Gustavo Koury Costa graduated in 1992 with a bachelor degree in Mechanical Engineering and has been teaching Fluid Power for 19 years at his current institution. He also holds a Doctorate degree in Computational Fluid Dynamics, having spent one year as a Postdoctoral Fellow at the University of Manitoba Fluid Power and Tele-Robotics Research Laboratory.Nariman Sepehri is a professor in Mechanical Engineering. He holds five patents and has published over 100 journal articles on various aspects of fluid power, including systems, manipulation, diagnosis and control. His current research focuses on self-healing, energy-efficient and reliable fluid power systems with applications to aircraft, hydraulic tele-manipulators and off-highway equipment. He is a Fellow and has served as Chair of the Fluid Power Systems and Technology Division of the American Society of Mechanical Engineers (ASME). He has served on editorial boards of eight journals including the International Journal of Fluid Power.

• Preface xiiiAcknowledgements xviiAbout the Companion Website xix1 Introduction to Power Transmission 11.1 Transmission Ratio 11.1.1 Generalities 11.1.2 Definition 31.1.3 Classification 31.2 Mechanical Transmissions 41.2.1 Gear Trains 41.2.2 Gearboxes 61.2.3 Efficiency 81.2.4 Continuously and Infinitely Variable Transmissions 111.3 Hydraulic Transmissions 151.4 Hydrostatic Transmissions 191.4.1 Operational Principles 191.4.2 Formal Definition of Hydrostatic Transmissions 321.4.3 Classification of Hydrostatic Transmissions 341.4.4 Efficiency Considerations 401.5 Hydromechanical Power-Split Transmissions 401.5.1 General Classification 411.5.2 Transmission Ratio 421.5.3 Lockup Point 441.5.4 Power Relations 441.6 Mechanical and Hydrostatic Actuators 511.6.1 Mechanical Actuators 511.6.2 Hydrostatic Actuators 521.6.3 Hydrostatic Actuation Versus Valve Control 531.6.4 Multiple Cylinder Actuators 55Exercises 56References 572 Fundamentals of Fluid Flows in Hydrostatic Transmissions 592.1 Fluid Properties 592.1.1 Viscosity 592.1.2 Compressibility 642.2 Fluid Flow in Hydraulic Circuits 792.2.1 Flow Regimes 792.2.2 Internal Flow in Conduits 812.2.3 Flow Through Orifices 852.2.4 Leakage Flow in Pumps and Motors 872.2.5 Other Loss Models 93Exercises 94References 963 Hydrostatic Pumps and Motors 983.1 Hydrostatic and Hydrodynamic Pumps and Motors 983.2 Hydrostatic Machine Output 1023.2.1 Average Input–Output Relations 1023.2.2 Instantaneous Pump Output 1043.2.3 Instantaneous Motor Output 1123.2.4 Further Efficiency Considerations 1163.3 Hydrostatic Pump and Motor Types 1173.3.1 Radial Piston Pumps and Motors 1173.3.2 Axial Piston Pumps and Motors 1193.3.3 Gear Pumps and Motors 1283.3.4 Vane Pumps and Motors 1303.3.5 Digital Displacement Pumps and Motors 1313.4 Energy Losses at Steady-State Operation 1353.4.1 Energy Balances 1353.4.2 Overall Efficiencies 1383.4.3 Simplified Efficiency Equations 1383.4.4 Efficiency Relations 1393.5 Modelling Pump and Motor Efficiencies 1413.5.1 Performance Curves 1413.5.2 Volumetric Efficiency Modelling 1443.5.3 Overall Efficiency Modelling 1543.5.4 Mechanical Efficiency 160Exercises 162References 1644 Basic Hydrostatic Transmission Design 1664.1 General Considerations 1664.1.1 Output Speed Control 1664.1.2 Transmission Losses 1674.2 Hydrostatic Transmission Efficiency 1684.2.1 Energy Balance 1694.2.2 Conduit Efficiency 1714.2.3 Minor Pressure Losses 1734.2.4 Practical Application 1764.3 Transmission Output 1834.4 Steady-State Design Applications 1844.4.1 Case Study 1. Fixed-Displacement Motor and Variable-Displacement Pump 1854.4.2 Case Study 2. Fixed-Displacement Pump and Variable-Displacement Motor 1924.5 External Leakages and Charge Circuit 1984.6 Heat Losses and Cooling 2014.6.1 Sizing of the Heat Exchanger 2014.6.2 Loop Flushing 203Exercises 204References 