robust concurrent design of engine lubricated components

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ROBUST CONCURRENT DESIGN OF AUTOMOBILE

ENGINE LUBRICATEDCOMPONENTS

A Thesis

Presented to

the Academic Faculty

by

Bharadwaj Rangarajan

In Partial Fulfillment

of the Requirements for the Degree ofMaster of Science in Mechanical Engineering

Georgia Institute of Technology


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February, 1998


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ROBUST CONCURRENT DESIGN OF AUTOMOBILE

ENGINE LUBRICATED COMPONENTS

____________________________

Bharadwaj Rangarajan

Approved:

_________________________________Farrokh Mistree, Committee ChairProfessorMechanical Engineering

_________________________________

Janet K. AllenSenior Research ScientistMechanical Engineering

_________________________________

Bert BrasAssistant ProfessorMechanical Engineering

_________________________________

Tony HayterAssociate ProfessorIndustrial Systems Engineering

_________________________________

Jagadish SorabSenior Technical SpecialistEngine and Processes DepartmentFord Research Laboratories


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_________________________________

Ward Winer

Professor andChairman, Department ofMechanical Engineering


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ACKNOWLEDGMENTS

There are several people I would like thank for helping me complete this thesis and I am

not sure if I would be doing justice their efforts with this write-up. First and foremost, my

advisor/orchestrator, Farrokh for his continued enthusiasm and guidance in helping me push my

research effort to new frontiers. One many occasions he has put me on the right track when I

have strayed and for this, I remain indebted to him. I am also thankful to my other committee

members, Janet Allen, for her patience and crucial advice on issues relating to uncertainty and

for the fabulous dinners, saving me the trouble of eating self-cooked food. Bert, for the

constructive criticism he has provided, both in my ME 6172 project and in my thesis, Dr.

Hayter and Dr. Winer, for their comments on my thesis from their respective viewpoints, Dr.

Jagadish Sorab, for providing me this wonderful opportunity to collaborate with Ford on this

industrial project and also for my summer internship at Ford. I would also like to express my

gratitude to Debbie Finney, for the cheerful and helpful person she has been.

The atmosphere in SRL is very congenial for research and for this I would like thank all the

members that comprise it and specifically, Tim Simpson and Pat Koch, my academic mentors.

They made graduate research life in the USA extremely easy to adjust for this guy from the

other end of the world with totally different ideas and perspectives. The advice and guidance


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Pat and Tim have provided during my stay here have been truly vital and I am thankful for my

association with them. I have learned a lot from my ME 6170 project mates Roberto and

Carrie and the times (both fun and frustration) we spent together working on the project was

perhaps my first face to face encounter with research.

The help provided by Dr. Jagadish Sorab, Ford Research Laboratories, Dearborn,

Michigan, in defining the engine design problem and in using the Engine Friction Anlalysis

Software (EnFAS) is greatly appreciated. We also gratefully acknowledge the monetary

support from Ford University Research Program and the NSF grant DMI-96-12365.

Finally, I thank God and my parents for giving me the strength, courage and tenacity to sail

through without any major problems.


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TABLE OF CONTENTS

LIST OF FIGURES XV

LIST OF TABLES XXXII

SUMMARY XXXII

NOMENCLATURE XXI

CHAPTER 1

GUIDING PRINCIPLES IN DESIGNING LARGE ENGINEERING SYSTEMS

1

1.1 PROBLEM SIGNIFICANCE AND MOTIVATION 4

1.2 OUR FRAME OF REFERENCE 8

1.2.1 Commitment to Designing Open Engineering Systems 8

1.2.2 Robust Concept Exploration Method (RCEM) 16

1.2.3 Modeling and Synthesizing Large Systems 22

1.2.4 Decision Making Based on Information Certainty for Designing Along a

Time Line 23

1.3 AN OVERVIEW OF THE ENGINE DESIGN CASE STUDY 27


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1.3.1 Problem Statement and Definition of the Case Study 28

1.3.2 Secondary Research Questions and Corresponding Tasks Under Investigation 28

1.3.3 Methodology for Addressing Research Questions and Related Tasks 35

1.4 ORGANIZATION OF THESIS 35

1.5 THE ROAD AHEAD 39

CHAPTER 2

MATHEMATICAL CONSTRUCTS USED IN AUTOMOBILE ENGINE

DESIGN 41

2.1 RESPONSE SURFACE METHODOLOGY 42

2.1.1 Creating Response Surface Models 44

2.1.2 Response Surface Model Regression Analysis And Validation 46

2.2 COMPROMISE DSP 48

2.2.1 The Compromise DSP: Math and Word Formulations 49

2.3 TAGUCHIS ROBUST DESIGN TECHNIQUES 55

2.3.1 Integration with Response Surface Models and the Compromise DSP 59

2.4 FUZZY SET THEORY 62

2.4.1 A Brief Description Of Fuzzy Set Theory Principles 63


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2.4.2 Abstraction of Fuzzy Set Theory to Decision Based Design: Fuzzy Compromise

DSP 66

2.5 BAYESIAN STATISTICS AND THE BAYESIAN COMPROMISE DSP 78

2.6 THE ROAD AHEAD... 82

CHAPTER 3

AN OVERVIEW OF ENGINE FRICTION AND LUBRICATION 83

3.1 SIGNIFICANCE OF ENGINE TRIBOLOGY 84

3.2 A COMPUTER MODEL FOR OVERALL ENGINE FRICTION AND

LUBRICATION ANALYSIS: (ENFAS) 88

3.3 FRICTION AND LUBRICATION MODELING FOR THE BEARINGS 90

3.4 FRICTION AND LUBRICATION MODELING FOR PISTON 95

3.5 FRICTION AND LUBRICATION MODELING FOR THE VALVE TRAIN 100

3.5.1 Flat Tappet Follower Valve Train Friction Analysis 101

3.5.2 Roller Follower Valve-Train Friction Model 103

3.6 ACCESSORIES FRICTION MODELING 106


CHAPTER 4


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DEVELOPING SYSTEM RESPONSE AND SOLUTION MODELS 111

4.1 LAYING DOWN THE DESIGN REQUIREMENTS AND FACTORS OF THE

DIFFERENT ENGINE COMPONENTS 115

4.1.1 Design Requirements and Factors for the Bearing Subsystem 116

4.1.2 Design Requirements and Factors for the Piston Subsystem 119

4.1.3 Design Requirements and Factors for the Valve Train Subsystem 121

4.1.4 Design Requirements and Factors for the Oil Pump Subsystem 123

4.2 IDENTIFYING SIGNIFICANT DESIGN FACTORS: SCREENING

EXPERIMENTS 125

4.3 ELABORATING SYSTEM RESPONSE MODELS 132

4.3.1 Developing Response Models for the Bearing Subsystem 137

4.3.2 Developing Response Models for the Piston Subsystem 140

4.3.3 Developing Response Models for the Valve Train Subsystem 141

4.3.4 Developing Response Models for the Oil Pump Subsystem 143

4.3.5 Validation of Response Surface Models 146

4.4 MATHEMATICAL MODELIN G OF ROBUSTNESS IN DESIGNING THE

ENGINE 150

4.4.1 Modeling Robustness at the System Level 150

4.4.2 Modeling Robustness at the Subsystem Level (Bearings) 155


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4.5 FORMULATION OF SOLUTION MODELS BASED ON LEVEL OF

INFORMATION CERTAINTY, FOR A SYSTEM LEVEL SYNTHESIS 159

4.5.1 Computer Implementation of the Compromise DSP Using DSIDES 177

4.5.2 Validation of the Engine Compromise DSP: Solution Convergence 178

4.6 THE ROAD AHEAD..... 185

CHAPTER 5

GENERATION OF TOP LEVEL DESIGN SPECIFICATIONS: INFERENCES,

VERIFICATION AND VALIDATION 186

5.1 INVESTIGATION OF DIFFERENT DESIGN SCENARIOS 188

5 .2 TOP LEVEL DESIGN SPECIFICATIONS FOR THE DIFFERENT

FORMULATIONS 190

5.2.1 Results of Crisp Formulation 192

5.2.2 Results of Fuzzy Formulation 197

5.2.3 Results of Bayesian Formulation 203

5.2.4 Developing Ranged Sets of Specifications for Different Compromise DSP

Formulations 208

5.3 EFFECT OF UNCERTAINTY ON ACHIEVING DESIRED

PERFORMANCE 213


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5.3.1 Influence of Uncertainty Parameter c on Goal Achievement 216

