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Numerical Modeling of Piston Secondary Motion and Skirt Lubricationin Internal Combustion Enginesby

Fiona McClureM.Eng., Mechanical EngineeringMcGill University, 2002

andB.Eng., Mechanical EngineeringB.S., Applied MathematicsThe University of Melbourne, 2000

Submitted to the Department of Mechanical Engineering in Partial Fulfillment of theRequirements for the Degree of Doctor of Philosophy in Mechanical Engineeringat the

Massachusetts Institute of TechnologySeptember 2007

C 2007 Massachusetts Institute of Technology. All rights reserved.

Signature of Author ............................ r. . . ..-. . . .V .. . . ..Department of Mechanical Engineering. Aiirun~t 91 2007Certified by ......... ........... ................................. Tian TianPrincipal Research Scientist, Department of Mechanical EngineeringI Thesis SupervisorCertified by ............ ................................................. John B. HeywoodSun Jae Proessor of Mechanical EngineeringThesis SupervisorAccepted by ............................ . - .l .........Lallit Anand

Chairman, Department Committee on Graduate StudiesDepartment of Mechanical EngineeringARCHIVES

MASSACOF

JALI

HURMI' IN SM.1 'TEOHNOLOGY

N03 20083RARIES- - _ I

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Numerical Modeling of Piston Secondary Motion andSkirt Lubrication in Internal Combustion Enginesby

Fiona McClureSubmitted to the Department of Mechanical Engineeringon August 21, 2007 in Partial Fulfillment of the Requirements for theDegree of Doctor of Philosophy in Mechanical Engineering

AbstractInternal combustion engines dominate transportation of people and goods, contributingsignificantly to air pollution, and requiring large amounts of fossil fuels. With increasingpublic concern about the environment and the reliability of oil supplies, automotivecompanies are pushed to improve engine design in order to reduce engine emissions andfuel consumption.This project aims to develop a numerical model of piston dynamics and lubrication ininternal combustion engines, enabling prediction of friction generation at the piston -cylinder bore interface, and oil transport in the power cylinder system. It is currentlyestimated that the piston - cylinder bore friction accounts for up to 25% of the power lossin a typical engine, while oil transported to the combustion chamber by the piston andring-pack contributes significantly to engine emissions.A dry piston model was first developed to allow fast calculation of approximate pistondynamics. An elastohydrodynamic lubrication model was then developed to allow directnumerical simulation of the effect of piston tooling marks, and comparison with resultsobtained using an Average Reynolds equation with flow factors. The lubrication modelwas incorporated into the piston dynamics model, enabling more accurate evaluation offriction and oil transport. Comparison between the dry and lubricated model resultsdemonstrate the effect of oil film thickness on piston lateral motion, tilt, frictiongeneration and oil transport.Thesis Supervisors:Tian TianPrincipal Research Scientist, Department of Mechanical EngineeringJohn B. HeywoodSun Jae Professor of Mechanical Engineering

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Acknowledgements

There are many people who I would like to thank for their contributions to this research,and to my time at MIT. In particular I would like to thank my supervisors, Dr. Tian Tianand Prof. John Heywood, for their support and guidance throughout my PhD. Theirdepth of knowledge and experience has significantly contributed to this research and tomy learning experience at MIT. I would also like to thank the members of my thesiscommittee, Prof. Rohan Abeyaratne and Prof. Gareth McKinley for their encouragement,constructive advice, and interest in our research.I would like to take this opportunity to thank our research sponsors, Mahle GmBh, ABVolvo, Peugeot PSA, Renault SA, and Dana Corporation for their financial support, andmore specifically, their representatives, Rolf-Gerhard Fiedler, Eduardo Tomanik, BengtOlson, Fredrick Stromstedt, Sebastien Messe, Gabriel Cavallaro, Randy Lunsford andRemi Rabute for their continued encouragement over the years, and for sharing theirextensive experience with me. Our regular meetings provided not only a motivation forcompleting work, but also an invaluable opportunity to share knowledge and obtainconstructive feedback. Without their help and guidance this research would not bepossible.I would also like to thank the members of the Sloan Automotive Laboratory for theirsupport and friendship. In particular I would like to thank Liang Liu and Yong Li fortheir repeated help and guidance with my work, and the significant contributions theyhave made to this research, and the other students of the Lubrication Consortium, StevePreszmitzki, Eric Senzer and Haijie Chen, for making the stressful times more fun. Iwould also like to thank Nancy Cook and Janet Maslow, not only for the great job theydo as administrators, but also for providing a kind and supportive ear whenever it wasneeded, and for the many laughs we have had.Finally, I would like to thank my friends and family for their love and support, which hasprovided me with so much comfort and strength.

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Table of Contents

Ab tract ................................................................................... ......................... 3Acknowledgements ................................................................................................. 5Lst o F gures .......................................................................................................... 11List of Tables ............................................................................................................ 17Chapter 1. Introduction ................................................................................ 19

1.1. Project Motivation ...................................................................................... 191.2. Introduction to Power Cylinder System ............................................................ 201.2.1. R ing Pack ................................................................. ........................... 211.2.2. Piston....... ............................................................................................... 221.2.3. W rist-Pin ................................................................ ............................. 231.2.4. Connecting-Rod .............................................................................. 241.2.5. Crankshaft ................................................................................................. 241.2.6. Cylinder B ore............................................................................................ 25

1.3. Previous Research ....................................................................................... 251.4. Project Objectives ............................................................................................ 26

Chapter 2. System Dynamics and Dry Piston Model ..................... 292.1. System Definition, Solution Outline and Nomenclature .................................. 292.2. Component Dynamics and Equations of Motion................................. 322.2.1. Crankshaft Dynamics............................................... 332.2.2. Connecting-Rod Dynamics and Equations of Motion .............................. 332.2.3. Wrist-Pin Dynamics and Equations of Motion ......................................... 352.2.4. Piston Dynamics and Equations of Motion .............................................. 362.3. Component Interface Models............................................................................ 382.3.1. Crankshaft - Connecting-Rod Interface: ....................................... 382.3.2. Connecting-Rod - Wrist-Pin and W rist-Pin - Piston Interfaces: ............. 382.3.3. Piston - Cylinder Bore Interface: ...................................... ........ 402.3.3.1 Contact Model:................................................. 422.3.3.2 Contact Friction Model: ........................................ ............ 442.3.3.3 Fluid Model:.................................................... 442.3.3.4 Compliance Matrix: ..................................... .... ............... 442.4. Externally Applied Forces and Inertia Terms................................ ..... 452.4.1. Combustion Chamber Pressure Force:................................. ....... 452.4.2. Gravity Force: ........................................................................................... 462.4.3. Inertia Term s: ............................................................ .......................... 462.5. Numerical Solution Method for Component Dynamics ................................ 47

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2.5.1. Globally Convergent Newton's Method ........................................ 472.5.2. Calculation of the Function Vector, FVEC................................. . 512.6. Numerical Solution Method for Dry Piston - Cylinder Bore Interface ............ 56Chapter 3. User Specification of System ...................................... 593.1. General Specifications ........................................................................... 593.2. Pressure Curve ................................................................ ............................ 603.3. Piston Geom etry Specification ......................................................................... 613.3.1. Cold Shape Specification ......................................... ............. 623.3.1.1 Nominal Radius ......................................................................... 623.3.1.2 Cold Shape Profile ................................................................................ 623.3.1.3 Ovality............................................ ................................................. 633.3.2. Radial Thermal Deformation ........................................ ..........643.3.3. Resulting Hot Shape Profile...................................................................... 653.4. Piston Structural Specifications ......................................... ............ 67

3.4.1. Piston Finite Element Model ........................................ ........... 673.4.2. Pressure Deformation............................................ 693.4.3. Inertia Deformation.............................................. 693.4.4. Compliance Matrix ......................................................................... 723.4.4.1 Generation of symmetric compliance matrix............................... 723.4.4.1 Generation of asymmetric compliance matrix ................................... 733.4.4.2 Typical compliance matrix features...................................................... 743.5. Cylinder Bore Specification........................................... 773.5.1. Cold Shape Specification .......................................................................... 783.5.2. Radial Thermal Deformation ........................................ .......... 80Chapter 4. Dry Model Results ..................................... ......... 81

4.1. Equations of Motion ......................................................................................... 824.1.1. Axial Force Balance on Piston................................... ............ 824.1.2. Axial Force Balance on Wrist-Pin ...................................... ....... 844.1.3. Moment Balance on Connecting-Rod.......................... ........... 854.1.4. Lateral Force Balance on Wrist-Pin............................ .. .......... 904.1.5. Moment Balance on Wrist-Pin...................................................... 914.1.6. Lateral Force Balance on Piston ...................................... ........ 944.1.7. Moment Balance on Piston ..................................... ... ............ 994.2. Piston and Wrist-Pin Motion ..................................... 1034.2.1. Lateral Motion ..................................... 1034.2.2. T lt.......................................................................................................... 1064.2.3. Piston Secondary Motion ..................................... 1084.3. Other Degrees of Freedom ............................... 1154.3.1. Motion along pin axis ................................................. ...................... 1154.3.2. Rotation about cylinder axis ..................................... 1164.3.3. Rotation about thrust axis ..................................... 1174.4. Effect of Parameter Uncertainties on Piston Dynamics.................................. 1174.4.1. Piston - Cylinder Bore Friction Coefficient ........................................ 1184.4.2. Wrist-Pin Bearing Friction Coefficient.......................... 120

