Yi Zhang is a Professor in the Department of Mechanical Engineering at the University of Michigan-Dearborn, USA. His current work focuses on the design, analysis and control of various transmissions for conventional automobiles. Other areas of research are theory of gearing and applications, hybrid vehicles, robotics, and mechanisms. Chris Mi is a Professor and the Chair of the Department of Electrical and Computer Engineering at San Diego State University, USA. He is also the Director of the GATE Center for Electric Drive Transportation funded by the DOE. His research focuses on hybrid electric vehicles and power electronics. He is an Area Editor and Associate Editor of three IEEE Transactions. He is also a Fellow of both the IEEE and the SAE.

• Series Preface xiPreface xiii1 Automotive Engine Matching 11.1 Introduction 11.2 Output Characteristics of Internal Combustion Engines 21.2.1 Engine Output Power and Torque 21.2.2 Engine Fuel Map 41.2.3 Engine Emission Map 51.3 Road Load, Driving Force, and Acceleration 61.3.1 Axle Loads 71.3.2 Road Loads 81.3.3 Powertrain Kinematics and Traction 91.3.4 Driving Condition Diagram 131.3.5 Ideal Transmission 151.3.6 Power–Speed Chart 171.4 Selection of Gear Ratios 181.4.1 Highest Gear Ratio 181.4.2 First Gear Ratio 191.4.3 Intermediate Gear Ratios 201.4.4 Finalization of Gear Ratios 23References 26Problem 262 Manual Transmissions 292.1 Introduction 292.2 Powertrain Layout and Manual Transmission Structure 302.3 Power Flows and Gear Ratios 372.4 Manual Transmission Clutches 402.4.1 Clutch Structure 402.4.2 Clutch Torque Capacity 432.4.3 Clutch Design 442.5 Synchronizer and Synchronization 452.5.1 Shift without Synchronizer 452.5.2 Shift with Synchronizer 472.6 Dynamic Modeling of Synchronization Process 522.6.1 Equivalent Mass Moment of Inertia 532.6.2 Equation of Motion during Synchronization 552.6.3 Condition for Synchronization 562.7 Shifting Mechanisms 59References 62Problems 623 Transmission Gear Design 65 3.1 Introduction 653.2 Gear Design Fundamentals 663.2.1 Conjugate Motion and Definitions   663.2.2 Property of Involute Curves   673.2.3 Involute Curves as Gear Tooth Profiles 683.2.4 Characteristics of Involute Gearing 693.3 Design of Tooth Element Proportions of Standard Gears 723.3.1 Gear Dimensional and Geometrical Parameters 723.3.2 Standardization of Tooth Dimensions 723.3.3 Tooth Dimensions of Standard Gears 743.3.4 Contact Ratio 743.3.5 Tooth Thickness and Space along the Tooth Height 763.4 Design of Non-Standard Gears 783.4.1 Standard and Non-Standard Cutter Settings 783.4.2 Avoidance of Tooth Undercutting and Minimum Number of Teeth 793.4.3 Systems of Non-standard Gears 813.4.4 Design of Long-Short Addendum Gear System 823.4.5 Design of General Non-Standard Gear System 833.5 Involute Helical Gears 863.5.1 Characteristics of Involute Helical Gearing 873.5.2 Design Parameters on the Normal and Transverse Sections 873.5.3 Tooth Dimensions of Standard Involute Helical Gears 893.5.4 Minimum Number of Teeth for Involute Helical Gears 893.5.5 Contact Ratio of Involute Helical Gears 903.5.6 Design of Non-standard Involute Helical Gears 913.6 Gear Tooth Strength and Pitting Resistance   913.6.1 Determination of Gear Forces 913.6.2 AGMA Standard on Bending Strength and Pitting Resistance 933.6.3 Pitting Resistance 