1
`
`PAICE 2211
`Ford Motor Co. v. PAICE LLC et al.
`IPR2014-00884
`
`

`
`Copyright 2003© Craig J. Hoff & Gregory W. Davis. All rights reserved.
`
`2
`
`

`
`Preface
`
`This book is intended for advanced engineering students and practicing automotive
`engineers who are interested in learning about the overall design of an automotive
`powertrain. It is an introductory text on the topic, but it will provide the interested reader
`with a basis for understanding the fundamentals of automotive engines and automotive
`transmissions, and more importantly how to select those components to provide the
`optimum compromise between acceleration performance, gradeability performance and
`fuel economy performance.
`The level of analysis used in the text is not particularly difficult (it is assumed that the
`reader has a good grasp of engineering mechanics), however the equations derived in the
`text become the basis for developing computer models that can be used to predict vehicle '
`performance.
`
`Acknowledgement; in
`
`
`
`The authors of this book would like to thank and to acknowledge the work and support of
`many others who have come before us.
`In particular, we would like to thank Dr. Colin
`‘ Jordan for his significant contributions to the original notes from which this book was
`drawn. Finally, we would like to acknowledge the works of others who have made many
`of the original illustrations in this edition. Unfortunately, we have not yet been able to
`track down the sources of some of these Works. We are working diligently to locate the
`authors and to replace illustrations as needed. This work is currently a pre-production
`work intended for educational use.
`i
`
`3
`
`

`
`4
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`

`
`‘Table of Contents
`
`Preface ................................................................................ .. 3
`
`Table of Contents ................................................................ .. 5
`
`1 Automotive Drivetrain Components and Layouts ........ .. 1 1
`1.1
`Typical Drivetrain Layouts ............................................................................. .. 11
`1.1.1
`Typical Rear Wheel Drive Configuration ............................................... .. 11
`1.1.2
`Typical Front Wheel Drive Configuration .............................................. .. 14
`1.1.3
`Rear Wheel Drive with Rear Engine ...................................................... .. 15
`1.1.4
`Typical Four Wheel Drive Configuration ............................................... .. 16
`1.1.5
`Drivetrain Packaging ................................................................
`............ .. 17
`1.2
`Driveline Components .................................................................................... .. 18
`1.2.1
`Clutches ................................................................................................... .. 18
`
`1.2.2
`1.2.3
`
`1.2.4
`
`1.2.5
`
`1.2.6
`1.2.7
`
`1.2.8
`
`Hydraulic Torque Converter ................................................................... .. 19
`Manual Transmission ................
`............................................................ .. 21
`
`Automatic Transmissions ........................................................................ .. 22
`
`Transaxles ............................................................................................... .. 23
`
`Driveshafts .............................................................................................. .. 24 1
`Differentials ............................................................................................ .. 25
`
`Rear Axle ................................................................................................ .. 26
`
`1 .3
`
`References ....................................................................................................... .. 26
`
`...................................... ..27
`Chapter 2 ..................................
`2 Road Loads ................................................................. .. 27
`2.1
`Introduction ..................................................................................................... .. 27
`
`2.2
`2.2.1
`2.2.2
`2.2.3
`2.2.4
`2.2.5
`
`Aerodynamic Lift and Drag ............................................................................ .. 29 _
`Inviscid Flow: Euler and Bernoulli Equations ................................. ... .... .. 30
`Application to an Automobile ................................................................. .. 32
`Viscid Flow: Boundary Layers .................................................. ... .......... .. 34
`Application to an Automobile ................................................................. .. 35
`Inviscid Flow over Bodies ...................................................................... .. 35
`
`2.2.6
`
`Viscid Flow over Bodies ......................................................................... .. 37
`
`Application to an Automobile ................................................................. .. 40
`2.2.7
`Experimental Techniques........................................................................ .. 40
`2.2.8
`Application to an Automobile ................................................................. .. 42
`2.2.9
`Vortex Shedding ..................................................................................... .. 46
`2.2.10
`Application to an Automobile ................................................................. .. 46
`2.2.11
`Automotive Drag Studies ........................................................................ .. 47
`2.2.12
`Afterbody Drag ....................................................................................... .. 48
`2.2.13
`2.2.14 Wheel and Wheel Wells .......................................................................... .. 49
`
`2.2.15
`2.2.16
`
`Forebody Effects ..................................................................................... .. 50
`Underbody Drag..................................
`................................................. .. 51
`
`5
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`

