**حل كتاب **

**Mechanical Design of Machine Elements and Machines – Solution Manual **

**A Failure Prevention Perspective **

**Second Edition **

**Jack A. Collins, Henry R. Busby & George H. Staab **

**The Ohio State University **

**Contents**

**Part One Engineering Principles **

**Chapter 1**

**Keystones of Design: Materials**

**Selection and Geometry Determination 1**

**1.1 Some Background Philosophy 1**

**1.2 The Product Design Team 2**

**1.3 Function and Form; Aesthetics and**

**Ergonomics 5**

**1.4 Concepts and Definition of Mechanical**

**Design 6**

**1.5 Design Safety Factor 7**

**1.6 Stages of Design 7**

**1.7 Steps in the Design Process 9**

**1.8 Fail Safe and Safe Life Design Concepts 9**

**1.9 The Virtues of simplicity 10**

**1.10 Lessons Learned Strategy 12**

**1.11 Machine Elements, Subassemblies, and**

**the Whole Machine 12**

**1.12 The Role of Codes and Standards in the**

**Design Process 13**

**1.13 Ethics in Engineering Design 13**

**1.14 Units 14**

**Chapter 2**

**The Failure Prevention Perspective 22**

**2.1 Role of Failure Prevention Analysis in**

**Mechanical Design 22**

**2.2 Failure Criteria 22**

**2.3 Modes of Mechanical Failure 23**

**2.4 Elastic Deformation, Yielding, and Ductile**

**Rupture 28**

**2.5 Elastic Instability and Buckling 34**

**Buckling of a Simple Pin-Jointed Mechanism 35**

**Buckling of a Pinned-End Column 36**

**Columns with Other End Constraints 38**

**Inelastic Behavior and Initially Crooked**

**Columns 39**

**Column Failure Prediction and Design**

**Considerations 40**

**Buckling of Elements Other Than Columns 43**

**2.6 Shock and Impact 46**

**Stress Wave Propagation Under Impact Loading**

**Conditions 46**

**Energy Method of Approximating Stress and**

**Deflection Under Impact Loading**

**Conditions 47**

**2.7 Creep and Stress Rupture 52**

**Predictions of Long-Term Creep Behavior 53**

**Creep under Uniaxial State of Stress 55**

**Cumulative Creep Prediction 57**

**2.8 Wear and Corrosion 59**

**Wear 59**

**Corrosion 64**

**2.9 Fretting, Fretting Fatigue, and Fretting**

**Wear 66**

**Fretting Fatigue 67**

**Fretting Wear 68**

**Minimizing or Preventing Fretting Damage 69**

**2.10 Failure Data and the Design Task 70**

**2.11 Failure Assessment and Retrospective**

**Design 70**

**2.12 The Role of Safety Factors; Reliability**

**Concepts 71**

**2.13 Selection and Use of a Design Safety**

**Factor 72**

**2.14 Determination of Existing Safety Factors**

**in a Completed Design: A Conceptual**

**Contrast 744.6 Stresses Caused by Curved Surfaces in**

**Contact 174**

**4.7 Load Sharing in Redundant Assemblies**

**and Structures 179**

**Machine Elements as Springs 180**

**4.8 Preloading Concepts 186**

**4.9 Residual Stresses 189**

**Estimating Residual Stress 190**

**4.10 Environmental Effects 194**

**Chapter 5**

**Failure Theories 205**

**5.1 Preliminary Discussions 205**

**5.2 Multiaxial States of Stress and Strain 205**

**Principal Stresses 205**

**Stress Cubic Equation 206**

**Mohr’s Circle Analogy for Stress 210**

**Strain Cubic Equation and Principal Strains 213**

**Mohr’s Circle Analogy for Strain 213**

**Elastic Stress-Strain Relationships**

**(Hooke’s Law) 214**

**5.3 Stress Concentration 215**

**Stress Concentration Effects 216**

**Multiple Notches 217**

**5.4 Combined Stress Theories of Failure 224**

**Maximum Normal Stress Theory**

**(Rankine’s Theory) 225**

**Maximum Shearing Stress Theory**

**(Tresca–Guest Theory) 226**

**Distortion Energy Theory**

**(Huber–von Mises–Hemcky Theory) 227**

**Failure Theory Selection 229**

**5.5 Brittle Fracture and Crack Propagation;**

**Linear Elastic Fracture Mechanics 233**

**5.6 Fluctuating Loads, Cumulative Damage,**

**and Fatigue Life 241**

**Fluctuating Loads and Stresses 242**

**Fatigue Strength and Fatigue Limit 244**

**Estimating S-N Curves 246**

**Stress-Life (S-N) Approach to Fatigue 248**

**Factors That May Affect S-N Curves 248**

**Nonzero-Mean Stress 258**

**Cumulative Damage Concepts and Cycle**

**Counting 266**

**Multiaxial Cyclic Stress 272**

**Fracture Mechanics (F-M) Approach to Fatigue 273**

**Crack Initiation Phase 273**

**Crack Propagation and Final Fracture Phases 276**

**x / Contents**

**2.15 Reliability: Concepts, Definitions, and**

**Data 76**

**System Reliability, Reliability Goals, and**

**Reliability Allocation 80**

**Reliability Data 83**

**2.16 The Dilemma of Reliability Specification**

**versus Design Safety Factor 84**

**Chapter 3**

**Materials Selection 93**

**3.1 Steps in Materials Selection 93**

**3.2 Analyzing Requirements of the**

**Application 93**

**3.3 Assembling Lists of Responsive**

**Materials 94**

**3.4 Matching Responsive Materials to**

**Application Requirements; Rank Ordered**

**Data Table Method 105**

**3.5 Matching Responsive Materials to**

**Application Requirements; Ashby chart**

**Method 114**

**Chapter 4**

**Response of Machine Elements to Loads**

**and Environments; Stress, Strain, and**

**Energy Parameters 123**

**4.1 Loads and Geometry 123**

**4.2 Equilibrium Concepts and Free-Body**

**Diagrams 123**

**4.3 Force Analysis 124**

**4.4 Stress Analysis; Common Stress Patterns**

**for Common Types of Loading 126**

**Direct Axial Stress 128**

**Bending; Load, Shear, and Moment**

**Diagrams 128**

**Bending; Straight Beam with Pure Moment 133**

**Bending; Initially Curved Beams 137**

**Bending; Straight Beam with Transverse**

**Forces 142**

**Direct Shear Stress and Transverse Shear**

**Stress 142**

**Torsional Shear; Circular Cross Section 150**

**Torsional Shear; Noncircular Cross Section 152**

**Torsional Shear; Shear Center in Bending 157**

**Surface Contact Stress 160**

**4.5 Deflection Analysis Common Types of**

**Loading 161**

**Stored Strain Energy 162**

**Castigliano’s Theorem 164Design Issues in Fatigue Life Prediction 280**

**Fatigue Stress Concentration Factors and**

**Notch Sensitivity Index 280**

**5.7 Multiaxial States of Cyclic Stress and**

**Multiaxial Fatigue Failure Theories 283**

**Chapter 6**

**Geometry Determination 305**

**6.1 The Contrast in Objectives Between**

**Analysis and Design 305**

**6.2 Basic Principles and Guidelines for**

**Creating Shape and Size 306**

**Direct Load Path Guideline 306**

**Tailored-Shape Guideline 307**

**Triangle-Tetrahedron Guideline 308**

**Buckling Avoidance Guideline 309**

**Hollow Cylinder and I-Beam Guideline 310**

**Conforming Surface Guideline 310**

**Lazy-Material Removal Guideline 311**

**Merging Shape Guideline 313**

**Strain Matching Guideline 313**

**Load Spreading Guideline 314**

**Contents / xi**

**6.3 Critical Sections and Critical Points 315**

**6.4 Transforming Combined Stress Failure**

**Theories into Combined Stress Design**

**Equations 317**

**6.5 Simplifying Assumptions: The Need and**

**the Risk 318**

**6.6 Iteration Revisited 319**

**6.7 Fits, Tolerances, and Finishes 323**

**Chapter 7**

**Design-Stage Integration of Manufacturing**

**and Maintenance Requirements 333**

**7.1 Concurrent Engineering 333**

**7.2 Design for Function, Performance, and**

**Reliability 334**

**7.3 Selection of the Manufacturing Process 334**

**7.4 Design for Manufacturing (DFM) 337**

**7.5 Design for Assembly (DFA) 337**

**7.6 Design for Critical Point Accessibility,**

**Inspectability, Disassembly, Maintenance,**

**and Recycling 339**

**Chapter 8**

**Power Transmission Shafting; Couplings,**

**Keys, and Splines 341**

**8.1 Uses and Characteristics of shafting 341**

**8.2 Potential Failure Modes 343**

**8.3 Shaft Materials 344**

**8.4 Design Equations–Strength Based 345**

**8.5 Design Equations–Deflection Based 353**

**8.6 Shaft Vibration and Critical Speed 358**

**8.7 Summary of Suggested Shaft Design**

**Procedure; General Guidelines for Shaft**

**Design 360**

**8.8 Couplings, Keys, and Splines 361**

**Rigid Couplings 361**

**Flexible Coupling 362**

**Keys, Splines, and Tapered Fits 365**

**Chapter 9**

**Pressurized Cylinders; Interference Fits 382**

**9.1 Uses and Characteristics of Pressurized**

**Cylinders 382**

**9.2 Interference Fit Applications 382**

**9.3 Potential Failure Modes 383**

**9.4 Materials for Pressure Vessels 383**

**9.5 Principles from Elasticity Theory 384**

**9.6 Thin-Walled Cylinders 385**

**9.7 Thick-Walled Cylinders 386**

**9.8 Interference Fits: Pressure and Stress 392**

**9.9 Design for Proper Interference 396**

**Chapter 10**

**Plain Bearings and Lubrication 403**

**10.1 Types of Bearings 403**

**10.2 Uses and Characteristics of Plain**

**Bearings 403**

**10.3 Potential Failure Modes 404**

**10.4 Plain Bearing Materials 405**

**10.5 Lubrication Concepts 405**

**10.6 Boundary-Lubricated Bearing Design 406**

**10.7 Hydrodynamic Bearing Design 409**

**Lubricant Properties 410**

**PART TWO DESIGN APPLICATIONSTightening Torque; Fastener Loosening 507**

**Multiply Bolted Joints; Symmetric and**

**Eccentric Loading 509**

**13.5 Rivets 517**

**Rivet Materials 517**

**Critical Points and Stress Analysis 518**

**13.6 Welds 522**

**Base Metals, Filler Materials, and Weldability 526**

**Butt Welds 528**

**Fillet Welds 529**

**13.7 Adhesive Bonding 538**

**Joint Design 538**

**Structural Adhesive Materials 540**

**Chapter 14**

**Springs 546**

**14.1 Uses and Characteristics of Springs 546**

**14.2 Types of Springs 546**

**14.3 Potential Failure Modes 548**

**14.4 Spring Materials 549**

**14.5 Axially Loaded Helical-Coil Springs;**

**Stress, Deflection, and Spring Rate 552**

**Deflection and Spring Rate 557**

**Buckling and Surging 559**

**14.6 Summary of Suggested Helical-Coil**

**Spring Design Procedure, and General**

**Guidelines for Spring Design 562**

**14.7 Beam Springs (Leaf Springs) 568**

**14.8 Summary of Suggested Leaf Spring**

**Design Procedure 574**

**14.9 Torsion Bars and Other Torsion Springs 578**

**14.10 Belleville (Coned-Disk) Springs 581**

**14.11 Energy Storage in Springs 582**

**Chapter 15**

**Gears and Systems of Gears 594**

**15.1 Uses and Characteristics of Gears 594**

**15.2 Types of Gears; Factors in Selection 595**

**15.3 Gear Trains; Reduction Ratios 600**

**15.4 Potential failure Modes 605**

**15.5 Gear Materials 607**

**15.6 Spur Gears; Tooth Profile and Mesh**

**Geometry 608**

**Involute Profiles and Conjugate Action 609**

**Gearing Nomenclature; Tooth Shape and**

**Size 610**

**Gear-Tooth Systems 612**

**Mesh Interactions 614**

**xii / Contents**

**Loading, Friction, and Lubricant Flow**

**Relationships 410**

**Thermal Equilibrium and Oil Film Temperature**

**Rise 416**

**Design Criteria and Assumptions 419**

**Suggested Design Procedure 420**

**10.8 Hydrostatic Bearing Design 425**

**Chapter 11**

**Rolling Element Bearings 429**

**11.1 Uses and Characteristics of Rolling**

**Element Bearings 429**

**11.2 Types of Rolling Element Bearings 430**

**11.3 Potential Failure Modes 433**

**11.4 Bearing Materials 433**

**11.5 Bearing Selection 434**

**Basic Load Ratings 435**

**Reliability Specifications 435**

**Suggested Selection Procedure for Steady**

**Loads 436**

**Suggested Selection Procedure for Spectrum**

**Loading 448**

**Lubrication 451**

**11.6 Preloading and Bearing Stiffness 453**

**11.7 Bearing Mounting and Enclosure 457**

**Chapter 12**

**Power Screw Assemblies 462**

**12.1 Uses and Characteristics of Power**

**Screws 462**

**12.2 Potential Failure Modes 466**

**12.3 Materials 466**

**12.4 Power Screw Torque and Efficiency 467**

**12.5 Suggested Power Screw Design Procedure 473**

**12.6 Critical Points and Thread Stresses 474**

**Chapter 13**

**Machine Joints and Fastening Methods 485**

**13.1 Uses and Characteristics of Joints in**

**Machine Assemblies 485**

**13.2 Selection of Joint Type and Fastening**

**Method 485**

**13.3 Potential Failure Modes 487**

**13.4 Threaded Fasteners 488**

**Screw Thread Standards and Terminology 489**

**Threaded Fastener Materials 492**

**Critical Points and Thread Stresses 494**

**Preloading Effects; Joint Stiffness and Gasketed**

**Joints 49715.7 Gear Manufacturing; Methods, Quality,**

**and Cost 618**

**Gear Cutting 618**

**Gear Finishing 620**

**Cutter Path Simulation, Mesh Deflection,**

**and Profile Modification 621**

**Accuracy Requirements, Measurement Factors,**

**and Manufacturing Cost Trends 622**

**15.8 Spur Gears; Force Analysis 624**

**15.9 Spur Gears; Stress Analysis and Design 626**

**Tooth Bending: Simplified Approach 626**

**Tooth Bending: Synopsis of AGMA Refined**

**Approach 631**

**Surface Durability: Hertz Contact Stresses and**

**Surface Fatigue Wear 639**

**Surface Durability: Synopsis of AGMA Refined**

**Approach 641**

**15.10 Lubrication and Heat Dissipation 645**

**15.11 Spur Gears; Summary of Suggested**

**Design Procedure 647**

**15.12 Helical Gears; Nomenclature, Tooth**

**Geometry, and Mesh Interaction 648**

**15.13 Helical Gears; Force Analysis 653**

**15.14 Helical Gears; Stress Analysis and**

**Design 654**

**15.15 Helical Gears; Summary of Suggested**

**Design Procedure 656**

**15.16 Bevel Gears; Nomenclature, Tooth**

**Geometry, and Mesh Interaction 662**

**15.17 Bevel Gears; Force Analysis 665**

**15.18 Bevel Gears; Stress Analysis and Design 666**

**15.19 Bevel Gears; Summary of Suggested**

**Design Procedure 668**

**15 20 Worm Gears and Worms; Nomenclature,**

**Tooth Geometry, and Mesh Interaction 675**

**15.21 Worm Gears and Worms; Force Analysis**

**and Efficiency 679**

**15.22 Worm Gears and Worms; Stress Analysis**

**and Design 682**

**15.23 Worm Gears and Worms; Suggested**

**Design Procedure 684**

**Chapter 16**

**Brakes and Clutches 701**

**16.1 Uses and Characteristics