933.6.4 Bending Strength 943.7 Design of Automotive Transmission Gears 953.8 Planetary Gear Trains 1033.8.1 Simple Planetary Gear Train 1063.8.2 Dual-Planet Planetary Gear Train 1073.8.3 Ravigneaux Planetary Gear Train 107References 108Problems 1094 Torque Converters  1114.1 Introduction 1114.2 Torque Converter Structure and Functions 1124.2.1 Torque Multiplication and Fluid Coupling 1144.2.2 Torque Converter Locking up 1154.3 ATF Circulation and Torque Formulation 1164.3.1 Terminologies and Definitions 1164.3.2 Velocity Diagrams 1194.3.3 Angular Momentum of ATF Flow and Torque Formulation 1224.4 Torque Capacity and Input–Output Characteristics 1244.4.1 Torque Converter Capacity Factor 1254.4.2 Input–Output Characteristics 1274.4.3 Joint Operation of Torque Converter and Engine 1284.4.4 Joint Operation of Torque Converter and Vehicle Powertrain 129References 133Problem 1345 Automatic Transmissions: Design, Analysis, and Dynamics 1375.1 Introduction 1375.2 Structure of Automatic Transmissions 1395.3 Ratio Analysis and Synthesis 1535.3.1 Ford FWD Six-Speed AT 1535.3.2 Ford six-speed RWD Ravigneaux AT 1605.3.3 ZF RWD Eight-Speed AT 1625.4 Transmission Dynamics 1645.4.1 Ford FWD Six-Speed AT 1655.4.2 Ford RWD Six-Speed AT 1705.4.3 ZF RWD Eight-Speed AT 1725.5 Qualitative Analysis on Transmission Shifting Dynamics 1755.6 General Vehicle Powertrain Dynamics 1865.6.1 General State Variable Equation in Matrix Form   1875.6.2 Specific State Variable Equation 1885.6.3 Solution of State Variables by Variable Substitution 1925.6.4 Vehicle System Integration 1935.7 Simulation of Vehicle Powertrain Dynamics 195References 198Problems 1986 Automatic Transmissions: Control and Calibration 2016.1 Introduction 2016.2 Components and Hydraulic Circuits for Transmission Control 2036.3 System Circuit Configurations for Transmission Control 2166.3.1 System Hydraulic Circuitry for the Previous Generation of ATs 2166.3.2 System Hydraulic Circuitry for ATs with Independent Clutch Pressure Control 2186.3.3 System Hydraulic Circuitry for ATs with Direct Clutch Pressure Control 2236.4 Transmission Control Strategy 2256.4.1 Transmission shift schedule 2256.4.2 Torque Converter Lock Control 2286.4.3 Lock-Release Schedule 2296.4.4 Lock-Release Operation 2316.4.5 Engine Torque Control During Shifts 2336.4.6 Shift Process Control 2366.4.7 Initial Clutch Pressure Profiles 2386.4.8 Initial Piston Stroke Attributes 2396.4.9 Feedback Shift Control 2396.4.10 Torque Based Shift Control 2416.4.11 System Diagnosis and Failure Mode Management 2456.5 Calibration of Transmission Control System 2456.5.1 Component Level Calibration 2466.5.2 System Level Calibration 247References 249Problem 2507 Continuously Variable Transmissions 2517.1 Introduction 2517.2 CVT Layouts and Key Components 253 7.2.1 Belt Structure 2547.2.2 Input and Output Pulleys 2547.2.3 Basic Ratio Equation 2557.3 Force Analysis for Belt CVT 2577.3.1 Forces Acting on a Metal Block 2577.3.2 Forces Acting on Pulley Sheaves 2587.3.3 Block Compression and Ring Tension 2627.3.4 Torque Transmitting Mechanism 2637.3.5 Forces Acting on the Whole Belt 2677.3.6 Relation between Thrusts on Input and Output Pulleys 2687.3.7 Ratio Changing Mechanism   2727.4 CVT Control System Design and Operation Control 2737.4.1 VBS Based Control System 2747.4.2 