Automotive Power Transmission Systems

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 xi

Preface xiii

1 Automotive Engine Matching 1

1.1 Introduction 1

1.2 Output Characteristics of Internal Combustion Engines 2

1.2.1 Engine Output Power and Torque 2

1.2.2 Engine Fuel Map 4

1.2.3 Engine Emission Map 5

1.3 Road Load, Driving Force, and Acceleration 6

1.3.1 Axle Loads 7

1.3.2 Road Loads 8

1.3.3 Powertrain Kinematics and Traction 9

1.3.4 Driving Condition Diagram 13

1.3.5 Ideal Transmission 15

1.3.6 Power–Speed Chart 17

1.4 Selection of Gear Ratios 18

1.4.1 Highest Gear Ratio 18

1.4.2 First Gear Ratio 19

1.4.3 Intermediate Gear Ratios 20

1.4.4 Finalization of Gear Ratios 23

References 26

Problem 26

2 Manual Transmissions 29

2.1 Introduction 29

2.2 Powertrain Layout and Manual Transmission Structure 30

2.3 Power Flows and Gear Ratios 37

2.4 Manual Transmission Clutches 40

2.4.1 Clutch Structure 40

2.4.2 Clutch Torque Capacity 43

2.4.3 Clutch Design 44

2.5 Synchronizer and Synchronization 45

2.5.1 Shift without Synchronizer 45

2.5.2 Shift with Synchronizer 47

2.6 Dynamic Modeling of Synchronization Process 52

2.6.1 Equivalent Mass Moment of Inertia 53

2.6.2 Equation of Motion during Synchronization 55

2.6.3 Condition for Synchronization 56

2.7 Shifting Mechanisms 59

References 62

Problems 62

3 Transmission Gear Design 65

3.1 Introduction 65

3.2 Gear Design Fundamentals 66

3.2.1 Conjugate Motion and Definitions   66

3.2.2 Property of Involute Curves   67

3.2.3 Involute Curves as Gear Tooth Profiles 68

3.2.4 Characteristics of Involute Gearing 69

3.3 Design of Tooth Element Proportions of Standard Gears 72

3.3.1 Gear Dimensional and Geometrical Parameters 72

3.3.2 Standardization of Tooth Dimensions 72

3.3.3 Tooth Dimensions of Standard Gears 74

3.3.4 Contact Ratio 74

3.3.5 Tooth Thickness and Space along the Tooth Height 76

3.4 Design of Non-Standard Gears 78

3.4.1 Standard and Non-Standard Cutter Settings 78

3.4.2 Avoidance of Tooth Undercutting and Minimum Number of Teeth 79

3.4.3 Systems of Non-standard Gears 81

3.4.4 Design of Long-Short Addendum Gear System 82

3.4.5 Design of General Non-Standard Gear System 83

3.5 Involute Helical Gears 86

3.5.1 Characteristics of Involute Helical Gearing 87

3.5.2 Design Parameters on the Normal and Transverse Sections 87

3.5.3 Tooth Dimensions of Standard Involute Helical Gears 89

3.5.4 Minimum Number of Teeth for Involute Helical Gears 89

3.5.5 Contact Ratio of Involute Helical Gears 90

3.5.6 Design of Non-standard Involute Helical Gears 91

3.6 Gear Tooth Strength and Pitting Resistance   91

3.6.1 Determination of Gear Forces 91

3.6.2 AGMA Standard on Bending Strength and Pitting Resistance 93

3.6.3 Pitting Resistance 93

3.6.4 Bending Strength 94

3.7 Design of Automotive Transmission Gears 95

3.8 Planetary Gear Trains 103

3.8.1 Simple Planetary Gear Train 106

3.8.2 Dual-Planet Planetary Gear Train 107

3.8.3 Ravigneaux Planetary Gear Train 107

References 108

Problems 109

4 Torque Converters  111

4.1 Introduction 111

4.2 Torque Converter Structure and Functions 112

4.2.1 Torque Multiplication and Fluid Coupling 114

4.2.2 Torque Converter Locking up 115

4.3 ATF Circulation and Torque Formulation 116

4.3.1 Terminologies and Definitions 116

4.3.2 Velocity Diagrams 119

4.3.3 Angular Momentum of ATF Flow and Torque Formulation 122

4.4 Torque Capacity and Input–Output Characteristics 124

4.4.1 Torque Converter Capacity Factor 125

4.4.2 Input–Output Characteristics 127

4.4.3 Joint Operation of Torque Converter and Engine 128

4.4.4 Joint Operation of Torque Converter and Vehicle Powertrain 129

References 133

Problem 134

5 Automatic Transmissions: Design, Analysis, and Dynamics 137

5.1 Introduction 137

5.2 Structure of Automatic Transmissions 139

5.3 Ratio Analysis and Synthesis 153

5.3.1 Ford FWD Six-Speed AT 153

5.3.2 Ford six-speed RWD Ravigneaux AT 160

5.3.3 ZF RWD Eight-Speed AT 162

5.4 Transmission Dynamics 164

5.4.1 Ford FWD Six-Speed AT 165

5.4.2 Ford RWD Six-Speed AT 170

5.4.3 ZF RWD Eight-Speed AT 172

5.5 Qualitative Analysis on Transmission Shifting Dynamics 175

5.6 General Vehicle Powertrain Dynamics 186

5.6.1 General State Variable Equation in Matrix Form   187

5.6.2 Specific State Variable Equation 188

5.6.3 Solution of State Variables by Variable Substitution 192

5.6.4 Vehicle System Integration 193

5.7 Simulation of Vehicle Powertrain Dynamics 195