5.3.2 Influence of Fuzziness Parameter on Solution Convergence 222

5.4 INFERENCES BASED ON TOP LEVEL DESIGN SPECIFICATIONS 228

5.4.1 Trade Off between Friction Losses and Lubricant Film Thickness 229

5.4.2 Trade-Off between Tolerance Design and System Sensitivity to

Tolerance 231

5.4.3 Implication of Robustness in Designing for Different Operating

Conditions 233

5.4.4 Link Between Information Certainty and Design Freedom along a Design Time

Line 236

5.4.5 Comparison of the Use of Taguchi Methods and Design Capability Indices in

Satisfying a Ranged Set of Design Requirements 243


CHAPTER 6

SUMMARY OF WORK DONE AND RESEARCH EXTENSIONS 254

6.1 A BRIEF OVERVIEW OF THE TASKS PERFORMED 255

6.1.1 Research Questions Revisited 256

6.1.2 Relevant Contributions through this Work 262


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6.2 RESEARCH EXTENSIONS STEMMING FORM THIS WORK 265

6.3 CLOSING REMARKS 267

APPENDIX A

RESULTS OF SCREENING EXPERIMENTS 268

A.1 BEARING SUBSYSTEM 269

A.2 PISTON SUBSYSTEM 270

A.3 VALVE-TRAIN SUBSYSTEM 271

APPENDIX B

RESPONSE SURFACE MODELING: RESULTS AND VALIDATION 272

B.1 BEARING RESPONSES 274

B.2 PISTON RESPONSES 283

B.3 VALVE-TRAIN RESPONSES 286

B.4 OIL PUMP RESPONSES 292

APPENDIX C

COMPUTER IMPLEMENTATION OF THE COMPROMISE DSP 298

C.1 FILES FOR COMPUTER IMPLEMENTATION OF COMPROMISE DSP 298


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C.1.1 FORTRAN File for Engine Compromise DSP 299

C.1.2 Data File for Engine Compromise DSP 307

C.2 CONVERGENCE PLOTS OF DESIGN VARIABLES 310

C.2.1 Convergence History for Bearing Subsystem 311

C.2.2 Convergence History for Piston Subsystem 314



C.3 BEARING COMPROMISE DSP FOR INVESTIGATING TOLERANCE DESIGN324

REFERENCES 328


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LIST OF TABLES

Table 1.1: The Fundamental Differences Between Open And Closed System

Paradigms ............................................................................................10

Table 1.2: Research Questions and Relevant Chapters...........................................35

Table 2.1: Research Questions Addressed in Chapter 2.........................................42

Table 2.2: Compromise DSP for Two Major Types of Robust Design

Application (Chen, et al., 1995)............................................................61

Table 2.3: A Comparison of Different Approaches in the Usage of Fuzzy Sets

in Optimization Models.........................................................................74

Table 4.1: Research Questions Addressed through Chapter 4 ..............................113

Table 4.2: Bearing Subsystem Factors and Ranges...............................................118

Table 4.3: Factors and Ranges for the Piston Subsystem......................................121

Table 4.4: Factors and Ranges for the Valve Train Subsystem..............................123

Table 4.5: Factors and Ranges for the Oil Pump Subsystem.................................124

Table 4.6: Most Significant Factors for the Bearing Subsystem.............................129

Table 4.7: Held Constant Factors for the Bearing Subsystem................................129

Table 4.8: Most Significant Factors for the Piston Subsystem...............................129

Table 4.9: Held Constant Factors for the Piston Subsystem..................................130


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Table 4.10: Most Significant Factors for the Valve Train Subsystem.......................130

Table 4.11: Held Constant Factors for the Valve Train Subsystem..........................130

Table 4.12: Details of BPOWLOS Response Model............................................138

Table 4.13: Details of BBFLMTHK Response Model..........................................139

Table 4.14: Details of MBFLMTHK Response Model.........................................140

Table 4.15: Details of PPOWLOS Response Model..............................................141

Table 4.16: Details of VPOWLOS Response Modeling.........................................142

Table 4.17: Details of VFLMTHK Response Modeling.........................................143

Table 4.18: Details of PUPOWLOS Response Modeling........................................144

Table 4.19: Details of OILFR Response Modeling..................................................145

Table 5.1: Different Scenarios for Formulation of the Deviation Function................190

Table 5.2: Top Level Specifications for Bearings for a Crisp Compromise

DSP...................................................................................................194

Table 5.3: Top Level Specifications for Piston for a Crisp Compromise

DSP...................................................................................................195

Table 5.4: Top Level Specifications for Valve-train for a Crisp Compromise

DSP...................................................................................................195

Table 5.5: Top Level Specifications for Oil Pump for a Crisp Compromise

DSP...................................................................................................196


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Table 5.6: Top Level Specifications for Bearings for a Fuzzy

Compromise DSP (c=0.05)................................................................199

Table 5.7: Top Level Specifications for Piston for a Fuzzy

Compromise DSP (c=0.03)...............................................................200

Table 5.8: Top Level Specifications for Valve-train for a Fuzzy

Compromise DSP (c=0.05)................................................................200

Table 5.9: Top Level Specifications for Bearings for a Bayesian

Compromise DSP (c=0.05)................................................................205

Table 5.10: Top Level Specifications for Piston for a Bayesian

Compromise DSP (c=0.03)................................................................206

Table 5.11: Top Level Specifications for Valve-train for a Bayesian

Compromise DSP (c=0.05)................................................................206

Table 5.12: Ranged Sets of Specifications for the Bearing Subsystem......................210

Table 5.13: Ranged Sets of Specifications for the Piston Subsystem........................211

Table 5.14: Ranged Sets of Specifications for the Valve-train Subsystem.................211

Table 5.15: Results for Bearing Subsystem For Different c Values in a

Fuzzy DSP .......................................................................................217

Table 5.16: Results for Piston Subsystem for Different c Values in a

Fuzzy DSP.........................................................................................218


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Table 5.17: Results for Valve- train Subsystem for Different c Values

in a Fuzzy DSP...................................................................................218

Table 5.18: Results for Bearing Subsystem for Different Values c in a Bayesian

DSP ...................................................................................................220

Table 5.19: Results for Piston Subsystem for Different Values c in a Bayesian

DSP ...................................................................................................221

Table 5.20: Results for Valve Subsystem for Different Values c in a

Bayesian DSP.....................................................................................221

Table 5.21: Two Design Configurations for Investigation of Robustness...................235

Table 5.22: DFI Values of Different Engine Subsystems Based on

Formulation.........................................................................................240

Table 5.23: Constraint and Target Values for the System Responses .......................246

Table 5.24: Ranged Set of Top Level Specifications Using Two Different

Models of Robustness.........................................................................249

Table 5.25: Design Freedom Indices for the Engine Subsystems based on

Two Different Robustness Models (Crisp Formulation) ........................251

Table A.1: Statistical Results for First Order Modeling of BPOWLOS...................269