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4.4.3. Piston Geometry................................. 1224.4.4 . Bore Geometry................................. 1264.5. Interesting Parameters............................... 13 14.5.1. Speed.................................... 13 14.5.2. Connecting-Rod Moment of Inertia, Mass and Centre of Gravity ......... 13 24.6. Effect of Operating Conditions on Piston Dynamics ................................ 13 3

4.7. Comparison with Experimental Results.............................. 13 44.8. Conclusions Based on Dry Model Analysis ..................................... 13 8Chapter 5. Lubrication Flow and Oil Transport Models ............. 143

5.1. Introduction to Lubricated Piston - Cylinder Bore Interface ...................... 1435.2. Governing Equations for Piston - Cylinder Bore Interface ............................ 1465.2.1. Lubrication Flow and Reynolds Equation .................... .................... 1465.2.2. Partial Film Phenomena............................... 1485.2.3. Universal Reynolds Equation ................................................................. 1495.2.4. Flow Factor Methods ..................................... 15 15.2.5. Combining the Piston - Cylinder Bore Interface Sub-Models .............. 15 2

5.3. Quasi-Steady Hydrodynamic Lubrication Model ........................................... 15 45.3.1. Numerical Solution Scheme ..................................... 1555.3.2. Quasi-Steady Sliding Results.............................. 15 75.3.2.1. Quasi-Steady Sliding of a Typical Piston Profile ........................... 15 75.3.2.2. Investigation of the Effect of Tooling Marks During Sliding......... 1625.3.2.3. Quasi-Steady Hydrodynamic Lubrication Flow Conclusions ........ 1685.4. Unsteady Hydrodynamic Lubrication Model ................................................. 1695.4.1. Numerical Solution Scheme ..................................... 1695.5. Elastohydrodynamic Lubrication Model ........................................................ 1705.5.1. Numerical Solution Scheme ..................................... 1715.6. Piston Oil Transport Model ..................................... 173

Chapter 6. Lubricated Piston Model Results ....................................... 1756.1. Expected Piston Secondary Motion ................................................................ 1756.2. Comparison of lubricated and dry model behaviour ................................. 1766.3. Piston Surface Representations.......................... 1836.3.1 Effect of Grid Size on Piston Dynamics and Friction.......................... 1866.3.2 Effect of Surface Representation on Piston Dynamics and Friction....... 1906.4. Piston Oil Transport Model Results.............................. 1926.5. Conclusions Based on Lubricated Model Results ..................................... 197

Chapter 7. Conclusions and Future Research ........... ..... 1997.1. Model Development.............................. 1997.2. Piston Dynamics ....................................... 2007.3. Friction Generation ..................................... 2017.4. Possible Areas for Future Research ..................................... 202Appendix 1. Derivation of Governing Equations ........................... 203Al.1. Review of Rigid Body Motion............................... 203

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Al.1.1. Conservation of Linear Momentum: ..................................... 203A1.1.2. Definition of Angular Momentum: ...................................................... 205A1.1.3. Conservation of Angular Momentum: .................................................... 206A1.2. Component Dynamics and Equations of Motion................. ................. 208A1.2.1. Crankshaft Dynamics ................................ 208A1.2.2. Connecting-Rod Dynamics and Equations of Motion ......................... 208Al.2.3. Wrist-Pin Dynamics and Equations of Motion ....................................... 213A1.2.4. Piston Dynamics and Equations of Motion ............................................ 215

Al.3. Contact Model: Blunt Wedge Against a Flat Plane ................................... 217Appendix 2. Fluid Model Equations and Results .............................. 221A2.1. Derivation of Lubrication Flow Equations ................................................. 221

A2.1.1. Mass Conservation ..................................... 221A2.1.2. Momentum Conservation ............................ 222A2.1.3. Lubrication Flow Approximation ........................................................... 223A2.2. Quasi-Steady Hydrodynamic Lubrication Model Results: ...................... 224A2.2.1. Plane Poiseuille Flow: ................................ 225A2.2.2. Plane Couette Flow ..................................... 229A2.2.3. Squeeze Flow : ........................................................................................ 234

B b liog raphy ............................................................................................................ 239

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List of Figures

Figure 1.1: Power Cylinder System ...................................................................... 21Figure 1.2: Piston profile ................................................................................................. 23Figure 1.3: Piston ovality.......................................... ................................................. 24Figure 2.1: Power Cylinder System ...................................................................... 29Figure 2.2: Crankshaft Dynamics .................................................................................... 33Figure 2.3: Connecting Rod Geometry and Dynamics .................................................... 34Figure 2.4: Wrist-Pin Dynamics ...................................................................................... 36Figure 2.5: Piston Geometry and Dynamics .................................................................... 37Figure 2.6: Bearing Forces Acting on Component 1 ...................................................... 39Figure 2.7: Direction of Bearing Forces .......................................................................... 39Figure 2.8: Diagram of Piston - Cylinder Bore Interface.......................................... 41Figure 2.9: Contact Model Representations...................................... 42Figure 2.10: Combustion Pressure Force and Moment ........................................ 45Figure 2.11: Globally Convergent Newton's Method ..................................................... 52Figure 2.12: Definition of Overlap, Radial Deformation and Rigid Radial Gap............. 57Figure 3.1: Combustion chamber pressure ...................................................................... 60Figure 3.2: Cold shape skirt profile, ovality and thermal deformation......................... 61Figure 3.3: Cold Shape Profile ................................................................................... 62Figure 3.4: Ovality Profile ............................................................................................... 63Figure 3.5: Piston temperature and thermal deformation profiles ................................ 64Figure 3.6: Piston Hot Shape Geometry .......................................................................... 65Figure 3.7: Piston Hot Shape Geometry - Adjusted ........................................................ 66Figure 3.8: Piston Hot Shape Profiles.............................................................................. 66Figure 3.9: FEA Piston Nodes ................................................................................... 68Figure 3.10: Subset of Piston Nodes Covering the Skirt and Lands ................................ 68Figure 3.11: Pressure Deformation Vector Plot ............................................................... 70Figure 3.12: Pressure Deformation, Radial Component Data ......................................... 70Figure 3.13: Axial Inertia Deformation Vector Plot ........................................................ 71Figure 3.14: Axial Inertia Deformation, Radial Component Data................................... 71Figure 3.15: Generation of Symmetric Compliance Matrix ............................................ 72Figure 3.16: Generation of Asymmetric Compliance Matrix ........................................... 74Figure 3.17: Compliance Matrix............................................................................ 75Figure 3.18: Diagonal of Compliance Matrix.................................................................. 76Figure 3.19: Row/Column Due to Load at Soft Centre of Skirt ................................... 76Figure 3.20: Row/Column Due to Load at Hard Top of Skirt ..................................... 77Figure 3.21: Bore Distortion Curves.................................................................... 79Figure 3.22: Bore Distortion Data ......................................................................... 79Figure 3.23: Cylinder Bore Temperature Distribution and Thermal Deformation.......... 80Figure 4.1: Baseline Piston and Bore Profiles ....................................... .........82Figure 4.2: Axial Force Balance on Piston .......................................................... 83Figure 4.3: Axial Force Balance on Wrist-Pin............................ ... ............. 84