References 198

Problems 198

6 Automatic Transmissions: Control and Calibration 201

6.1 Introduction 201

6.2 Components and Hydraulic Circuits for Transmission Control 203

6.3 System Circuit Configurations for Transmission Control 216

6.3.1 System Hydraulic Circuitry for the Previous Generation of ATs 216

6.3.2 System Hydraulic Circuitry for ATs with Independent Clutch Pressure Control 218

6.3.3 System Hydraulic Circuitry for ATs with Direct Clutch Pressure Control 223

6.4 Transmission Control Strategy 225

6.4.1 Transmission shift schedule 225

6.4.2 Torque Converter Lock Control 228

6.4.3 Lock-Release Schedule 229

6.4.4 Lock-Release Operation 231

6.4.5 Engine Torque Control During Shifts 233

6.4.6 Shift Process Control 236

6.4.7 Initial Clutch Pressure Profiles 238

6.4.8 Initial Piston Stroke Attributes 239

6.4.9 Feedback Shift Control 239

6.4.10 Torque Based Shift Control 241

6.4.11 System Diagnosis and Failure Mode Management 245

6.5 Calibration of Transmission Control System 245

6.5.1 Component Level Calibration 246

6.5.2 System Level Calibration 247

References 249

Problem 250

7 Continuously Variable Transmissions 251

7.1 Introduction 251

7.2 CVT Layouts and Key Components 253 7.2.1 Belt Structure 254

7.2.2 Input and Output Pulleys 254

7.2.3 Basic Ratio Equation 255

7.3 Force Analysis for Belt CVT 257

7.3.1 Forces Acting on a Metal Block 257

7.3.2 Forces Acting on Pulley Sheaves 258

7.3.3 Block Compression and Ring Tension 262

7.3.4 Torque Transmitting Mechanism 263

7.3.5 Forces Acting on the Whole Belt 267

7.3.6 Relation between Thrusts on Input and Output Pulleys 268

7.3.7 Ratio Changing Mechanism   272

7.4 CVT Control System Design and Operation Control 273

7.4.1 VBS Based Control System 274

7.4.2 Servo Mechanism Control System 277

7.4.3 Comparison of the Two Control System Designs 285

7.5 CVT Control Strategy and Calibration 287

7.5.1 Line Pressure Control 287

7.5.2 Continuous Ratio Control Strategy 288

7.5.3 Stepped Ratio Control Strategy 292

7.5.4 CVT Control Calibration 293

References 295

Problems 296

8 Dual Clutch Transmissions 299

8.1 Introduction 299

8.2 DCT Layouts and Key Components 300

8.2.1 Dry Dual Clutch Transmissions 301

8.2.2 Wet Dual Clutch Transmissions 306

8.3 Modeling of DCT Vehicle Dynamics 307

8.3.1 Equations of Motion during Launch and Shifts 307

8.4 DCT Clutch Control 313

8.5 Clutch Torque Formulation 322

8.5.1 Correlation on Clutch Torque and Control Variable 322

8.5.2 Case Study on Clutch Torque and Control Variable Correlation 325

8.5.3 Algorithm for Clutch Torque Calculation under Real Time Conditions 327

8.5.4 Case Study for the Clutch Torque Algorithm 328

References 330

Problems 331

9 Electric Powertrains 333

9.1 Basics of Electric Vehicles 333

9.2 Current Status and Trends for EVs 333

9.3 Output Characteristic of Electric Machines 336

9.4 DC Machines 337

9.4.1 Principle of DC Machines 338

9.4.2 Excitation Types of DC Machines 342

9.4.3 Speed Control of DC Machines 343

9.5 Induction Machines 347

9.5.1 Principle of Induction Motors 348

9.5.2 Equivalent Circuit of Induction Motors 349

9.5.3 Speed Control of Induction Machine 352

9.5.4 Variable Frequency, Variable Voltage Control of Induction Motors 354

9.5.5 Efficiency and Losses of Induction Machine 355

9.5.6 Field-Oriented Control of Induction Machine 356

9.6 Permanent Magnet Motor Drives 361

9.6.1 Basic Configuration of PM Motors 361

9.6.2 Basic Principle and Operation of PM Motors 364

9.7 Switched Reluctance Motors 370

9.8 EV Transmissions 372

9.8.1 Single-Speed EV Transmission 372

9.8.2 Multiple Ratio EV Transmissions 374

9.9 Conclusions 379

Bibliography 380

10 Hybrid Powertrains 389

10.1 Series HEVs 390

10.2 Parallel HEVs 391

10.3 Series–Parallel HEVs 394

10.4 Complex HEVs 400

10.4.1 GM Two-Mode Hybrid Transmission 400

10.4.2 Dual Clutch Hybrid Transmissions 407

10.4.3 Hybrid Transmission Proposed by Zhang, et al. 413

10.4.4 Renault IVT Hybrid Transmission 415

10.4.5 Timken Two-Mode Hybrid Transmission 416

10.4.6 Tsai’s Hybrid Transmission 419

10.4.7 Hybrid Transmission with Both Speed and Torque Coupling Mechanism 421

10.4.8 Toyota Highlander and Lexus Hybrid, e-Four Wheel Drive 423

10.4.9 CAMRY Hybrid 424

10.4.10 Chevy Volt Powertrain 425

10.5 Non-Ideal Gears in the Planetary System   427

10.6 Dynamics of Planetary Gear Based Transmissions 427

10.7 Conclusions 428

References 429

Index 431