Table A.2: Statistical Results for First Order Modeling of PPOWLOS...................270

Table A.3: Statistical Results for First Order Modeling of VPOWLOS...................271

Table C.1: Design Scenarios Investigated For The Bearing Compromise DSP.......326


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Table C.2: Design Specifications from Bearing Compromise DSP. ........................327


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LIST OF FIGURES

Figure 1.1: Primary Research Question and Chapter 1 Structure................................4

Figure 1.2: Typical Energy Distribution in an Automobile

Engine (Sorab, 1997)............................................................................5

Figure 1.3: Typical Friction Distribution Among Various

Components (Sorab, 1997)...................................................................6

Figure 1.4: Reducing Time-To-Market by Increasing Design Knowledge

and Maintaining Design Freedom.........................................................11

Figure 1.5: The Robust Concept Exploration Modules ............................................18

Figure 1.6: Principal Research Question, Key Phrases, and Secondary

Research Questions and Tasks: A Mental Model.................................29

Figure 1.7: Hierarchic and Non-hierarchic Representation of Systems

(Koch, 1997)......................................................................................30

Figure 1.8: Component Level Engine Representation.............................................31

Figure 1.9: Steps in Using the RCEM for Engine Design Case Study......................36

Figure 1.10: A Road Map for the Thesis..................................................................38

Figure 1.11: Running Icon for the Thesis ..................................................................39

Figure 2.1 Second-Order Response Surface Model..............................................43


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Figure 2.2: Creating Response Surface Models ......................................................44

Figure 2.3: Three Variables Central Composite Design...........................................46

Figure 2.4: A Single Objective Optimization Problem (a) and the Multi goal

Compromise Decision Support Problem (b).........................................51

Figure 2.5: Mathematical Form of a Compromise DSP ..........................................53

Figure 2.6: A Comparison of Two Types of Robust Design

(Chen, et al., 1995).............................................................................57

Figure 2.7: Mapping form the Design Space to the Membership Space.............. 64

Figure 2.8: The Different Kinds of Fuzzy Memberships ............................................65

Figure 2.9: Mathematical Formulation of a Fuzzy Compromise DSP.........................72

Figure 2.10: A Fuzzy Goal around a Crisp Target ......................................................76

Figure 2.11: Mathematical Formulation of a Bayesian Compromise DSP

(adapted from Vadde, et al., 1994b).....................................................81

Figure 3.1: Role of EnFAS (Simulation Model) within the RCEM Structure..............84

Figure 3.2 Typical Energy Distribution in an Automotive Engine

(Taylor, 1993)......................................................................................85

Figure 3.3: Lubrication Regimes (Shigley and Mischke, 1989)..................................86

Figure 3.4: EnFAS Analysis Module Structure (Rangarajan, 1997)...........................90

Figure 3.5: Big End Bearing Loading and Load Diagram Shapes (Taylor, 1993).......91

Figure 3.6: Bearing Lubrication (Sorab, 1997).........................................................92


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Figure 3.7: Flow Chart for Bearing Friction Computer Analysis ................................94

Figure 3.8: Crank Angle Resolved Connecting Rod Bearing Loads and

Power Loss (Sorab, 1997)...................................................................95

Figure 3.9: Piston Lubrication (Sorab, 1997) ..........................................................96

Figure 3.10: Flow Chart for Piston Friction Computer Modeling................................99

Figure 3.11: Graph of Piston Ring Power Loss Vs. Crank Angle (Sorab, 1997) ......100

Figure 3.12: Cam and Flat Tappet Follower (Rangarajan,1997)..............................101

Figure 3.13: End Pivot Rocker Roller Follower Cam Mechanism

(Heywood, 1988)...............................................................................103

Figure 3.14: Flow Chart for Valve Train Friction Computer Modeling .....................105

Figure 3.15: Graph of Friction Torque of Valve Train Vs. Cam Angle

(Sorab, 1997) ....................................................................................106

Figure 3.16: Flow Chart for Oil Pump Friction Modeling.........................................107

Figure 3.17: Oil Viscosity Contribution for Pump At 00C (Sorab, 1997).................108

Figure 3.18: Overall Engine Friction Estimates from EnFAS (Sorab, 1997)..............109

Figure 3.19 Pictorial Review of Issues Addressed in the First Three Chapters...110

Figure 4.1: A Pictorial Representation of Issues Addressed in Chapter 4 ..............112

Figure 4.2: Case Study Implementation Process Diagram..........................114

Figure 4.3: A Typical Normal Distribution for Engine Speed..................................119

Figure 4.4: General Procedure for Performing Screening Experiments


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for Each Subsystem............................................................................127

Figure 4.5: A General Method for Generating Engine Subsystem

Response Models ...............................................................................135

Figure 4.6: Prediction Profile for BPOWLOS........................................................138

Figure 4.7: Prediction Profile for BBFLMTHK......................................................138

Figure 4.8: Prediction Profile for MBFLMTHK .....................................................139

Figure 4.9: Prediction Profile for PPOWLOS........................................................140

Figure 4.10: Prediction Profile for VPOWLOS........................................................142

Figure 4.11: Prediction Profile for VFLMTHK ........................................................142

Figure 4.12: Prediction Profile for PUPOWLOS......................................................144

Figure 4.13: Prediction Profile for OILFR................................................................145

Figure 4.14: Comparison of Actual (a) and Predicted Response Surface (b)

for BPOWLOS..................................................................................147

Figure 4.15: Actual vs. Predicted Values of BPOWLOS..........................................148

Figure 4.16: Residual vs. Predicted Values of BPOWLOS.......................................149

Figure 4.17 : Probability Distribution of Engine Speed...............................................151

Figure 4.18: A Typical Normal Distribution for Bearing Dimensions..........................156

Figure 4.19: Preference Function and Possibility Parameter in a Fuzzy

Compromise DSP ..............................................................................166

Figure 4.20: A Gaussian Distribution for Representing an Uncertain Parameter


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Figure 5.5: Mathematical Formulation of Engine Bayesian Compromise DSP.........204

Figure 5.6: Convergence of Deviation Function for Different Values of

c in a Fuzzy Compromise DSP...........................................................223

Figure 5.7: Convergence of Deviation Function for Different Values of

c in a Bayesian Compromise DSP......................................................223

Figure 5.8: Convergence of Main Bearing Clearance (MCLR, ? m) for

Different Values of c in a Fuzzy Formulation........................................225

Figure 5.9: Convergence of Oil Ring Tension (OT, MPa) for Different

Values of c in a Fuzzy Formulation......................................................225

Figure 5.10: Convergence of Valve Closing Load (VCL. gms) for Different

Values of c in a Fuzzy Formulation......................................................226

Figure 5.11: Convergence of Main Bearing Clearance (MCLR, ? m) for Different

Values of c in a Bayesian Formulation. ................................................227

Figure 5.12: Convergence of Oil Ring Tension (OT, MPa) for Different


Figure 5.13: Convergence of Valve Closing Load (VCL, gms) for Different


Figure 5.14: Deviation Variables for Bearing Power Loss (BPOWLOS)

and Film Thickness (BBFLMTHK and MBFLMTHK)

for Three Scenarios (Table 5.1) ..........................................................230


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Figure 5.15: Deviation Variables for Valve-train Power Loss (VPOWLOS)

and (Cam And Follower Film Thickness) VFLMTHK

for Three Scenarios (Table 5.1). .........................................................231

Figure 5.16: Plot for Investigation Trade-Off between Tolerance

Design and System Sensitivity to Tolerance .........................................233

Figure 5.17: Comparison of Two Designs with respect to Total Engine

System Power Loss............................................................................236