of Brakes**

**and Clutches 701**

**16.2 Types of Brakes and Clutches 702**

**16.3 Potential Failure Modes 704**

**16.4 Brake and Clutch Materials 704**

**Contents / xiii**

**16.5 Basic Concepts for Design of Brakes**

**and Clutches 705**

**16.6 Rim (Drum) Brakes with Short Shoes 708**

**16.7 Rim (Drum) Brakes with Long Shoes 719**

**16.8 Band Brakes 727**

**16.9 Disk Brakes and Clutches 732**

**Uniform Wear Assumption 733**

**Uniform Pressure Assumption 735**

**16.10 Cone Clutches and Brakes 738**

**Chapter 17**

**Belts, Chains, Wire Rope, and Flexible**

**Shafts 746**

**17.1 Uses and Characteristics of Flexible**

**Power Transmission Elements 746**

**17.2 Belt Drives; Potential Failure Modes 750**

**17.3 Belts; Materials 752**

**17.4 Belt Drives; Flat Belts 752**

**17.5 Belt Drives; V-Belts 757**

**17.6 Belt Drives; Synchronous Belts 769**

**17.7 Chain Drives; Potential Failure Modes 769**

**17.8 Chain Drives; Materials 770**

**17.9 Chain Drives; Precision Roller Chain 771**

**17.10 Roller Chain Drives; Suggested Selection**

**Procedure 774**

**17.11 Chain Drives; Inverted-Tooth Chain 779**

**17.12 Wire Rope; Potential Failure Modes 779**

**17.13 Wire Rope; Materials 782**

**17.14 Wire Rope; Stresses and Strains 782**

**17.15 Wire Rope; Suggested Selection**

**Procedure 786**

**17.16 Flexible Shafts 791**

**Chapter 18**

**Flywheels and High-Speed Rotors 798**

**18.l Uses and Characteristics of Flywheels 798**

**18.2 Fluctuating Duty Cycles, Energy**

**Management, and Flywheel inertia 799**

**18.3 Types of Flywheels 804**

**18.4 Potential Failure Modes 805**

**18.5 Flywheel Materials 805**

**18.6 Spoke-and-Rim Flywheels 806**

**Stresses in a Rotating Free Ring 807**

**Bending Stresses in Flywheel Rim 808**

**Spoke-Axial Tensile Stresses 809**

**18.7 Disk Flywheels of Constant Thickness 809**

**18.8 Disk Flywheels of Uniform Strength 81519.5 Summary of Suggested Crankshaft**

**Design Procedure 826**

**Chapter 20**

**Completing the Machine 843**

**20.1 Integrating the Components; Bases,**

**Frames, and Housings 843**

**20.2 Safety Issues; Guards, Devices, and**

**Warnings 850**

**20.3 Design Reviews; Releasing the Final**

**Design 855**

**xiv / Contents**

**18.9 Uniform-Strength Disk Flywheel with**

**a Rim 816**

**18.10 Flywheel-to-Shaft Connections 820**

**Chapter 19**

**Cranks and Crankshafts 824**

**19.1 Uses and Characteristics of Crankshafts 824**

**19.2 Types of Crankshafts 825**

**19.3 Potential Failure Modes 826**

**19.4 Crankshaft Materials 826**

**Table A-4**

**Section Properties of Selected S**

**(Standard 1) Shapes 870**

**Table A-5**

**Section Properties of Selected C**

**(Channel) Shapes 871**

**Table A-6**

**Section Properties of Selected Equal-Leg**

**L (Angle) Shapes 872**

**NSPE Code of Ethics for Engineers 859**

**Table A-1**

**Coefficients of Friction 864**

**Table A-2**

**Mass Moments of Inertia J and Radii of**

**Gyration k for Selected Homogeneous Solid**

**Bodies Rotating About Selected Axes, as**

**Sketched 867**

**Table A-3**

**Section Properties of Selected W**

**(Wide Flange) Shapes 868**

**APPENDIX**

**REFERENCES 873**

**PHOTO CREDITS 881**

**INDEX **

**Index**

**883**

**Abrasive wear, 23, 25, 59, 62**

**Acme threads, 463, 464, 470, 471**

**Adhesive bonding, 538–542**

**Adhesive wear, 23, 25, 59, 62**

**American Bearing Manufacturers**

**Association (ABMA), 430**

**American Gear Manufacturers Association**

**(AGMA), 607**

**Angle shapes (equal leg), section**

**properties, 872**

**Angular velocity ratio, 595, 600–605**

**Anthropometrics, 5**

**Archard adhesive wear constant, 60**

**Area moment of inertia (table), 135**

**Ashby charts, 105–111, 114–120**

**ASME Boiler and Pressure Vessel Code, 382**

**Asperities, surface, 59, 409**

**Assembly, design for, 337, 338**

**Assembly process, selection, 337, 338**

**Backlash (gears), 618**

**Ball screws (see power screws)**

**Baseplates, 843, 844**

**Bases, 843**

**Beam springs, 568–578 (also see springs)**

**Bearings:**

**antifrictional (see rolling element bearings)**

**basic load rating, 62**

**journal (see plain bearings)**

**plain (see plain bearings)**

**rolling element (see rolling element**

**bearing)**

**sleeve (see plain bearings)**

**sliding (see plain bearings)**

**Belleville springs (coned disk), 581, 582**

**Belts:**

**failure modes, 750, 751**

**flat, 752–756**

**flat belt selection. 754–756**

**materials, 752**

**synchronous, 769**

**timing, 769**

**uses, 746**

**V-belts, 756–768**

**V-belt datum system, 759**

**V-belt pitch system, 759**

**V-belt selection, 763–768**

**Bending:**

**curved beams, 137–142**

**gear teeth (see gears)**

**load, shear, and moment diagrams (table),**

**128–133**

**neutral axis, 134, 138, 144**

**pure bending, 134**

**spring rate, 180, 181**

**straight beams, 128–137**

**transverse loads, 142–150**

**transverse shear, 142–150**

**Bevel gears, 662–675 (also see gears)**

**Biaxial brittle fracture strength data, 226**

**Biaxial state of stress, 127, 205–213**

**Biaxial yield strength data, 227**

**Body force, 123**

**Boundary conditions, 385, 387, 388**

**Bolts, (see fasteners)**

**Brakes:**

**band, 727–732**

**caliper, 735, 736**

**cone, 738, 739**

**design procedure, 705–707**

**disk, 732–738**

**external shoe, 703, 708, 724**

**failure mode, 704**

**friction coefficient (table), 706**

**friction lining material, 706**

**internal shoe, 703, 708, 724**

**long-shoe drum type, 719–727**

**multiple disk, 732–738**

**materials, 704–706**

**self-energizing, 708**

**self-locking, 708**

**short-shoe drum type, 708–719**

**temperature rise, 711, 712**

**types, 702–704**

**uniform pressure assumption (disk), 735**

**uniform wear assumption (disk), 733, 734**

**uses, 701, 702**

**Brinnelling, 23, 24**

**Brittle fracture, 23, 24, 225, 233–241**

**Buckling, 23, 27, 34–45**

**Buckling:**

**column, 35, 36**

**critical buckling load, 35–44**

**critical unit load, 40**

**effective column length, 38**

**effective slenderness ratio, 39**

**end support influence, 36, 38**

**Euler’s critical load, 38**

**Euler-Engesser equation, 39**

**externally pressurized thin-walled**

**tubes, 44**

**helical coil springs, 559–561**

**initially crooked columns, 39, 40**

**local buckling, 41**

**long columns, 41**

**long thin rod, 43, 44**

**onset of, 35**

**pin-jointed mechanisms, 35, 36**

**primary buckling, 41**

**secant formula, 39, 40**

**short columns, 40, 41**

**thin deep beams, 44**

**Buckling avoidance guideline, 309, 310**

**Butt welds, 528**

**Buttress thread, 463, 464**

**Castigliano’s theorem, 164–171**

**Cathodic protection, 66**

**Chains:**

**chordial action, 773, 774**

**failure modes, 769, 770**

**inverted tooth, 779**

**materials, 770, 771**

**multiple strand factor (table), 773**

**precision roller chain, 771–779**

**precision roller chain, selection, 774–779**

**polygonal action, 773, 774**

**silent, 779**

**uses, 746**

**Channel shape, section properties, 871**

**Clutches:**

**band, 727–732**

**cone, 738, 739**

**design procedure, 705–707**

**disk, 732–738Clutches (Continued)**

**failure modes, 704**

**friction coefficients (table), 706**

**friction lining material, 706**

**materials, 704–706**

**multiple disk, 732–738**

**temperature rise, 711, 712**

**types, 702–704**

**uniform pressure assumption (disk), 735**

**uniform wear assumption (disk), 733,**

**734**

**uses, 701, 702**

**Code of ethics (NSPE), 14, 15, 859–863**

**Codes, 13**

**Codes and standards, 13**

**Coefficient of speed fluctuations**

**(flywheels), 800, 801**

**Cold-rolling, 189**

**Columns (see buckling)**

**Combined creep and fatigue, 23–28**

**Combined stress design equations, 317, 318**

**Combines stress theory of failure, 33,**

**224–233, 317, 318**

**Conceptual design, 8**

**Concurrent design, 333, 336**

**Concurrent engineering, 333, 336**

**Conforming surface guideline, 310, 311**

**Configurational guidelines, 306–315**

**Configurational guidelines:**

**buckling avoidance, 309, 310**

**conforming surfaces, 310, 311**

**direct load path, 306, 307**

**hollow cylinder and I-beam, 310**

**lazy material removal, 311, 312**

**load spreading, 314**

**merging shape, 313**

**strain matching, 313, 314**

**triangle-tetrahedron, 308, 309**

**tailored shape, 307, 308**

**Constant thickness disk flywheel, 809–815**

**(also see flywheels)**

**Contact stress (Hertz), cylinders, 176–179**

**Contact stress (Hertz), spheres, 174–175**

**Corrosion:**

**biological corrosion, 23, 25, 64**

**cathodic protection, 66**

**cavitation corrosion, 23, 25, 64, 65**

**direct chemical attack, 23, 25, 64**

**erosion corrosion, 23, 25, 64**

**galvanic corrosion, 23, 25, 64, 65**

**hydrogen damage, 23, 25, 64**

**intergranular corrosion, 23, 25, 65**

**pitting corrosion, 23, 25, 65**

**protection, 65**

**sacrificial anode, 65**

**selective leaching, 23, 25, 64**

**stress corrosion, 23, 25, 64–66**

**Corrosion fatigue, 23, 28, 64**

**Corrosion fatigue strength properties**

**(table), 102**

**Corrosion wear, 23, 28**

**Couplings:**

**bellows, 363, 364**

**elastomeric disk, 363, 364**

**failure modes, 363–365**

**flexible, 361, 363–365**

**flexible disk, 362, 363**

**gear, 363, 364**

**rigid, 361, 362, 369–372**

**roller chain, 363, 364**

**rubber cap, 364**

**sliding disk, 363, 364**

**spring, 363, 364**

**universal joint (U-joint), 365**

**Crack:**

**initiation, 241, 242, 273–279**

**length, 233**

**opening mode (Mode I), 233**

**propagation, 233, 241, 276–279**

**size, unstable (critical), 241, 276–279**

**surface, 233**

**surface flaw shape parameter, 233, 236**

**through-the-thickness, 234–237**

**Crankshaft:**

**center cranks, 825**

**design procedure, 826–841**

**disk cranks, 825**

**failure modes, 826**

**materials, 826**

**side cranks, 825**

**types, 825**

**uses, 824, 825**

**Creep, 23, 26, 52–58**

**Creep:**

**constant creep rate, 56**

**cumulative creep, 57, 58**

**Larson-Miller theory, 54**

**logarithmic creep, 56**

**log-log stress-time creep, 65**

**long-term creep, 53–58**

**parabolic creep, 56**

**Robinson hypothesis, 57, 58**

**Stage I transient creep, 56**

**Stage II steady-state creep, 56**

**true creep strain, 56**

**under axial stress, 55–58**

**Creep buckling, 23, 28**

**Creep deformation, 53**

**Creep-limited maximum stress (table), 98**

**Creep strain, 52**

**Creep rupture, 52, 53**

**Creep testing:**

**abridged method, 53**

**mechanical acceleration method, 53**

**thermal acceleration method, 53**

**Critical points, 315–317, 474–481,**

**494–497, 582, 583**

**Critical point accessibility, design for, 339,**

**340**

**Critical sections, 315–317**

**Critical speed, rotating shafts, 358–360**

**Critical stress intensity factor, 234, 237, 238**

**Cumulative creep prediction, 57, 58**

**Cumulative damage, 241, 242, 266–272**

**Cumulative distribution function, 253**

**Curved beams, 137–142**

**Curved surfaces in contact, 174–179**

**Customer attributes, 3, 4**

**Customer perceptions, 5**

**CV joints, 365**

**Cycle counting, rain flow method, 266–272**

**Cyclic equivalent stress, 283–291**

**Cyclic multiaxial state of stress, 283–291**

**Cyclic stresses, 242–291**

**Deflection:**

**axial loading, 161**

**bending, 129–133, 162, 164**

**Castigliano’s theorem, 164–171**

**cylinders in contact, 176**

**shafts, 353–358**

**spheres in contact, 174**

**Hertz contact, 161, 174, 176**

**torsional loading, 161**

**Deflection analysis, 126**

**Design:**

**concurrent, 333, 336**

**detail design, 8**

**embodiment design, 8**

**fail safe design, 9**

**intermediate design, 8**

**mechanical design, 1**

**preliminary design, 7, 8**

**safe life design, 9**

**Design equations, combined stress, 317, 318**

**Design for assembly (DFA), 337, 338**

**Design for manufacturing (DFM), 337**

**Design for “X” (DFX), 333, 334**

**Design reviews, 10, 855**

**Design safety factors, 7, 33, 71–74, 84**

**Design steps, 9–11**

**Detail design, 8**

**Development and field service, 9**

**Dilatation energy per unit volume, 227, 228**

**Direct load path guideline, 306, 307**

**Direct shear, spring rate, 181**

**Disassembly, design for, 339, 340**

**Distortion energy design equation, 228**

**Distortion energy failure theory, 33, 224,**

**225, 227–232**

**Distortion energy per unit volume, 228**

**Distribution function (see probability**

**density function)**

**Ductile rupture, 23, 24, 33, 34**

**Ductility properties (table), 99, 100**

**Durability of gear teeth (see gears)**

**Effective stress, 228**

**Efficiency:**

**power screws, 467–473**

**worm gears, 679–682**

**Elastic instability (see buckling)**

**Elastic strain, 31, 32**

**884 IndexElastic stress-strain relationships, 214, 215**

**Elasticity theory (see theory of elasticity)**

**Elevated temperature strength (table), 96, 97**

**Embodiment design, 8**

**Energy methods:**

**Castigliano’s theorem, 164–171**

**Impact, 47–52**

**Engineering strain, 29, 30**

**Engineering stress-strain diagram, 30**

**Environmental effects, 194, 195**

**Epicylic gears, 600–605**

**Equilibrium, 123, 124, 385, 393, 412**

**Equivalent alternating stress amplitude,**

**283–291**

**Equivalent cyclic stress, 283–291**

**Equivalent mean stress, 283–291**

**Equivalent stress, 228, 272, 283–291**

**Ergonomics, 5**

**Ethics, 13, 14**

**Ethics, code of, 14, 15, 859–863**

**Ethical dilemma, 14**

**Euler’s critical load, 38**

**External energy, 47**

**Fail safe design, 9, 82**

**Failure analysis, 70, 71**

**Failure criteria, 22**

**Failure modes, 23–28 (also see mechanical**

**failure)**

**Failure