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Figure 4.4: Moment Balance on Connecting-Rod ...................................... ....... 86Figure 4.5: Moments Acting on Connecting-Rod............................................................ 87Figure 4.6: Driving and Reacting Connecting-Rod Moments ..................................... 87Figure 4.7: Wrist-Pin - Connecting-Rod Force, Angle of Action ............................... 88Figure 4.8: Forces Relative to Connecting-Rod Axis ...................................................... 89Figure 4.9: Forces Transmitted to Crankshaft ...................................... ......... 89Figure 4.10: Lateral Force Balance on Wrist-Pin ..................................... ....... 90Figure 4.11: Effect of Component Inertias .......................................................... 91Figure 4.12: Moment Balance on Wrist-Pin ....................................... .......... 92Figure 4.13: Wrist-Pin Angular Moments and Velocity.................................................. 93Figure 4.14: Component Angular Motions ........................................ ........... 94Figure 4.15: Lateral Force Balance on Piston............................................................ 95Figure 4.16: Piston Forces - Lateral Direction ................................................................ 96Figure 4.17: Piston Side Force......................................................................................... 96Figure 4.18: Piston Slap Timing ........................................................................... 97Figure 4.19: M oments Acting on Piston ........................................................................ 100Figure 4.20: M oments Acting on Piston ........................................................................ 101Figure 4.21: Piston Moments Close to Combustion TDC ................... ..................... 101Figure 4.22: Moments Acting on Piston During Intake and Exhaust Strokes ............... 102Figure 4.23: Piston - Cylinder Bore Moments ..................................... 102Figure 4.24: Timing of Piston Lateral Motion.............................. 104Figure 4.25: Piston Lateral Motion.................................... 104Figure 4.26: Piston Lateral Motion.................................... 105Figure 4.27: Piston Tilt ........................................ 107Figure 4.28: Stable Piston Tilt ....................................................................................... 108Figure 4.29: Piston Secondary Motion 0-1 1CA ........................................................... 109Figure 4.30: Piston Secondary Motion 24-67 0 CA......................................................... 109Figure 4.31: Piston Secondary Motion 70-83 0 CA ..................................... 110Figure 4.32: Piston Secondary Motion 99-123CA ..................................... 110Figure 4.33: Piston Secondary Motion 180-2420 CA ..................................................... 11Figure 4.34: Piston Secondary Motion 249-305 0 CA ..................................................... 111Figure 4.35: Piston Secondary Motion 326-356 0 CA..................................................... 112Figure 4.36: Piston Secondary Motion 362-3700CA........................ 113Figure 4.37: Piston Secondary Motion 376-445 0CA........................ 11 4Figure 4.38: Piston Secondary Motion 461-543 0 CA ....................... 114Figure 4.39: Net Force Along the Pin Axis ..................................... 116Figure 4.40: Net Moment About the Cylinder Axis .................................... 116Figure 4.41: Net Moment About the Thrust Axis................................ 117Figure 4.42: Effect of Piston Friction Coefficient on Lateral Motion ........................ 118Figure 4.43: Effect of Piston Friction Coefficient on Piston Tilt ............................... 119Figure 4.44: Effect of Piston Friction Coefficient with an Interference Fit............... 119Figure 4.45: Effect of Piston Friction Coefficient on Piston Tilt ............................... 119Figure 4.46: Effect of Friction Coefficient on Cylinder Bore - Piston Moments ......... 120Figure 4.47: Effect of Wrist-Pin Friction on Component Angular Motion ................ 12 1Figure 4.48: Effect of Wrist-Pin Friction on Force Generation and Lateral Motion..... 121Figure 4.49: Effect of Difference Between Wrist-Pin Bearing Friction Coefficients ... 122

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Figure 4.50: Simple Piston Profiles .................................... ...................Figure 4.51: Effect of Piston Profile on Piston Secondary Motion ............................Figure 4.52: Piston Hot Shape Profiles..............................................Figure 4.53: Effect of Piston Profile on Lateral Motion ...........................................Figure 4.54: Effect of Piston Hot Shape on Piston tilt....................................................Figure 4.55: Simple Bore G eometries ...........................................................................Figure 4.56: Effect of Simple Bore Geometry on Piston Motion ..................................Figure 4.57: Realistic Bore Geometries.............................................Figure 4.58: Effect of Simple and Realistic Bore Geometries on Piston Motion..........Figure 4.59: Bore Geometry as a Function of Load ......................................................Figure 4.60: Effect of Load Related Bore Variation on Piston Dynamics ....................Figure 4.61: Effect of Speed on Axial Piston Forces......................................................Figure 4.62: Effect of Speed on Piston Dynamics .........................................................Figure 4.63: Effect of Connecting-Rod Moment of Inertia on CR Moments ................Figure 4.64: Effect of Connecting-Rod Moment of Inertia on Piston Motion ..............Figure 4.65: Effect of Speed and Load on Lateral Motion ............................................Figure 4.66: Effect of Speed and Load on Piston Tilt ...................................................Figure 5.1: Diagram of Piston - Cylinder Bore Interface...............................................Figure 5.2: Diagram of Piston - Cylinder Bore Interface Lubrication Flow.............Figure 5.3: Fixed Control Volum e .................................................................................Figure 5.4: Cavitation, Fluid Separation and Inlet Oil Starvation .................................Figure 5.5: Partial Film Representation .........................................................................Figure 5.6: Comparison of Rough and Smooth Surface Flow Rates ...........................Figure 5.7: Solution Procedure for Piston - Cylinder Bore Interface.........................Figure 5.8: Quasi-Steady Hydrodynamic Lubrication....................... ..............Figure 5.9: Quasi-Steady Hydrodynamic Lubrication Solution Algorithm ..................Figure 5.10: Quasi-Steady Sliding of a Typical Piston Profile.................................Figure 5.11: Effect of Grid Size on Normal and Friction Force Generation .................Figure 5.12: Effect of Gap Height on Pressure and Friction Generation...................Figure 5.13: Effect of Gap Height on Oil Film Thickness .........................................Figure 5.14: Effect of Dynamic Viscosity on Lubrication Flow ................................Figure 5.15: Effect of Speed on Lubrication Flow ...............................................Figure 5.16: Tooling Marks - 2D Surface Position, Relative to Flat Sliding Surface...Figure 5.17: Pressure Distribution for 2D Sliding .........................................................Figure 5.18: Cavitation Region for 2D Sliding ..............................................................Figure 5.19: Centreline Pressure Distribution for 3D Sliding .......................................Figure 5.20: Pressure Distribution for 3D Sliding .........................................................Figure 5.21: Centreline Axial Flow Rates .....................................................................Figure 5.22: Onset of Contact ........................................................................................Figure 5.23: Wave-averaged pressure distribution ...............................................Figure 5.24: Centreline average pressure distributions....................... .............Figure 5.25: Average pressure distributions ..................................... ...............Figure 5.26: Normal Force.......................................................Figure 5.27: Side Flow Rate ..........................................................Figure 5.28: Unsteady Hydrodynamic Lubrication ..................................... ........Figure 5.29: Numerical Algorithm for Elastohydrodynamic Lubrication ...................

12312312512512612712712812913 013 013 113 213 213 313 513 614414414714814915 115415 415 615 715 815 915 9160161162163163164164164165165166166167167169172

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Figure 5.30: Oil Transport Model .................................. 174Figure 6.1: Dry Model - Piston Lateral Motion ............................................................ 175Figure 6.2: Bore and Piston Geometry .......................................................................... 177Figure 6.3: Effect of OFT on Lateral Position .................................... 178Figure 6.4: Effect of OFT on Piston Tilt........................................................................ 179Figure 6.5: Effect of OFT on Driving Forces .................................... 179Figure 6.6: Effect of OFT on Component Positions ..................................... 18 0Figure 6.7: Effect of OFT on Piston - Cylinder Bore Interface Forces..................... 181Figure 6.8: Effect of OFT on Piston - Cylinder Bore Interface Moments and Tilt....... 18 1Figure 6.9: Effect of OFT on Piston - Cylinder Bore Interface Friction Coefficient.... 182Figure 6.10: Combined Piston - Cylinder Bore Interface Friction Coefficient ............. 18 2Figure 6.11: Piston Surface Representations ................................................................. 183Figure 6.12: Discretization Error in Gap Height ........................................................... 184Figure 6.13: Effect of Grid Size on Piston Dynamics - Mean Surface Line ................. 18 6Figure 6.14: Effect of Grid Size on Piston Dynamics - Outer Surface Line........... 187Figure 6.15: Effect of Grid Size on Piston Dynamics - Flow Factor Method........... 187Figure 6.16: Effect of Grid Size on Friction Generation - Mean Surface Line ............ 188Figure 6.17: Effect of Grid Size on Friction Generation - Outer Surface Line ............. 189Figure 6.18: Effect of Grid Size on Friction Generation - Outer Surface Line....... 18 9Figure 6.19: Effect of Surface Representations on Piston Dynamics........................ 190Figure 6.20: Effect of Surface Representation on Friction Generation ......................... 191Figure 6.21: Oil Transport Model .................................. 192Figure 6.22: Oil Film Distribution - 50 pm Inlet OFT .................................................. 194Figure 6.23: Changes to Oil Film Distribution .............................................................. 195Figure 6.24: Effect of Oil Transport Model on Piston Dynamics............................ 196Figure 6.25: Comparison of Oil Transport Model Results with Dry Model ................. 196Figure 6.26: Effect of Oil Transport Model on Friction ................................................ 19 7Figure 6.27: Comparison of Oil Transport Model and Dry Model Friction Forces ...... 197Figure Al.1: Particle Dynamics ................................ 203Figure A1.2: Rigid Body Dynamics .............................................................................. 204Figure A1.3: Angular Momentum about the Centre of Gravity ................................. 205Figure A1.4: Angular Momentum about an Arbitrary Point, Q ................................. 206Figure A 1.5: Crankshaft Dynam ics ............................................................................... 209Figure A1.6: Connecting Rod Geometry and Dynamics .................... .................... 209Figure A1.7: Connecting Rod Force and Moment Balance............................. 212Figure A1.8: Piston Pin Dynamics ................................ 213Figure A 1.9: Piston Geometry and Dynamics ..................................... 215Figure Al.10: Blunt Wedge Against a Flat Plane............................... 217Figure A2.1: Lubrication Flow ..................................... 224Figure A2.2: Plane Poiseuille Flow ..................................... 225Figure A2.3: Plane Poiseuille Flow - Centreline Results............................. 226Figure A2.4: Plane Poiseuille Flow - Normal Force............................... 227Figure A2.5: Plane Poiseuille Flow - Friction Force .................................... 228Figure A2.6: Plane Poiseuille Flow - Flow Rate................................ 228Figure A2.7: Plane Poiseuille Flow - Negative Pressure Gradients.......................... 229Figure A2.8: Plane Couette Flow .................................. 230