Figure 5.18: Target Performance and Feasible Performance Ranges

for Measuring Design Freedom...........................................................238

Figure 5.19: Graph between DFI and Information Certainty for

Different Engine Subsystems ...............................................................240

Figure 5.20: Design Process Time Line for Automobile Engine Design. ....................241

Figure 5.21: Bilevel Modeling of Robustness...........................................................244

Figure 5.22: A System Level Crisp Compromise DSP using Design

Capability Indices...............................................................................247

Figure 5.23: Research Issues Addressed through Chapter 5. ...................................253

Figure 6.1: A Schematic Representation of the Mode of Addressing

Research Issues..................................................................................256

Figure A.1: Pareto Plot for BPOWLOS ................................................................269

Figure A.2: Pareto Plot for PPOWLOS.................................................................270


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Figure A.3: Pareto Plot for VPOWLOS................................................................271

Figure B.1: Comparison of Actual (a) and Predicted Response Surface (b)

for BPOWLOS.................................................................................274

Figure B.2: Plots of First (a) and Second Order (b) Effects

for BPOWLOS.................................................................................275

Figure B.3: Plots of Predicted Vs. Actual Response (a) and Residual Plot (b)

from JMP for BPOWLOS.................................................................276

Figure B.4: Comparison of Actual (a) and Predicted Response

Surface (b) for BBFLMTHK.............................................................277

Figure B.5: Plots of First (a) and Second Order (b) Effects for BBFLMTHK........278


from JMP For BBFLMTHK ..............................................................279


for MBFLMTHK...............................................................................280

Figure B.8: Plots of First (a) and Second Order (b) Effects for MBFLMTHK........281


from JMP for MBFLMTHK...............................................................282

Figure B.10: Comparison of Actual (a) And Predicted Response

Surface (b) for PPOWLOS................................................................283

Figure B.11: Plots of First (a) and Second Order (b) Effects for PPOWLOS ...........284


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Figure B.12: Plots of Predicted Vs. Actual Response (a) and Residual

Plot (b) from JMP for PPOWLOS .....................................................285


Surface (b) for VPOWLOS................................................................286

Figure B.14: Plots of First (a) and Second Order (b) Effects

for VPOWLOS..................................................................................287

Figure B.15: Plots of Predicted Vs. Actual Response (a) and Residual

Plot (b) from JMP for VPOWLOS.....................................................288


Surface (b) for VFLMTHK................................................................289

Figure B.17: Plots of First (a) and Second Order (b) Effects for VFLMTHK ...........290

Figure B.18: Plots of Predicted Vs. Actual Response (a) And Residual

Plot (b) from JMP for VFLMTHK .....................................................291


Surface (b) for PUPOWLOS .............................................................292

Figure B.20: Plots of First (a) and Second Order (b) Effects for PUPOWLOS.........293


from JMP for PUPOWLOS...............................................................294


for OILFR..........................................................................................295


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Figure B.23: Plots of First (a) And Second Order (b) Effects for OILFR..................296

Figure B.24: Plots of Predicted Vs. Actual Response (a) And Residual Plot (b)

from JMP for OILFR.........................................................................297

Figure C.1: Convergence of BCLR from 3 Different Starting Points

in a Fuzzy Compromise DSP ..............................................................311

Figure C.2: Convergence of MCLR from 3 Different Starting Points



in a Bayesian Compromise DSP..........................................................312




in a Crisp Compromise DSP...............................................................313



Figure C.7: Convergence of BORE From 3 Different Starting Points


Figure C.8: Convergence of OT from 3 Different Starting Points in

a Fuzzy Compromise DSP..................................................................314

Figure C.9: Convergence of RW1 from 3 Different Starting Points


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Figure C.10: Convergence of BORE From 3 Different Starting Points




Figure C.12: Convergence of OT from 3 Different Starting Points


Figure C.13: Convergence of BORE from 3 Different Starting Points




Figure C.15: Convergence of OT from 3 Different Starting Points


Figure C.16: Convergence of VCL from 3 Different Starting Points


Figure C.17: Convergence of SR from 3 Different Starting Points






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Figure C.22: Convergence of R1 from 3 Different Starting Points


Figure C.23: Convergence of R2 from 3 Different Starting Points


Figure C.24: Convergence of B from 3 Different Starting Points


Figure C.25: Mathematical Formulation of Bearing Compromise DSP

for Tolerance Design...........................................................................325


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NOMENCLATURE

ANOVA Analysis of Variance

CCD Central Composite Design

C-DSP Compromise Decision Support Problem

Cdk , Cdu, Cdl Design capability indices

DBD Decision Based Design

Design freedom A measure of the extent to which a system can be adjusted while

still meeting the requirements

DOE Design of Experiments

DSIDES Decision Support in Designing Engineering Systems (used to solve

compromise DSPs)

DSP Decision Support Problem

EnFAS Engine Friction Analysis Software

JMP Statistical Software Package developed by SAS Institute.

LRL Lower Requirement Limit

RSM Response Surface Methodology

RCEM Robust Concept Exploration Method

TDC Top Dead Center

URL Upper Requirement Limit


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xi Design variable

y Response

? Mean of a response

? Standard Deviation of a response

A~

A fuzzy parameter

Variables Used in the Case Study

Bearings

BDIAM Big end bearing diameter

BLEN Big end bearing length

BCLR Big end bearing clearance:

SPEED Engine speed:

MDIAM Main bearing diameter

MLEN Main bearing length:

MCLR Main bearing clearance

TOLBD Manufacturing Tolerance on BDIAM

TOLMD Manufacturing Tolerance on MDIAM

TOLMC Manufacturing Tolerance on MCLR

TOLBC Manufacturing Tolerance on BCLR

BORE Bore diameter of the piston


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WF Weight of the flywheel

CONROD Length of the connecting rod

BPOWLOS Total power loss in the bearings

BBFLMTHK Big end or connecting rod bearing film thickness

MBFLMTHK Main or crankshaft bearing film thickness

Piston assembly

RW1 Width of compression ring 1

RW2 Width of compression ring 2

RO1 Offset of compression ring 1

RO2 Offset of compression ring 2

RT1 Tension in compression ring 1

RT2 Tension in compression ring 2

BORE Bore diameter of the piston

CONROD Length of the connecting rod

RS Ring surface roughness

OT Oil control ring tension

OWIDTH Oil ring width

RCURV Ring face radius of curvature

PPOWLOS Power loss in the piston assembly


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Valve train

VCL Valve closing load

SR Valve spring rate

BASRAD Cam base circle radius

RT Tappet radius

TBL Tappet bore length

BCLOAD Load on the cam base circle

WROLL Roller mass

RCAGE Mean radius of the roller bearing cage

CSRM Composite surface roughness

CFL Cam follower contact length

WVALS Valve spring weight

VPOWLOS Total valve train friction power loss

VFLMTHK Film thickness in the cam follower interface

Oil pump

R1 Radius of the rotor

R2 Radius of the outer gear

B Width of the gear


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DINLET Diameter of the inlet tube

LINLET Length of the inlet tube

S Area between engaging gear teeth

OILFR Lubricant/oil flow rate through the pump

PUPOWLOS Friction loss in the oil pump.