prevention perspective, 22–70,**

**233–280**

**Failure theories:**

**distortional energy theory (also known as**

**octahedral shear stress theory,**

**Huber-von-Mises- Henky theory, or**

**von-Mises theory), 33, 225**

**fatigue, 224–232, 241–291**

**maximum normal stress theory (also**

**known as Rankine theory), 225**

**maximum shearing stress theory (also**

**known as Tresca Guest theory), 226,**

**227**

**selection of, 229**

**Fasteners:**

**bolts, 487, 496, 497**

**critical points, 494–497, 518–522**

**failure modes, 495–497**

**head styles, 488**

**lead (thread), 489**

**materials, 492–494**

**metric threads, 491**

**multiple threads, 489**

**reduced-body bolts, 487**

**rivets, 517–522**

**screw thread standards, 488, 489**

**thread angle, 489**

**thread series, 492**

**thread major diameter, 489**

**thread minor diameter, 489**

**thread specifications, 492**

**thread stresses, 494–497**

**tightening, 507, 508**

**torque coefficient, 508**

**unified inch, threads, 490, 491**

**Fastener loosening, 507–508**

**Fatigue:**

**completely reversed stress, 242, 258**

**corrosion fatigue, 28**

**crack growth rate, 276**

**crack initiation, 241, 242, 273–279**

**crack propagation, 233, 241, 276–279**

**critical (unstable) crack size, 241, 276–279**

**cumulative damage, 241, 242, 266–272**

**cycle ratio, 266–269**

**cyclic strain-hardening exponent, 274,**

**275**

**cyclic strength coefficients, 274, 275**

**damage fraction, 266–269**

**definitions for constant-amplitude stress**

**time pattern, 242, 243**

**estimating properties of a part, 257**

**elastic strain amplitude, 274, 275**

**estimating S-N curves, 246–248**

**factors that may affect S-N curves,**

**248–258**

**failure theories, 283–291**

**fatigue life, 241**

**fatigue limit, 244, 245**

**fatigue strength, 244, 245**

**final fracture, 276–278**

**fluctuating loads, 241**

**fracture mechanics approach**

**(F-M approach), 242**

**fretting fatigue, 23, 26, 66, 67, 69**

**high-cycle fatigue, 23, 24, 241–280**

**histogram, 245**

**impact fatigue, 23**

**infinite life diagram, 256**

**life improvement from residual stress,**

**288–291**

**life improvement form shot-peening,**

**288–291**

**linear damage rule, 266–269**

**loading spectra, 242**

**local stress-strain approach to crack**

**initiation, 273–279**

**low-cycle fatigue, 23, 24, 242**

**master diagram, 258, 259**

**modified Goodman relationships, 260,**

**261–266**

**multiaxial cyclic stress, 272**

**Neuber rule, 274**

**nonzero mean stress, 243, 258–266**

**Palmgren-Miner hypothesis, 266–269**

**Paris law, 277**

**plastic strain amplitude, 274, 275**

**probability of failure, 245**

**rain flow cycle counting, 254, 266–272**

**range of stress, 243, 276**

**released tension, 243**

**reliability, 245**

**reversals to failure, 274, 275**

**sample standard deviation, 245**

**sample mean, 245**

**scatter of life diagram, 244, 245**

**S-N curves, 244**

**SNP curves, 244, 245**

**standard deviation of fatigue strength, 253**

**strain-controlled fatigue (see low-cycle**

**fatigue)**

**stress life approach (S-N approach), 242,**

**243, 248**

**strength-influencing factors for S-N**

**curves, 247–258**

**strength reliability factors, 247**

**stress intensity factor range, 276, 277**

**stress spectra, 242, 266**

**surface fatigue, 23, 24**

**test method influence on S-N data, 248**

**thermal fatigue, 23, 24**

**total strain amplitude, 274, 275**

**zero-mean stress, 243, 258**

**Fatigue limit, 244, 246**

**Fatigue strength, 244, 246**

**Fatigue strength reduction factor, 281–283**

**Fatigue stress concentration factor, 280–283**

**Fillet welds, 529–537**

**Finishes, 328, 330**

**Fits, 323–329**

**Flexible shafts:**

**maximum operating torque (tables), 792,**

**793**

**selection procedure, 793–795**

**uses, 748–750**

**Fluctuating loads, 242**

**Flywheels:**

**bending in flywheel rims, 808, 809**

**coefficient of speed fluctuation, 800, 801**

**connection to shaft, 820, 821**

**constant thickness disk, 809–815**

**design for speed control, 799–804**

**energy management, 799–804**

**failure modes, 805**

**fluctuating duty cycle, 799–804**

**materials, 805, 806**

**rotating free ring, 807, 808**

**spoke-and-rim, 806–809**

**tension in flywheel spokes, 808, 809**

**types, 804, 805**

**uniform strength disk, 815, 816**

**uniform strength disk with rim, 816, 817**

**uses, 798**

**Force analysis, 124–126**

**Force flow lines, 124,125, 215**

**Force-induced elastic deformation, 23, 24,**

**28–31**

**Fracture mechanics, 233–241**

**Fracture mechanics approach to fatigue,**

**273–279**

**Fracture toughness, plane strain, 237**

**Frames:**

**C-frame, 844**

**design procedure, 845–850**

**Index 885Frames (Continued)**

**failure modes, 844**

**materials, 844**

**O-frame, 844**

**open truss, 843, 844**

**stressed-skin structure, 843, 844**

**thin-walled shell, 843, 844**

**Free body diagram, 123–126, 191, 386, 467**

**Fretting, 23, 26, 66–70**

**Fretting:**

**fretting action, 26, 66**

**fretting corrosion, 23, 26, 66**

**fretting fatigue, 23, 26, 66–68**

**fretting wear, 23, 26, 66, 68, 69**

**maps, 69**

**minimizing or preventing fretting**

**damage, 69, 70**

**Friction coefficients (table), 864–866**

**Friction wheel drives, 594, 595**

**Galling, 23, 27, 61**

**Gasketed joint, 497–507**

**Gasket materials, (table), 503**

**Gears:**

**angular velocity ratio, 595, 600–605, 609**

**backlash, 618**

**bevel:**

**applications, 597, 598**

**bending (tooth) – AGMA refined**

**approach, 667, 668**

**design procedure, 668–675**

**force analysis, 665, 666**

**nomenclature, 662–665**

**standard AGMA tooth proportions,**

**(table), 665**

**stress analysis, 666–668**

**surface durability using AGMA refined**

**approach, 667, 668**

**compound, 600–605**

**epicyclic, 600–605**

**external, 594, 595**

**face gear, 598**

**failure modes, 605–607**

**fundamental law, 595**

**helical:**

**applications, 597**

**bending (tooth) – AGMA refined**

**approach, 654, 655**

**contact-pattern, 649**

**design procedure, 656–662**

**force analysis, 653, 654**

**nomenclature, 648, 650**

**standard AGMA tooth proportions,**

**(table), 651**

**stress analysis, 654, 655**

**surface durability using AGMA refined**

**approach, 654, 655**

**herringbone, 597**

**hypoid, 598**

**internal, 594, 595**

**involute, 608–618**

**Lewis equation (bending), 626–629**

**Lewis form factor, 628**

**line of action (pressure line), 609**

**manufacturing cost trends, 624**

**manufacturing methods:**

**accuracy requirements (table), 623,**

**624**

**gear cutting, 618–620**

**gear finishing, 620**

**profile modification, 621, 622**

**materials, 607, 608**

**rack and pinion, 597**

**reduction ratios, 600–605**

**selection of type, 595–600**

**simple, 600–605**

**spiroid, 598**

**straight tooth spur:**

**angular velocity ratio, 595, 600–605,**

**609**

**applications, 595, 597**

**approximate actual size, 614**

**bending (tooth) – AGMA refined**

**approach, 631–638**

**bending (tooth) – simplified approach,**

**626–631**

**conjugate action, 609**

**design procedure, 647, 648**

**force analysis, 624–626**

**involute profile, 608–618**

**lubrication, 645–647**

**nomenclature, 594, 610**

**standard AGMA tooth proportions,**

**(table), 613**

**stress analysis, 631–645**

**surface durability using AGMA refined**

**approach, 641–645**

**surface durability using Hertz contact**

**stresses, 639–641**

**tooth profile, 608–618**

**surface durability, 62, 639–645, 655, 667,**

**668**

**tooth bending, 626–638, 654, 655, 667,**

**668**

**tooth durability, 632–645, 655, 667, 668**

**trains, 600–605**

**types, 595–600**

**uses, 594, 595**

**worm:**

**allowable tangential gear force, 682,**

**683**

**applications, 599**

**bending (tooth), 682**

**common thread profiles, 676**

**design procedure, 684–691**

**efficiency, 679–682**

**force analysis, 679–682**

**nomenclature, 675**

**stress analysis, 682, 683**

**surface durability, 682**

**typical tooth profiles, (table), 677**

**Zerol, 597, 598**

**Geometric compatibility, 385, 387, 392**

**Geometry determination, 305–330**

**Hardness properties, (table), 101**

**Heat affected zone (HAZ), 528**

**Helical coil springs, 546, 552–568**

**(also see springs)**

**Helical gears, 648–662 (also see gears)**

**Hertz contact deflection, 177, 453–457**

**Hertz contact spring rate, 181–182, 453**

**Hertz contact stress, 24, 62, 160, 161,**

**174–179**

**High-speed-rotors (see flywheels)**

**Hollow cylinder guidelines, 310**

**Hooke’s Law, 32, 47, 162, 214, 215, 228,**

**385, 387, 393**

**Horsepower relationship, 152**

**Housing, 844**

**Huber-von-Mises-Hencky Theory**

**(see distortional energy theory)**

**Human factors engineering, 5**

**House of quality, 3**

**I-beam guidelines, 308**

**I-beams, section properties, 870**

**Impact, 23, 26**

**Impact:**

**deflection, 47–52**

**deformation, 23, 26**

**energy method, 47–52**

**fatigue, 23**

**fracture, 23, 26**

**fretting, 23**

**stress, 47–52**

**stress wave propagation, 46**

**suddenly applied load, 46, 48**

**wear, 23, 26**

**Industrial designers, 2**

**Inspectability, 9**

**Inspectability, design for 339, 340**

**Interference fits:**

**design procedures, 396–400**

**failure modes, 386**

**uses, 382, 386**

**Intermediate design, 8**

**Involute gear teeth, 609–618**

**Involute splines, 373, 374**

**Iteration, 7, 319**

**Jack screws (see power screws)**

**Joints:**

**adhesively bonded, 538–542**

**advantages of adhesive bonding, 838**

**bolted, 486, 487–516**

**butt weld, 528**

**centroid of bolt pattern, 510, 511**

**centroid of weld pattern, 530**

**eccentric loading, 509–516, 529–537**

**failure modes, 487, 488**

**fillet welds, 529–537**

**gasketed, 497–507**

**886 IndexJoints (Continued)**

**moment of inertia, 510, 512**

**multiply bolted, 509**

**multiply riveted, 519**

**multiply welded, 529–537**

**preload, 495–507**

**rivet material, 517**

**riveted, 517–522**

**stiffness, 497–507**

**torsion-like shear, 509–516**

**types, 485, 486**

**weld edge preparation, 525, 526**

**weld electrode specifications, 527**

**weld types, 525, 526**

**weldability, 527**

**welded, 522–537**

**weld heat affected zone (HAZ), 528**

**weld stress concentration factors, 525**

**weld symbol, 524**

**Keys, 361–372**

**Keys:**

**failure modes, 366**

**square, 365–372**

**stress concentration factors (keyway),**

**220, 367, 369**

**Woodruff, 365, 367**

**Kinematic viscosity, 410, 411, 414**

**Larson-Miller parameter, 54**

**Lazy-material removal guideline, 611, 612**

**Lead screw (see power screws)**

**Leaf springs, 568–578 (also see springs)**

**Lessons learned strategy, 12**

**Lewis equation (see gears), 626–629**

**Line of action (see gears), 609**

**Linear actuators (see power screws)**

**Linear elastic fracture mechanics (LEFM),**

**233–241**

**Load sharing, 179–186**

**Load spreading guideline, 314**

**Loading severity parameter, 225**

**Lubrication:**

**boundary, 406–409**

**elastohydrodynamic (squeeze film), 406,**

**452, 645–647**

**hydrodynamic, 406, 409–425**

**hydrostatic, 409**

**Petroff’s equation, 411**

**pV product, 406–409**

**Raimondi and Boyd data, 413–417**

**Reynolds equation, 412, 413**

**plain bearings, 403, 405–425**

**rolling element bearings, 452**

**solid film, 406**

**Sommerfield data, 413–417**

**thick film (full film), 405, 409–425**

**thin film (partial film), 405–409**

**Tower experiments, 412**

**viscosity, 410, 411, 414**

**zero film, 405**

**Machinability index (table), 104**

**Maintenance, design for, 333, 339, 340**

**Manufacturing, 333–340**

**Manufacturing, design for, 337**

**Manufacturing process, selection, 334–337**

**Manufacturing process suitability (table), 103**

**Marketing specialists, 1, 2**

**Mass moments of inertia (table), 867**

**Materials:**

**application requirements, 94**

**Ashby charts, 105–111, 114–120**

**mechanical properties (tables), 95–105,**

**106–109, 238**

**performance evaluation indices, 94**

**selection by Ashby method, 105–111,**

**114–120**

**selection by rank-ordered data (table),**

**105–114**

**selection steps, 93**

**Materials cost index, 104**

**Maximum shearing stress design**

**equation, 318**

**Maximum shearing stress failure**

**theory, 225–227**

**Maximum normal stress design equation, 318**

**Maximum normal stress failure theory, 225,**

**226**

**Mean, 77**

**Mechanical design:**

**concepts, 6**

**definition, 6**

**failure prevention perspective, 22–75**

**Mechanical failure:**

**brinnelling, 23, 24**

**brittle fracture, 23, 24, 233–241**

**buckling, 23, 27, 34–45**

**combined creep and fatigue, 23, 28**

**corrosion, 23, 24, 64–66**

**corrosion fatigue, 23, 28, 64**

**corrosion wear, 23, 28, 64**

**creep, 23, 26, 27, 52–58**

**creep buckling, 23, 28**

**ductile rupture, 23, 24, 33, 34**

**fatigue, 23, 24, 241–291**

**force-induced elastic deformation, 23,**

**24, 30**

**fretting, 23, 26, 66–70**

**galling, 23, 27, 61**

**impact, 23, 26, 46–52**

**modes of, 23–28**

**radiation damage, 23, 27, 102, 103**

**seizure, 23, 27, 61**

**spalling, 23, 27**

**stress corrosion, 23, 28, 65, 66**

**stress rupture, 23, 27, 52–58**

**temperature-induced elastic deformation,**

**23, 24, 31, 32**

**thermal relaxation, 23, 27**

**thermal shock, 23, 27**

**wear, 23, 25, 59–63**

**yielding, 23, 24, 32, 33**

**Membrane analogy, 153–155**

**Merging shape guidelines, 313**

**Mode I crack displacement, 233**

**Mode II crack displacement, 233**

**Mode III crack displacement, 233**