Servo Mechanism Control System 2777.4.3 Comparison of the Two Control System Designs 2857.5 CVT Control Strategy and Calibration 2877.5.1 Line Pressure Control 2877.5.2 Continuous Ratio Control Strategy 2887.5.3 Stepped Ratio Control Strategy 2927.5.4 CVT Control Calibration 293References 295Problems 2968 Dual Clutch Transmissions 2998.1 Introduction 2998.2 DCT Layouts and Key Components 3008.2.1 Dry Dual Clutch Transmissions 3018.2.2 Wet Dual Clutch Transmissions 3068.3 Modeling of DCT Vehicle Dynamics 3078.3.1 Equations of Motion during Launch and Shifts 3078.4 DCT Clutch Control 3138.5 Clutch Torque Formulation 3228.5.1 Correlation on Clutch Torque and Control Variable 3228.5.2 Case Study on Clutch Torque and Control Variable Correlation 3258.5.3 Algorithm for Clutch Torque Calculation under Real Time Conditions 3278.5.4 Case Study for the Clutch Torque Algorithm 328References 330Problems 3319 Electric Powertrains 3339.1 Basics of Electric Vehicles 3339.2 Current Status and Trends for EVs 3339.3 Output Characteristic of Electric Machines 3369.4 DC Machines 3379.4.1 Principle of DC Machines 3389.4.2 Excitation Types of DC Machines 3429.4.3 Speed Control of DC Machines 3439.5 Induction Machines 3479.5.1 Principle of Induction Motors 3489.5.2 Equivalent Circuit of Induction Motors 3499.5.3 Speed Control of Induction Machine 3529.5.4 Variable Frequency, Variable Voltage Control of Induction Motors 3549.5.5 Efficiency and Losses of Induction Machine 3559.5.6 Field-Oriented Control of Induction Machine 3569.6 Permanent Magnet Motor Drives 3619.6.1 Basic Configuration of PM Motors 3619.6.2 Basic Principle and Operation of PM Motors 3649.7 Switched Reluctance Motors 3709.8 EV Transmissions 3729.8.1 Single-Speed EV Transmission 3729.8.2 Multiple Ratio EV Transmissions 3749.9 Conclusions 379Bibliography 38010 Hybrid Powertrains 38910.1 Series HEVs 39010.2 Parallel HEVs 39110.3 Series–Parallel HEVs 39410.4 Complex HEVs 40010.4.1 GM Two-Mode Hybrid Transmission 40010.4.2 Dual Clutch Hybrid Transmissions 40710.4.3 Hybrid Transmission Proposed by Zhang, et al. 41310.4.4 Renault IVT Hybrid Transmission 41510.4.5 Timken Two-Mode Hybrid Transmission 41610.4.6 Tsai’s Hybrid Transmission 41910.4.7 Hybrid Transmission with Both Speed and Torque Coupling Mechanism 42110.4.8 Toyota Highlander and Lexus Hybrid, e-Four Wheel Drive 42310.4.9 CAMRY Hybrid 42410.4.10 Chevy Volt Powertrain 42510.5 Non-Ideal Gears in the Planetary System   42710.6 Dynamics of Planetary Gear Based Transmissions 42710.7 Conclusions 428References 429Index 431

Yi Zhang is a Professor in the Department of Mechanical Engineering at the University of Michigan-Dearborn, USA. His current work focuses on the design, analysis and control of various transmissions for conventional automobiles. Other areas of research are theory of gearing and applications, hybrid vehicles, robotics, and mechanisms. Chris Mi is a Professor and the Chair of the Department of Electrical and Computer Engineering at San Diego State University, USA. He is also the Director of the GATE Center for Electric Drive Transportation funded by the DOE. His research focuses on hybrid electric vehicles and power electronics. He is an Area Editor and Associate Editor of three IEEE Transactions. He is also a Fellow of both the IEEE and the SAE.