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xxxvii

SUMMARY

One of the major underlying issues in designing fuel efficient automobile engines is that

tribological problems relating to friction and lubrication are unearthed after the product

development process (testing phase), leading to reduced quality and durability. To facilitate

simultaneous engineering and concurrent determination of performance targets for different

components, the usage of an overall engine friction model is proposed, so that tribological

considerations are abstracted to the parametric design stages itself. The case study under

investigation involves developing top level design specifications for automobile engine lubricated

components (bearings, pistons, valves, etc.). The Robust Concept Exploration Method

(developed in the Systems Realization Lab., Georgia Tech.) is adopted in implementing this case

study. This involves three major action items,

1. Design space exploration (design of experiments),

2. System modeling (engine friction computer modeling and system approximation

using response surface methods), and

3. System synthesis (Compromise DSP).

Additionally through the use of fuzzy sets and Bayesian statistics the relationship between quality

of information about issues relating to friction and lubrication and the ranged set of top level

specifications generated, at different stages in a design process, is captured. The details of the

case study, the implication of the results and the conclusions that can be drawn, are elaborated

in this thesis.


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1.

CHAPTER 1

GUIDING PRINCIPLES IN DESIGNING LARGEENGINEERING SYSTEMS

Complex engineering systems are characterized as having multiple interdependent

subsystems and conflicting design requirements, making a trade off between these requirements

indispensable. While designing such systems it is extremely essential to represent them as close

to reality as possible and to ensure effectiveness and efficiency in their synthesis. One such

complex system is an automobile engine and one of the associated concerns is designing fuel

efficient engines. To achieve a competitive advantage in the field of automobile engine design it

is necessary to seek holistic and robust design processes in which considerations of fuel

efficiency and durability are included. Traditional approaches to design involve design

processes with sequential decisions that increasingly constrain a design. This involves fixing

parameters at one level before moving to the next level of detail. Newer methods that help a

designer partition the problem to a set of related tasks and facilitate concurrent decision making

to address different product issues (performance, durability, cost, etc.) must be developed. The

main points of focus in this thesis, in dealing with automobile engine design include,

?? representing the engine system and its components accurately,


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?? increasing the effectiveness and efficiency of the process of synthesis,

?? addressing issues relating to friction and lubrication through the notion of simulation

based design, and

?? seeking satisficing rather than optimal solutions to models that accurately represent

the real world. By satisficing solutions we refer to those solutions that are good

enough and not necessarily the best. Seeking satisficing solutions is considered a

more practical approach than seeking optimal solutions in real life complex systems

design. The notion of satisficing was introduced by Herbert Simon and in (Simon,

1988) he states,

Of course the decision that is optimal for the simplified approximation will rarely

be optimal in the real world, but experience shows it will often be satisfactory.

The alternative method provided by Artificial Intelligence (AI), most often in the

form of heuristic search (selective search using rules of thumb), find decisions that

are good enough, that satisfice

The case study that is investigated in this thesis involves concurrent design of a system

consisting of lubricated engine components. The primary concern in this case study deals with

including tribological considerations in design. At this juncture the principal research question

addressed through this thesis is posed.

How can issues like friction and lubrication be effectively and efficiently

addressed in system level design to generate robust top level design specifications along a

design timeline and avoid rework?


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Top-level design specifications provide the foundation of the preliminary design

of complex systems. They define system/subsystem concept alternatives, representing the

primary descriptors of a complex system. (Koch, et al., 1996)

This principal research question serves as an ideal starting point to discuss the structure

of this chapter as presented in Figure 1.1. The motivation for addressing the principal research

question and significance of the same is established through the next section. As shown in

Figure 1.1, designing open engineering systems serves as a guiding paradigm in developing

ranged sets of top level design specifications to satisfy the engine system requirements. The

defining characteristics of open engineering systems and its relevance in generating ranged sets

of top level design specifications in early design stages is presented in Section 1.2.1.

Associated with open engineering systems design are issues involving modeling large systems,

incorporating robustness and modeling uncertainty in early design stages. The Robust Concept

Exploration Method (RCEM) (Chen, et al., 1996a) is used as a design framework that enables

us address the aforementioned issues and to integrate tribological considerations in designing

open engineering systems efficiently. A discussion on this method is presented in Section 1.2.2

and its particularization to the case study summarized in Section 1.3.3. Since we are interested

in a system level design process, a clear representation of the engine components and their

interactions is necessary to use the RCEM for system synthesis. A discussion on different


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approaches to system level modeling and synthesis and the approach adopted in this thesis is

presented in Section 1.2.3. The issue of robustness as viewed in this case study is highlighted in

Section 1.2.1 under the discussion of open engineering systems. It must be remembered that

specifications generated in preliminary (early) phases of engine development are seldom final. In

other words, further down a design timeline, detailed component level analysis and synthesis

processes are carried out which may necessitate a change in the specifications generated in the

previous phases of design. Moreover, preliminary design phases are typically characterized by

a lot of uncertain information (Vadde, et al., 1994b), and it is necessary to (a) recognize the

extent of uncertainty prevalent in the information available to a designer and (b) model it

suitably. A discussion on the role of uncertainty and the ways to model it is presented in Section

1.2.4.


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Principal ResearchQuestion

Problem Significance and Motivation(Section 1.1) } Why addressthe question?

How toaddress

the question?

Guiding Paradigm:Desiging Open Engineering Systems

ModelingLarge Systems

IncorporatingRobustness

ModelingUncertainty

(Section 1.2.1)

(Section 1.2.3) (Section 1.2.1) (Section 1.2.4)

RCEM: A Design Framework for SystemLevel Design (Section 1.2.2)

Figure 1.1: Primary Research Question and Chapter 1 Structure

In Section 1.3 an overview of the engine design case study, the relevant research

questions and the tasks involved are presented. This chapter is concluded with a road map and

a running icon for the thesis, which outline the remaining chapters of this thesis.

1.1 PROBLEM SIGNIFICANCE AND MOTIVATION

In this thesis we are interested in designing automobile engine lubricated components

concurrently, for reduced friction losses and sufficient lubrication. Reducing engine friction

improves the thermal efficiency of the engine and consequently reduces vehicle fuel


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consumption. Stringent government laws pertaining to environmental pollution regulation and

control, and strong competitive market forces, have resulted in a renewed interest in

understanding the mechanisms of engine friction and applying this understanding to designing low

friction engine components. In order to do this, we need to understand

?? how friction is generated,

?? the variation of friction losses with engine conditions,

?? the distribution of these losses among engine components, and

?? the interaction of component geometry, surfaces and engine oil parameters and their

effects on engine friction

A typical energy distribution in an automobile engine is shown in Figure 1.2.

Exhaust32%

Brake HP25%

Pumping6%

Engine

Friction

8%

Cylindercooling

29%

Figure 1.2: Typical Energy Distribution in an Automobile Engine (Sorab, 1997)


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From Figure 1.2 it is evident that magnitude of losses in an engine (pumping + friction)

are very much comparable to the brake power generated. In Figure 1.3 the distribution of

friction among the various engine components is illustrated.

Connecting RodBearings

MainBearings18%

PistonRings26%

PistonSkirt11%

Valve train19%

Accessories12% 14%

Figure 1.3: Typical Friction Distribution Among Various Components (Sorab, 1997)

Friction distribution among the various components varies from engine to engine and as

seen from Figure 1.3, it is dominated by the piston assembly, bearings and valve train. Hence in

this study, generation of top level design specifications for these three components is

investigated in detail, so that the engine configurations generated ensure improved fuel efficiency.

In addition design of the oil pump which supplies the lubricant is also studied, so that lubricant

flow rate and power loss requirements of the pump are also included in the design.


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The development process for a new engine proceeds through a series of consecutive

stages including formation of a concept, planning, determination of performance targets, design

synthesis of the components, trial production of prototypes, experimentation for checking

performance and durability and reliability tests for assuring quality (Hamai, et al., 1990). One of

the major shortcomings of such a development process is that problems relating to friction and

lubrication are unearthed only in the durability and reliability evaluation stage, making

implementation of changes an arduous task. To facilitate simultaneous engineering and

concurrent determination of performance targets, tribological considerations should be

abstracted and introduced into to the preliminary design stages itself. This idea serves as a

motivating factor in the case study investigated in this thesis. Tribological issues are captured

through the usage of an overall engine friction prediction model (given in Chapter 3) which is

used to determine part configurations of different engine components and also estimate engine

losses. With the help of this model and other mathematical tools that are elaborated in later

parts (Chapter 2) of this thesis, it is possible to examine different engine configurations and their

relative merits from the point of view of engine friction and lubrication before finalizing the engine

type and configuration.