2055 Dynamic Analysis of Hydrostatic Transmissions 2075.1 Introduction 2075.1.1 Pressure Surges during Transients 2085.1.2 Mechanical Vibrations and Noise 2115.1.3 Natural Circuit Oscillations 2145.1.4 Resonance and Beating 2175.1.5 Summary 2195.2 Modelling and Simulation 2195.2.1 Basic Equations 2205.2.2 Case Study 1. Purely Inertial Load with a Step Input 2235.2.3 Case Study 2. Variable Pump Flow 231Exercises 240References 2416 Hydrostatic Actuators 2436.1 Introductory Concepts 2436.1.1 Circuit Operational Quadrants 2436.1.2 Energy Management 2446.1.3 Cylinder Stiffness 2456.1.4 Double-Rod and Single-Rod Actuators 2456.2 Hydrostatic Actuator Circuits 2476.2.1 Design 1. Dual-Pump, Open-Circuit, Displacement-Controlled Actuator 2476.2.2 Design 2. Dual-Pump, Closed-Circuit, Displacement-Controlled Actuator 2496.2.3 Design 3. Dual-Pump Electrohydrostatic Actuator with Accumulators 2516.2.4 Design 4. Circuit with an Inline Hydraulic Transformer 2536.2.5 Design 5. Single-Pump Circuit with a Directional Valve 2576.2.6 Design 6. Single-Pump Circuit with Pilot-Operated Check Valves 2606.2.7 Design 7. Single-Pump Circuit with Inline Check Valves 2636.2.8 Design 8. Energy Storage Circuit 2676.2.9 Design 9. Double-Rod Actuator 2736.3 Common Pressure Rail and Hydraulic Transformers 275Exercises 281References 2827 Dynamic Analysis of Hydrostatic Actuators 2837.1 Introduction 2837.2 Mathematical Model 2847.2.1 Basic Equations 2847.2.2 Cylinder Friction 2887.2.3 Pilot-Operated Check Valves 2947.3 Case Study 2987.3.1 Determination of the Pump Flow Period 2997.3.2 Numerical Simulation 300Exercises 304References 3068 Practical Applications 3078.1 Infinitely Variable Transmissions in Vehicles 3078.2 Heavy Mobile Equipment 3108.3 Hybrid Vehicles 3138.3.1 Definition 3158.3.2 Electric Hybrids 3158.3.3 Hydraulic Hybrids 3168.3.4 CPR-Based Hybrids 3218.4 Wind Turbines 3238.4.1 Asynchronous Generators 3248.4.2 Synchronous Generators 3268.4.3 General Aspects of Power Transmission in Wind Turbines 3288.4.4 Hydrostatic Transmission in Wind Turbines 3298.5 Wave Energy Extraction 3318.6 Aeronautical Applications 334References 336Appendix A Hydraulic Symbols 339Appendix B Mathematics Review 345B.1 The Nabla Operator (∇) 345B.2 Ordinary Differential Equations (ODEs) 346B.2.1 General Aspects and Definitions for ODEs 347B.2.2 The Laplace Transform Method 351References 360Appendix C Fluid Dynamics Equations 361C.1 Introduction 361C.2 Fluid Stresses and Distortion Rates 363C.3 Differential Fluid Dynamics Equations 365C.3.1 Conservation of Mass 365C.3.2 Conservation of Momentum 367C.3.3 Navier–Stokes Equations in Cylindrical Coordinates 370C.4 Control Volume Analysis 371C.4.1 The Reynolds Transport Theorem 371C.4.2 Mass and Momentum Conservation 373C.4.3 Conservation of Energy 375References 378Index 379

Gustavo Koury Costa graduated in 1992 with a bachelor degree in Mechanical Engineering and has been teaching Fluid Power for 19 years at his current institution. He also holds a Doctorate degree in Computational Fluid Dynamics, having spent one year as a Postdoctoral Fellow at the University of Manitoba Fluid Power and Tele-Robotics Research Laboratory.Nariman Sepehri is a professor in Mechanical Engineering. He holds five patents and has published over 100 journal articles on various aspects of fluid power, including systems, manipulation, diagnosis and control. His current research focuses on self-healing, energy-efficient and reliable fluid power systems with applications to aircraft, hydraulic tele-manipulators and off-highway equipment. He is a Fellow and has served as Chair of the Fluid Power Systems and Technology Division of the American Society of Mechanical Engineers (ASME). He has served on editorial boards of eight journals including the International Journal of Fluid Power.