• Series Preface xiPreface xiii1 Automotive Engine Matching 11.1 Introduction 11.2 Output Characteristics of Internal Combustion Engines 21.2.1 Engine Output Power and Torque 21.2.2 Engine Fuel Map 41.2.3 Engine Emission Map 51.3 Road Load, Driving Force, and Acceleration 61.3.1 Axle Loads 71.3.2 Road Loads 81.3.3 Powertrain Kinematics and Traction 91.3.4 Driving Condition Diagram 131.3.5 Ideal Transmission 151.3.6 Power–Speed Chart 171.4 Selection of Gear Ratios 181.4.1 Highest Gear Ratio 181.4.2 First Gear Ratio 191.4.3 Intermediate Gear Ratios 201.4.4 Finalization of Gear Ratios 23References 26Problem 262 Manual Transmissions 292.1 Introduction 292.2 Powertrain Layout and Manual Transmission Structure 302.3 Power Flows and Gear Ratios 372.4 Manual Transmission Clutches 402.4.1 Clutch Structure 402.4.2 Clutch Torque Capacity 432.4.3 Clutch Design 442.5 Synchronizer and Synchronization 452.5.1 Shift without Synchronizer 452.5.2 Shift with Synchronizer 472.6 Dynamic Modeling of Synchronization Process 522.6.1 Equivalent Mass Moment of Inertia 532.6.2 Equation of Motion during Synchronization 552.6.3 Condition for Synchronization 562.7 Shifting Mechanisms 59References 62Problems 623 Transmission Gear Design 65 3.1 Introduction 653.2 Gear Design Fundamentals 663.2.1 Conjugate Motion and Definitions   663.2.2 Property of Involute Curves   673.2.3 Involute Curves as Gear Tooth Profiles 683.2.4 Characteristics of Involute Gearing 693.3 Design of Tooth Element Proportions of Standard Gears 723.3.1 Gear Dimensional and Geometrical Parameters 723.3.2 Standardization of Tooth Dimensions 723.3.3 Tooth Dimensions of Standard Gears 743.3.4 Contact Ratio 743.3.5 Tooth Thickness and Space along the Tooth Height 763.4 Design of Non-Standard Gears 783.4.1 Standard and Non-Standard Cutter Settings 783.4.2 Avoidance of Tooth Undercutting and Minimum Number of Teeth 793.4.3 Systems of Non-standard Gears 813.4.4 Design of Long-Short Addendum Gear System 823.4.5 Design of General Non-Standard Gear System 833.5 Involute Helical Gears 863.5.1 Characteristics of Involute Helical Gearing 873.5.2 Design Parameters on the Normal and Transverse Sections 873.5.3 Tooth Dimensions of Standard Involute Helical Gears 893.5.4 Minimum Number of Teeth for Involute Helical Gears 893.5.5 Contact Ratio of Involute Helical Gears 903.5.6 Design of Non-standard Involute Helical Gears 913.6 Gear Tooth Strength and Pitting Resistance   913.6.1 Determination of Gear Forces 913.6.2 AGMA Standard on Bending Strength and Pitting Resistance 933.6.3 Pitting Resistance 933.6.4 Bending Strength 943.7 Design of Automotive Transmission Gears 953.8 Planetary Gear Trains 1033.8.1 Simple Planetary Gear Train 1063.8.2 Dual-Planet Planetary Gear Train 1073.8.3 Ravigneaux Planetary Gear Train 107References 108Problems 1094 Torque Converters  1114.1 Introduction 1114.2 Torque Converter Structure and Functions 1124.2.1 Torque Multiplication and Fluid Coupling 1144.2.2 Torque Converter Locking up 1154.3 ATF Circulation and Torque Formulation 1164.3.1 Terminologies and Definitions 1164.3.2 Velocity Diagrams 1194.3.3 Angular Momentum of ATF Flow and Torque Formulation 1224.4 Torque Capacity and Input–Output Characteristics 1244.4.1 Torque Converter Capacity Factor 1254.4.2 Input–Output Characteristics 1274.4.3 Joint Operation of Torque Converter and Engine 1284.4.4 Joint Operation of Torque Converter and Vehicle Powertrain 129References 133Problem 1345 Automatic Transmissions: Design, Analysis, and Dynamics 1375.1 Introduction 