Another motivating factor in this study deals with the idea of robustness or generating

engine configurations that are insensitive to small variations in dimensions and also have the

capacity to function effectively under different operating conditions. The theoretical foundations


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of robustness and its particularization for this case study are presented in Sections 2.3 and 4.4

respectively.

Related literature on the tribological considerations in design include (Rosenberg, 1982)

and (Hamai, et al., 1990) in which techniques for predicting and reducing engine friction losses

are presented. In (Katoh and Yasuda, 1994) friction reduction techniques for valve train

mechanisms in new generation light weight engines are summarized. Bartz (Bartz, 1985), gives

an overview of lubricant effects on engine friction and potential fuel savings by adopting low

friction engine oils. Through this thesis an attempt is made to use a lot of domain specific

tribological information (friction and lubrication parameters of engine components) in

conjunction with domain independent robust design techniques in configuring an automobile

engine. The problem significance and motivation being established, in the next section our frame

of reference or a set of guiding principles is presented.

1.2 OUR FRAME OF REFERENCE

In this section a discussion on Open Engineering Systems, the Robust Concept

Exploration Method (RCEM), system decomposition and the role of uncertainty in design is

presented from the point of view of their relevance to this case study.

1.2.1 Commitment to Designing Open Engineering Systems

Open engineering systems are systems of products, processes, and/or services which

are readily adaptable to changes in the systems comprehensive environment (Simpson, et al.,


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1997a). An open engineering system allows producers to remain competitive in a global

marketplace through continuous improvement and indefinite growth of an existing base. More

firms are striving to deliver greater quality, more customization, faster response, more innovative

designs and lower prices (Bower and Hout, 1988; Stalk and Hout, 1990). World-class

manufacturers have responded by adopting product design and manufacturing systems that are

more flexible, responsive and cost effective than ever before, (Clark and Fujimoto, 1991;

Drucker, 1990; Womack, et al., 1990)

In essence, an open engineering system resembles a readily adapting system. In a

continuously changing environment, the traditional means of retiring and redesigning is too

inefficient and expensive for society to maintain and still remain competitive. Remaining open

during the early stages of solution formulation and opting for a satisficing rather than an optimal

solution to system requirements produces a system that more rapidly accommodates even those

changes that cannot be predicted. If every new artifact that is manufactured has to be

developed from scratch, then this would result in a colossal waste of time and effort. How can

this issue be tackled? One way of doing this is to consider product features in the early design

stages itself and come up with concepts that would to a certain extent circumvent the necessity

for an absolute change. Designing open engineering systems provides the answer to the

questions of a changing competitive global marketplace.


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Going back to the principal research question posed in Section 1.1, we see that by

addressing tribological issues in design we are in a way reducing downstream changes that are

necessitated by reliability and durability problems. In essence we are interested in designing the

automobile engine as an open engineering system. Inherent benefits of designing open

engineering systems include increased quality, decreased time-to-market, improved

customization, and increased return on investmentwhich are enhanced through the system's

capability to be adapted to change. System in this case refers to the product, process, and/or

service as well as the producers and the customers. Consider the following analogy: like a

species that cannot adapt itself to a changing environment, a system that cannot be adapted to a

changing marketplace becomes extinct. We now proceed to the actual definition of an open

engineering system,

Open engineering systems are systems of industrial products, services, and/or

processes that are readily adaptable to changes in their environment and enable

producers to remain competitive in a global marketplace through continuous

improvement and indefinite growth of an existing base. (Simpson, et al., 1996).

The basic premise in designing an open engineering system, is to get a quality product to

market quickly and then remain competitive in the marketplace through continuous development

of the product line. Shown in Table 1.1 are the primary differences between the open and

closed systems paradigm.


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Table 1.1: The Fundamental Differences Between Open And Closed System

Paradigms

Closed System Paradigm Open System Paradigm

short term profit long-term investmentpressure to constrain design quickly keep design freedom opensingle point solution in early stages satisficing solutions in early stages

design-for-manufacture design-for-life cyclelittle growth capability indefinite growth potential

ri gi d de si gn s flexible designsmass production mass customization

designed for current technology adaptable to current and future technology

What is the relevance of open engineering systems specifically in automobile engine

design?

Designing automobile engines as open engineering systems provides the inherent

advantage of adaptability to new requirements and eliminates redesign to a great extent. The

process of redesigning an engine is a cumbersome and costly process. In this thesis open

engineering systems are chosen as a guiding paradigm in designing the engine effectively and

avoiding rework due to durability or reliability problems. Designing open engineering systems as

mentioned before help us achieve better quality products, reduced time to market, and

increased return on investment. To achieve all these benefits we have to model a design

process suitably. In the following two sections the characteristics of design processes under

open systems and the product features under an open engineering environment, and their

relevance to this thesis are discussed.

Characteristics of open engineering design processes

The design of open engineering is anchored on the three important requirements:


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1. Increasing design knowledge during early design phases

2. Maintaining design freedom during early design phases.

3. Increasing efficiency of the design process.

This notion is graphically represented in Figure 1.4 where the shifts in the design

knowledge and design freedom, in early design stages, when designing open systems is shown.

The reason for increasing design knowledge and maintaining design freedom, during early design

stages, a lot of flexibility is provided for the later design stages and the amount of rework is also

reduced. The specifications obtained using a design process in the early design phases, are

used in quest for superior solutions as more information flows in along a design time line. Hence

it is desirable to maintain some design freedom through the specifications generated. Designing

open engineering systems helps achieve this.


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Rework

Preliminary

Concept

Detail

Detail

Prelimina

ry

Concept

DesignTime-Line

DesignFreedom

Knowledgeabout Design

CUMULATIVE

100%

0%

Potential TimeSavings

Prototype

Rework

Prototype

MaintainFreedom

Increase

Knowledge

Figure 1.4: Reducing Time-To-Market by Increasing Design Knowledge andMaintaining Design Freedom (Simpson, 1995)

What are the ramifications of these requirements.?

An increase in design knowledge helps us develop a better understanding of the

system and get a feel for the system sensitivity. Also included in this is the abstraction of

principles to early stages of design so that downstream design changes may be avoided. This

also improves the possibility of developing adaptable products as the future needs of the

product are predicted if greater information is available in the early design stages. Increase in

design knowledge implies the ability to answer questions usually posed in the later stages of

product development and avoid rework. If issues like reliability, manufacturability are abstracted

to the early design stages (where changes are implemented more easily), then a design process


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becomes holistic, as different issues along a product timeline are addressed in the design phase

itself.

Maintaining design freedom implies that it would be unwise to restrict the choices

that are available quite early in the design. In designing complex systems it is desirable to keep

design freedom as open as possible so that changes are implemented more easily. Also, keeping

design freedom open reduces the probability of neglecting competent designs on the basis of

qualitative information.

Increasing efficiency implies making the process quicker in terms of the computations

involved and making wise approximations in order to increase the computational efficiency of

the process. Wherever possible the process should be automated.

In this case study, the preceding features are incorporated in the following ways.