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Figure A2.9: Plane Couette Flow - Centreline Results ..................................... 231Figure A2.10: Plane Couette Flow - Normal Force ..................................... 232Figure A2.11: Plane Couette Flow - Friction Force ...................................................... 232Figure A2.12: Plane Couette Flow - Flow Rate ..................................... 233Figure A2.13: Plane Couette Flow - Negative Sliding Velocities .............................. 233Figure A 2.14: Squeeze Flow .......................................................................................... 234Figure A2.15: Squeeze Flow - Centreline Results ........................................................ 235Figure A2.16: Squeeze Flow - Normal Force ............................................................... 236Figure A2.17: Squeeze Flow - Friction Force............................... 236Figure A2.18: Squeeze Flow - Flow Rates ................................................................... 237

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List of Tables

Table 2.1: Nomenclature Guidelines .................................................................... 32Table 4.1: Baseline Model Parameters .......................................... ............................... 81Table 4.2: Axial Piston Forces...................................... ............................................. 83Table 4.3: Axial W rist-Pin Forces ......................................................................... 85Table 4.4: Connecting-Rod Moments..................................................................... 88Table 4.5: Connecting-Rod Forces ....................................................................... 90Table 4.6: Lateral Wrist-Pin Forces.............................................................................. 91Table 4.7: Wrist-Pin Moments......................................................94Table 4.8: Lateral Piston Forces ........................................................................... 98Table 4.9: Piston Moments ....................................... 100Table 5.1: Nomenclature............................. 146Table 5.2: Comparison of Solution Methods.............................. 167Table 6.1: Piston Surface Representations.......................... 185

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1. Introduction

1.1. Project MotivationInternal combustion engines dominate transportation of people and goods, contributingsignificantly to air pollution, and requiring large amounts of fossil fuels. As concern forthe environment, and the effects of global warning, increase, governments continue tointroduce more stringent emissions criteria. Additionally, increasing political concernregarding dependence on foreign oil and political instability in the middle east, andcorresponding increases in fuel prices, push for increased mileage per gallon. These twoconcerns, in parallel, are motivating automotive companies to improve engine design inorder to reduce engine emissions and fuel consumption, while maintaining at least thecurrent standards of noise, performance and maintenance requirements. An improvedunderstanding of interactions within the engine is therefore required.It is useful to separate engine emissions into emissions due to fuel and those due to oilconsumption. Fuel consumption and engine emissions due to fuel can be reducedthrough improvements in combustion, fuel delivery and friction reduction. Currentengine designs tend to have overall efficiencies of 38-41%, with 4-15% of the energybeing lost to mechanical friction. It is estimated that 40-55% of the friction losses aredue to the power cylinder system, made up of the piston (25-47%), ring-pack (28-45%)and connecting-rod bearings (18-33%) [1]. Friction generated in the power cylindersystem therefore represents a significant proportion of the energy loss in the engine, and acorresponding opportunity for improvement in engine efficiency.In order to better understand friction generation on the piston, we first must accuratelymodel piston dynamics, which also significantly impact ring pack dynamics and frictiongenerated within the ring pack. The piston dynamics are predominantly driven by thepressure load and connecting-rod angle, and constrained by the piston's interaction withthe cylinder bore. Ideally, the piston has only one degree of freedom, allowing areciprocating motion along the cylinder axis, which is commonly referred to as itsprimary motion. More realistically, the piston has six degrees of freedom, with the rangeof allowable motion in each direction varying significantly. The secondary motion of thepiston is made up of translation perpendicular to the cylinder and piston pin axes, androtation about the piston pin axis. This motion allows the piston to collide with thecylinder bore, a phenomenon referred to as piston slap. In a typical car engine thedisplacements in the axial direction are of the order of 100 mm, while the displacementsinvolved in the secondary motion of the piston are of the order of 100 pm [2-4], and thepiston tilts are of the order of 0.001 rad [3]. The piston's motion due to the remainingthree degrees of freedom is currently believed to be significantly smaller than both itsprimary and secondary motions and is neglected for the purposes of this project.

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Piston slap is initiated when the connecting-rod side force changes direction either due tochanges in the connecting-rod angle, or the connecting-rod force (from compression totension or vice versa). The piston's impact against the cylinder bore is a significantsource of noise, vibration and energy loss, and can lead to cavitation wear on the coolingside of the liner, while its motion along the cylinder bore generates friction and transportsoil, thereby affecting wear of the piston, rings and liner, and contributing to oilconsumption.Piston skirt lubrication is provided by lubrication oil, which is, in general, picked up fromthe oil sump and thrown onto the cylinder bore by the motion of the crankshaft. In someengines, lubrication oil is also sprayed onto the underside of the piston or other locationswithin the power cylinder system. The lubrication oil is then transported along thecylinder bore by the motion of the piston and piston rings, and by gravity. Lubrication oilis also transported around the system when it is entrained in blow-by gases. Thelubrication oil leaves the cylinder bore in three ways: oil returns to the sump; oilentrained in the blow-by gas leaves the system via the crank case; or oil is consumed inthe combustion chamber. The last two options create a significant source of engineemissions due to oil consumption.Due to the complex nature of oil transport within this system, and the inaccessibility forexperimental observation, it is often impossible to accurately predict the location andthickness of oil films within the system. Previous research, both experimental andcomputational, indicates average oil film thicknesses in the range 1-100 m [2, 4-8].Depending on the amount of oil present, the side load and the sliding speed, regions ofboundary, mixed and elastohydrodynamic lubrication may all be present simultaneouslyon the piston skirt throughout the cycle. On the lower end, oil film thicknesses of around1gtm, which is significantly smaller than typically piston tooling mark wave heights, willresult in boundary lubrication with significant solid-solid contact and friction generation.Significantly thicker oil film thicknesses, such as 100 gim may be sufficient to support theside load via elastohydrodynamic lubrication, eliminating solid-solid con tact and wear.A detailed model of the piston - cylinder bore interface and oil film distribution isrequired for estimating lubrication conditions, friction generation and oil transport on thepiston.

1.2. Introduction to Power Cylinder SystemThe Power Cylinder System can be considered to be made up of 6 components, each witha separate role:1. Ring Pack2. Piston3. Wrist-Pin

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Connecting-RodCrankshaftCylinder Bore

Cylinde

1. Ring pack -

Thrust .

Figu

Cylinder borePistonWrist-pin

,ntrelineshaft

)tation

ire 1.1: Power Cylinder SystemThe chemical energy in the fuel is converted to kinetic energy during combustion andtransmitted from the combustion chamber, through the piston, pin and connecting-rod tothe crankshaft. The geometric arrangement of the power cylinder system allows thelinear motion of the piston to be converted into the rotational motion of the crankshaft.The angle of the connecting-rod causes lateral motion of the piston, and interaction withthe bore, combined with the lateral motion and friction at the wrist-pin bearing tends tocauses piston tilt.

1.2.1. Ring PackThe Ring Pack plays two roles within the power cylinder system:1. Seals the gases in the combustion chamber, both during compression andcombustion, minimizing energy losses and emissions due to blow-by.2. Transport oil along the cylinder bore, balancing conflicting criteria ofproviding oil to reduce friction, while reducing oil consumption.

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A typical ring pack is made up of two or three rings, with the top one or two ringsfocusing on sealing the combustion chamber, and the lower ring acting as an oil controlring. Significant research has been completed in the areas of ring pack dynamics, frictiongeneration and oil transport [5,6]. In terms of interactions between the piston and ringpack:* The piston dynamics significant impact the ring pack, and an accurate model ofpiston motion is required as an input for ring pack analysis.* Normal and friction forces generated between the piston and rings, whilesignificant for the purposes of determining ring motion, are not significant indetermining piston dynamics. The ring pack is therefore neglected for thepurposes of this project.

1.2.2. PistonThe main role of the piston is to transmit the pressure force generated during combustionthrough the pin and connecting-rod to the crankshaft, thereby converting the energy ofthe expanding gases to the essentially linear kinetic energy of the piston, and finally tothe rotational kinetic energy of the crankshaft. While ideally the piston travels in theaxial direction only, in reality the connecting-rod angle results in significant side forcesbeing transmitted through the piston, causing lateral motion. The resulting motion, oftenreferred to as piston slap, occurs:* when the connecting-rod angle changes sign, which is determined by engine

geometry, and for an engine design with no crankshaft offset occurs at 0, 180,360 and 540 *CA, and* when the connecting-rod force changes sign, that is, from compression to tension,or vice versa, which is essentially a function of the pressure trace and componentaxial inertias, and typically occurs during the intake and exhaust strokes aroundmid-stroke.

