Designing Precision Machines

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Principles and Techniques for Designing Precision Machines
Layton Carter Hale
LAWRENCE LIVERMORE NATIONAL LABORATORY

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1 Introduction 24
1.1 Contributions of this Thesis 25
1.2 Introduction to Case Studies 27
1.2.1 The Large Optics Diamond Turning Machine (LODTM) 27
1.2.2 Accuracy Enhancement of High-Productivity Machine Tools 31
1.2.3 The National Ignition Facility (NIF) 34
1.2.4 Extreme Ultraviolet Lithography Projection Optics 36
2 Precision Engineering Principles 3 8
2.1 Determinism 38
2.1.1 The Error Budget as a Deterministic Tool 39
2.1.2 An Editorial Note on Determinism 44
2.2 Alignment Principles 46
2.3 Symmetry 47
2.4 Separation of Metrology and Structural Loops 48
2.5 Separation of Systematic Errors 48
2.5.1 Reversal Techniques 49
2.5.2 Multi-Step Averaging 59
2.5.3 Closure and Subdivision 60
2.5.4 Self Calibration of 2-D Artifacts 62
2.5.5 Volumetric Error Mapping 66
2.6 Exact-Constraint Design 67
2.7 Elastic Averaging 82
2.8 Thermal Management 83
2.9 Materials Selection 89
3 Design Techniques 9 4
3.1 Conceptual Design 95
3.1.1 Understanding the Problem 95
3.1.2 Generating Concepts 96
3.1.3 Visualization Techniques 97
3.2 Design Axioms 98
3.3 The Analytic Hierarchy Process 104
3.3.1 A New Formulation of the AHP 105
3.3.2 The Reciprocal Matrix and Redundancy 107
3.3.3 Duality in the Decision Vector 112
4 Structural Design 114
4.1 Guidelines from Structural Mechanics 114
4.2 Modeling Complex Structures 134
4.3 Shear Panel Models 137
4.4 A Case Study of the MaximÔ Column 140
5 Deterministic Damping 148
5.1 Viscoelastic Constrained-Layer Damping 148
5.2 Squeeze-Film Damping 156
5.3 Tuned-Mass Damping 164
5.4 Damping Experiments 168
5.4.1 Constrained-Layer Damping on the Maxim Column 168
5.4.2 Dynamic Compliance Tests on the LLNL Maxim Column 172
6 Practical Exact-Constraint Design 174
6.1 Useful Constraint Devices and Arrangements 174
6.1.1 Basic Blade Flexures 175
6.1.2 Basic Kinematic Couplings 177
6.1.3 Extensions of Basic Types 179
6.2 Analytical Design of Flexures 184
6.2.1 Comparison of Flexure Profiles 185
6.2.2 A Study on Fillets for Blade Flexures 187
6.2.3 The Compact Pivot Flexure 191
6.2.4 Helical Blades for a Ball-Screw Isolation Flexure 194
6.2.5 A General Approach for Analyzing Flexure Systems 197
6.3 Friction-Based Design of Kinematic Couplings 205
6.3.1 Friction Effects in Kinematic Couplings 205
6.3.2 Centering Ability of the Basic Kinematic Couplings 206
6.3.3 A General Approach for Optimizing Centering Ability 209
6.4 MathcadÔ Documents for Generalized Kinematic Modeling 213
6.4.1 Flexure System Analysis Program 213
6.4.2 Kinematic Coupling Analysis Program 218
7 Examples of Exact-Constraint Designs 224
7.1 Optic Mounts for EUVL Projection Optics 224
7.2 A Gravity-Compensating Optic Mount for EUVL 227
7.3 qx-qy-Z Flexure Stage for EUVL Projection Optics 229
7.4 X-Y Flexure Stage for EUVL Projection Optics 231
7.5 Kinematic Mounts for NIF Optics Assemblies 233
7.6 Tip-Tilt Mounts for NIF Large-Aperture Optics 240
8 Anti-Backlash Transmission Design 242
8.1 Preloaded Rolling-Element Bearings 243
8.2 Preloaded Gear Trains 249
8.2.1 Modeling Preloaded Gear Trains 250
8.2.2 Designing Preloaded Gear Trains 253
8.3 Dual-Motor Drives 260
8.4 Commercial Differential Drives 263
8.4.1 The Cycloidal Drive 265
8.4.2 The Harmonic Drive 267
8.4.3 The Epicyclic Drive 267
8.4.4 Experimental Results 268
8.4.5 Conclusions 271
8.5 The NIF Precision Linear Actuator 272
8.5.1 The Differential Friction Drive 274
8.5.2 Test Results for the NIF Actuator 280
9 Conceptual Design of a Horizontal Machining Center 286
9.1 Developing Specifications 287
9.1.1 Machining Study 288
9.1.2 Spindle Power, Torque and Speed 288
9.1.3 Axis Velocity, Acceleration and Thrust 292
9.1.4 Part Size and Weight .. 294
9.1.5 Ranges of Travel 294
9.1.6 Volumetric Accuracy 295
9.1.7 Static and Dynamic Stiffness (or Compliance) 298
9.2 Design Strategies 300
9.2.1 Accuracy 300
9.2.2 Thermal Stability 307
9.2.3 Structural Stability 309
9.2.4 Stiffness 311
9.2.5 Productivity 312
9.2.6 Manufacturability 315
9.3 Selecting a Configuration of Axes 316
9.3.1 AHP Criteria 317
9.3.2 Discussion of Results 320
9.4 Design Layouts 322
9.5 Analytical Results 328
9.5.1 The Spindle Carrier Model 328
9.5.2 The Column Model 329
9.5.3 The Work Carriage Model 333
9.5.4 The Base Model 334
9.5.5 The Assembly Model 338
9.5.6 Tool-to-Work Compliance 339
9.5.7 Predicted Error Motion 341
9.6 Recommendations 348