1375.2 Structure of Automatic Transmissions 1395.3 Ratio Analysis and Synthesis 1535.3.1 Ford FWD Six-Speed AT 1535.3.2 Ford six-speed RWD Ravigneaux AT 1605.3.3 ZF RWD Eight-Speed AT 1625.4 Transmission Dynamics 1645.4.1 Ford FWD Six-Speed AT 1655.4.2 Ford RWD Six-Speed AT 1705.4.3 ZF RWD Eight-Speed AT 1725.5 Qualitative Analysis on Transmission Shifting Dynamics 1755.6 General Vehicle Powertrain Dynamics 1865.6.1 General State Variable Equation in Matrix Form   1875.6.2 Specific State Variable Equation 1885.6.3 Solution of State Variables by Variable Substitution 1925.6.4 Vehicle System Integration 1935.7 Simulation of Vehicle Powertrain Dynamics 195References 198Problems 1986 Automatic Transmissions: Control and Calibration 2016.1 Introduction 2016.2 Components and Hydraulic Circuits for Transmission Control 2036.3 System Circuit Configurations for Transmission Control 2166.3.1 System Hydraulic Circuitry for the Previous Generation of ATs 2166.3.2 System Hydraulic Circuitry for ATs with Independent Clutch Pressure Control 2186.3.3 System Hydraulic Circuitry for ATs with Direct Clutch Pressure Control 2236.4 Transmission Control Strategy 2256.4.1 Transmission shift schedule 2256.4.2 Torque Converter Lock Control 2286.4.3 Lock-Release Schedule 2296.4.4 Lock-Release Operation 2316.4.5 Engine Torque Control During Shifts 2336.4.6 Shift Process Control 2366.4.7 Initial Clutch Pressure Profiles 2386.4.8 Initial Piston Stroke Attributes 2396.4.9 Feedback Shift Control 2396.4.10 Torque Based Shift Control 2416.4.11 System Diagnosis and Failure Mode Management 2456.5 Calibration of Transmission Control System 2456.5.1 Component Level Calibration 2466.5.2 System Level Calibration 247References 249Problem 2507 Continuously Variable Transmissions 2517.1 Introduction 2517.2 CVT Layouts and Key Components 253 7.2.1 Belt Structure 2547.2.2 Input and Output Pulleys 2547.2.3 Basic Ratio Equation 2557.3 Force Analysis for Belt CVT 2577.3.1 Forces Acting on a Metal Block 2577.3.2 Forces Acting on Pulley Sheaves 2587.3.3 Block Compression and Ring Tension 2627.3.4 Torque Transmitting Mechanism 2637.3.5 Forces Acting on the Whole Belt 2677.3.6 Relation between Thrusts on Input and Output Pulleys 2687.3.7 Ratio Changing Mechanism   2727.4 CVT Control System Design and Operation Control 2737.4.1 VBS Based Control System 2747.4.2 Servo Mechanism Control System 2777.4.3 Comparison of the Two Control System Designs 2857.5 CVT Control Strategy and Calibration 2877.5.1 Line Pressure Control 2877.5.2 Continuous Ratio Control Strategy 2887.5.3 Stepped Ratio Control Strategy 2927.5.4 CVT Control Calibration 293References 295Problems 2968 Dual Clutch Transmissions 2998.1 Introduction 2998.2 DCT Layouts and Key Components 3008.2.1 Dry Dual Clutch Transmissions 3018.2.2 Wet Dual Clutch Transmissions 3068.3 Modeling of DCT Vehicle Dynamics 3078.3.1 Equations of Motion during Launch and Shifts 3078.4 DCT Clutch Control 3138.5 Clutch Torque Formulation 3228.5.1 Correlation on Clutch Torque and Control Variable 3228.5.2 Case Study on Clutch Torque and Control Variable Correlation 3258.5.3 Algorithm for Clutch Torque Calculation under Real Time Conditions 3278.5.4 Case Study for the Clutch Torque Algorithm 328References 330Problems 3319 Electric Powertrains 3339.1 Basics of Electric Vehicles 3339.2 Current Status and Trends for EVs 3339.3 Output Characteristic of Electric Machines 3369.4 DC Machines 3379.4.1 Principle of DC Machines 3389.4.2 Excitation Types of DC Machines 3429.4.3 Speed Control