`
`6
`
`A
`
`Introduction to Automotive Powertrains
`
`2.2.17
`2.2.18
`
`Optimization Study ...................................................... ... ........................ .. 52
`Effect of Wind ......................................................................................... .. 53
`
`54
`..........................
`Complete Aerodynamic Forces of a Vehicle .........
`2.2.19
`Density of Air ..........................
`............................................................. .. 55
`2.2.20
`Alternate Form for Drag Equation .......................................................... .. 57
`2.2.21
`2.3
`Rolling Resistance .......................................................................................... .. 5 9
`2.3.1
`Simple Model for Rolling Resistance ..................................................... .. 60
`2.3.2
`Effect of Road Surface ............................................................................ .. 61
`
`' 2.3.3
`2.3.4
`
`2.3.5
`2.3.6
`
`Effect of Temperature on Rolling Resistance ......................................... .. 61
`Effect of Tire Inflation Pressure ............................................................. .. 62
`
`Effect of Tire Speed ........................................................................... .. 62
`Effect of Tire Materials ........................................................................... .. 62
`
`2.3.7 I
`2.3.8
`2.4
`2.5
`
`Effect of Tire Slip Angle......................................................................... .. 63
`Other Models for Rolling Resistance ...................................................... .. 64
`Coast Down Testing ........................................................................................ .. 64
`Grade Resistance ............................................................................................. .. 65
`
`2.6
`2.7
`
`The Proving Ground Equation ........................................................................ .. 66
`References ....................................................................................................... .. 68
`
`3 Power Systems .............. ... ........................................... .. 69
`3 .1
`Introduction to Internal Combustion Engines and Their Performance ........... .. 69 —
`3.1.1
`Spark—ignited (S1) or Gasoline Four-stroke Engines .............................. .. 69
`3.1.2
`Compression—ignition (D1) or Diesel Four—stroke Engines ..................... .. 70
`3.2
`Engine Brake Torque and Power .................................................................... .. 72
`3.2.1
`Brake Power ............................................................................................ .. 73
`
`3.2.2
`3.2.3
`3.2.4
`3.2.5
`3.3
`
`Friction Power (FP) ................................................................................. .. 75
`Indicated Power (IP) ............................................................................... .. 75
`Specific Power ........................................................................................ .. 75
`Mean Effective Pressure (MEP) ............................................................. .. 75
`Efficiencies ..................................................................................................... .. 78
`
`3.3.1
`3.3.2
`3 .3 .3
`3.3.4
`3.3.5
`3 .3 .6
`3.4
`
`Mechanical Efficiency ............................................................................ .. 78
`Overall Thermal Efficiency (or Fuel Efficiency) .................................... .. 78
`Combustion Efficiency ........................................................................... .. 80
`Thermal Efficiency (or Specific Efficiency) ........................................... .. 80
`Specific Fuel Consumption (SFC) .......................................................... .. 81
`Volumetric Efficiency ............................................................................. .. 81
`Fuels ................................................................................................................ .. 81
`
`3.4.1
`3.4.2
`3.4.3
`3.5
`
`Octane Rating.......................................................................................... .. 82
`Decane Rating ......................................................................................... .. 82
`Determination of Fuel Specific Gravity and Heating Value ................... .. 82
`Emissions ............................................................ .; .......................................... .. 82
`
`3.6
`3.6.1
`3.6.2
`3.7
`3.7.1
`3.7.2
`
`Other Engine Parameters ................................................................................ .. 83
`Mean Piston Speed (S) ......
`.................................................................... .. 83
`Inlet Air Velocity .................................................................................... .. 83
`Typical Engine Performance Data .................................................................. .. 83
`Full Load Performance Comparison of SI and CI Engines .................... .. 83
`SAE Net Versus Gross Performance ...................................................... .. 86
`
`6
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`