In general, the outer surface of a piston is specified by a nominal radius, cold profile andovality. There is also significant design of the internal structure of the piston, therebyinfluencing the:* mass and weight distribution,* heat transfer, and therefore temperature distribution and thermal expansion, and* structural response to pressure, inertia and skirt loadsDesign criteria for a piston are often conflicting in nature:1. Piston - Bore Clearance: In order to minimize frictional losses, a smallerpiston diameter is desired, allowing increased clearance between the pistonand bore, while in order to reduce noise and impact losses, a large pistondiameter is desired, with decreased clearances reducing lateral movement.2. Piston structural stiffness: The piston must be structurally strong enough towithstand the large forces transmitted both axially and laterally, requiringstiffness around the pin bore where forces are transmitted to the wrist-pin, and

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sufficient stiffness in the skirt, while a flexible skirt is more desirable for noisereduction and minimizing local contact pressures. Similarly there is anoptimal flexibility for the skirt in terms of friction reduction.3. Piston Mass: Decreased piston mass reduces the loss of energy to pistoninertia, but sufficient mass must be provided for the required structuralstiffness.4. Piston profile: Significantly affects pressure generation, oil transport andfriction generation at the piston-cylinder interface. As the piston slides axiallyalong the liner, pressure tends to be generated by the converging gap at theleading edge of the piston which also acts to scrape oil along the cylinderbore, thereby altering the oil film thickness.

Pidtnn .nlrI hana Prnfiln0.14Cylinderaxis m)0.120.1

0.080.060.040.02

n

Thrust axis lpm)Figure 1.2: Piston profile

5. Piston ovality: With increased ovality the pressure generated at the piston-cylinder bore interface is centralized, thereby supporting the side load moreefficiently, and the portion of the skirt that is fully flooded is reduced, therebydecreasing hydrodynamic friction, but also decreasing pressure generation fora given surface separation. Increased beyond an optimal value, the ovalitywill result in solid-solid contact due to decreased surface separation, and asignificant rise in contact friction.

1.2.3. Wrist-PinThe wrist-pin transmits forces between the piston and connecting-rod while allowing thepiston and connecting-rod to rotate relatively independently of each other. At high loads,however, particularly around combustion TDC, significant torque is transmitted from theconnecting-rod to the piston, even for small friction coefficients, thereby influencing thepiston tilt. At these high loads, it is expected that there will be significant bending of thepin, but for the purposes of this work the pin is assumed to be rigid.

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Cylinderaxis (m)

Ovality Lrm)Figure 1.3: Piston ovality

1.2.4. Connecting-RodThe connecting-rod transmits force from the wrist-pin to the crankshaft. The loadstransmitted by the crankshaft are typically of the order of 100 kN, generating moments of5 kNm. The small end of the connecting-rod connects to the wrist-pin, carrying out axialmotion equal to twice the crankshaft radius (- 100 mm), and lateral motion of the orderof 100 jm. The large end of the connecting-rod connects to the crankshaft and rotates ina circular motion at the crankshaft radius. The longer the connecting-rod, the smaller theconnecting-rod angle and the corresponding side force and bending moments, but the lesscompact the engine design, and the larger the connecting-rod mass and resulting energyloss due to component inertia. The connecting-rod must be sufficiently strong to transmitthese loads without significant bending, and is assumed to be rigid for the purposes ofthis model.

1.2.5. CrankshaftThe crankshaft helps to convert the piston motion into a continuous rotation of the drivetrain and wheels with its large rotational inertia and rigid structure smoothing out thecombustion pressure impulses. The connecting-rod - crankshaft joint represents the endof the power cylinder system for the purposes of this project. It is assumed that theconnecting-rod - crankshaft bearing can be modeled as a frictionless pin joint, and thatthe crankshaft's motion is purely rotational.

i& /'.i4,

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1.2.6. Cylinder BoreThe cylinder bore acts to create the combustion chamber, and constrain piston motion.There are many different engine block designs including cylinder liners, coolantpassages, bolt configurations, reinforcements etc. which significantly affect the heattransfer, temperature and thermal deformation distributions, mechanical deformations,and structural stiffness. There are also a wide range of surface finishing methods whichimpact the surface roughness and bore distortion.For the purposes of this project, we are solely interested in the geometry of the internalsurface of the cylinder, which is typically provided by a nominal radius, cold boredistortion and thermal deformation profiles. The deformation of he cylinder bore, due tointeractions with the piston are neglected, as is the effect of the axial temperaturedistribution on oil viscosity.

1.3. Previous ResearchA significant amount of research into piston motion has been carried out over the pastfour decades, initially focusing on investigating piston slap as a significant source ofengine noise and then gradually developing to predicting piston secondary motion,friction generation and oil transport. There is still much to be learnt about this systemthough, and while simulation programs already exist, reports from industry suggest thatthere con tinue to be problems of instability, long running times, and inflexibility, andtherefore that they do not currently meet the needs of industrial research facilities.Early work in this area [9-13] was focused on reducing engine noise and vibration, andbegan with rigid body, frictionless models of the piston-cylinder system based onidealized joint constraints and a variety of additional simplifications. These models wereinitially used to solve for the crank angles at which the lateral force on the piston isreversed, causing piston slap to occur, and to develop an idea of which parameters werelikely to affect piston motion. They were later developed into more sophisticated modelsthat were used to investigate the effect of variations in piston-cylinder bore clearance andwrist-pin offset. Experimental results obtained by Griffiths and Skorecki [9] confirmedthat piston slap is a significant source of engine noise, particularly in the range of 2000 to4000 Hz, and were used both to confirm the trends predicted by the model simulationsand to investigate the effect of varying lubrication conditions on piston slap.In the early 1980's, focus shifted to minimizing piston assembly friction and models ofhydrodynamic lubrication based on the Reynold's equation were developed for thissystem by Knoll and Peeken [14], and then combined with a rigid body model withidealized joint constraints by Li, Rohde and Ezzat [15]. The addition of thermal and

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elastic deformations by Oh, Li and Goenka [16], thereby extending the lubrication modelto elastohydrodynamic lubrication, further improved the accuracy of these models.More recent work has increasingly focused on modeling of the oil film. The averageReynolds equation developed by Patir and Cheng [17] was used by Zhu et al [18-19] totake into account surface roughness and waviness, and models have been extended fromessentially two-dimensional kinematic models to quasi-three-dimensional models whichmake use of the two-dimensional Reynolds equation, which was applied over a variablecircumferential extent by Dursunkaya, Keribar and Ganapathy [20]. Boundary conditionsfor the oil film were initially modeled as fully-flooded and the pressure distribution wassimply restricted to being non-negative, but increasingly efforts have been made toaccurately model oil starvation [21-22], and Duyar et al [23] make use of a finite volumesolution to correctly satisfy mass and momentum conservation in the oil film.There has been a significant amount of research completed on the effect of surfaceroughness on lubrication flows, and several average flow models have been developed.The Average Reynolds equation developed by Patir and Cheng [17] was expanded byTripp [24] to include general roughness distributions, and by Harp and Salant [25] toinclude inter-asperity cavitation. Prat et al [26] and Bayada et al [27] have alsodeveloped more rigorous approaches to average flows. As a starting point, we havechosen to compare direction numerical simulation results with the baseline Patir andCheng flow factor method.

1.4. Project ObjectivesThe overall aim of this research is to develop an accurate numerical model of pistonsecondary motion, and to improve understanding of piston dynamics, skirt lubrication,friction generation and oil transport. In order to achieve this, the project was broken intoseveral objectives:* To develop a fast, quasi-dry model of piston secondary motion.* To develop an elastohydrodynamic lubrication model to investigate piston skirtlubrication.* To develop a detailed, lubricated model of piston secondary motion.* To develop a piston oil transport model.One of the major challenges of this research is to provide a practical set of piston analysistools that are sufficiently accurate and numerically robust, but also fast enough to bepractically useful. Currently available lubricated piston models can take days to run,whereas a dry model can run in a matter of minutes or hours. It is also critical that themodel is flexible, able to be applied to range of engine designs and data formats, welldocumented, and modular in design to allow for future improvements.

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The first step in this process, the development of a fast, quasi-dry model of pistonsecondary motion allowed the overall program architecture, inputs and outputs to beestablished, and an understanding of the components dynamics and force generation andtransmission to be developed. It also provides a significantly faster running analysis tool,than the lubricated model, and comparison with the lubricated model results allows anestimate of the dry model's accuracy and limitations to be established. The quasi-drymodel can be used to investigate the affect of many system parameters on componentdynamics and force generation, and to assess the degree to which current uncertainties inthe system, such as wrist-pin friction, can influence these results. The governingequations for component dynamics and force generation due to both componentinteractions and external influences are presented in Chapter 2, while the userspecifications of the power cylinder system are outlined in Chapter 3.Results of the dry model, including discussion of component dynamics, particularlypiston secondary motion, and the affect of system parameters and uncertainties arepresented in Chapter 4. Experimental results obtained and processed by our sponsors,and corresponding input files for modeling the same engine, enabled comparisons to bemade between the simulated and experimental piston dynamics, over a range of operatingconditions. These comparisons are included in Chapter 4.A set of lubrication flow models were then developed, beginning with a quasi-steadyhydrodynamic lubrication flow model, based on the Universal Reynolds equation toallow for partial film regions while maintaining conservation of oil mass. The quasi-steady lubrication model was used to investigate the effects of piston skirt tooling markson pressure and friction generation in sliding flow, as predicted by different surfacerepresentations.The unsteady term and surface deformation were added in steps, resulting in an unsteadyhydrodynamic lubrication model and finally unsteady elastohydrodynamic lubricationmodel. Each of these models provides a useful stand-alone tool for investigatingdifferent lubrication flow behaviors, independent of piston dynamics, and enabling moredetailed analysis of surface texture effects within reasonable calculation times.Numerical solution of unsteady elastohydrodynamic lubrication presents a significantchallenge due to the complicated geometries of the piston - cylinder bore interface,combined with rapidly varying side loads, including impacts and squeezing throughoutthe cycle, and the corresponding structural deformations that are the same order ofmagnitude as the nominal piston - cylinder bore clearance. This model is furthercomplicated by the lack of information regarding oil supply conditions which areexpected to vary significantly, resulting in regions of boundary, mixed andelastohydrodynamic lubrication.In parallel, a set of lubrication flow models using an Average Universal Reynoldsequation, based on the flow factor methods introduced by Patir and Cheng [17], weredeveloped in order to assess the degree to which these methods can provide a sufficientlyaccurate representation of the effect of piston skirt tooling marks. The development ofeach of the lubrication flow models and their results are presented in Chapter 5.