of DC Machines 3439.5 Induction Machines 3479.5.1 Principle of Induction Motors 3489.5.2 Equivalent Circuit of Induction Motors 3499.5.3 Speed Control of Induction Machine 3529.5.4 Variable Frequency, Variable Voltage Control of Induction Motors 3549.5.5 Efficiency and Losses of Induction Machine 3559.5.6 Field-Oriented Control of Induction Machine 3569.6 Permanent Magnet Motor Drives 3619.6.1 Basic Configuration of PM Motors 3619.6.2 Basic Principle and Operation of PM Motors 3649.7 Switched Reluctance Motors 3709.8 EV Transmissions 3729.8.1 Single-Speed EV Transmission 3729.8.2 Multiple Ratio EV Transmissions 3749.9 Conclusions 379Bibliography 38010 Hybrid Powertrains 38910.1 Series HEVs 39010.2 Parallel HEVs 39110.3 Series–Parallel HEVs 39410.4 Complex HEVs 40010.4.1 GM Two-Mode Hybrid Transmission 40010.4.2 Dual Clutch Hybrid Transmissions 40710.4.3 Hybrid Transmission Proposed by Zhang, et al. 41310.4.4 Renault IVT Hybrid Transmission 41510.4.5 Timken Two-Mode Hybrid Transmission 41610.4.6 Tsai’s Hybrid Transmission 41910.4.7 Hybrid Transmission with Both Speed and Torque Coupling Mechanism 42110.4.8 Toyota Highlander and Lexus Hybrid, e-Four Wheel Drive 42310.4.9 CAMRY Hybrid 42410.4.10 Chevy Volt Powertrain 42510.5 Non-Ideal Gears in the Planetary System   42710.6 Dynamics of Planetary Gear Based Transmissions 42710.7 Conclusions 428References 429Index 431

Yi Zhang is a Professor in the Department of Mechanical Engineering at the University of Michigan-Dearborn, USA. His current work focuses on the design, analysis and control of various transmissions for conventional automobiles. Other areas of research are theory of gearing and applications, hybrid vehicles, robotics, and mechanisms. Chris Mi is a Professor and the Chair of the Department of Electrical and Computer Engineering at San Diego State University, USA. He is also the Director of the GATE Center for Electric Drive Transportation funded by the DOE. His research focuses on hybrid electric vehicles and power electronics. He is an Area Editor and Associate Editor of three IEEE Transactions. He is also a Fellow of both the IEEE and the SAE.

• Series Preface xiPreface xiii1 Automotive Engine Matching 11.1 Introduction 11.2 Output Characteristics of Internal Combustion Engines 21.2.1 Engine Output Power and Torque 21.2.2 Engine Fuel Map 41.2.3 Engine Emission Map 51.3 Road Load, Driving Force, and Acceleration 61.3.1 Axle Loads 71.3.2 Road Loads 81.3.3 Powertrain Kinematics and Traction 91.3.4 Driving Condition Diagram 131.3.5 Ideal Transmission 151.3.6 Power–Speed Chart 171.4 Selection of Gear Ratios 181.4.1 Highest Gear Ratio 181.4.2 First Gear Ratio 191.4.3 Intermediate Gear Ratios 201.4.4 Finalization of Gear Ratios 23References 26Problem 262 Manual Transmissions 292.1 Introduction 292.2 Powertrain Layout and Manual Transmission Structure 302.3 Power Flows and Gear Ratios 372.4 Manual Transmission Clutches 402.4.1 Clutch Structure 402.4.2 Clutch Torque Capacity 432.4.3 Clutch Design 442.5 Synchronizer and Synchronization 452.5.1 Shift without Synchronizer 452.5.2 Shift with Synchronizer 472.6 Dynamic Modeling of Synchronization Process 522.6.1 Equivalent Mass Moment of Inertia 532.6.2 Equation of Motion during Synchronization 552.6.3 Condition for Synchronization 562.7 Shifting Mechanisms 59References 62Problems 623 Transmission Gear Design 65 3.1 Introduction 653.2 Gear Design Fundamentals 663.2.1 Conjugate Motion and Definitions   663.2.2 Property of Involute Curves   673.2.3 Involute Curves as