Bibliography 352
A Transformation Matrices 360
A.1 The Rotation Matrix 361
A.2 The Inverse Problem, Finding the Angles of Rotation 364
A.3 The Homogeneous Transformation Matrix (HTM) 367
A.4 The Cross Product Matrix 368
A.5 Equations of Compatibility and Equilibrium 368
A.6 The [6 x 6] Transformation Matrix 370
A.7 Dynamic Simulations Involving Large-Angle Motion 371
A.8 MatlabÔ Functions for Transformation Matrices 375
B Least-Squares Fitting 384
B.1 Solution by Singular Value Decomposition 386
B.2 Nonlinear Least Squares 389
B.3 Planar Fit 390
B.4 Spherical Fit 391
B.5 Linear Fit 392
B.6 Fitting Surfaces of Revolution 393
B.6.1 Cylindrical Fit 393
B.6.2 Conical Fit 395
B.6.3 Fitting a General-Form Revolution 397
B.7 Fitting Quadratic Surfaces 397
B.8 Fitting Cubic Splines 399
B.9 MatlabÔ Functions for Least-Squares Fitting 403
C Contact Mechanics 414
C.1 Circular Contact 418
C.2 Elliptical Contact 419
C.3 Line Contact 421
C.4 Sphere and Cone Contact 422
C.5 Tangential Loading of an Elliptical Contact 422
C.5.1 Stationary Elliptical Contact, Variable Tangential Force
C.6 MathcadÔ Documents for Contact Mechanics 427
D Determinism in Die Throwing and the Transition to Chaos 438
D.1 Developing the Dynamic Model 439
D.2 Developing the Sensitivity Model 442
D.3 Simulation Results 446
D.4 An Example from the Chaos Literature 451
E Orthogonal Machining Model 454
F Friction and Backlash in Servo Mechanisms 458
F.1 Developing the Dynamic Model 458
F.2 Simulation Results 464
G AHP Spreadsheet and Configuration Drawings 468

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