• Preface xiiiAcknowledgements xviiAbout the Companion Website xix1 Introduction to Power Transmission 11.1 Transmission Ratio 11.1.1 Generalities 11.1.2 Definition 31.1.3 Classification 31.2 Mechanical Transmissions 41.2.1 Gear Trains 41.2.2 Gearboxes 61.2.3 Efficiency 81.2.4 Continuously and Infinitely Variable Transmissions 111.3 Hydraulic Transmissions 151.4 Hydrostatic Transmissions 191.4.1 Operational Principles 191.4.2 Formal Definition of Hydrostatic Transmissions 321.4.3 Classification of Hydrostatic Transmissions 341.4.4 Efficiency Considerations 401.5 Hydromechanical Power-Split Transmissions 401.5.1 General Classification 411.5.2 Transmission Ratio 421.5.3 Lockup Point 441.5.4 Power Relations 441.6 Mechanical and Hydrostatic Actuators 511.6.1 Mechanical Actuators 511.6.2 Hydrostatic Actuators 521.6.3 Hydrostatic Actuation Versus Valve Control 531.6.4 Multiple Cylinder Actuators 55Exercises 56References 572 Fundamentals of Fluid Flows in Hydrostatic Transmissions 592.1 Fluid Properties 592.1.1 Viscosity 592.1.2 Compressibility 642.2 Fluid Flow in Hydraulic Circuits 792.2.1 Flow Regimes 792.2.2 Internal Flow in Conduits 812.2.3 Flow Through Orifices 852.2.4 Leakage Flow in Pumps and Motors 872.2.5 Other Loss Models 93Exercises 94References 963 Hydrostatic Pumps and Motors 983.1 Hydrostatic and Hydrodynamic Pumps and Motors 983.2 Hydrostatic Machine Output 1023.2.1 Average Input–Output Relations 1023.2.2 Instantaneous Pump Output 1043.2.3 Instantaneous Motor Output 1123.2.4 Further Efficiency Considerations 1163.3 Hydrostatic Pump and Motor Types 1173.3.1 Radial Piston Pumps and Motors 1173.3.2 Axial Piston Pumps and Motors 1193.3.3 Gear Pumps and Motors 1283.3.4 Vane Pumps and Motors 1303.3.5 Digital Displacement Pumps and Motors 1313.4 Energy Losses at Steady-State Operation 1353.4.1 Energy Balances 1353.4.2 Overall Efficiencies 1383.4.3 Simplified Efficiency Equations 1383.4.4 Efficiency Relations 1393.5 Modelling Pump and Motor Efficiencies 1413.5.1 Performance Curves 1413.5.2 Volumetric Efficiency Modelling 1443.5.3 Overall Efficiency Modelling 1543.5.4 Mechanical Efficiency 160Exercises 162References 1644 Basic Hydrostatic Transmission Design 1664.1 General Considerations 1664.1.1 Output Speed Control 1664.1.2 Transmission Losses 1674.2 Hydrostatic Transmission Efficiency 1684.2.1 Energy Balance 1694.2.2 Conduit Efficiency 1714.2.3 Minor Pressure Losses 1734.2.4 Practical Application 1764.3 Transmission Output 1834.4 Steady-State Design Applications 1844.4.1 Case Study 1. Fixed-Displacement Motor and Variable-Displacement Pump 1854.4.2 Case Study 2. Fixed-Displacement Pump and Variable-Displacement Motor 1924.5 External Leakages and Charge Circuit 1984.6 Heat Losses and Cooling 2014.6.1 Sizing of the Heat Exchanger 2014.6.2 Loop Flushing 203Exercises 204References 2055 Dynamic Analysis of Hydrostatic Transmissions 2075.1 Introduction 2075.1.1 Pressure Surges during Transients 2085.1.2 Mechanical Vibrations and Noise 2115.1.3 Natural Circuit Oscillations 2145.1.4 Resonance and Beating 2175.1.5 Summary 2195.2 Modelling and Simulation 2195.2.1 Basic Equations 2205.2.2 Case Study 1. Purely Inertial Load with a Step Input 2235.2.3 Case Study 2. Variable Pump Flow 231Exercises 240References 2416 Hydrostatic Actuators 2436.1 Introductory Concepts 2436.1.1 