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Combining the unsteady elastohydrodynamic lubrication model with the dry pistondynamics model led to the creation a lubricated piston dynamics model. The addition ofoil reservoirs at the top and base of the piston skirt, and the development of simple rulesfor the filling and emptying of these reservoirs form the basis of the piston oil transportmodel, as described in Chapter 5.Results of the lubricated piston dynamics model are presented in Chapter 6. A range ofinlet oil film thickness were investigated and the effect of oil film thickness on pistondynamics and friction generation described. Different surface representations were thencompared and evaluated, demonstrating clear differences between the accuracy requiredfor prediction of piston dynamics and that required for accurate evaluation of friction.The piston skirt oil transport model was then used to investigate a range oil supplyconfigurations.The development of these models, and the preliminary analysis presented in this thesisare just the first steps in achieving a better understanding of piston motion and lubricationbehavior. It is hoped that as our knowledge of his system increases, it will be possible toimprove this complex system, leading in the longer term to reductions in engineemissions and fuel consumption.

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2. System Dynamics and Dry Piston Model

This chapter aims to:* Introduce the power cylinder system, and define its components as represented bythe model.* Provide the equations of motion governing component dynamics.* Provide the equations governing interface and external force generation.* Outline the numerical algorithm used to solve for component dynamics.* Outline the numerical algorithm used to solve for the dry piston - cylinder boreinterface force and corresponding piston deformation.

2.1. System Definition, Solution Outline and NomenclatureThe power cylinder system is made up of the crankshaft, connecting-rod, wrist-pin,piston, ring pack and cylinder bore, as shown in Figure 2.1.

Cylinder Bore Axis Op

Thrust ,

ore

Figure 2.1: Power Cylinder System

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For a given crankshaft speed and engine geometry, the ideal axial motions of theconnecting-rod, wrist-pin and piston are defined by:r/,o = [- rcs sin(OCA) + YcsoIj +rcs cos(OCA)k

rpo = [rcs cos(OA) + 1cR cos(CR)]k=cRrcsin Ycso - rcs sin(OcA)I C R CR ic

In this project we aim to solve for piston secondary motion, that is, the lateral motion (inthe y-direction) of the piston, xpy, and its rotation about the pin-bore axis, bps. Theresulting motion of the power cylinder system is then defined by:rF o = Pyj + [rcs cos(OCA )+ CR cos(CR)]

=cR arcsin Ycso rCS sin( )-XI CR CRCRThis solution is obtained iteratively, as explained in more detail in Section 2.5, by:* estimating the lateral motion, xpy, and piston tilt, 5Ps,* applying axial force balances on the piston and wrist-pin to calculate the axialforce transmitted to the connecting-rod* applying a moment balance, on the connecting-rod, about the x-axis at point Q, toobtain the lateral force and friction torque at the connecting-rod small endbearing,* applying a lateral force balance on the wrist-pin to determine the lateral forcetransmitted to the piston,* checking to see whether the lateral force balance on the piston, and x-momentbalance on the piston and wrist-pin are satisfied,* improving the estimated lateral motion, xep, and piston tilt, qps, until convergence

is achieved.In order to achieve this solution, we must first define:* the dynamics of the each of the components,* the force and moment balances that govern their motion, and* the equations governing interface and external force generation.For the purposes of this project, our system is defined by the following assumptions:* The crankshaft is rigid, and carries out purely rotational motion.* The crankshaft - connecting-rod bearing is an ideal frictionless pin joint, allowingrelative rotational motion of the two components without friction generation orrelative displacement at point Q.* The connecting-rod is rigid, with a distributed mass.

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* The connecting-rod - wrist-pin and wrist-pin - piston bearings are defined by asimple bearing model which generates a friction force acting perpendicular totheir normal load, and corresponding friction moment, as described in Section2.3.2. While there are significant clearances in each of these bearings, for thepurposes of his project it is assumed that the connecting-rod small end, wrist-pinand piston have no relative displacement at point P.* The wrist-pin is rigid, with a distributed mass.* The piston is rigid, with a distributed mass, for the purposes of describing themotion of its centre of gravity. Structural deformations of the piston skirt andlands, due to interaction with the cylinder bore, are considered when determiningthe forces generated at the piston - cylinder-bore interface, as described inSection 2.3.3, and are of the order of 100 ptm. Any variations in the moment ofinertia or position of the centre of gravity, due to these deformations areconsidered to be negligible.* The ring pack is neglected for the purposes of this project as the forces betweenthe ring pack and piston are small compared to the other forces acting on thepiston.* The cylinder bore is assumed to be stationary and rigid. Depending on thecombination of materials, cylinder bore deformation can be as significant aspiston deformation, however, as a starting point, for the purposes of this project,cylinder bore deformation is neglected.

Given the large number of equations contained in this chapter, and the repetitive nature ofthe symbols used, it is convenient to define some general guidelines for nomenclature,which are assumed to apply unless otherwise specified.Location Symbol Explanation of VariableMain text

a Vector accelerationF Vector forceF Scalar force, direction usually specified by subscriptg Gravity vectori Unit vector in the x-directionj Unit vector in the y-directionk Unit vector in the z-direction1 LengthM Vector momentM Scalar momentm Massp Pressurer Vector positionr Radiust Timex Vector positionx Scalar position, direction usually specified by subscript,otherwise, in x-directiony Scalar position in y-directionycso Crankshaft offsetz Scale position in z-direction

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Angular position, velocity and accelerationoCA, ca Crankshaft angle, speed and acceleration

r Scalar torque or momentwCA Crankshaft speed (angular) CA Degrees of crankshaft angleSubscripti/j Dynamics: Pertaining to i, relative toj.Forces and Moments: Due to component i, acting oncomponentj.O Referring to an initial configuration or geometricspecification/A With respect to reference frame A

ANG Pertaining to angular momentum/B With respect to reference frame BB Pertaining to the bearing modelbore Pertaining to, or relative to the Cylinder BoreCB Pertaining to, or relative to the Cylinder BoreCG Pertaining to the component's centre of gravityCR Pertaining to, or relative to the Connecting-RodCS Pertaining to, or relative to the Crankshaftext ExternalF Friction componentN Normal component (generally acting radially)0 Pertaining to, or relative to the point O, located at theideal centre of the crankshaft.P Pertaining to, or relative to the point O, located at theideal centre of the wrist-pin, pin boss and connecting-rod small end bearing.P Pertaining to the combustion chamber pressure.PS Pertaining to, or relative to the PistonQ Pertaining to, or relative to the point O, located at theideal centre of the connecting-rod large end bearing.

WP Pertaining to, or relative to the Wrist-Pinx, X Component in the x-directionXX Relative to the x-axis (Moment of Inertia)y, Y Component in the y-directionz, Z Component in the z-directionTable 2.1: Nomenclature Guidelines

2.2. Component Dynamics and Equations of MotionThis section contains a summary of the equations defining the component dynamics, andthe force and moment balances governing their motion. A more detailed derivation ofthese equations is provided in Appendix 1.

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2.2.1. Crankshaft DynamicsIt is assumed that the crankshaft has no linear motion, and rotates about its axis with agiven angular speed, cOCA(t). The motion of the centre of the connecting-rod large endbearing, point Q, as a function of crankshaft angle, 8CA(t), relative to reference frame A,is therefore given by: r o = [-rcs sin(OcA)+ Ycso +rc cos(OCA)k

Reference Frame A: (X. Y. Z}

Figure 2.2: Crankshaft Dynamics

2.2.2. Connecting-Rod Dynamics and Equations of MotionThe connecting-rod connects the wrist-pin to the crankshaft, helping to convert the linearmotion of the piston into the angular motion of the crankshaft. It is assumed that:* There is no relative displacement between the centre of the large end of theconnecting-rod and the corresponding point on the crankshaft, Q.* The large end of the connecting-rod is attached to the crankshaft via bearingswhich are assumed to be frictionless, and therefore provide no moment to theconnecting-rod.* The connecting-rod is considered to be rigid for the purposes of this work.* There is no relative displacement between the small end of the connecting-rod,the wrist-pin and piston at point P.