`
`Automotive Drivetrain Components and Layouts
`
`7
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`3.7.3
`
`Part Load Performance ........................................................................... .. 86
`
`3.8
`3.8.1
`3.8.2
`
`Other Power Systems ...................................................................................... .. 87
`Gasoline Direct Injection (GDI) Spark—Ignited Engines ........................ .. 87
`Electric Motors ........................................................................................ .. 89
`
`3.8.3
`3.9
`
`Hybrid Electric Power Systems .............................................................. .. 90
`References ....................................................................................................... .. 92
`
`Chapter 4 .......................................................................... .. 93
`4 Driveline ....................................................................... ..93
`4.1
`Introduction ..................................................................................................... .. 93
`
`4.2
`
`Driveline ......................................................................................................... .. 96
`
`4.2.1
`4.2.2
`
`Ideal Driveline .............................. .. ................................. .. ..................... .. 96
`Driveline Losses ...................................................................................... .. 99
`
`4.3
`4.3.1
`4.3.2
`
`Tires (Idealized Model) ................................................................................. .. 103
`N/V Ratio (Idealized Tire) .................................................................... .. 103
`Available Tractive Power ..................................................................... .. 108
`
`4.3.3
`
`Available Tractive Effort ...................................................................... .. 111
`
`4.3.4
`4.4
`4.4.1
`
`Actual Tractive Power and Tractive Effort ........................................... .. 115
`Tires (Better Model) ..................................................................................... .. 118
`Tire Forces and Moments ............................................................... .; .... .. 118
`
`4.4.2
`4.4.3
`4.4.4
`
`Tire Slip ................................................................................................ .. 119
`NN Ratio (Better Model) ..................................................................... .. 122
`' Tractive Effort ....................................................................... .; .............. .. 122
`
`Example — Effect of Tire Slip ............................................................... .. 124
`4.4.5
`Slip Angle ............................................................................................. .. 127
`4.4.6
`The Friction Ellipse....................................................................................... .. 130
`4.5
`4.5.1
`Rolling Resistance (Revisited) .............................................................. .. 134
`4.5.2
`A Final Note on Tires ........................................................................... .. 135
`
`4.6 Move-off Elements ................................................. ..' .................................... .. 135
`
`References..................................................................................................... .. 137
`4.7
`5 Gear Ratio Selection .................................................. .. 139
`
`5.1
`5.2
`5.2.1
`5.2.2
`5.2.3
`
`Typical Gear Ratios Selected for Passenger Vehicles .................................. .. 143
`A Procedure for Selecting Gear Ratios ......................................................... .. 149
`Selection of a top gear N/V ratio .......................................................... .. 149
`Determination of Top Gear Ratio and Axle Ratio ................................ .. 153
`Low Gear Ratio Determination ............................................................. .. 154
`
`5.2.4
`5.3
`5.3.1
`5.3.2
`5.3.3
`
`159
`Selecting Intermediate Gear ratios ...................................................
`Example ........................................................................................................ .. 168
`Select a Top Gear N/V ratio.................................................................. .. 169
`Select a top gear ratio ............................................................................ .. 169
`Select an axle ratio ................................................................................ .. 169
`
`5.3.4
`5.3.5
`5.3.6
`
`Select first gear ratio ............................................................................. .. 170
`Select intermediate gear ratios .............................................................. .. 170
`Evaluate Gear Ratios ............................................................................. .. 172
`
`5.4
`
`5.5
`
`Homework....
`
`............................................................................................... .. 172
`
`References .................................................... .2 ............................................... .. 173
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`7
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`

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`8
`
`Introduction to Automotive Powertrains
`
`6 Acceleration Performance ....................... ..'. ............... .. 175
`
`6.1
`6.2
`
`6.3
`
`6.4
`6.5
`
`Predicting Acceleration Performance ........................................................... .. 178
`Power-Limited Acceleration ..........................................
`............................. .. 180
`
`Power-Limited Acceleration — Calculation Procedure .......... .; ..................... .. 188
`
`Examples: Power-Lirnited Acceleration — Manual Transmission ................ .. 190
`Acceleration — Automatic Transmission ....................................................... .. 209
`
`6.5.1
`6.5.2
`6.6
`6.7
`6.7.1
`6.7.2
`6.7.3
`6.8
`
`Torque Converter Basics ....................................................................... .. 209
`Matching of the engine and torque converter ....................................... .. 212
`Examples: Power—Limited Acceleration — Automatic Transmission............ .. 218
`Dynamic Axle Loads ................................................ .; .................................. .. 224
`Special Case: Static Loads on Level Ground without a Trailer ............ .. 228
`Determining the Location of the Vehicle CG ....................................... .. 228
`Low-Speed Acceleration....................................................................... .. 230
`Traction-Limited Acceleration...................................................................... .. 232
`
`6.8.1
`
`Maximum Possible Acceleration .......................................................... .. 232
`
`6.8.2
`6.8.3
`6.9
`
`...................... .. 235
`Actual Maximum Acceleration — Low Speed...............
`Traction Limited Acceleration - Example ............................................ .. 237
`Final Comments ............................................................................................ .. 238
`
`. 7 Gradeability Performance .......................................... .. 239
`7.1»
`Power—Limited Gradeability ......................................................................... .. 239
`7.2
`Traction—Limited Gradeability ................................
`.................................... .. 2471
`7 .3
`Gradeability with a Trailer ............................................................................ .. 251
`7.3 .1
`Power—Limited Gradeability ................................................................. .. 251
`7.3.2
`Traction-Limited Gradeability .............................................................. .. 253
`7.4
`References ..................................................................................................... .. 258 .
`
`Chapter 8 ........................................................................ ..259
`8 Fuel Economy Performance ...................................... ..259
`8.1
`Engine Fuel Consumption............................................................................. .. 259
`8.2 WOT Fuel Economy ..................................................................................... .. 264
`8.3
`POT Fuel Economy....................................................................................... .. 266
`8.3.1
`Example Problem .................................................................................. .. 267
`8.4
`Corporate Average Fuel Economy (CAFE).................................................. .. 277
`8.5
`Vehicle Emissions Performance ................................................................... .. 289
`
`Selecting Powertrain Components ................................................................ .. 294
`8.6
`9 Manual Transmissions ............................................... ..299
`
`9.1
`9.2
`9.2.1
`
`Clutch Systems.............................................................................................. .. 299
`Analysis of a Clutch ...................................................................................... .. 310
`Uniform Pressure Model ....................................................................... .. 311
`
`9.2.2
`
`Uniform Rate of Wear Model ............................................................... .. 312
`
`9.3
`
`Manual Transmission Gearboxes .............................
`
`.................................. .. 315
`
`Operation of a Constant Mesh Transmission ........................................ .. 321
`9.3.1
`Typical Overdrive Transmission........................................................... .. 324
`9.3.2
`10 Automatic Transmissions ........................................... .. 327
`
`10.1
`
`Introduction ................................................................................................... .. 327
`
`8
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`