**Modified square thread, 463, 464**

**Mohr’s circle (strain), 213, 214**

**Mohr’s circle (stress), 210, 211**

**Moment diagrams, bending (table),**

**129–133**

**Moment of inertia, area (table), 135**

**Moment of inertia, mass (table), 867**

**Multiaxial cyclic stress, 283–291**

**Multiaxial fatigue failure theories, 283–291**

**Multiaxial state of stress, 127, 205–215**

**Multiple threads, 464, 465**

**National Society of Professional Engineers**

**(NSPE), Code of Ethics, 14, 15,**

**859–863**

**Neuber rule, 274**

**Newtonian fluid, 410**

**Newton’s law of cooling:**

**bearings, 418**

**brakes, 712**

**gears, 646**

**Nondestructive evaluation (NDE), 339**

**Normal (Gaussian) distribution, 76–80**

**Normal stress, 126, 127**

**Notch sensitivity, 280–283**

**Octahedral shear stress theory of failure (see**

**distortion energy failure theory)**

**Paris law (fatigue), 277**

**Petroff’s equation, 411**

**Pins, 376, 377**

**Plain bearings:**

**advantages, 403, 404**

**design criteria, 419, 420**

**design procedure, 420–425**

**eccentricity ratio, 413, 421**

**failure modes, 404**

**lubrication, 403, 405–425**

**materials, 405**

**oil film temperature rise, 416, 418**

**recommended clearances (table), 420, 421**

**uses, 403, 404**

**Plane cross section properties (table), 135**

**Plane strain:**

**critical stress intensity factor, 237**

**definition, 237**

**minimum thickness for, 237**

**Plain strain fracture toughness, 237, 276**

**Plane stress, critical stress intensity factor,**

**237**

**Planetary gears, 600–605**

**Plastic strain, 32**

**Policy of least commitment, 3**

**Power, as related to torque and speed, 151,**

**152**

**Index 887Power screws:**

**Acme threads, 463, 464, 470, 471**

**back driving, 467**

**ball screw, 465**

**buttress thread, 463, 464**

**design procedures, 473, 474**

**efficiency, 467–473**

**failure modes, 466**

**helix angle, 464**

**lead (thread), 464**

**lead angle, 464, 469**

**materials, 466**

**modified square thread, 463, 464**

**multiple threads, 464, 465**

**overhauling, 469**

**pitch, 464**

**self-locking, 469**

**square thread, 463, 464**

**thread angle, 463**

**threads, 463–470**

**torque, 467–473**

**uses, 462**

**Preliminary design, 7, 8**

**Preloading, 186–189, 453–457**

**Presetting, 189**

**Pressure vessels:**

**ASME Boiler and Pressure Vessel Code,**

**382**

**failure modes, 383**

**longitudinal stress, 386**

**materials, 383, 384**

**tangential (hoop) stress, 385**

**thick wall, 382, 386–392**

**thin wall, 382, 385, 386**

**uses, 382**

**Prestressing, 190–192**

**Principal normal stress, 205–213**

**Principal planes, 205–213**

**Principal stresses, 205–213, 389**

**Principal shearing stress, 205–213**

**Projected area, 386**

**Probability density function, 76–79**

**Probability of failure, 76–79, 245**

**Probabilistic design, 76**

**Product design team, 1, 2, 3**

**Product marketing concept, 3**

**Radiation damage, 23, 27, 102, 103**

**Radiation exposure influence on properties**

**(table), 102, 103**

**Rain flow cycle counting (fatigue), 254,**

**266–272**

**Rankine’s theory (see maximum normal**

**stress theory)**

**Recycling, design for, 339, 340**

**Redundant assemblies, 179–186**

**Redundant supports, 166–169, 179–186**

**Redundancy, component level, 82, 83**

**Redundancy, sub-assembly level, 82, 83**

**Reliability, 76–84, 245**

**Reliability:**

**allocation, 80**

**block diagrams, 81**

**definition, 76**

**equal apportionment, 83**

**functional block diagrams, 81–83**

**goals, 80, 81**

**log-normal distribution, 76**

**normal cumulative distribution, 77–79**

**normal distribution, 77–80**

**parallel components, 82, 83**

**population mean, 77**

**population standard deviation, 77**

**population variance, 77**

**redundancy at component level, 82, 83**

**redundancy at subsystem level, 82, 83**

**series components, 82**

**Six Sigma, 81**

**standard normal variable (table), 78**

**system, 80–83**

**specification, 84**

**Weibull distribution, 76**

**Residual stresses, 189–194, 525**

**Residual stresses:**

**cold-rolling, 190**

**estimating, 190–194**

**fatigue life improvement, 288–291**

**presetting, 189**

**prestressing, 190–192**

**shot-peening, 190, 526**

**weldments, 525, 526**

**Resilience properties (table), 100**

**Resonance, 344, 359**

**Retrospective design, 70, 71**

**Reynolds equation, 412**

**Rivets (see fasteners)**

**Rolling element bearings:**

**ball, 430, 431**

**basic dynamic load rating, 435**

**basic static load rating, 435**

**enclosure, 457, 458**

**failure modes, 433**

**force-deflection curves, 453–457**

**lubrication, 451, 452**

**materials, 433, 434**

**mounting practices, 457, 458**

**preloading, 453, 457**

**reliability, 435, 436**

**roller, 430, 432**

**selection for spectrum loading, 434,**

**448–451**

**selection for steady loads, 434, 436–448**

**stiffness, 453–457**

**types, 430–432**

**uses, 429**

**Rotors, high-speed (see flywheels)**

**Rotating free ring, 407, 408**

**Safe life design, 9**

**Safety factor:**

**design, 7, 33, 72–74, 84**

**existing, 75**

**rating factors, 73**

**rating numbers, 72, 73, 84**

**Safety issues:**

**devices, 850, 852–854**

**guards, 850, 851**

**hazards, 850**

**risk, 850**

**Sample mean, 245**

**Sample standard deviation, 245**

**Screw threads:**

**Acme, 463, 464, 470, 471**

**buttress, 463, 464**

**failure modes, 466**

**helix angle, 464**

**lead, 464**

**lead angle, 464, 469**

**modified square, 463, 464**

**multiple threads, 464, 465**

**pitch, 464**

**square, 563, 464, 468**

**thread angle, 463**

**Screws, power (see power screws)**

**Seizure, 23, 27, 61**

**Setscrews, 365, 275, 376**

**Setscrews:**

**holding power, 376**

**types of points, 375**

**Shaft deflection, 353–358**

**Shaft strength, 345–353**

**Shafts:**

**connection to flywheels, 820, 821**

**critical speed, 358–360**

**design equations, deflection based,**

**353–358**

**design equations, strength based,**

**345–353**

**design layout, 343**

**design procedure, 360, 361**

**failure modes, 343, 344**

**flexible (see flexible shafts)**

**materials, 344, 345**

**standard for design of, 345**

**uses, 341–343**

**vibration, 358–360**

**Shear center, 158–160**

**Shearing stress, 126, 127, 142–148**

**Shock (see impact)**

**Shot-peening, 190**

**Shot-peening, fatigue life improvement,**

**288–291**

**Simplifying assumptions, 318**

**Six Sigma, 81**

**Slider-crank mechanism, 824**

**Solid bodies, properties of (table), 867**

**Spalling, 23, 27**

**Specification, reliability, 84**

**Specifications, engineering, 2, 8, 11, 93**

**Specifications, thread, 492**

**S-N curves, estimating, 246–248**

**S-N curves, strength-influencing factors,**

**247–258**

**888 IndexSplines, 361, 373, 374**

**Splines:**

**failure mode, 373**

**fits, 373**

**involute, 374**

**straight, 373, 374**

**stress concentration factors, 374**

**Spoke-and-rim flywheel, 806–809**

**(also see flywheel)**

**Spring index, 554**

**Springs:**

**Belleville (coned disk), 581, 582**

**buckling of helical coil, 559, 560**

**curvature factor in helical coil, 554**

**end loop stress concentration, 555, 556**

**energy storage, 582–586**

**fatigue shearing strength (table), 563**

**helical coil, 546, 552–568, 579**

**helical coil design procedure, 562–568**

**helical coil nomenclature, 552**

**helical coil spring index, 554**

**helical coil spring rate, 558**

**leaf springs, 568–578**

**leaf spring design procedure, 574–578**

**leaf spring spring-rate, 572**

**linear, 181**

**machine elements as, 180–186**

**nonlinear softening, 181**

**nonlinear stiffening (hardening), 181**

**parallel, 176–186**

**series, 179–186**

**shackles, 572–573**

**spiral torsion, 579, 580**

**surging of helical coil, 561**

**torsion bar, 578–581**

**torsion in helical coil, 553**

**torsion springs, 578–581**

**torsion tubes, 578**

**torsional shear yield strength (table), 560**

**transverse shear in helical coil, 553**

**Wahl factor, 554, 555**

**Spring rate (spring constant), 29, 179–186,**

**557, 558**

**Spring rate:**

**axial, 30, 181**

**bending, 181**

**direct shear, 181**

**helical coil, 557–559**

**Hertz contact, 181**

**leaf spring, 572**

**linearized, 181, 453**

**torsional, 181**

**Spur gears, 608–618 (also see gears)**

**Square thread, 463, 464, 469**

**Stages of design, 7–9**

**Standard deviation, 77**

**Standard normal variable, 253, (table), 78**

**Standards, 13**

**State of stress:**

**biaxial, 127, 205–213, 386**

**multiaxial, 127, 205–213, 225**

**multiaxial cyclic, 272, 283–291**

**triaxial, 127, 205**

**uniaxial, 127, 225**

**Stiffness, joint, 497–507**

**Stiffness properties of materials (table),**

**99**

**Straight toothy spur gears, 608–648**

**(also see gears)**

**Strain amplitude, elastic, 274, 275**

**Strain amplitude, plastic, 274, 275**

**Strain amplitude, total, 274, 275**

**Strain cubic equation, 213**

**Strain energy, 47, 126, 162–173, 227**

**Strain energy per unit volume, 227**

**Strain gage, 214**

**Strain-matching guideline, 313**

**Strain rosette, 241**

**Strength at elevated temperature (table),**

**96, 97**

**Strength properties (table), 95, 96**

**Strength reduction factor, 281**

**Strength/weight ratio (table), 96**

**Stress (see “stress patterns” and “state of**

**stress”)**

**Stress, equivalent, 272**

**Stress concentration, 215–224**

**Stress concentration:**

**actual local stress, 216**

**highly local, 216–224**

**multiple notches, 217, 223**

**nominal stress, 216**

**notch root, 216**

**notch sensitivity index, 280–283**

**strength reduction factor, 281**

**widely distributed, 138, 139, 216**

**Stress concentration factors:**

**crankshaft fillet, 222**

**curved beams, 138, 139**

**cyclic multiaxial states of stress, 281,**

**282**

**end-of hub pressed on shaft, 223**

**fatigue, 216, 217**

**fatigue of brittle materials, 282**

**fatigue of ductile materials, 282**

**flat bar with shoulder fillet, 221**

**gear tooth fillet, 222**

**helical coil spring in torsion, 580**

**intermediate and low-cycle range,**

**282**

**keyways (profiled, slender runner), 367,**

**369**

**keyways (Woodruff), 367**

**screw threads, 217**

**shaft diametral hole, 220**

**shaft fillet, 218**

**shaft groove, 219**

**shaft keyway, 220, 366–369**

**shaft splines, 220, 374**

**theoretical elasticity, 216**

**torsion of helical coil spring, 580**

**weldment, 525**

**Stress corrosion, 23, 28, 64**

**Stress cubic equation, 206–209**

**Stress intensity:**

**critical, 234**

**stress intensity factor, 233**

**Stress intensity factor, 233–237**

**Stress patterns:**

**bending, 128–137**

**direct stress, 128**

**surface contact stress, 128, 160**

**torsional shear, 128, 150–160**

**transverse shear, 128, 142–150**

**Stress relaxation, 27**

**Stress rupture, 23, 27, 52–58**

**Stress rupture strength (table), 97**

**Stress wave propagation, 46**

**Structural adhesives (table), 541**

**Structural shapes, section properties,**

**867–872**

**Suddenly applied load, 48**

**Superposition, principal of, 32**

**Surface contact stress, 160**

**Surface forces, 123**

**Surging, helical coil springs, 561**

**System reliability, 80–83**

**Tailored-shape guidelines, 307, 308**

**Tapered fits, 274, 375**

**Temperature-induced elastic deformation,**

**23, 24, 31, 32**

**Theoretical stress concentration factor, 216**

**Theories of failure:**

**distortional energy theory, 225, 227,**

**228**

**maximum shearing stress theory,**

**225–227**

**maximum normal stress theory, 225,**

**226**

**selection of, 229**

**Theory of elastic principles, 384–386**

**Thermal conductivity (table), 104, 105**

**Thermal expansion coefficients (table), 98**

**Thermal shock, 23, 27**

**Thermal relaxation, 23, 27**

**Thermal stress (temperature induces stress),**

**32**

**Threads:**

**fasteners, 488–497**

**power screws, 463–470**

**Tolerances, 323–329**

**Tooth bending, 631–639, 654, 655, 667, 668**

**(also see gears)**

**Topological interference, 824**

**Torsion:**

**circular cross section, 150–156**

**deflection, 161**

**noncircular cross section, 152–155**

**shear center in bending, 157–160**

**spring rate, 181**

**Torsion bar springs, 578–581 (also see**

**springs)**

**Index 889Total strain energy per unit volume, 227**

**Toughness properties (tables), 100, 238**

**Transverse shear, 142–147**

**Tresca-Guest theory (see maximum**

**shearing stress theory)**

**Triangle-tetrahedron guideline, 308, 309**

**Uniaxial state of stress, 127, 225, 233**

**Unit inertia (table), 532, 533**

**Units, 14–20**

**Units:**

**absolute system, 15, 16**

**base units, 15**

**conversion table, 17**

**derived units, 15**

**foot-pound-second system (fps), 14**

**gravitational system, 15**

**inch-pound-second system (ips), 14**

**International system (SI), 14**

**standard prefixes, 17**

**Universal joint, 365**

**Variance, 77**

**Virtues of simplicity, 10**

**Viscosity, 410, 411, 414**

**von Mises stress, 228**

**von Mises theory (see distortional**

**energy theory)**

**Whal factor, 554, 555**

**Wear, 23, 25, 59–63**

**Wear:**

**abrasive wear, 23, 25, 59, 61, 62**

**abrasive wear constant, 62**

**adhesive wear, 23, 25, 59, 61, 62**

**Archard adhesive wear constant, 60**

**corrosion wear, 23, 25, 59**

**deformation wear, 23, 26, 59**

**fretting wear, 23, 26, 66, 68**

**impact wear, 23, 26**

**mean normal contact pressure, 60, 61**

**principle of conversion, 61**

**principle of diversion, 61**

**principle of protective layers, 61**

**surface fatigue wear, 23, 25, 59, 62**

**three-body