Split Transmissions 40
1.5.1 General Classification 41
1.5.2 Transmission Ratio 42
1.5.3 Lockup Point 44
1.5.4 Power Relations 44
1.6 Mechanical and Hydrostatic Actuators 51
1.6.1 Mechanical Actuators 51
1.6.2 Hydrostatic Actuators 52
1.6.3 Hydrostatic Actuation Versus Valve Control 53
1.6.4 Multiple Cylinder Actuators 55
Exercises 56
References 57
2 Fundamentals of Fluid Flows in Hydrostatic Transmissions 59
2.1 Fluid Properties 59
2.1.1 Viscosity 59
2.1.2 Compressibility 64
2.2 Fluid Flow in Hydraulic Circuits 79
2.2.1 Flow Regimes 79
2.2.2 Internal Flow in Conduits 81
2.2.3 Flow Through Orifices 85
2.2.4 Leakage Flow in Pumps and Motors 87
2.2.5 Other Loss Models 93
Exercises 94
References 96
3 Hydrostatic Pumps and Motors 98
3.1 Hydrostatic and Hydrodynamic Pumps and Motors 98
3.2 Hydrostatic Machine Output 102
3.2.1 Average Inputâ"Output Relations 102
3.2.2 Instantaneous Pump Output 104
3.2.3 Instantaneous Motor Output 112
3.2.4 Further Efficiency Considerations 116
3.3 Hydrostatic Pump and Motor Types 117
3.3.1 Radial Piston Pumps and Motors 117
3.3.2 Axial Piston Pumps and Motors 119
3.3.3 Gear Pumps and Motors 128
3.3.4 Vane Pumps and Motors 130
3.3.5 Digital Displacement Pumps and Motors 131
3.4 Energy Losses at Steady-State Operation 135
3.4.1 Energy Balances 135
3.4.2 Overall Efficiencies 138
3.4.3 Simplified Efficiency Equations 138
3.4.4 Efficiency Relations 139
3.5 Modelling Pump and Motor Efficiencies 141
3.5.1 Performance Curves 141
3.5.2 Volumetric Efficiency Modelling 144
3.5.3 Overall Efficiency Modelling 154
3.5.4 Mechanical Efficiency 160
Exercises 162
References 164
4 Basic Hydrostatic Transmission Design 166
4.1 General Considerations 166
4.1.1 Output Speed Control 166
4.1.2 Transmission Losses 167
4.2 Hydrostatic Transmission Efficiency 168
4.2.1 Energy Balance 169
4.2.2 Conduit Efficiency 171
4.2.3 Minor Pressure Losses 173
4.2.4 Practical Application 176
4.3 Transmission Output 183
4.4 Steady-State Design Applications 184
4.4.1 Case Study 1. Fixed-Displacement Motor and Variable-Displacement Pump 185
4.4.2 Case Study 2. Fixed-Displacement Pump and Variable-Displacement Motor 192
4.5 External Leakages and Charge Circuit 198
4.6 Heat Losses and Cooling 201
4.6.1 Sizing of the Heat Exchanger 201
4.6.2 Loop Flushing 203
Exercises 204
References 205
5 Dynamic Analysis of Hydrostatic Transmissions 207
5.1 Introduction 207
5.1.1 Pressure Surges during Transients 208
5.1.2 Mechanical Vibrations and Noise 211
5.1.3 Natural Circuit Oscillations 214
5.1.4 Resonance and Beating 217
5.1.5 Summary 219
5.2 Modelling and Simulation 219
5.2.1 Basic Equations 220
5.2.2 Case Study 1. Purely Inertial Load with a Step Input 223
5.2.3 Case Study 2. Variable Pump Flow 231
Exercises 240
References 241
6 Hydrostatic Actuators 243
6.1 Introductory Concepts 243
6.1.1 Circuit Operational Quadrants 243
6.1.2 Energy Management 244
6.1.3 Cylinder Stiffness 245
6.1.4 Double-Rod and Single-Rod Actuators 245
6.2 Hydrostatic Actuator Circuits 247
6.2.1 Design 1. Dual-Pump, Open-Circuit, Displacement-Controlled Actuator 247
6.2.2 Design 2. Dual-Pump, Closed-Circuit, Displacement-Controlled Actuator 249
6.2.3 Design 3. Dual-Pump Electrohydrostatic Actuator with Accumulators 251
6.2.4 Design 4. Circuit with an Inline Hydraulic Transformer 253
6.2.5 Design 5. Single-Pump Circuit with a Directional Valve 257
6.2.6 Design 6. Single-Pump Circuit with Pilot-Operated Check Valves 260
6.2.7 Design 7. Single-Pump Circuit with Inline Check Valves 263
6.2.8 Design 8. Energy Storage Circuit 267
6.2.9 Design 9. Double-Rod Actuator 273
6.3 Common Pressure Rail and Hydraulic Transformers 275
Exercises 281
References 282
7 Dynamic Analysis of Hydrostatic Actuators 283
7.1 Introduction 283
7.2 Mathematical Model 284
7.2.1 Basic Equations 284
7.2.2 Cylinder Friction 288
7.2.3 Pilot-Operated Check Valves 294
7.3 Case Study 298
7.3.1 Determination of the Pump Flow Period 299
7.3.2 Numerical Simulation 300
Exercises 304
References 306
8 Practical Applications 307
8.1 Infinitely Variable Transmissions in Vehicles 307
8.2 Heavy Mobile Equipment 310
8.3 Hybrid Vehicles 313
8.3.1 Definition 315
8.3.2 Electric Hybrids 315
8.3.3 Hydraulic Hybrids 316
8.3.4 CPR-Based Hybrids 321
8.4 Wind Turbines 323
8.4.1 Asynchronous Generators 324
8.4.2 Synchronous Generators 326
8.4.3 General Aspects of Power Transmission in Wind Turbines 328
8.4.4 Hydrostatic Transmission in Wind Turbines 329
8.5 Wave Energy Extraction 331
8.6 Aeronautical Applications 334
References 336
Appendix A Hydraulic Symbols 339
Appendix B Mathematics Review 345
B.1 The Nabla Operator (â) 345
B.2 Ordinary Differential Equations (ODEs) 346
B.2.1 General Aspects and Definitions for ODEs 347
B.2.2 The Laplace Transform Method 351
References 360
Appendix C Fluid Dynamics Equations 361
C.1 Introduction 361
C.2 Fluid Stresses and Distortion Rates 363
C.3 Differential Fluid Dynamics Equations 365
C.3.1 Conservation of Mass 365
C.3.2 Conservation of Momentum 367
C.3.3 Navierâ"Stokes Equations in Cylindrical Coordinates 370
C.4 Control Volume Analysis 371
C.4.1 The Reynolds Transport Theorem 371
C.4.2 Mass and Momentum Conservation 373
C.4.3 Conservation of Energy 375
References 378
Index 379