Gear Tooth Profiles 683.2.4 Characteristics of Involute Gearing 693.3 Design of Tooth Element Proportions of Standard Gears 723.3.1 Gear Dimensional and Geometrical Parameters 723.3.2 Standardization of Tooth Dimensions 723.3.3 Tooth Dimensions of Standard Gears 743.3.4 Contact Ratio 743.3.5 Tooth Thickness and Space along the Tooth Height 763.4 Design of Non-Standard Gears 783.4.1 Standard and Non-Standard Cutter Settings 783.4.2 Avoidance of Tooth Undercutting and Minimum Number of Teeth 793.4.3 Systems of Non-standard Gears 813.4.4 Design of Long-Short Addendum Gear System 823.4.5 Design of General Non-Standard Gear System 833.5 Involute Helical Gears 863.5.1 Characteristics of Involute Helical Gearing 873.5.2 Design Parameters on the Normal and Transverse Sections 873.5.3 Tooth Dimensions of Standard Involute Helical Gears 893.5.4 Minimum Number of Teeth for Involute Helical Gears 893.5.5 Contact Ratio of Involute Helical Gears 903.5.6 Design of Non-standard Involute Helical Gears 913.6 Gear Tooth Strength and Pitting Resistance   913.6.1 Determination of Gear Forces 913.6.2 AGMA Standard on Bending Strength and Pitting Resistance 933.6.3 Pitting Resistance 933.6.4 Bending Strength 943.7 Design of Automotive Transmission Gears 953.8 Planetary Gear Trains 1033.8.1 Simple Planetary Gear Train 1063.8.2 Dual-Planet Planetary Gear Train 1073.8.3 Ravigneaux Planetary Gear Train 107References 108Problems 1094 Torque Converters  1114.1 Introduction 1114.2 Torque Converter Structure and Functions 1124.2.1 Torque Multiplication and Fluid Coupling 1144.2.2 Torque Converter Locking up 1154.3 ATF Circulation and Torque Formulation 1164.3.1 Terminologies and Definitions 1164.3.2 Velocity Diagrams 1194.3.3 Angular Momentum of ATF Flow and Torque Formulation 1224.4 Torque Capacity and Input–Output Characteristics 1244.4.1 Torque Converter Capacity Factor 1254.4.2 Input–Output Characteristics 1274.4.3 Joint Operation of Torque Converter and Engine 1284.4.4 Joint Operation of Torque Converter and Vehicle Powertrain 129References 133Problem 1345 Automatic Transmissions: Design, Analysis, and Dynamics 1375.1 Introduction 1375.2 Structure of Automatic Transmissions 1395.3 Ratio Analysis and Synthesis 1535.3.1 Ford FWD Six-Speed AT 1535.3.2 Ford six-speed RWD Ravigneaux AT 1605.3.3 ZF RWD Eight-Speed AT 1625.4 Transmission Dynamics 1645.4.1 Ford FWD Six-Speed AT 1655.4.2 Ford RWD Six-Speed AT 1705.4.3 ZF RWD Eight-Speed AT 1725.5 Qualitative Analysis on Transmission Shifting Dynamics 1755.6 General Vehicle Powertrain Dynamics 1865.6.1 General State Variable Equation in Matrix Form   1875.6.2 Specific State Variable Equation 1885.6.3 Solution of State Variables by Variable Substitution 1925.6.4 Vehicle System Integration 1935.7 Simulation of Vehicle Powertrain Dynamics 195References 198Problems 1986 Automatic Transmissions: Control and Calibration 2016.1 Introduction 2016.2 Components and Hydraulic Circuits for Transmission Control 2036.3 System Circuit Configurations for Transmission Control 2166.3.1 System Hydraulic Circuitry for the Previous Generation of ATs 2166.3.2 System Hydraulic Circuitry for ATs with Independent Clutch Pressure Control 2186.3.3 System Hydraulic Circuitry for ATs with Direct Clutch Pressure Control 2236.4 Transmission Control Strategy 2256.4.1 Transmission shift schedule 2256.4.2 Torque Converter Lock Control 2286.4.3 Lock-Release Schedule 2296.4.4 Lock-Release Operation 2316.4.5 Engine Torque Control During Shifts 2336.4.6 Shift Process Control 2366.4.7 