wear, 61**

**two-body wear, 61**

**Weibull distribution, 76**

**Weldability, 526**

**Welded joints (see joints, welded)**

**Weld symbol, 524–526**

**Wide flange beam, section properties, 868,**

**869**

**Wire rope:**

**failure modes, 779–781**

**fatigue data, 785**

**materials, 782**

**selection procedure, 786–791**

**stresses, 782, 784–791**

**uses, 748, 749**

**Worm gears, 675–691 (also see gears)**

**Yielding, 23, 24, 32, 33**

**Yield strength (table), 95Mechanical Design of Machine Elements and Machines – Solution Manual **

**A Failure Prevention Perspective **

**Second Edition **

**Jack A. Collins, Henry R. Busby & George H. Staab **

**The Ohio State University **

**Contents**

**Part One Engineering Principles **

**Chapter 1**

**Keystones of Design: Materials**

**Selection and Geometry Determination 1**

**1.1 Some Background Philosophy 1**

**1.2 The Product Design Team 2**

**1.3 Function and Form; Aesthetics and**

**Ergonomics 5**

**1.4 Concepts and Definition of Mechanical**

**Design 6**

**1.5 Design Safety Factor 7**

**1.6 Stages of Design 7**

**1.7 Steps in the Design Process 9**

**1.8 Fail Safe and Safe Life Design Concepts 9**

**1.9 The Virtues of simplicity 10**

**1.10 Lessons Learned Strategy 12**

**1.11 Machine Elements, Subassemblies, and**

**the Whole Machine 12**

**1.12 The Role of Codes and Standards in the**

**Design Process 13**

**1.13 Ethics in Engineering Design 13**

**1.14 Units 14**

**Chapter 2**

**The Failure Prevention Perspective 22**

**2.1 Role of Failure Prevention Analysis in**

**Mechanical Design 22**

**2.2 Failure Criteria 22**

**2.3 Modes of Mechanical Failure 23**

**2.4 Elastic Deformation, Yielding, and Ductile**

**Rupture 28**

**2.5 Elastic Instability and Buckling 34**

**Buckling of a Simple Pin-Jointed Mechanism 35**

**Buckling of a Pinned-End Column 36**

**Columns with Other End Constraints 38**

**Inelastic Behavior and Initially Crooked**

**Columns 39**

**Column Failure Prediction and Design**

**Considerations 40**

**Buckling of Elements Other Than Columns 43**

**2.6 Shock and Impact 46**

**Stress Wave Propagation Under Impact Loading**

**Conditions 46**

**Energy Method of Approximating Stress and**

**Deflection Under Impact Loading**

**Conditions 47**

**2.7 Creep and Stress Rupture 52**

**Predictions of Long-Term Creep Behavior 53**

**Creep under Uniaxial State of Stress 55**

**Cumulative Creep Prediction 57**

**2.8 Wear and Corrosion 59**

**Wear 59**

**Corrosion 64**

**2.9 Fretting, Fretting Fatigue, and Fretting**

**Wear 66**

**Fretting Fatigue 67**

**Fretting Wear 68**

**Minimizing or Preventing Fretting Damage 69**

**2.10 Failure Data and the Design Task 70**

**2.11 Failure Assessment and Retrospective**

**Design 70**

**2.12 The Role of Safety Factors; Reliability**

**Concepts 71**

**2.13 Selection and Use of a Design Safety**

**Factor 72**

**2.14 Determination of Existing Safety Factors**

**in a Completed Design: A Conceptual**

**Contrast 744.6 Stresses Caused by Curved Surfaces in**

**Contact 174**

**4.7 Load Sharing in Redundant Assemblies**

**and Structures 179**

**Machine Elements as Springs 180**

**4.8 Preloading Concepts 186**

**4.9 Residual Stresses 189**

**Estimating Residual Stress 190**

**4.10 Environmental Effects 194**

**Chapter 5**

**Failure Theories 205**

**5.1 Preliminary Discussions 205**

**5.2 Multiaxial States of Stress and Strain 205**

**Principal Stresses 205**

**Stress Cubic Equation 206**

**Mohr’s Circle Analogy for Stress 210**

**Strain Cubic Equation and Principal Strains 213**

**Mohr’s Circle Analogy for Strain 213**

**Elastic Stress-Strain Relationships**

**(Hooke’s Law) 214**

**5.3 Stress Concentration 215**

**Stress Concentration Effects 216**

**Multiple Notches 217**

**5.4 Combined Stress Theories of Failure 224**

**Maximum Normal Stress Theory**

**(Rankine’s Theory) 225**

**Maximum Shearing Stress Theory**

**(Tresca–Guest Theory) 226**

**Distortion Energy Theory**

**(Huber–von Mises–Hemcky Theory) 227**

**Failure Theory Selection 229**

**5.5 Brittle Fracture and Crack Propagation;**

**Linear Elastic Fracture Mechanics 233**

**5.6 Fluctuating Loads, Cumulative Damage,**

**and Fatigue Life 241**

**Fluctuating Loads and Stresses 242**

**Fatigue Strength and Fatigue Limit 244**

**Estimating S-N Curves 246**

**Stress-Life (S-N) Approach to Fatigue 248**

**Factors That May Affect S-N Curves 248**

**Nonzero-Mean Stress 258**

**Cumulative Damage Concepts and Cycle**

**Counting 266**

**Multiaxial Cyclic Stress 272**

**Fracture Mechanics (F-M) Approach to Fatigue 273**

**Crack Initiation Phase 273**

**Crack Propagation and Final Fracture Phases 276**

**x / Contents**

**2.15 Reliability: Concepts, Definitions, and**

**Data 76**

**System Reliability, Reliability Goals, and**

**Reliability Allocation 80**

**Reliability Data 83**

**2.16 The Dilemma of Reliability Specification**

**versus Design Safety Factor 84**

**Chapter 3**

**Materials Selection 93**

**3.1 Steps in Materials Selection 93**

**3.2 Analyzing Requirements of the**

**Application 93**

**3.3 Assembling Lists of Responsive**

**Materials 94**

**3.4 Matching Responsive Materials to**

**Application Requirements; Rank Ordered**

**Data Table Method 105**

**3.5 Matching Responsive Materials to**

**Application Requirements; Ashby chart**

**Method 114**

**Chapter 4**

**Response of Machine Elements to Loads**

**and Environments; Stress, Strain, and**

**Energy Parameters 123**

**4.1 Loads and Geometry 123**

**4.2 Equilibrium Concepts and Free-Body**

**Diagrams 123**

**4.3 Force Analysis 124**

**4.4 Stress Analysis; Common Stress Patterns**

**for Common Types of Loading 126**

**Direct Axial Stress 128**

**Bending; Load, Shear, and Moment**

**Diagrams 128**

**Bending; Straight Beam with Pure Moment 133**

**Bending; Initially Curved Beams 137**

**Bending; Straight Beam with Transverse**

**Forces 142**

**Direct Shear Stress and Transverse Shear**

**Stress 142**

**Torsional Shear; Circular Cross Section 150**

**Torsional Shear; Noncircular Cross Section 152**

**Torsional Shear; Shear Center in Bending 157**

**Surface Contact Stress 160**

**4.5 Deflection Analysis Common Types of**

**Loading 161**

**Stored Strain Energy 162**

**Castigliano’s Theorem 164Design Issues in Fatigue Life Prediction 280**

**Fatigue Stress Concentration Factors and**

**Notch Sensitivity Index 280**

**5.7 Multiaxial States of Cyclic Stress and**

**Multiaxial Fatigue Failure Theories 283**

**Chapter 6**

**Geometry Determination 305**

**6.1 The Contrast in Objectives Between**

**Analysis and Design 305**

**6.2 Basic Principles and Guidelines for**

**Creating Shape and Size 306**

**Direct Load Path Guideline 306**

**Tailored-Shape Guideline 307**

**Triangle-Tetrahedron Guideline 308**

**Buckling Avoidance Guideline 309**

**Hollow Cylinder and I-Beam Guideline 310**

**Conforming Surface Guideline 310**

**Lazy-Material Removal Guideline 311**

**Merging Shape Guideline 313**

**Strain Matching Guideline 313**

**Load Spreading Guideline 314**

**Contents / xi**

**6.3 Critical Sections and Critical Points 315**

**6.4 Transforming Combined Stress Failure**

**Theories into Combined Stress Design**

**Equations 317**

**6.5 Simplifying Assumptions: The Need and**

**the Risk 318**

**6.6 Iteration Revisited 319**

**6.7 Fits, Tolerances, and Finishes 323**

**Chapter 7**

**Design-Stage Integration of Manufacturing**

**and Maintenance Requirements 333**

**7.1 Concurrent Engineering 333**

**7.2 Design for Function, Performance, and**

**Reliability 334**

**7.3 Selection of the Manufacturing Process 334**

**7.4 Design for Manufacturing (DFM) 337**

**7.5 Design for Assembly (DFA) 337**

**7.6 Design for Critical Point Accessibility,**

**Inspectability, Disassembly, Maintenance,**

**and Recycling 339**

**Chapter 8**

**Power Transmission Shafting; Couplings,**

**Keys, and Splines 341**

**8.1 Uses and Characteristics of shafting 341**

**8.2 Potential Failure Modes 343**

**8.3 Shaft Materials 344**

**8.4 Design Equations–Strength Based 345**

**8.5 Design Equations–Deflection Based 353**

**8.6 Shaft Vibration and Critical Speed 358**

**8.7 Summary of Suggested Shaft Design**

**Procedure; General Guidelines for Shaft**

**Design 360**

**8.8 Couplings, Keys, and Splines 361**

**Rigid Couplings 361**

**Flexible Coupling 362**

**Keys, Splines, and Tapered Fits 365**

**Chapter 9**

**Pressurized Cylinders; Interference Fits 382**

**9.1 Uses and Characteristics of Pressurized**

**Cylinders 382**

**9.2 Interference Fit Applications 382**

**9.3 Potential Failure Modes 383**

**9.4 Materials for Pressure Vessels 383**

**9.5 Principles from Elasticity Theory 384**

**9.6 Thin-Walled Cylinders 385**

**9.7 Thick-Walled Cylinders 386**

**9.8 Interference Fits: Pressure and Stress 392**

**9.9 Design for Proper Interference 396**

**Chapter 10**

**Plain Bearings and Lubrication 403**

**10.1 Types of Bearings 403**

**10.2 Uses and Characteristics of Plain**

**Bearings 403**

**10.3 Potential Failure Modes 404**

**10.4 Plain Bearing Materials 405**

**10.5 Lubrication Concepts 405**

**10.6 Boundary-Lubricated Bearing Design 406**

**10.7 Hydrodynamic Bearing Design 409**

**Lubricant Properties 410**

**PART TWO DESIGN APPLICATIONSTightening Torque; Fastener Loosening 507**

**Multiply Bolted Joints; Symmetric and**

**Eccentric Loading 509**

**13.5 Rivets 517**

**Rivet Materials 517**

**Critical Points and Stress Analysis 518**

**13.6 Welds 522**

**Base Metals, Filler Materials, and Weldability 526**

**Butt Welds 528**

**Fillet Welds 529**

**13.7 Adhesive Bonding 538**

**Joint Design 538**

**Structural Adhesive Materials 540**

**Chapter 14**

**Springs 546**

**14.1 Uses and Characteristics of Springs 546**

**14.2 Types of Springs 546**

**14.3 Potential Failure Modes 548**

**14.4 Spring Materials 549**

**14.5 Axially Loaded Helical-Coil Springs;**

**Stress, Deflection, and Spring Rate 552**

**Deflection and Spring Rate 557**

**Buckling and Surging 559**

**14.6 Summary of Suggested Helical-Coil**

**Spring Design Procedure, and General**

**Guidelines for Spring Design 562**

**14.7 Beam Springs (Leaf Springs) 568**

**14.8 Summary of Suggested Leaf Spring**

**Design Procedure 574**

**14.9 Torsion Bars and Other Torsion Springs 578**

**14.10 Belleville (Coned-Disk) Springs 581**

**14.11 Energy Storage in Springs 582**

**Chapter 15**

**Gears and Systems of Gears 594**

**15.1 Uses and Characteristics of Gears 594**

**15.2 Types of Gears; Factors in Selection 595**

**15.3 Gear Trains; Reduction Ratios 600**

**15.4 Potential failure Modes 605**

**15.5 Gear Materials 607**

**15.6 Spur Gears; Tooth Profile and Mesh**

**Geometry 608**

**Involute Profiles and Conjugate Action 609**

**Gearing Nomenclature; Tooth Shape and**

**Size 610**

**Gear-Tooth Systems 612**

**Mesh Interactions 614**

**xii / Contents**

**Loading, Friction, and Lubricant Flow**

**Relationships 410**

**Thermal Equilibrium and Oil Film Temperature**

**Rise 416**

**Design Criteria and Assumptions 419**

**Suggested Design Procedure 420**

**10.8 Hydrostatic Bearing Design 425**

**Chapter 11**

**Rolling Element Bearings 429**

**11.1 Uses and Characteristics of Rolling**

**Element Bearings 429**

**11.2 Types of Rolling Element Bearings 430**

**11.3 Potential Failure Modes 433**

**11.4 Bearing Materials 433**

**11.5 Bearing Selection 434**

**Basic Load Ratings 435**

**Reliability Specifications 435**

**Suggested Selection Procedure for Steady**

**Loads 436**

**Suggested Selection Procedure for Spectrum**

**Loading 448**

**Lubrication 451**

**11.6 Preloading and Bearing Stiffness 453**

**11.7 Bearing Mounting and Enclosure 457**

**Chapter 12**

**Power Screw Assemblies 462**

**12.1 Uses and Characteristics of Power**

**Screws 462**

**12.2 Potential Failure Modes 466**

**12.3 Materials 466**

**12.4 Power Screw Torque and Efficiency 467**

**12.5 Suggested Power Screw Design Procedure 473**

**12.6 Critical Points and Thread Stresses 474**

**Chapter 13**

**Machine Joints and Fastening Methods 485**

**13.1 Uses and Characteristics of Joints in**

**Machine Assemblies 485**

**13.2 Selection of Joint Type and Fastening**

**Method 485**

**13.3 Potential Failure Modes 487**

**13.4 Threaded Fasteners 488**

**Screw Thread Standards and Terminology 489**

**Threaded Fastener Materials 492**

**Critical Points and Thread Stresses 494**

**Preloading Effects; Joint Stiffness and Gasketed**

**Joints 49715.7 Gear Manufacturing; Methods, Quality,**

**and Cost 618**

**Gear Cutting 618**

**Gear Finishing 620**

**Cutter Path Simulation, Mesh Deflection,**

**and Profile Modification 621**

**Accuracy Requirements, Measurement Factors,**

**and Manufacturing Cost Trends 622**

**15.8 Spur Gears; Force Analysis 624**

**15.9 Spur Gears; Stress Analysis and Design 626**

**Tooth Bending: Simplified Approach 626**

**Tooth Bending: Synopsis of AGMA Refined**

**Approach 631**

**Surface Durability: Hertz Contact Stresses and**

**Surface Fatigue Wear 639**

**Surface Durability: Synopsis of AGMA Refined**

**Approach 641**

**15.10 Lubrication and Heat Dissipation 645**

**15.11 Spur Gears; Summary of Suggested**

**Design Procedure 647**

**15.12 Helical Gears; Nomenclature, Tooth**

**Geometry, and Mesh Interaction 648**

**15.13 Helical Gears; Force Analysis 653**

**15.14 Helical Gears; Stress Analysis and**

**Design 654**

**15.15 Helical Gears; Summary of Suggested**

**Design Procedure 656**

**15.16 Bevel Gears; Nomenclature, Tooth**

**Geometry, and Mesh Interaction 662**

**15.17 Bevel Gears; Force Analysis 665**

**15.18 Bevel Gears; Stress Analysis and