Circuit Operational Quadrants 2436.1.2 Energy Management 2446.1.3 Cylinder Stiffness 2456.1.4 Double-Rod and Single-Rod Actuators 2456.2 Hydrostatic Actuator Circuits 2476.2.1 Design 1. Dual-Pump, Open-Circuit, Displacement-Controlled Actuator 2476.2.2 Design 2. Dual-Pump, Closed-Circuit, Displacement-Controlled Actuator 2496.2.3 Design 3. Dual-Pump Electrohydrostatic Actuator with Accumulators 2516.2.4 Design 4. Circuit with an Inline Hydraulic Transformer 2536.2.5 Design 5. Single-Pump Circuit with a Directional Valve 2576.2.6 Design 6. Single-Pump Circuit with Pilot-Operated Check Valves 2606.2.7 Design 7. Single-Pump Circuit with Inline Check Valves 2636.2.8 Design 8. Energy Storage Circuit 2676.2.9 Design 9. Double-Rod Actuator 2736.3 Common Pressure Rail and Hydraulic Transformers 275Exercises 281References 2827 Dynamic Analysis of Hydrostatic Actuators 2837.1 Introduction 2837.2 Mathematical Model 2847.2.1 Basic Equations 2847.2.2 Cylinder Friction 2887.2.3 Pilot-Operated Check Valves 2947.3 Case Study 2987.3.1 Determination of the Pump Flow Period 2997.3.2 Numerical Simulation 300Exercises 304References 3068 Practical Applications 3078.1 Infinitely Variable Transmissions in Vehicles 3078.2 Heavy Mobile Equipment 3108.3 Hybrid Vehicles 3138.3.1 Definition 3158.3.2 Electric Hybrids 3158.3.3 Hydraulic Hybrids 3168.3.4 CPR-Based Hybrids 3218.4 Wind Turbines 3238.4.1 Asynchronous Generators 3248.4.2 Synchronous Generators 3268.4.3 General Aspects of Power Transmission in Wind Turbines 3288.4.4 Hydrostatic Transmission in Wind Turbines 3298.5 Wave Energy Extraction 3318.6 Aeronautical Applications 334References 336Appendix A Hydraulic Symbols 339Appendix B Mathematics Review 345B.1 The Nabla Operator (∇) 345B.2 Ordinary Differential Equations (ODEs) 346B.2.1 General Aspects and Definitions for ODEs 347B.2.2 The Laplace Transform Method 351References 360Appendix C Fluid Dynamics Equations 361C.1 Introduction 361C.2 Fluid Stresses and Distortion Rates 363C.3 Differential Fluid Dynamics Equations 365C.3.1 Conservation of Mass 365C.3.2 Conservation of Momentum 367C.3.3 Navier–Stokes Equations in Cylindrical Coordinates 370C.4 Control Volume Analysis 371C.4.1 The Reynolds Transport Theorem 371C.4.2 Mass and Momentum Conservation 373C.4.3 Conservation of Energy 375References 378Index 379

Gustavo Koury Costa graduated in 1992 with a bachelor degree in Mechanical Engineering and has been teaching Fluid Power for 19 years at his current institution. He also holds a Doctorate degree in Computational Fluid Dynamics, having spent one year as a Postdoctoral Fellow at the University of Manitoba Fluid Power and Tele-Robotics Research Laboratory.Nariman Sepehri is a professor in Mechanical Engineering. He holds five patents and has published over 100 journal articles on various aspects of fluid power, including systems, manipulation, diagnosis and control. His current research focuses on self-healing, energy-efficient and reliable fluid power systems with applications to aircraft, hydraulic tele-manipulators and off-highway equipment. He is a Fellow and has served as Chair of the Fluid Power Systems and Technology Division of the American Society of Mechanical Engineers (ASME). He has served on editorial boards of eight journals including the International Journal of Fluid Power.