Increase Design Knowledge in Early Design Sages


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Design PhaseTesting Phase

Issues relating to frictionand lubrication

Simulation

by incorporating tribological considerations in design phase itself

by identifying the impact of system parameters on performance

by identifying the significant factors or the design (friction) drivers

by studying changes in the design variables due to different scenarios or trade off

studies

by answering several what-if questions during the design process

Increase Design Freedom

Level of uncertainty

Ranged sets ofspecificationsas against pointoptimal solutions

?? by searching for satisficing ranged sets of solutions rather than optimal or point

solutions.

?? incorporating robustness into the design by making the design insensitive to changes

in the later design stages


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?? by enhancing concept exploration by not restricting the number of parameters

considered or limiting their ranges.

?? by mathematically modeling the quality of information and not restricting the feasible

design space based on uncertain information

Increase Efficiency

y

Factor A

FactorB

Factor C

A1 A2A3

B 1

B 2

B 3

C1

C2

C3

by using response surfaces (Section 2.1) to develop models for system

performances to improve computational efficiency.

by utilizing statistical techniques like Design of Experiments (Section 2.1) to obtain

various design parameter settings quickly.

Having addressed design process issues for open systems, we now look at the product

features in an open engineering system.

Product features in open engineering systems

The next important issue that needs to be considered deals with the characteristics that

have to be incorporated into a product that is designed as an open system. One way is to

design flexible products that are adapted in response to a large number of changes in customer


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requirements by changing a small number of components (Chen, et al., 1994). Another way is

to develop robust designs which evolve into a design family of variants which meet a variety of

changing market needs and requirements. This leads us into the investigation the characteristics

of open engineering systems. Flexibility is one primary feature of an open engineering system

without which the system is no longer adaptable to change. Flexibility encompasses the other

features of open engineering system namely, adaptability, robustness, modularity and mutability.

In (Simpson, 1995) these characteristics are defined. The main emphasis in this thesis is on

robustness.

Robustness is the capability of the system to function properly despite small

environmental changes or noise (Simpson, 1995). It implies an insensitivity to small variations.

The philosophy behind robust design and its particularization to the case study under

investigation is elaborated in Sections 2.3 and 4.4 respectively. Robustness in this particular

case is viewed from two different stand points:

?? making the system insensitive to variations that may occur in manufacturing

?? designing the system in such a way that it functions effectively under different

operating conditions (satisfying a ranged set of design requirements)

Robustness is modeled at two levels, system and subsystem level. At the system level

robustness implies the capacity to satisfy a ranged set of design requirements, under different

operating conditions. At the subsystem level robustness is viewed as reducing system sensitivity


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to manufacturing noise. The applications of Taguchis robust design principles and the usage of

design capability indices (Chen, et al., 1996c) in designing a robust engine capable of meeting

ranged sets of design requirements is presented in this thesis.

Thus one of the prime guiding notions in this thesis is the idea of designing open

engineering systems, wherein design knowledge is increased, design freedom is maintained,

design process efficiency is improved and system robustness ensured. As mentioned in the

beginning of this chapter, in order to design the engine system as an open engineering system, it

is essential to model the components of the system and their interactions and also address the

issue of uncertainty in preliminary engine design. In the next section a discussion on the Robust

Concept Exploration Method (RCEM) (Chen, et al., 1996a) which provides an ideal platform

to address these issues and implement open engineering systems process and product features

that include tribological considerations is presented.

1.2.2 Robust Concept Exploration Method (RCEM)

The main function of the Robust Concept Exploration Method (RCEM) (Chen, et al.,

1996a) is to improve the efficiency and effectiveness of decisions made in the early stages of

design. It utilizes a combination of Taguchis robust design principles, Response Surface

Methodology, and the compromise Decision Support Problem in order to determine top-level

design specifications (Pg. 2). In (Chen, et al., 1996a) it is shown that RCEM is used to explore

airframe configurations and propulsion system designs and determine robust top-level design


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specifications for the HSCT (High Speed Civil Transport) system. In (Simpson, et al., 1996)

the use of RCEM in the conceptual design of a family of products is illustrated with the specific

example of a general aviation aircraft.

The method allows for:

rapid evaluation of different design alternatives,

generation of robust top-level design specifications which incorporate considerations

from different disciplines, and

acquisition and shaping of knowledge to reduce or reorganize the design models without

risking high costs.

There are several other approaches that have the same goals as the RCEM but fall short

of these goals in some form. Included among these alternate methods are the Concept

Exploration Model and Taguchis principles.

The Concept Exploration Model (CEM) (Chen, 1995) is an approach that utilizes

simulations to predict the performance of a concept. In the early stages, design concepts are

evaluated through this simulation of their performance and the ones that show the most promise

form the top-level design specifications for further design. This becomes a very limiting

approach due to the fact that the number of concepts and areas of the design space in which

they should be generated have no scientific basis. This makes it not only difficult to locate an


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adequate starting point but also requires extensive computation which can become quite

expensive.

Taguchis principles of quality engineering (Taguchi, 1987) and statistical techniques

have become a widely recognized and accepted method for increasing the robustness of

designs. However, there are also difficulties associated with such methods. Critics have argued

that many of the statistical methods associated with Taguchis principles are unnecessarily

inefficient and complicated. There are also various mathematical difficulties associated with the

loss-model approach which involves Taguchis signal-to-noise-ratio (Taguchi, 1987). In

response to this criticism, the response-model approach was developed which combines the

control and noise factors within a single array. This enables the modeling of the actual response

rather than the expected loss. However, these proposed alterations only provide for a single

performance measure.

The Robust Concept Exploration Method (Figure 1.5) consists of four main steps

(Chen, et al., 1996a):

classify design parameters

screening experiments

elaborate the response surface models


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generate top-level design specifications with quality considerations

C. SimulationPrograms

(Rigorous AnalysisTools)

Overall DesignRequirements

D. Experiments Analyzer

Eliminate unimportant factorsReduce the design space to the region

of interest

Plan additional experiments

Robust, Top-LevelDesign Specifications

A. Factors and Ranges

Product/Process

Noise zFactors

yResponse

xControlFactors

F. The Compromise DSP

FindControl Variables

SatisfyConstraintsGoals"Mean on Target""Minimize Deviation"Maximize the independence

Bounds Minimize

Deviation Function

B. Point Generator

Design of ExperimentsPlackett-Burman

Full Factorial DesignFractional Factorial DesignTaguchi Orthogonal ArrayCentral Composite Design

etc.

E. Response Surface Model

y=f( x, z)

? y = f( x, ? z)

? ? y= ?i=1

k fzi( )

2? ? z

i i=1

lfx i( )

2? ? x

i+ ?

Input and Output

Processor

Simulation Program

Figure 1.5: The Robust Concept Exploration Modules

Step 1: Classify Design Parameters

The first step consists of using robust design terminology and principles to classify the

design parameters. The design parameters are classified as either control factors, noise factors,

responses or constant design parameters. Each of these terms are defined as follows:

Control factors - to be determined, top level design parameters which describe

characteristics of the design at the system level (discrete or continuous)


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Noise factors - uncontrollable design parameters associated with the unstable operating

environment or manufacturing process or uncertain design parameters associated with

downstream design considerations (continuous)

Responses - system performance parameters which are used for evaluating the overall

design requirements (continuous)

Constant Design Parameters - those that a designer keeps constant during the study

(discrete or continuous)

Step 2: Screening Experiments

The second step of RCEM utilizes computer simulation as well as the tools and methods

of response surface methodology (Box and Draper, 1987). It consists of an initial set of

experiments whose purpose is to reduce the size of the problem and provide information for

organizing secondary experiments. The results of these experiments are used to identify the

significance of main effects. Those that are determined to be trivial are eliminated by holding

them constant at suitable values for later experiments.