Design 666**

**15.19 Bevel Gears; Summary of Suggested**

**Design Procedure 668**

**15 20 Worm Gears and Worms; Nomenclature,**

**Tooth Geometry, and Mesh Interaction 675**

**15.21 Worm Gears and Worms; Force Analysis**

**and Efficiency 679**

**15.22 Worm Gears and Worms; Stress Analysis**

**and Design 682**

**15.23 Worm Gears and Worms; Suggested**

**Design Procedure 684**

**Chapter 16**

**Brakes and Clutches 701**

**16.1 Uses and Characteristics of Brakes**

**and Clutches 701**

**16.2 Types of Brakes and Clutches 702**

**16.3 Potential Failure Modes 704**

**16.4 Brake and Clutch Materials 704**

**Contents / xiii**

**16.5 Basic Concepts for Design of Brakes**

**and Clutches 705**

**16.6 Rim (Drum) Brakes with Short Shoes 708**

**16.7 Rim (Drum) Brakes with Long Shoes 719**

**16.8 Band Brakes 727**

**16.9 Disk Brakes and Clutches 732**

**Uniform Wear Assumption 733**

**Uniform Pressure Assumption 735**

**16.10 Cone Clutches and Brakes 738**

**Chapter 17**

**Belts, Chains, Wire Rope, and Flexible**

**Shafts 746**

**17.1 Uses and Characteristics of Flexible**

**Power Transmission Elements 746**

**17.2 Belt Drives; Potential Failure Modes 750**

**17.3 Belts; Materials 752**

**17.4 Belt Drives; Flat Belts 752**

**17.5 Belt Drives; V-Belts 757**

**17.6 Belt Drives; Synchronous Belts 769**

**17.7 Chain Drives; Potential Failure Modes 769**

**17.8 Chain Drives; Materials 770**

**17.9 Chain Drives; Precision Roller Chain 771**

**17.10 Roller Chain Drives; Suggested Selection**

**Procedure 774**

**17.11 Chain Drives; Inverted-Tooth Chain 779**

**17.12 Wire Rope; Potential Failure Modes 779**

**17.13 Wire Rope; Materials 782**

**17.14 Wire Rope; Stresses and Strains 782**

**17.15 Wire Rope; Suggested Selection**

**Procedure 786**

**17.16 Flexible Shafts 791**

**Chapter 18**

**Flywheels and High-Speed Rotors 798**

**18.l Uses and Characteristics of Flywheels 798**

**18.2 Fluctuating Duty Cycles, Energy**

**Management, and Flywheel inertia 799**

**18.3 Types of Flywheels 804**

**18.4 Potential Failure Modes 805**

**18.5 Flywheel Materials 805**

**18.6 Spoke-and-Rim Flywheels 806**

**Stresses in a Rotating Free Ring 807**

**Bending Stresses in Flywheel Rim 808**

**Spoke-Axial Tensile Stresses 809**

**18.7 Disk Flywheels of Constant Thickness 809**

**18.8 Disk Flywheels of Uniform Strength 81519.5 Summary of Suggested Crankshaft**

**Design Procedure 826**

**Chapter 20**

**Completing the Machine 843**

**20.1 Integrating the Components; Bases,**

**Frames, and Housings 843**

**20.2 Safety Issues; Guards, Devices, and**

**Warnings 850**

**20.3 Design Reviews; Releasing the Final**

**Design 855**

**xiv / Contents**

**18.9 Uniform-Strength Disk Flywheel with**

**a Rim 816**

**18.10 Flywheel-to-Shaft Connections 820**

**Chapter 19**

**Cranks and Crankshafts 824**

**19.1 Uses and Characteristics of Crankshafts 824**

**19.2 Types of Crankshafts 825**

**19.3 Potential Failure Modes 826**

**19.4 Crankshaft Materials 826**

**Table A-4**

**Section Properties of Selected S**

**(Standard 1) Shapes 870**

**Table A-5**

**Section Properties of Selected C**

**(Channel) Shapes 871**

**Table A-6**

**Section Properties of Selected Equal-Leg**

**L (Angle) Shapes 872**

**NSPE Code of Ethics for Engineers 859**

**Table A-1**

**Coefficients of Friction 864**

**Table A-2**

**Mass Moments of Inertia J and Radii of**

**Gyration k for Selected Homogeneous Solid**

**Bodies Rotating About Selected Axes, as**

**Sketched 867**

**Table A-3**

**Section Properties of Selected W**

**(Wide Flange) Shapes 868**

**APPENDIX**

**REFERENCES 873**

**PHOTO CREDITS 881**

**INDEX **

**Index**

**883**

**Abrasive wear, 23, 25, 59, 62**

**Acme threads, 463, 464, 470, 471**

**Adhesive bonding, 538–542**

**Adhesive wear, 23, 25, 59, 62**

**American Bearing Manufacturers**

**Association (ABMA), 430**

**American Gear Manufacturers Association**

**(AGMA), 607**

**Angle shapes (equal leg), section**

**properties, 872**

**Angular velocity ratio, 595, 600–605**

**Anthropometrics, 5**

**Archard adhesive wear constant, 60**

**Area moment of inertia (table), 135**

**Ashby charts, 105–111, 114–120**

**ASME Boiler and Pressure Vessel Code, 382**

**Asperities, surface, 59, 409**

**Assembly, design for, 337, 338**

**Assembly process, selection, 337, 338**

**Backlash (gears), 618**

**Ball screws (see power screws)**

**Baseplates, 843, 844**

**Bases, 843**

**Beam springs, 568–578 (also see springs)**

**Bearings:**

**antifrictional (see rolling element bearings)**

**basic load rating, 62**

**journal (see plain bearings)**

**plain (see plain bearings)**

**rolling element (see rolling element**

**bearing)**

**sleeve (see plain bearings)**

**sliding (see plain bearings)**

**Belleville springs (coned disk), 581, 582**

**Belts:**

**failure modes, 750, 751**

**flat, 752–756**

**flat belt selection. 754–756**

**materials, 752**

**synchronous, 769**

**timing, 769**

**uses, 746**

**V-belts, 756–768**

**V-belt datum system, 759**

**V-belt pitch system, 759**

**V-belt selection, 763–768**

**Bending:**

**curved beams, 137–142**

**gear teeth (see gears)**

**load, shear, and moment diagrams (table),**

**128–133**

**neutral axis, 134, 138, 144**

**pure bending, 134**

**spring rate, 180, 181**

**straight beams, 128–137**

**transverse loads, 142–150**

**transverse shear, 142–150**

**Bevel gears, 662–675 (also see gears)**

**Biaxial brittle fracture strength data, 226**

**Biaxial state of stress, 127, 205–213**

**Biaxial yield strength data, 227**

**Body force, 123**

**Boundary conditions, 385, 387, 388**

**Bolts, (see fasteners)**

**Brakes:**

**band, 727–732**

**caliper, 735, 736**

**cone, 738, 739**

**design procedure, 705–707**

**disk, 732–738**

**external shoe, 703, 708, 724**

**failure mode, 704**

**friction coefficient (table), 706**

**friction lining material, 706**

**internal shoe, 703, 708, 724**

**long-shoe drum type, 719–727**

**multiple disk, 732–738**

**materials, 704–706**

**self-energizing, 708**

**self-locking, 708**

**short-shoe drum type, 708–719**

**temperature rise, 711, 712**

**types, 702–704**

**uniform pressure assumption (disk), 735**

**uniform wear assumption (disk), 733, 734**

**uses, 701, 702**

**Brinnelling, 23, 24**

**Brittle fracture, 23, 24, 225, 233–241**

**Buckling, 23, 27, 34–45**

**Buckling:**

**column, 35, 36**

**critical buckling load, 35–44**

**critical unit load, 40**

**effective column length, 38**

**effective slenderness ratio, 39**

**end support influence, 36, 38**

**Euler’s critical load, 38**

**Euler-Engesser equation, 39**

**externally pressurized thin-walled**

**tubes, 44**

**helical coil springs, 559–561**

**initially crooked columns, 39, 40**

**local buckling, 41**

**long columns, 41**

**long thin rod, 43, 44**

**onset of, 35**

**pin-jointed mechanisms, 35, 36**

**primary buckling, 41**

**secant formula, 39, 40**

**short columns, 40, 41**

**thin deep beams, 44**

**Buckling avoidance guideline, 309, 310**

**Butt welds, 528**

**Buttress thread, 463, 464**

**Castigliano’s theorem, 164–171**

**Cathodic protection, 66**

**Chains:**

**chordial action, 773, 774**

**failure modes, 769, 770**

**inverted tooth, 779**

**materials, 770, 771**

**multiple strand factor (table), 773**

**precision roller chain, 771–779**

**precision roller chain, selection, 774–779**

**polygonal action, 773, 774**

**silent, 779**

**uses, 746**

**Channel shape, section properties, 871**

**Clutches:**

**band, 727–732**

**cone, 738, 739**

**design procedure, 705–707**

**disk, 732–738Clutches (Continued)**

**failure modes, 704**

**friction coefficients (table), 706**

**friction lining material, 706**

**materials, 704–706**

**multiple disk, 732–738**

**temperature rise, 711, 712**

**types, 702–704**

**uniform pressure assumption (disk), 735**

**uniform wear assumption (disk), 733,**

**734**

**uses, 701, 702**

**Code of ethics (NSPE), 14, 15, 859–863**

**Codes, 13**

**Codes and standards, 13**

**Coefficient of speed fluctuations**

**(flywheels), 800, 801**

**Cold-rolling, 189**

**Columns (see buckling)**

**Combined creep and fatigue, 23–28**

**Combined stress design equations, 317, 318**

**Combines stress theory of failure, 33,**

**224–233, 317, 318**

**Conceptual design, 8**

**Concurrent design, 333, 336**

**Concurrent engineering, 333, 336**

**Conforming surface guideline, 310, 311**

**Configurational guidelines, 306–315**

**Configurational guidelines:**

**buckling avoidance, 309, 310**

**conforming surfaces, 310, 311**

**direct load path, 306, 307**

**hollow cylinder and I-beam, 310**

**lazy material removal, 311, 312**

**load spreading, 314**

**merging shape, 313**

**strain matching, 313, 314**

**triangle-tetrahedron, 308, 309**

**tailored shape, 307, 308**

**Constant thickness disk flywheel, 809–815**

**(also see flywheels)**

**Contact stress (Hertz), cylinders, 176–179**

**Contact stress (Hertz), spheres, 174–175**

**Corrosion:**

**biological corrosion, 23, 25, 64**

**cathodic protection, 66**

**cavitation corrosion, 23, 25, 64, 65**

**direct chemical attack, 23, 25, 64**

**erosion corrosion, 23, 25, 64**

**galvanic corrosion, 23, 25, 64, 65**

**hydrogen damage, 23, 25, 64**

**intergranular corrosion, 23, 25, 65**

**pitting corrosion, 23, 25, 65**

**protection, 65**

**sacrificial anode, 65**

**selective leaching, 23, 25, 64**

**stress corrosion, 23, 25, 64–66**

**Corrosion fatigue, 23, 28, 64**

**Corrosion fatigue strength properties**

**(table), 102**

**Corrosion wear, 23, 28**

**Couplings:**

**bellows, 363, 364**

**elastomeric disk, 363, 364**

**failure modes, 363–365**

**flexible, 361, 363–365**

**flexible disk, 362, 363**

**gear, 363, 364**

**rigid, 361, 362, 369–372**

**roller chain, 363, 364**

**rubber cap, 364**

**sliding disk, 363, 364**

**spring, 363, 364**

**universal joint (U-joint), 365**

**Crack:**

**initiation, 241, 242, 273–279**

**length, 233**

**opening mode (Mode I), 233**

**propagation, 233, 241, 276–279**

**size, unstable (critical), 241, 276–279**

**surface, 233**

**surface flaw shape parameter, 233, 236**

**through-the-thickness, 234–237**

**Crankshaft:**

**center cranks, 825**

**design procedure, 826–841**

**disk cranks, 825**

**failure modes, 826**

**materials, 826**

**side cranks, 825**

**types, 825**

**uses, 824, 825**

**Creep, 23, 26, 52–58**

**Creep:**

**constant creep rate, 56**

**cumulative creep, 57, 58**

**Larson-Miller theory, 54**

**logarithmic creep, 56**

**log-log stress-time creep, 65**

**long-term creep, 53–58**

**parabolic creep, 56**

**Robinson hypothesis, 57, 58**

**Stage I transient creep, 56**

**Stage II steady-state creep, 56**

**true creep strain, 56**

**under axial stress, 55–58**

**Creep buckling, 23, 28**

**Creep deformation, 53**

**Creep-limited maximum stress (table), 98**

**Creep strain, 52**

**Creep rupture, 52, 53**

**Creep testing:**

**abridged method, 53**

**mechanical acceleration method, 53**

**thermal acceleration method, 53**

**Critical points, 315–317, 474–481,**

**494–497, 582, 583**

**Critical point accessibility, design for, 339,**

**340**

**Critical sections, 315–317**

**Critical speed, rotating shafts, 358–360**

**Critical stress intensity factor, 234, 237, 238**

**Cumulative creep prediction, 57, 58**

**Cumulative damage, 241, 242, 266–272**

**Cumulative distribution function, 253**

**Curved beams, 137–142**

**Curved surfaces in contact, 174–179**

**Customer attributes, 3, 4**

**Customer perceptions, 5**

**CV joints, 365**

**Cycle counting, rain flow method, 266–272**

**Cyclic equivalent stress, 283–291**

**Cyclic multiaxial state of stress, 283–291**

**Cyclic stresses, 242–291**

**Deflection:**

**axial loading, 161**

**bending, 129–133, 162, 164**

**Castigliano’s theorem, 164–171**

**cylinders in contact, 176**

**shafts, 353–358**

**spheres in contact, 174**

**Hertz contact, 161, 174, 176**

**torsional loading, 161**

**Deflection analysis, 126**

**Design:**

**concurrent, 333, 336**

**detail design, 8**

**embodiment design, 8**

**fail safe design, 9**

**intermediate design, 8**

**mechanical design, 1**

**preliminary design, 7, 8**

**safe life design, 9**

**Design equations, combined stress, 317, 318**

**Design for assembly (DFA), 337, 338**

**Design for manufacturing (DFM), 337**

**Design for “X” (DFX), 333, 334**

**Design reviews, 10, 855**

**Design safety factors, 7, 33, 71–74, 84**

**Design steps, 9–11**

**Detail design, 8**

**Development and field service, 9**

**Dilatation energy per unit volume, 227, 228**

**Direct load path guideline, 306, 307**

**Direct shear, spring rate, 181**

**Disassembly, design for, 339, 340**

**Distortion energy design equation, 228**

**Distortion energy failure theory, 33, 224,**

**225, 227–232**

**Distortion energy per unit volume, 228**

**Distribution function (see probability**

**density function)**

**Ductile rupture, 23, 24, 33, 34**

**Ductility properties (table), 99, 100**

**Durability of gear teeth (see gears)**

**Effective stress, 228**

**Efficiency:**

**power screws, 467–473**

**worm gears, 679–682**

**Elastic instability (see buckling)**

**Elastic strain, 31, 32**

**884 IndexElastic stress-strain relationships, 214, 215**

**Elasticity theory (see theory of elasticity)**

**Elevated temperature strength (table), 96, 97**

**Embodiment design, 8**

**Energy methods:**

**Castigliano’s theorem, 164–171**

**Impact, 47–52**

**Engineering strain, 29, 30**

**Engineering stress-strain diagram, 30**

**Environmental effects, 194, 195**

**Epicylic gears, 600–605**

**Equilibrium, 123, 124, 385, 393, 412**

**Equivalent alternating