• Preface xiiiAcknowledgements xviiAbout the Companion Website xix1 Introduction to Power Transmission 11.1 Transmission Ratio 11.1.1 Generalities 11.1.2 Definition 31.1.3 Classification 31.2 Mechanical Transmissions 41.2.1 Gear Trains 41.2.2 Gearboxes 61.2.3 Efficiency 81.2.4 Continuously and Infinitely Variable Transmissions 111.3 Hydraulic Transmissions 151.4 Hydrostatic Transmissions 191.4.1 Operational Principles 191.4.2 Formal Definition of Hydrostatic Transmissions 321.4.3 Classification of Hydrostatic Transmissions 341.4.4 Efficiency Considerations 401.5 Hydromechanical Power-Split Transmissions 401.5.1 General Classification 411.5.2 Transmission Ratio 421.5.3 Lockup Point 441.5.4 Power Relations 441.6 Mechanical and Hydrostatic Actuators 511.6.1 Mechanical Actuators 511.6.2 Hydrostatic Actuators 521.6.3 Hydrostatic Actuation Versus Valve Control 531.6.4 Multiple Cylinder Actuators 55Exercises 56References 572 Fundamentals of Fluid Flows in Hydrostatic Transmissions 592.1 Fluid Properties 592.1.1 Viscosity 592.1.2 Compressibility 642.2 Fluid Flow in Hydraulic Circuits 792.2.1 Flow Regimes 792.2.2 Internal Flow in Conduits 812.2.3 Flow Through Orifices 852.2.4 Leakage Flow in Pumps and Motors 872.2.5 Other Loss Models 93Exercises 94References 963 Hydrostatic Pumps and Motors 983.1 Hydrostatic and Hydrodynamic Pumps and Motors 983.2 Hydrostatic Machine Output 1023.2.1 Average Input–Output Relations 1023.2.2 Instantaneous Pump Output 1043.2.3 Instantaneous Motor Output 1123.2.4 Further Efficiency Considerations 1163.3 Hydrostatic Pump and Motor Types 1173.3.1 Radial Piston Pumps and Motors 1173.3.2 Axial Piston Pumps and Motors 1193.3.3 Gear Pumps and Motors 1283.3.4 Vane Pumps and Motors 1303.3.5 Digital Displacement Pumps and Motors 1313.4 Energy Losses at Steady-State Operation 1353.4.1 Energy Balances 1353.4.2 Overall Efficiencies 1383.4.3 Simplified Efficiency Equations 1383.4.4 Efficiency Relations 1393.5 Modelling Pump and Motor Efficiencies 1413.5.1 Performance Curves 1413.5.2 Volumetric Efficiency Modelling 1443.5.3 Overall Efficiency Modelling 1543.5.4 Mechanical Efficiency 160Exercises 162References 1644 Basic Hydrostatic Transmission Design 1664.1 General Considerations 1664.1.1 Output Speed Control 1664.1.2 Transmission Losses 1674.2 Hydrostatic Transmission Efficiency 1684.2.1 Energy Balance 1694.2.2 Conduit Efficiency 1714.2.3 Minor Pressure Losses 1734.2.4 Practical Application 1764.3 Transmission Output 1834.4 Steady-State Design Applications 1844.4.1 Case Study 1. Fixed-Displacement Motor and Variable-Displacement Pump 1854.4.2 Case Study 2. Fixed-Displacement Pump and Variable-Displacement Motor 1924.5 External Leakages and Charge Circuit 1984.6 Heat Losses and Cooling 2014.6.1 Sizing of the Heat Exchanger 2014.6.2 Loop Flushing 203Exercises 204References 