Step 3: Elaborate the Response Surface Models

The third step involves secondary experiments whose purpose is to fit second order

response surface models. These models are used to replace original expensive analysis


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programs as the fast analysis module. The results of these experiments are used to increase the

designers knowledge about the significance of different design factors and their interactions.

Step 4: Generate Top-Level Design Specifications with Quality Considerations

The purpose of the fourth step in the RCEM is to determine the top level design

specifications which are the values of the control factors. This includes the incorporation of

quality considerations such as robustness and flexibility. The compromise DSP is used to

integrate different considerations and make trade offs between conflicting objectives. The

original analysis program is replaced by response surface models as functions of both control

and noise factors. Deviations associated with the control factors are considered. The overall

goals are to bring the mean on target and to minimize the variation. These are modeled as goals

in the compromise DSP (Section 2.2).

The main components of the RCEM (compromise DSP, Taguchis Design, Response

Surface Methodology) are discussed further in Chapter 2. A brief review of the computer

infrastructure of the RCEM is presented in the following. The relationship between the key

elements of the RCEM as illustrated in (Chen, et al., 1996a) is shown in Figure 1.5. The robust

concept exploration method consists of a simulator and three processors.

The relationship between these components and the software used is summarized as

follows:


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Module A - different design parameters are classified as control factors, noise factors,

or responses and ranges are specified.

Module B - point generator - identifies simulations to be conducted based on the design

of experiments.

Module C - the simulator - the center of the structure - a numerical processor which

takes values of control, noise and held constant factors as input and generates values of system

performance as output.

Module D- the experiments analyzer- a mathematical tool that helps in screening

unimportant factors based on statistical tests of significance.

Module E - response surface model processor - fits a surface model which represents

a quick mapping from decision space to performance space. In addition, mean and variance of

performance is predicted. Trivial design effects are removed.

In this case, a statistical software package called JMP (Developed by SAS Institute) is

used as the point generator, experiments analyzer and response surface model processor.


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Module F - the compromise DSP (Mistree, et al., 1993a) solver (DSIDES) (Reddy, et

al., 1992) - values of control factors are determined to achieve a performance as close as

possible to the target mean and to minimize variations around these targets.

The Robust Concept Exploration Method provides a general framework for design at

any level of hierarchy (component or system level). RCEM is anchored in the notion of

Decision Based Design (Muster and Mistree, 1988), according to which the primary role of a

designer in a design process under Decision Based Design is to make decisions. The

compromise DSP which is the cornerstone of the RCEM is used as a decision support tool in

this thesis in the quest for top level ranged sets of specifications. In order to use this framework

for system level design, a scheme for representing the system and the components is essential.

In the next section a review of different techniques that are used to represent, decompose,

model and synthesize large systems is discussed.

1.2.3 Modeling and Synthesizing Large Systems

The decomposition or partitioning of complex systems, such as automobile engines has

long been viewed as beneficial to the efficient solution of a system. Although breaking up a

system into smaller, less complex subsystems may allow for effective solution at the subsystem

level, decomposition makes system design more complicated by requiring the coordination of

subsystem solutions. Hence depending on the magnitude of the problem a single level or


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multilevel system synthesis may be adopted. This choice is guided by the amount and quality of

information in a system model at any point in the design process.

Decomposition schemes historically have been hierarchical in nature. An excellent

review of hierarchical decomposition is presented in (Renaud, 1992; Koch, 1997). On the

other hand many systems lend themselves to non-hierarchic decomposition schemes instead of

hierarchical ones. A review of non-hierarchic decomposition is also presented in (Renaud,

1992). Various decomposition and coordination strategies have been developed and

implemented based on the Global Sensitivity Equations approach (GSE) (Sobieszczanski-

Sobieski, 1988) in coupling non-hierarchic subsystems (see, e.g., Balling and Sobieski, 1994).

In (Kroo, et al., 1994) compatibility constraints are used at the system and subsystem levels to

account for coupling between levels. In (Renaud and Tapetta, 1997) a collaborative strategy is

presented in dealing with system level design with multiple subsystem objectives and

compatibility constraints. In (Kuppuraju, et al., 1985) a single level system synthesis template is

used in a hierarchical design problem.

In the case study investigated, while there is a component level analysis and modeling,

the system synthesis is done at a single system level. The interaction between the components

are handled by using the notion of state variables and formulating the response surface equations

using the state variables. State variables are those factors of a system that affect system


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performance, but are controlled by other designers (different from the one designing the system

under consideration). In a similar fashion system compatibility is also ascertained when system

synthesis is performed.

Having dealt with the problem of decomposing and synthesizing the system, the next

step is to investigate the idea of design along a timeline based on the quality of information or

complementarily, design freedom available at various design stages. In the next section the role

and kinds of uncertainty in early design stages and ways to handle them for designing along a

timeline is presented.

1.2.4 Decision Making Based on Information Certainty for Designing Along a TimeLine

Any design process is characterized by different phases of decision making under

different levels of information certainty. The field of decision making is commonly classified

(Luce and Raiffa, 1957) as decisions under:

?? Certainty: If a decision is known to lead invariably to a specific outcome.

?? Risk: If a decision leads to one of a set of possible outcomes, each of these having an

associated probability, the probabilities being known to the designer also called stochastic

uncertainty (Wood, et al., 1990).

?? Uncertainty: If a decision could lead to a set of possible outcomes and there is no

information regarding the associated probabilities.


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indicator of likelihood, while modeling fuzzy numbers, which is addressed in this thesis (Section

2.4). Based on this discussion, uncertainty is viewe d as encompassing both imprecision

(semantic uncertainty) and risk (stochastic uncertainty) in the remainder of this

thesis.

The nature (imprecision or risk) of uncertainty in the design parameters varies along a

design time-line. The magnitudes of imprecision and risk decreases along a design time line as

more information becomes available. The decrease in uncertainty along a design time-line is a

result of a reduction in the number of uncertain parameters as well as a reduction in the extent of

uncertainty of the parameter. A decrease in the extent of uncertainty refers to a reduction in the

range of values in which an uncertain parameter may lie. To be able to make decisions and

progress with the design of the system it is necessary to incorporate this uncertainty in a design

model. It is desirable to develop a baseline model that is applicable to all phases of a design

process. The philosophy behind modeling uncertainty is to represent appropriately the available

information rather than seeking unavailable information. The ability to model soft information is

of key significance in starting a design process. A major limitation of traditional design

processes is that they require precisely defined information about the design environment. A

mathematical construct called the compromise Decision Support Problem (C-DSP) (Mistree, et

al., 1992) is used as the base line model for this case study. The three kinds of decision making


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activities (Luce and Raiffa, 1957) mentioned earlier are modeled using three formulations of the

compromise DSP:

?? Crisp C-DSP (Mistree, et al., 1992): Decisions under certainty

?? Fuzzy C-DSP (Zhou, 1988): Decisions made with imprecise information

?? Bayesian C-DSP (Vadde, et al., 1994b): Decisions under risk or stochastic uncertainty

A procedure that utilizes fuzzy parameters (Section 2.4) adequately represents

imprecise information (Wood, et al., 1990). A design using such a fuzzy model may not be

accurate to conclude the design process, but could very well be used to give a designer more

information about the behavior of the model. At some point later in the design time-line, the

availability of a statistically significant sample set (probability distribution), may make it

appropriate to switch to the usage of stochastic parameters (Section 2.5) to model uncertainty.

Further, fuzzy set theory or Bayesian statistics could be used to handle all forms of uncertainty

(Vadde, et al., 1994b). When clear and well defined information is available, a crisp

formulation is used. Thus the usage of such mathematical models for uncertainty is very useful,

in making progressive refinements to design processes as more information becomes available.

The rationale for using uncertain parameters in this thesis is that there are n

robust concurrent design of engine lubricated components

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