stress amplitude,**

**283–291**

**Equivalent cyclic stress, 283–291**

**Equivalent mean stress, 283–291**

**Equivalent stress, 228, 272, 283–291**

**Ergonomics, 5**

**Ethics, 13, 14**

**Ethics, code of, 14, 15, 859–863**

**Ethical dilemma, 14**

**Euler’s critical load, 38**

**External energy, 47**

**Fail safe design, 9, 82**

**Failure analysis, 70, 71**

**Failure criteria, 22**

**Failure modes, 23–28 (also see mechanical**

**failure)**

**Failure prevention perspective, 22–70,**

**233–280**

**Failure theories:**

**distortional energy theory (also known as**

**octahedral shear stress theory,**

**Huber-von-Mises- Henky theory, or**

**von-Mises theory), 33, 225**

**fatigue, 224–232, 241–291**

**maximum normal stress theory (also**

**known as Rankine theory), 225**

**maximum shearing stress theory (also**

**known as Tresca Guest theory), 226,**

**227**

**selection of, 229**

**Fasteners:**

**bolts, 487, 496, 497**

**critical points, 494–497, 518–522**

**failure modes, 495–497**

**head styles, 488**

**lead (thread), 489**

**materials, 492–494**

**metric threads, 491**

**multiple threads, 489**

**reduced-body bolts, 487**

**rivets, 517–522**

**screw thread standards, 488, 489**

**thread angle, 489**

**thread series, 492**

**thread major diameter, 489**

**thread minor diameter, 489**

**thread specifications, 492**

**thread stresses, 494–497**

**tightening, 507, 508**

**torque coefficient, 508**

**unified inch, threads, 490, 491**

**Fastener loosening, 507–508**

**Fatigue:**

**completely reversed stress, 242, 258**

**corrosion fatigue, 28**

**crack growth rate, 276**

**crack initiation, 241, 242, 273–279**

**crack propagation, 233, 241, 276–279**

**critical (unstable) crack size, 241, 276–279**

**cumulative damage, 241, 242, 266–272**

**cycle ratio, 266–269**

**cyclic strain-hardening exponent, 274,**

**275**

**cyclic strength coefficients, 274, 275**

**damage fraction, 266–269**

**definitions for constant-amplitude stress**

**time pattern, 242, 243**

**estimating properties of a part, 257**

**elastic strain amplitude, 274, 275**

**estimating S-N curves, 246–248**

**factors that may affect S-N curves,**

**248–258**

**failure theories, 283–291**

**fatigue life, 241**

**fatigue limit, 244, 245**

**fatigue strength, 244, 245**

**final fracture, 276–278**

**fluctuating loads, 241**

**fracture mechanics approach**

**(F-M approach), 242**

**fretting fatigue, 23, 26, 66, 67, 69**

**high-cycle fatigue, 23, 24, 241–280**

**histogram, 245**

**impact fatigue, 23**

**infinite life diagram, 256**

**life improvement from residual stress,**

**288–291**

**life improvement form shot-peening,**

**288–291**

**linear damage rule, 266–269**

**loading spectra, 242**

**local stress-strain approach to crack**

**initiation, 273–279**

**low-cycle fatigue, 23, 24, 242**

**master diagram, 258, 259**

**modified Goodman relationships, 260,**

**261–266**

**multiaxial cyclic stress, 272**

**Neuber rule, 274**

**nonzero mean stress, 243, 258–266**

**Palmgren-Miner hypothesis, 266–269**

**Paris law, 277**

**plastic strain amplitude, 274, 275**

**probability of failure, 245**

**rain flow cycle counting, 254, 266–272**

**range of stress, 243, 276**

**released tension, 243**

**reliability, 245**

**reversals to failure, 274, 275**

**sample standard deviation, 245**

**sample mean, 245**

**scatter of life diagram, 244, 245**

**S-N curves, 244**

**SNP curves, 244, 245**

**standard deviation of fatigue strength, 253**

**strain-controlled fatigue (see low-cycle**

**fatigue)**

**stress life approach (S-N approach), 242,**

**243, 248**

**strength-influencing factors for S-N**

**curves, 247–258**

**strength reliability factors, 247**

**stress intensity factor range, 276, 277**

**stress spectra, 242, 266**

**surface fatigue, 23, 24**

**test method influence on S-N data, 248**

**thermal fatigue, 23, 24**

**total strain amplitude, 274, 275**

**zero-mean stress, 243, 258**

**Fatigue limit, 244, 246**

**Fatigue strength, 244, 246**

**Fatigue strength reduction factor, 281–283**

**Fatigue stress concentration factor, 280–283**

**Fillet welds, 529–537**

**Finishes, 328, 330**

**Fits, 323–329**

**Flexible shafts:**

**maximum operating torque (tables), 792,**

**793**

**selection procedure, 793–795**

**uses, 748–750**

**Fluctuating loads, 242**

**Flywheels:**

**bending in flywheel rims, 808, 809**

**coefficient of speed fluctuation, 800, 801**

**connection to shaft, 820, 821**

**constant thickness disk, 809–815**

**design for speed control, 799–804**

**energy management, 799–804**

**failure modes, 805**

**fluctuating duty cycle, 799–804**

**materials, 805, 806**

**rotating free ring, 807, 808**

**spoke-and-rim, 806–809**

**tension in flywheel spokes, 808, 809**

**types, 804, 805**

**uniform strength disk, 815, 816**

**uniform strength disk with rim, 816, 817**

**uses, 798**

**Force analysis, 124–126**

**Force flow lines, 124,125, 215**

**Force-induced elastic deformation, 23, 24,**

**28–31**

**Fracture mechanics, 233–241**

**Fracture mechanics approach to fatigue,**

**273–279**

**Fracture toughness, plane strain, 237**

**Frames:**

**C-frame, 844**

**design procedure, 845–850**

**Index 885Frames (Continued)**

**failure modes, 844**

**materials, 844**

**O-frame, 844**

**open truss, 843, 844**

**stressed-skin structure, 843, 844**

**thin-walled shell, 843, 844**

**Free body diagram, 123–126, 191, 386, 467**

**Fretting, 23, 26, 66–70**

**Fretting:**

**fretting action, 26, 66**

**fretting corrosion, 23, 26, 66**

**fretting fatigue, 23, 26, 66–68**

**fretting wear, 23, 26, 66, 68, 69**

**maps, 69**

**minimizing or preventing fretting**

**damage, 69, 70**

**Friction coefficients (table), 864–866**

**Friction wheel drives, 594, 595**

**Galling, 23, 27, 61**

**Gasketed joint, 497–507**

**Gasket materials, (table), 503**

**Gears:**

**angular velocity ratio, 595, 600–605, 609**

**backlash, 618**

**bevel:**

**applications, 597, 598**

**bending (tooth) – AGMA refined**

**approach, 667, 668**

**design procedure, 668–675**

**force analysis, 665, 666**

**nomenclature, 662–665**

**standard AGMA tooth proportions,**

**(table), 665**

**stress analysis, 666–668**

**surface durability using AGMA refined**

**approach, 667, 668**

**compound, 600–605**

**epicyclic, 600–605**

**external, 594, 595**

**face gear, 598**

**failure modes, 605–607**

**fundamental law, 595**

**helical:**

**applications, 597**

**bending (tooth) – AGMA refined**

**approach, 654, 655**

**contact-pattern, 649**

**design procedure, 656–662**

**force analysis, 653, 654**

**nomenclature, 648, 650**

**standard AGMA tooth proportions,**

**(table), 651**

**stress analysis, 654, 655**

**surface durability using AGMA refined**

**approach, 654, 655**

**herringbone, 597**

**hypoid, 598**

**internal, 594, 595**

**involute, 608–618**

**Lewis equation (bending), 626–629**

**Lewis form factor, 628**

**line of action (pressure line), 609**

**manufacturing cost trends, 624**

**manufacturing methods:**

**accuracy requirements (table), 623,**

**624**

**gear cutting, 618–620**

**gear finishing, 620**

**profile modification, 621, 622**

**materials, 607, 608**

**rack and pinion, 597**

**reduction ratios, 600–605**

**selection of type, 595–600**

**simple, 600–605**

**spiroid, 598**

**straight tooth spur:**

**angular velocity ratio, 595, 600–605,**

**609**

**applications, 595, 597**

**approximate actual size, 614**

**bending (tooth) – AGMA refined**

**approach, 631–638**

**bending (tooth) – simplified approach,**

**626–631**

**conjugate action, 609**

**design procedure, 647, 648**

**force analysis, 624–626**

**involute profile, 608–618**

**lubrication, 645–647**

**nomenclature, 594, 610**

**standard AGMA tooth proportions,**

**(table), 613**

**stress analysis, 631–645**

**surface durability using AGMA refined**

**approach, 641–645**

**surface durability using Hertz contact**

**stresses, 639–641**

**tooth profile, 608–618**

**surface durability, 62, 639–645, 655, 667,**

**668**

**tooth bending, 626–638, 654, 655, 667,**

**668**

**tooth durability, 632–645, 655, 667, 668**

**trains, 600–605**

**types, 595–600**

**uses, 594, 595**

**worm:**

**allowable tangential gear force, 682,**

**683**

**applications, 599**

**bending (tooth), 682**

**common thread profiles, 676**

**design procedure, 684–691**

**efficiency, 679–682**

**force analysis, 679–682**

**nomenclature, 675**

**stress analysis, 682, 683**

**surface durability, 682**

**typical tooth profiles, (table), 677**

**Zerol, 597, 598**

**Geometric compatibility, 385, 387, 392**

**Geometry determination, 305–330**

**Hardness properties, (table), 101**

**Heat affected zone (HAZ), 528**

**Helical coil springs, 546, 552–568**

**(also see springs)**

**Helical gears, 648–662 (also see gears)**

**Hertz contact deflection, 177, 453–457**

**Hertz contact spring rate, 181–182, 453**

**Hertz contact stress, 24, 62, 160, 161,**

**174–179**

**High-speed-rotors (see flywheels)**

**Hollow cylinder guidelines, 310**

**Hooke’s Law, 32, 47, 162, 214, 215, 228,**

**385, 387, 393**

**Horsepower relationship, 152**

**Housing, 844**

**Huber-von-Mises-Hencky Theory**

**(see distortional energy theory)**

**Human factors engineering, 5**

**House of quality, 3**

**I-beam guidelines, 308**

**I-beams, section properties, 870**

**Impact, 23, 26**

**Impact:**

**deflection, 47–52**

**deformation, 23, 26**

**energy method, 47–52**

**fatigue, 23**

**fracture, 23, 26**

**fretting, 23**

**stress, 47–52**

**stress wave propagation, 46**

**suddenly applied load, 46, 48**

**wear, 23, 26**

**Industrial designers, 2**

**Inspectability, 9**

**Inspectability, design for 339, 340**

**Interference fits:**

**design procedures, 396–400**

**failure modes, 386**

**uses, 382, 386**

**Intermediate design, 8**

**Involute gear teeth, 609–618**

**Involute splines, 373, 374**

**Iteration, 7, 319**

**Jack screws (see power screws)**

**Joints:**

**adhesively bonded, 538–542**

**advantages of adhesive bonding, 838**

**bolted, 486, 487–516**

**butt weld, 528**

**centroid of bolt pattern, 510, 511**

**centroid of weld pattern, 530**

**eccentric loading, 509–516, 529–537**

**failure modes, 487, 488**

**fillet welds, 529–537**

**gasketed, 497–507**

**886 IndexJoints (Continued)**

**moment of inertia, 510, 512**

**multiply bolted, 509**

**multiply riveted, 519**

**multiply welded, 529–537**

**preload, 495–507**

**rivet material, 517**

**riveted, 517–522**

**stiffness, 497–507**

**torsion-like shear, 509–516**

**types, 485, 486**

**weld edge preparation, 525, 526**

**weld electrode specifications, 527**

**weld types, 525, 526**

**weldability, 527**

**welded, 522–537**

**weld heat affected zone (HAZ), 528**

**weld stress concentration factors, 525**

**weld symbol, 524**

**Keys, 361–372**

**Keys:**

**failure modes, 366**

**square, 365–372**

**stress concentration factors (keyway),**

**220, 367, 369**

**Woodruff, 365, 367**

**Kinematic viscosity, 410, 411, 414**

**Larson-Miller parameter, 54**

**Lazy-material removal guideline, 611, 612**

**Lead screw (see power screws)**

**Leaf springs, 568–578 (also see springs)**

**Lessons learned strategy, 12**

**Lewis equation (see gears), 626–629**

**Line of action (see gears), 609**

**Linear actuators (see power screws)**

**Linear elastic fracture mechanics (LEFM),**

**233–241**

**Load sharing, 179–186**

**Load spreading guideline, 314**

**Loading severity parameter, 225**

**Lubrication:**

**boundary, 406–409**

**elastohydrodynamic (squeeze film), 406,**

**452, 645–647**

**hydrodynamic, 406, 409–425**

**hydrostatic, 409**

**Petroff’s equation, 411**

**pV product, 406–409**

**Raimondi and Boyd data, 413–417**

**Reynolds equation, 412, 413**

**plain bearings, 403, 405–425**

**rolling element bearings, 452**

**solid film, 406**

**Sommerfield data, 413–417**

**thick film (full film), 405, 409–425**

**thin film (partial film), 405–409**

**Tower experiments, 412**

**viscosity, 410, 411, 414**

**zero film, 405**

**Machinability index (table), 104**

**Maintenance, design for, 333, 339, 340**

**Manufacturing, 333–340**

**Manufacturing, design for, 337**

**Manufacturing process, selection, 334–337**

**Manufacturing process suitability (table), 103**

**Marketing specialists, 1, 2**

**Mass moments of inertia (table), 867**

**Materials:**

**application requirements, 94**

**Ashby charts, 105–111, 114–120**

**mechanical properties (tables), 95–105,**

**106–109, 238**

**performance evaluation indices, 94**

**selection by Ashby method, 105–111,**

**114–120**

**selection by rank-ordered data (table),**

**105–114**

**selection steps, 93**

**Materials cost index, 104**

**Maximum shearing stress design**

**equation, 318**

**Maximum shearing stress failure**

**theory, 225–227**

**Maximum normal stress design equation, 318**

**Maximum normal stress failure theory, 225,**

**226**

**Mean, 77**

**Mechanical design:**

**concepts, 6**

**definition, 6**

**failure prevention perspective, 22–75**

**Mechanical failure:**

**brinnelling, 23, 24**

**brittle fracture, 23, 24, 233–241**

**buckling, 23, 27, 34–45**

**combined creep and fatigue, 23, 28**

**corrosion, 23, 24, 64–66**

**corrosion fatigue, 23, 28, 64**

**corrosion wear, 23, 28, 64**

**creep, 23, 26, 27, 52–58**

**creep buckling, 23, 28**

**ductile rupture, 23, 24, 33, 34**

**fatigue, 23, 24, 241–291**

**force-induced elastic deformation, 23,**

**24, 30**

**fretting, 23, 26, 66–70**

**galling, 23, 27, 61**

**impact, 23, 26, 46–52**

**modes of, 23–28**

**radiation damage, 23, 27, 102, 103**

**seizure, 