`
`Automotive Drivetrain Components and Layouts
`
`9
`
`Torque Converters ........................................................................................ .. 329
`10.2
`10.2.1
`Fluid Couplings ..................................................................................... .. 329
`10.2.2
`Torque Converters ................................................................................ .. 332
`10.3
`Planetary (Epicyclic) Gear Trains ................................................................. .. 340
`10.3.1
`Kinematics of a Planetary Gear Train................................................... .. 342
`10.3.2
`Speed and Torque Ratios for Simply Planetary Gear Trains ................ .. 342 _
`10.3.3
`Summary of Equations for Simply Planetary Gear Sets and Example... 345
`10.3.4
`Compound Planetary Gearsets .............................................................. .. 346
`10.4 Control Elements .......................................................................................... .. 347
`
`Control of a Simple Planetary Gearset.................................................. .. 354
`10.4.1
`Example — Allison AT540 Transmission................. ... .......................... .. 355
`10.4.2
`10.5 Other Considerations .................................................................................... .. 362
`
`Transmission And Engine Oil Coolers ................................................. .. 362
`10.5.1
`Parking ............................ ...................................................................... .. 364
`10.5.2
`1 1 Differentials ................................................................ .. 365
`11.1
`Introduction ................................................................................................... .. 365
`
`11.2 Open Differentials ......................................................................................... .. 367
`11.2.1
`Vehicle traveling in a straight line ........................................................ .. 368
`11.2.2
`Vehicle Turning ................................................. .; ................................. .. 370
`11.3
`Limited Slip Differentials ....................................................... ..' .................... .. 373
`11.4
`Locking Differentials .................................................................................... .. 374
`11.5
`Planetary gear set as a Differential ....................... ... ..................................... .. 375
`Table of Figures .............................................................. .. 377
`
`9
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`

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`Power Systems
`
`This leads to the following relationship:
`
`nth
`
`= CF -Power _
`
`Afuel 'QLHV '77s
`
`81
`
`(3.16)
`
`3.3.5 Specific Fuel Consumption (SFC)
`
`Specific fuel consumption is inversely proportional to the efficiency and is defined as,
`
`SFC =
`
`#1fuel
`Power
`
`(3.17)
`
`Depending on the value used for power, either indicated or brake, specific fuel
`consumption is either called indicated specific fuel consumption (ISFC), or brake specific
`fuel consumption (BSFC). A lower value of specific fuel consumption is an indicator of
`higher engine efficiency.
`
`3.3.6 Volumetric Efficiency
`
`Volumetric efficiency relates the actual air used by an engine compared to the theoretical
`maximum level of air that could be used by the engine at that engine speed. Engines are
`limited by the amount of air that can be induced into the engine. More air input allows
`for more fuel to be added, leading to a higher engine power output. A good maximum
`value of volumetric efficiency for a naturally aspirated engine is approximately 80-90 %.
`To increase the volumetric efficiency of naturally aspirated engines,
`the
`automotive industry has used multi—valve engines, and ram tuning. Additionally,
`turbochargers and superchargers are used to force additional air into the engine. A 4
`cylinder engine utilizing a turbocharger may be able to provide the same performance as
`a naturally aspirated 6 cylinder engine.
`Volumetric efficiency can be expressed as:
`
`22. = 3'
`ml
`
`(3.18)
`
`Where
`
`ma = actual mass air flow rate,
`
`m, = theoretical maximum air flow rate = p ' VD - N / z ,
`
`p = air density.
`
`The air density is usually based upon the inlet air conditions or standard conditions if this
`is not known. Sometimes, particularly when an engine is turbo-or supercharged, the air
`density is based upon the intake manifold conditions.
`
`3.4 Fuels
`
`There are several important parameters for fossil fuels. These parameters describe the
`combustion properties of these fuels in engines.
`
`10
`
`10