Initial Clutch Pressure Profiles 2386.4.8 Initial Piston Stroke Attributes 2396.4.9 Feedback Shift Control 2396.4.10 Torque Based Shift Control 2416.4.11 System Diagnosis and Failure Mode Management 2456.5 Calibration of Transmission Control System 2456.5.1 Component Level Calibration 2466.5.2 System Level Calibration 247References 249Problem 2507 Continuously Variable Transmissions 2517.1 Introduction 2517.2 CVT Layouts and Key Components 253 7.2.1 Belt Structure 2547.2.2 Input and Output Pulleys 2547.2.3 Basic Ratio Equation 2557.3 Force Analysis for Belt CVT 2577.3.1 Forces Acting on a Metal Block 2577.3.2 Forces Acting on Pulley Sheaves 2587.3.3 Block Compression and Ring Tension 2627.3.4 Torque Transmitting Mechanism 2637.3.5 Forces Acting on the Whole Belt 2677.3.6 Relation between Thrusts on Input and Output Pulleys 2687.3.7 Ratio Changing Mechanism   2727.4 CVT Control System Design and Operation Control 2737.4.1 VBS Based Control System 2747.4.2 Servo Mechanism Control System 2777.4.3 Comparison of the Two Control System Designs 2857.5 CVT Control Strategy and Calibration 2877.5.1 Line Pressure Control 2877.5.2 Continuous Ratio Control Strategy 2887.5.3 Stepped Ratio Control Strategy 2927.5.4 CVT Control Calibration 293References 295Problems 2968 Dual Clutch Transmissions 2998.1 Introduction 2998.2 DCT Layouts and Key Components 3008.2.1 Dry Dual Clutch Transmissions 3018.2.2 Wet Dual Clutch Transmissions 3068.3 Modeling of DCT Vehicle Dynamics 3078.3.1 Equations of Motion during Launch and Shifts 3078.4 DCT Clutch Control 3138.5 Clutch Torque Formulation 3228.5.1 Correlation on Clutch Torque and Control Variable 3228.5.2 Case Study on Clutch Torque and Control Variable Correlation 3258.5.3 Algorithm for Clutch Torque Calculation under Real Time Conditions 3278.5.4 Case Study for the Clutch Torque Algorithm 328References 330Problems 3319 Electric Powertrains 3339.1 Basics of Electric Vehicles 3339.2 Current Status and Trends for EVs 3339.3 Output Characteristic of Electric Machines 3369.4 DC Machines 3379.4.1 Principle of DC Machines 3389.4.2 Excitation Types of DC Machines 3429.4.3 Speed Control of DC Machines 3439.5 Induction Machines 3479.5.1 Principle of Induction Motors 3489.5.2 Equivalent Circuit of Induction Motors 3499.5.3 Speed Control of Induction Machine 3529.5.4 Variable Frequency, Variable Voltage Control of Induction Motors 3549.5.5 Efficiency and Losses of Induction Machine 3559.5.6 Field-Oriented Control of Induction Machine 3569.6 Permanent Magnet Motor Drives 3619.6.1 Basic Configuration of PM Motors 3619.6.2 Basic Principle and Operation of PM Motors 3649.7 Switched Reluctance Motors 3709.8 EV Transmissions 3729.8.1 Single-Speed EV Transmission 3729.8.2 Multiple Ratio EV Transmissions 3749.9 Conclusions 379Bibliography 38010 Hybrid Powertrains 38910.1 Series HEVs 39010.2 Parallel HEVs 39110.3 Series–Parallel HEVs 39410.4 Complex HEVs 40010.4.1 GM Two-Mode Hybrid Transmission 40010.4.2 Dual Clutch Hybrid Transmissions 40710.4.3 Hybrid Transmission Proposed by Zhang, et al. 41310.4.4 Renault IVT Hybrid Transmission 41510.4.5 Timken Two-Mode Hybrid Transmission 41610.4.6 Tsai’s Hybrid Transmission 41910.4.7 Hybrid Transmission with Both Speed and Torque Coupling Mechanism 42110.4.8 Toyota Highlander and Lexus Hybrid, e-Four Wheel Drive 42310.4.9 CAMRY Hybrid 42410.4.10 Chevy Volt Powertrain 42510.5 Non-Ideal Gears in the Planetary System   42710.6 Dynamics of Planetary Gear Based Transmissions 42710.7 Conclusions 428References 429Index 431