2055 Dynamic Analysis of Hydrostatic Transmissions 2075.1 Introduction 2075.1.1 Pressure Surges during Transients 2085.1.2 Mechanical Vibrations and Noise 2115.1.3 Natural Circuit Oscillations 2145.1.4 Resonance and Beating 2175.1.5 Summary 2195.2 Modelling and Simulation 2195.2.1 Basic Equations 2205.2.2 Case Study 1. Purely Inertial Load with a Step Input 2235.2.3 Case Study 2. Variable Pump Flow 231Exercises 240References 2416 Hydrostatic Actuators 2436.1 Introductory Concepts 2436.1.1 Circuit Operational Quadrants 2436.1.2 Energy Management 2446.1.3 Cylinder Stiffness 2456.1.4 Double-Rod and Single-Rod Actuators 2456.2 Hydrostatic Actuator Circuits 2476.2.1 Design 1. Dual-Pump, Open-Circuit, Displacement-Controlled Actuator 2476.2.2 Design 2. Dual-Pump, Closed-Circuit, Displacement-Controlled Actuator 2496.2.3 Design 3. Dual-Pump Electrohydrostatic Actuator with Accumulators 2516.2.4 Design 4. Circuit with an Inline Hydraulic Transformer 2536.2.5 Design 5. Single-Pump Circuit with a Directional Valve 2576.2.6 Design 6. Single-Pump Circuit with Pilot-Operated Check Valves 2606.2.7 Design 7. Single-Pump Circuit with Inline Check Valves 2636.2.8 Design 8. Energy Storage Circuit 2676.2.9 Design 9. Double-Rod Actuator 2736.3 Common Pressure Rail and Hydraulic Transformers 275Exercises 281References 2827 Dynamic Analysis of Hydrostatic Actuators 2837.1 Introduction 2837.2 Mathematical Model 2847.2.1 Basic Equations 2847.2.2 Cylinder Friction 2887.2.3 Pilot-Operated Check Valves 2947.3 Case Study 2987.3.1 Determination of the Pump Flow Period 2997.3.2 Numerical Simulation 300Exercises 304References 3068 Practical Applications 3078.1 Infinitely Variable Transmissions in Vehicles 3078.2 Heavy Mobile Equipment 3108.3 Hybrid Vehicles 3138.3.1 Definition 3158.3.2 Electric Hybrids 3158.3.3 Hydraulic Hybrids 3168.3.4 CPR-Based Hybrids 3218.4 Wind Turbines 3238.4.1 Asynchronous Generators 3248.4.2 Synchronous Generators 3268.4.3 General Aspects of Power Transmission in Wind Turbines 3288.4.4 Hydrostatic Transmission in Wind Turbines 3298.5 Wave Energy Extraction 3318.6 Aeronautical Applications 334References 336Appendix A Hydraulic Symbols 339Appendix B Mathematics Review 345B.1 The Nabla Operator (∇) 345B.2 Ordinary Differential Equations (ODEs) 346B.2.1 General Aspects and Definitions for ODEs 347B.2.2 The Laplace Transform Method 351References 360Appendix C Fluid Dynamics Equations 361C.1 Introduction 361C.2 Fluid Stresses and Distortion Rates 363C.3 Differential Fluid Dynamics Equations 365C.3.1 Conservation of Mass 365C.3.2 Conservation of Momentum 367C.3.3 Navier–Stokes Equations in Cylindrical Coordinates 370C.4 Control Volume Analysis 371C.4.1 The Reynolds Transport Theorem 371C.4.2 Mass and Momentum Conservation 373C.4.3 Conservation of Energy 375References 378Index 379