----- ~--~-`

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Reference FranFran

Figure 2.3: Connecting Rod Geometry and DynamicsThe connecting-rod angle, CR, is defined by:

cR =arcsin Ycso rCs sin(OCA)- XP_ICR 1CR CR

The lateral motion of point P does not significantly impact the connecting-rod angle, butthe resulting changes to the connecting-rod angular acceleration, and the correspondingconnecting-rod, wrist-pin and piston inertia terms, are important.The motion of the centre of gravity of the connecting-rod can be expressed in terms of hecrankshaft motion and engine geometry:

rCR_CGIO = rQ + rCR_CG/Q= [- rcs sin(Oc) +Ycsolb +rcs cos(OcA)k + rCR_CGIQ

aCRCG/A = aQA + Ci)CRX _CG Q+ CR) [(CR)X rCR_CG QS[- Orcscos(O) + C 2rc sin(OC)i - [cArcs sin(OcA) + 9 A rcs cos(OcA)

+ [(CRi)X rCR_CG /Q RI(O CRi)x rCR_CG/ Qwhere the position of the centre of gravity, of the connecting-rod, relative to pointQ, rcR CG/Q, is defined as:

rCR_C = XCR_CGOi + [COS(cR)-- CR_CGO sin(cjR)Ji + [YCRCGO sin(qCR) ZCR_CGO COS(CR)k

F WP/CR

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As shown in Figure 2.3, the connecting-rod is subject to external forces from theinterfaces it shares with the crankshaft and wrist-pin, Fcs/cR and FwP/CR respectively, anddue to gravity. The calculation of these forces is described in Sections 2.3 and 2.4.Conservation of linear momentum for the connecting-rod yields the following equation:FCsICR + FwpiCR + mcRg = mcRaCR CG/A

Assuming that the motion of the connecting-rod is two-dimensional, conservation ofangular momentum for the connecting-rod, about the point Q, yields the followingequation:ICR_XYXCR = WPICRX +c F z -CR_PQYFWPICR rCRPICG/QFW + mRgZ

-rCR_CG/QZmCRgY - rCR_CG/QymCRaCR_CG/AZ + CR_CG/QZmCRaCR_CG/Ay

Rearranging this equation, we can express that angular motion of the connecting-rod interms of known quantities, and the three unknown forces and moments acting at theconnecting-rod - wrist-pin interface, FWP/CR z, FWP/CR y, nd rwP/cRx:

S=PCRX + rCR_P/QyFw + rCRCG/QymCRgZ - rCRCG/QZCRgYFWP/CRY -WPCR--rCR_P/QZ rCR_P/QZ - rCR CG/QCRCRaCR_CG/AZ + CR_CG/QZmCRaCR_CG/Ay -IcR_xxCRjThe axial force acting at the connecting-rod - wrist-pin interface can be defined by axialforce balances on the piston and wrist-pin, leaving the lateral force and moment to besolved for simultaneously from the above equation and the simple bearing modeldescribed in Section 2.3.2.

2.2.3. Wrist-Pin Dynamics and Equations of MotionThe wrist-pin connects the connecting-rod to the piston, allowing the piston to rotaterelative to the connecting-rod. It can be fixed to the connecting-rod, fixed to the piston,or able to rotate independently of both the connecting-rod and piston (floating pin). Forthe purposes of this project we assume that the wrist-pin is rigid, and that there is norelative displacement between the wrist-pin, piston and small end of the connecting-rodat point P.The motion of the centre of gravity of the wrist-pin can be expressed as:rwP CG/ O rWP PIO + WPCG/WP_P

= x,,j+ [rcs cos(Oc)+ Ic os OcR)]k + rP_CG WPP

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aWPCGIA = WP P/A + [(kPi) rwP_CG/WPP +(PWP)XWi)x rWP_CG/WP P= ,ipyj- crcs sin(c ) + 9CA2rcs cos(OcA) + 'cRlcRsin CR)+ ~5 2CR COS(R)+ POi)x WP CGIWP ]+ Wp)XP O)X rWP CG/WP P]

where the position of the centre of gravity, of the wrist-pin, relative to pointWP_P, rwp CG/WP_p, is defined as:

rWPCG/WPP = WPCGO + WPCGO COS(WP)- ZWPCGO sin(p)+ YWp CGOSin(WP)+ZWP CGOCOS(WP)

IIFigure 2.4: Wrist-Pin Dynamics

The wrist-pin is subject to external forces from the interfaces it shares with theconnecting-rod and piston, FcR/wp and Fps/wP respectively, and due to gravity. Thecalculation of these forces is described in Sections 2.3 and 2.4. Conservation of linearmomentum for the wrist-pin yields the following equation:Fes/WP +FcIwp + mwpg = mwpaWP CGIA

Assuming that the motion of the wrist-pin is two-dimensional, conservation of angularmomentum for the wrist-pin, about point P,yields the following equation:IWp_XX9WP = rpsIWpx + TCRIWPX + rWP_CGIWP_Py X mWP Z -rWPCG/W_PZ x mwg

- rWP_CG/WP_Py XmWPaWP_CGIAZ +rWPCGIWP_PZ x mWPaWP_CG/Ay

2.2.4. Piston Dynamics and Equations of MotionThe piston is connected to the wrist-pin and constrained by the cylinder bore. Duringcombustion the pressure force pushes the piston along the cylinder bore, therebyconverting the chemical energy in the fuel into kinetic energy. The piston also carries thering pack, which act to seal the combustion gases and control the transport of lubricatingoil along the cylinder bore. The piston rotates relative to the wrist-pin, but it is assumedfor the purposes of this model that there is no relative displacement between the twocomponents at point P.

rrLAL

,,

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YFigure 2.5: Piston Geometry and Dynamics

The motion of the centre of gravity of the piston can be expressed as:rPS CGO PS PlO +PS CGIPS P= Xj + [rcs cos(OA )+ 1CR cos(cR)] + rPS_CG/PS_P

aPSCG/ aPS_P/A + PSX TPSCG/PS_P+ (PSi)X PSiX PSCG/PS_P= pj [Arcs sin(Oca)+ ca2rCS cos()+CA + clc sin ()+ c2CR cos(cR)+ [(i) rPSCG PS_P ]+ (PSi [()X PS CG/PS ]

where the position of the centre of gravity, of the piston, relative to point PS_P,rps CG/PS P, is defined as:PS CG/PS P = XPS CGO+ YPS CGO COS(p)-ZPS CGOsin )J+ YPS CGO Sin(Ops)+ ZPS CGO COS(ps)

The piston is subject to external forces from the interfaces it shares with wrist-pin andcylinder bore, Fwp/Ps and FCB/Ps respectively, and due to combustion chamber pressure,Fp/ps, and gravity. The calculation of these forces is described in Sections 2.3 and 2.4.Conservation of linear momentum for the piston yields the following equation:

FwpP +FCBPS + FPPS +mpsg = mpsaps CGIAAssuming that the motion of the piston is two-dimensional, conservation of angularmomentum for the piston, about the ideal centre of the pin bore, point P, yields thefollowing equation:

PS PS rCBPSP XFCB/PS +rP/PS Px FpPS+rPs XG/PSP PS P CGPS_ I PSmpsaps CGIA X

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2.3. Component Interface Models

2.3.1. Crankshaft - Connecting-Rod Interface:The Crankshaft - Connecting-Rod interface is assumed to be an idealized frictionless pin-joint with no relative displacement between the two components at point Q. The forcestransmitted at this joint are not considered in this analysis, apart from assuming that nomoment is generated at the joint.

2.3.2. Connecting-Rod - Wrist-Pin and Wrist-Pin - Piston Interfaces:Depending on the engine design, the Wrist-Pin may be fixed to Connecting-Rod, fixed tothe Piston, or float freely between the two. Cold wrist-pin - piston clearances aregenerally of the order of 5-25 plm, expanding with speed and load to around 80gpm [28,29]. Previous hydrodynamic modeling results [28] indicate that most of the wrist-pinmotion, relative to the piston, is in the axial direction, with relative lateral motions ofabout one quarter of the operating clearance. Taking these motions into account wouldrequire a significantly more complicated wrist-pin bearing model, and correspondingincrease in computational time. As a starting point it is assumed that there is no relativedisplacement between these three components at point P, but that the Wrist-Pin rotatesindependently of the other two, generating a friction m oment, and that we must solve forthis angular motion.The Connecting-Rod - Wrist-Pin and Wrist-Pin - Piston interfaces can be considered aslubricated bearings whenever there is relative angular motion between the twocomponents. The load supported by the bearing is considered to be made up of wocomponents as shown in Figure 2.6:* FN: A normal force, which acts radially to the ideal bearing centre.

* FF: A friction force, which acts circumferentially to the ideal bearing centre, atthe same location as the normal force, in order to resist relative rotation of the twocomponents.The magnitude of the friction force is assumed to be related to the magnitude of thenormal force by a friction coefficient function of the form:f =a pRLA a(R )af IF c

I I =IENIwherefis the friction coefficient, al,a2, and a3 are user supplied constantsdescribing the wrist-pin bearing's friction behavior, pt is the viscosity of the

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z

lubrication oil in the bearing, R is the bearing radius, L is the bearing length, c is

the bearing clearance, F is the load on the bearing, FN is the nonnal load on the

bearing, FF is the friction force, and f1~ is the relative angular velocity of

component I with respect to component 2.

Component 1

Figure 2.6: Bearing Forces Acting on Component 1

Many different correlations are available for bearing friction. Petroff slaw [30] is one of

the simplest of these:

where N = relative rotational speed in revis, P = pressure

The friction coefficient is a constant, aI, when a2 and aJ are set equal to zero. Previous

research [29] provides experimentally obtained friction coefficient values of 0.005 to 0.1

throughout the region around combustion TDC, with lower values (0.02-0.04) during

peak loads. The oil temperature during these experiments was 140-150C.

The direction of the friction force is detennined by the angle at which the nonnal force

acts, and the sign of the relative rotational speed of the components.

I t>~=~ -~ >0 I

y

Figure 2.7: Direction of Bearing Forces

39

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9OB= arctanK jFF = -sign(A )flFNI[- sin(9,)j + cos(9B)k ]

where OB is the angle at which the normal load on the bearing acts, as defined inFigure 2.7.In some case, particularly when the coefficient of friction is a constant, small changes inrotational speeds may change the direction of relative rotation, and thereby significantlychange the friction force, leading to system instability. In order to reduce this effect, asmoothing function has been added to the friction coefficient function. The smoothedfriction coefficient is given by:

fs = l-exp - fwherefs is the smoothed friction coefficient, and a is the friction coefficientbandwidth.

The resulting equation governing bearing friction force is:FF= -sign(A)fs F,I[- in(0 )j + cos(o9)k]Combining the friction and normal components, the total force acting on the bearing isgiven by:F, = IF,I os(B,)+ sign(A)fs sin(OB)}j+ IF, {sin(B,)- sign(AO)fs cos(9B)}kThe normal force is assumed to act radially, and therefore generate no moment. Themoment generated by the friction force, about the ideal centre of the bearing, is given by:

MB = -sign(A )fslFRi

2.3.3. Piston - Cylinder Bore Interface:The piston - cylinder bore interface is essentially made up of three components:

1. The deformed piston surface geometry, taking into account piston motion.2. The cylinder bore geometry, which is considered to be stationary and rigid forthe purposes of this project.3. The oil film thickness distribution, which is neglected for the purposes of thedry piston model, but included in the lubricated piston model, as discussed inChapter 5.

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Piston - cylinder bore clearances are typically in the range of 0-100 p.m. The variationsin bore geometry are significant and lead to a height distribution w hich varies in time,relative to the piston. The combined surface roughness is of the order of 0.5 pm [31].When piston tooling marks are present, they tend to have surface gradients of the order of1/30, and are expected to dominate over any surface roughness effects.

Cylinder Bore ,0.40.35Lateral Motionand Tilt Indicator>0.3

I I

I I I

I I

.200 -100 0 100 200RadialVertion from65.4 mn (Mcrons)Radmilariationrom05.4 u (microns)

- Piston Lands

- Piston Skirt

Figure 2.8: Diagram of Piston - Cylinder Bore InterfaceThe piston's axial sliding velocity ranges from 0-10 m/s. There is significant lateralmotion of the piston both during piston slap events, and throughout the rest of the cycledue to the applied side load. Peak lateral velocities are expected to be around 0.01 m/s.In the absence of oil, the side load is supported by solid-solid contact between the pistonand cylinder bore, generating significant friction.The elasticity of the piston, as described by a compliance matrix, leads to structuraldeformations of the piston skirt and lands due to combustion chamber pressure, axialinertia, and pressure generated at the piston - cylinder bore interface. Thesedeformations significantly alter profile of the piston, and resulting piston - cylinder boreclearance distribution.The piston - cylinder bore interface model can be considered to be made up of four sub-models:* Contact model: Determines pressure generation as a function of surface overlap.* Contact friction model: Determines friction force as a function of normal forceand relative surface velocity.* Fluid model: Determines hydrodynamic pressure generation, shear stress and oilflow as a function of surface motion and oil film thickness.* Compliance matrix: Determines piston surface deformation as a function ofnormal force.

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These sub-models form a highly non-linear system which must be solved iteratively,using the algorithms described in Sections 2.6 and 5.5, to determine:* net forces and moments acting on the piston,* hydrodynamic and contact pressure distributions,* shear stress and contact friction distributions,* piston deformation, and* oil film thickness distribution and oil transport by the piston skirt.

2.3.3.1 Contact Model:A contact model describes the way in which pressure is generated by solid-solid contactas two surfaces approach each other, as shown in Figure 2.9. We assume that thepressure generation can be described by three constants, C1,C2, and hp, nd a functionof the form: P C(hp,-hh>h

where p,, is the average asperity contact pressure, h is the local gap heightbetween the mean surface lines, h, is a measure of asperity or tooling markheight, as appropriate, and C, and C2 are the corresponding user suppliedconstants.Cvlinder bore

Piston pr Triangular Tooling Marks

itact eh~ = fl /2

Figure 2.9: Contact Model RepresentationsWhen the piston skirt has tooling marks, their geometry dominates the generation ofcontact pressure. For triangular tooling marks, the analytical solution for a blunt wedgeagainst a flat plane [32,18] provides an appropriate description of the relationshipbetween contact pressure and surface separation:

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S2-1= t O.6366(l(2ni - +10779' ,h 2E*= -v1 +- 2El E2

where A s the wavelength of the tooling marks, O is the peak to valleywaveheight of the tooling marks, E, is the Young's Modulus of surface i, and vi isthe Poisson's Ratio of the surface i.For a given set of surface properties, curve-fitting over an appropriate range of Sresultsin an expression of the form assumed above.A=250m IV1.0652

C = 7 panm p = 4.9065 x1013 - hE* = 47 GPaA 40 pm o112.069S= 20 pm Pasp = 2.013 x 1013 (- h)E* = 47 GPa

A detailed derivation of the analytical solution and numerical integrals is provided inAppendix 1.When there are no tooling marks, or the waveheight is of the same order as the surfaceroughness, an asperity contact model is more appropriate. Greenwood and Tripp's modelof contact pressure generated by two nominally flat surfaces [33] has been widely used todescribe the relationship between contact pressure and surface overlap for both the piston- cylinder bore and ring-pack - cylinder bore interfaces [5, 6, 20, 23, 34]. A convenientformula for this model was proposed by Hu et al [34]:

= A(4.0a - h)6.804 h < 4.0aP h > 4.0o16JZ (NP a)2, 1A = 4.4068 x10-5 x (N 1 215 a ' 1 -, 2+

El E2A = 2.0884 x10 4 (Ni o-)E*vaff

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(Nf o ) - 0.03 - 0.06S-0.001-0.3

E* - 7x1010 -9x10'0 [31, 33, 34]where N is the number of asperities per unit contact area, f' is the asperity radiusof curvature, and a is the variance of the composite surface roughness.

2.3.3.2 Contact Friction Model:A simple friction model is used to describe the contact friction force generated as thepiston slides along the cylinder bore, as a function of contact force and a constantcoefficient of friction: F, = -sign(A )JfFk

wherefis the coefficient of friction, FN is the contact force generated at thesurface, and Aiz is the axial velocity of the piston, relative to the cylinder bore.

2.3.3.3 Fluid Model:An elastohydrodynamic lubrication model is included in the lubricated piston model, asdescribed in detail in Chapter 5. It describes the way in which pressure and shear stressare generated within the oil film between the piston and cylinder bore, and the way inwhich the oil is transported. In the dry model, the effect of lubricant is neglected.

2.3.3.4 Compliance Matrix:The compliance matrix is used to describe the radial mechanical deformation of thepiston due to the combined loading of the contact and fluid pressures acting normal to thesurface of the piston skirt and lands. The piston has a complicated structure with varyingwall thicknesses ranging from a few millimeters to the full diameter of the piston,reinforcing struts, bearing surfaces, wear resistant inserts, and other variations inmaterial. There are many different ways of generating such a matrix, and some of theseare discussed in more detail in Section 3.4.4. For the purposes of this project, it isassumed that the user supplies a suitable compliance matrix, generated using an FEAprogram. This matrix is then used to calculate the radial deformation of the piston due tothe normal forces generated due to the combined loading of the contact and fluidpressures.

{Radial Deformation)= [Compliance Matrix]{Normal Force)

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2.4. Externally Applied Forces and Inertia Terms

2.4.1. Combustion Chamber Pressure Force:

The pressure force applied to the piston is assumed to act at a specified position in the

plane perpendicular to the cylinder axis, at a specified height from the wrist-pin, as

shown in Figure 2.10. Typically the pressure force is assumed to act at the ideal centre of

the cylinder bore.

Xcy/ Xpb

Z / Z bCY"l\ J\ P

"- ~

FP2

~

~

rpo~ ;\ .....

\ i

~

, y

!

- -Figure 2.10: Combustion Pressure Force and Moment

When the piston tilts, the magnitude of the axial component of the pre