23, 27, 61**

**spalling, 23, 27**

**stress corrosion, 23, 28, 65, 66**

**stress rupture, 23, 27, 52–58**

**temperature-induced elastic deformation,**

**23, 24, 31, 32**

**thermal relaxation, 23, 27**

**thermal shock, 23, 27**

**wear, 23, 25, 59–63**

**yielding, 23, 24, 32, 33**

**Membrane analogy, 153–155**

**Merging shape guidelines, 313**

**Mode I crack displacement, 233**

**Mode II crack displacement, 233**

**Mode III crack displacement, 233**

**Modified square thread, 463, 464**

**Mohr’s circle (strain), 213, 214**

**Mohr’s circle (stress), 210, 211**

**Moment diagrams, bending (table),**

**129–133**

**Moment of inertia, area (table), 135**

**Moment of inertia, mass (table), 867**

**Multiaxial cyclic stress, 283–291**

**Multiaxial fatigue failure theories, 283–291**

**Multiaxial state of stress, 127, 205–215**

**Multiple threads, 464, 465**

**National Society of Professional Engineers**

**(NSPE), Code of Ethics, 14, 15,**

**859–863**

**Neuber rule, 274**

**Newtonian fluid, 410**

**Newton’s law of cooling:**

**bearings, 418**

**brakes, 712**

**gears, 646**

**Nondestructive evaluation (NDE), 339**

**Normal (Gaussian) distribution, 76–80**

**Normal stress, 126, 127**

**Notch sensitivity, 280–283**

**Octahedral shear stress theory of failure (see**

**distortion energy failure theory)**

**Paris law (fatigue), 277**

**Petroff’s equation, 411**

**Pins, 376, 377**

**Plain bearings:**

**advantages, 403, 404**

**design criteria, 419, 420**

**design procedure, 420–425**

**eccentricity ratio, 413, 421**

**failure modes, 404**

**lubrication, 403, 405–425**

**materials, 405**

**oil film temperature rise, 416, 418**

**recommended clearances (table), 420, 421**

**uses, 403, 404**

**Plane cross section properties (table), 135**

**Plane strain:**

**critical stress intensity factor, 237**

**definition, 237**

**minimum thickness for, 237**

**Plain strain fracture toughness, 237, 276**

**Plane stress, critical stress intensity factor,**

**237**

**Planetary gears, 600–605**

**Plastic strain, 32**

**Policy of least commitment, 3**

**Power, as related to torque and speed, 151,**

**152**

**Index 887Power screws:**

**Acme threads, 463, 464, 470, 471**

**back driving, 467**

**ball screw, 465**

**buttress thread, 463, 464**

**design procedures, 473, 474**

**efficiency, 467–473**

**failure modes, 466**

**helix angle, 464**

**lead (thread), 464**

**lead angle, 464, 469**

**materials, 466**

**modified square thread, 463, 464**

**multiple threads, 464, 465**

**overhauling, 469**

**pitch, 464**

**self-locking, 469**

**square thread, 463, 464**

**thread angle, 463**

**threads, 463–470**

**torque, 467–473**

**uses, 462**

**Preliminary design, 7, 8**

**Preloading, 186–189, 453–457**

**Presetting, 189**

**Pressure vessels:**

**ASME Boiler and Pressure Vessel Code,**

**382**

**failure modes, 383**

**longitudinal stress, 386**

**materials, 383, 384**

**tangential (hoop) stress, 385**

**thick wall, 382, 386–392**

**thin wall, 382, 385, 386**

**uses, 382**

**Prestressing, 190–192**

**Principal normal stress, 205–213**

**Principal planes, 205–213**

**Principal stresses, 205–213, 389**

**Principal shearing stress, 205–213**

**Projected area, 386**

**Probability density function, 76–79**

**Probability of failure, 76–79, 245**

**Probabilistic design, 76**

**Product design team, 1, 2, 3**

**Product marketing concept, 3**

**Radiation damage, 23, 27, 102, 103**

**Radiation exposure influence on properties**

**(table), 102, 103**

**Rain flow cycle counting (fatigue), 254,**

**266–272**

**Rankine’s theory (see maximum normal**

**stress theory)**

**Recycling, design for, 339, 340**

**Redundant assemblies, 179–186**

**Redundant supports, 166–169, 179–186**

**Redundancy, component level, 82, 83**

**Redundancy, sub-assembly level, 82, 83**

**Reliability, 76–84, 245**

**Reliability:**

**allocation, 80**

**block diagrams, 81**

**definition, 76**

**equal apportionment, 83**

**functional block diagrams, 81–83**

**goals, 80, 81**

**log-normal distribution, 76**

**normal cumulative distribution, 77–79**

**normal distribution, 77–80**

**parallel components, 82, 83**

**population mean, 77**

**population standard deviation, 77**

**population variance, 77**

**redundancy at component level, 82, 83**

**redundancy at subsystem level, 82, 83**

**series components, 82**

**Six Sigma, 81**

**standard normal variable (table), 78**

**system, 80–83**

**specification, 84**

**Weibull distribution, 76**

**Residual stresses, 189–194, 525**

**Residual stresses:**

**cold-rolling, 190**

**estimating, 190–194**

**fatigue life improvement, 288–291**

**presetting, 189**

**prestressing, 190–192**

**shot-peening, 190, 526**

**weldments, 525, 526**

**Resilience properties (table), 100**

**Resonance, 344, 359**

**Retrospective design, 70, 71**

**Reynolds equation, 412**

**Rivets (see fasteners)**

**Rolling element bearings:**

**ball, 430, 431**

**basic dynamic load rating, 435**

**basic static load rating, 435**

**enclosure, 457, 458**

**failure modes, 433**

**force-deflection curves, 453–457**

**lubrication, 451, 452**

**materials, 433, 434**

**mounting practices, 457, 458**

**preloading, 453, 457**

**reliability, 435, 436**

**roller, 430, 432**

**selection for spectrum loading, 434,**

**448–451**

**selection for steady loads, 434, 436–448**

**stiffness, 453–457**

**types, 430–432**

**uses, 429**

**Rotors, high-speed (see flywheels)**

**Rotating free ring, 407, 408**

**Safe life design, 9**

**Safety factor:**

**design, 7, 33, 72–74, 84**

**existing, 75**

**rating factors, 73**

**rating numbers, 72, 73, 84**

**Safety issues:**

**devices, 850, 852–854**

**guards, 850, 851**

**hazards, 850**

**risk, 850**

**Sample mean, 245**

**Sample standard deviation, 245**

**Screw threads:**

**Acme, 463, 464, 470, 471**

**buttress, 463, 464**

**failure modes, 466**

**helix angle, 464**

**lead, 464**

**lead angle, 464, 469**

**modified square, 463, 464**

**multiple threads, 464, 465**

**pitch, 464**

**square, 563, 464, 468**

**thread angle, 463**

**Screws, power (see power screws)**

**Seizure, 23, 27, 61**

**Setscrews, 365, 275, 376**

**Setscrews:**

**holding power, 376**

**types of points, 375**

**Shaft deflection, 353–358**

**Shaft strength, 345–353**

**Shafts:**

**connection to flywheels, 820, 821**

**critical speed, 358–360**

**design equations, deflection based,**

**353–358**

**design equations, strength based,**

**345–353**

**design layout, 343**

**design procedure, 360, 361**

**failure modes, 343, 344**

**flexible (see flexible shafts)**

**materials, 344, 345**

**standard for design of, 345**

**uses, 341–343**

**vibration, 358–360**

**Shear center, 158–160**

**Shearing stress, 126, 127, 142–148**

**Shock (see impact)**

**Shot-peening, 190**

**Shot-peening, fatigue life improvement,**

**288–291**

**Simplifying assumptions, 318**

**Six Sigma, 81**

**Slider-crank mechanism, 824**

**Solid bodies, properties of (table), 867**

**Spalling, 23, 27**

**Specification, reliability, 84**

**Specifications, engineering, 2, 8, 11, 93**

**Specifications, thread, 492**

**S-N curves, estimating, 246–248**

**S-N curves, strength-influencing factors,**

**247–258**

**888 IndexSplines, 361, 373, 374**

**Splines:**

**failure mode, 373**

**fits, 373**

**involute, 374**

**straight, 373, 374**

**stress concentration factors, 374**

**Spoke-and-rim flywheel, 806–809**

**(also see flywheel)**

**Spring index, 554**

**Springs:**

**Belleville (coned disk), 581, 582**

**buckling of helical coil, 559, 560**

**curvature factor in helical coil, 554**

**end loop stress concentration, 555, 556**

**energy storage, 582–586**

**fatigue shearing strength (table), 563**

**helical coil, 546, 552–568, 579**

**helical coil design procedure, 562–568**

**helical coil nomenclature, 552**

**helical coil spring index, 554**

**helical coil spring rate, 558**

**leaf springs, 568–578**

**leaf spring design procedure, 574–578**

**leaf spring spring-rate, 572**

**linear, 181**

**machine elements as, 180–186**

**nonlinear softening, 181**

**nonlinear stiffening (hardening), 181**

**parallel, 176–186**

**series, 179–186**

**shackles, 572–573**

**spiral torsion, 579, 580**

**surging of helical coil, 561**

**torsion bar, 578–581**

**torsion in helical coil, 553**

**torsion springs, 578–581**

**torsion tubes, 578**

**torsional shear yield strength (table), 560**

**transverse shear in helical coil, 553**

**Wahl factor, 554, 555**

**Spring rate (spring constant), 29, 179–186,**

**557, 558**

**Spring rate:**

**axial, 30, 181**

**bending, 181**

**direct shear, 181**

**helical coil, 557–559**

**Hertz contact, 181**

**leaf spring, 572**

**linearized, 181, 453**

**torsional, 181**

**Spur gears, 608–618 (also see gears)**

**Square thread, 463, 464, 469**

**Stages of design, 7–9**

**Standard deviation, 77**

**Standard normal variable, 253, (table), 78**

**Standards, 13**

**State of stress:**

**biaxial, 127, 205–213, 386**

**multiaxial, 127, 205–213, 225**

**multiaxial cyclic, 272, 283–291**

**triaxial, 127, 205**

**uniaxial, 127, 225**

**Stiffness, joint, 497–507**

**Stiffness properties of materials (table),**

**99**

**Straight toothy spur gears, 608–648**

**(also see gears)**

**Strain amplitude, elastic, 274, 275**

**Strain amplitude, plastic, 274, 275**

**Strain amplitude, total, 274, 275**

**Strain cubic equation, 213**

**Strain energy, 47, 126, 162–173, 227**

**Strain energy per unit volume, 227**

**Strain gage, 214**

**Strain-matching guideline, 313**

**Strain rosette, 241**

**Strength at elevated temperature (table),**

**96, 97**

**Strength properties (table), 95, 96**

**Strength reduction factor, 281**

**Strength/weight ratio (table), 96**

**Stress (see “stress patterns” and “state of**

**stress”)**

**Stress, equivalent, 272**

**Stress concentration, 215–224**

**Stress concentration:**

**actual local stress, 216**

**highly local, 216–224**

**multiple notches, 217, 223**

**nominal stress, 216**

**notch root, 216**

**notch sensitivity index, 280–283**

**strength reduction factor, 281**

**widely distributed, 138, 139, 216**

**Stress concentration factors:**

**crankshaft fillet, 222**

**curved beams, 138, 139**

**cyclic multiaxial states of stress, 281,**

**282**

**end-of hub pressed on shaft, 223**

**fatigue, 216, 217**

**fatigue of brittle materials, 282**

**fatigue of ductile materials, 282**

**flat bar with shoulder fillet, 221**

**gear tooth fillet, 222**

**helical coil spring in torsion, 580**

**intermediate and low-cycle range,**

**282**

**keyways (profiled, slender runner), 367,**

**369**

**keyways (Woodruff), 367**

**screw threads, 217**

**shaft diametral hole, 220**

**shaft fillet, 218**

**shaft groove, 219**

**shaft keyway, 220, 366–369**

**shaft splines, 220, 374**

**theoretical elasticity, 216**

**torsion of helical coil spring, 580**

**weldment, 525**

**Stress corrosion, 23, 28, 64**

**Stress cubic equation, 206–209**

**Stress intensity:**

**critical, 234**

**stress intensity factor, 233**

**Stress intensity factor, 233–237**

**Stress patterns:**

**bending, 128–137**

**direct stress, 128**

**surface contact stress, 128, 160**

**torsional shear, 128, 150–160**

**transverse shear, 128, 142–150**

**Stress relaxation, 27**

**Stress rupture, 23, 27, 52–58**

**Stress rupture strength (table), 97**

**Stress wave propagation, 46**

**Structural adhesives (table), 541**

**Structural shapes, section properties,**

**867–872**

**Suddenly applied load, 48**

**Superposition, principal of, 32**

**Surface contact stress, 160**

**Surface forces, 123**

**Surging, helical coil springs, 561**

**System reliability, 80–83**

**Tailored-shape guidelines, 307, 308**

**Tapered fits, 274, 375**

**Temperature-induced elastic deformation,**

**23, 24, 31, 32**

**Theoretical stress concentration factor, 216**

**Theories of failure:**

**distortional energy theory, 225, 227,**

**228**

**maximum shearing stress theory,**

**225–227**

**maximum normal stress theory, 225,**

**226**

**selection of, 229**

**Theory of elastic principles, 384–386**

**Thermal conductivity (table), 104, 105**

**Thermal expansion coefficients (table), 98**

**Thermal shock, 23, 27**

**Thermal relaxation, 23, 27**

**Thermal stress (temperature induces stress),**

**32**

**Threads:**

**fasteners, 488–497**

**power screws, 463–470**

**Tolerances, 323–329**

**Tooth bending, 631–639, 654, 655, 667, 668**

**(also see gears)**

**Topological interference, 824**

**Torsion:**

**circular cross section, 150–156**

**deflection, 161**

**noncircular cross section, 152–155**

**shear center in bending, 157–160**

**spring rate, 181**

**Torsion bar springs, 578–581 (also see**

**springs)**

**Index 889Total strain energy per unit volume, 227**

**Toughness properties (tables), 100, 238**

**Transverse shear, 142–147**

**Tresca-Guest theory (see maximum**

**shearing stress theory)**

**Triangle-tetrahedron guideline, 308, 309**

**Uniaxial state of stress, 127, 225, 233**

**Unit inertia (table), 532, 533**

**Units, 14–20**

**Units:**

**absolute system, 15, 16**

**base units, 15**

**conversion table, 17**

**derived units, 15**

**foot-pound-second system (fps), 14**

**gravitational system, 15**

**inch-pound-second system (ips), 14**

**International system (SI), 14**

**standard prefixes, 17**

**Universal joint, 365**

**Variance, 77**

**Virtues of simplicity, 10**

**Viscosity, 410, 411, 414**

**von Mises stress, 228**

**von Mises theory (see distortional**

**energy theory)**

**Whal factor, 554, 555**

**Wear, 23, 25, 59–63**

**Wear:**

**abrasive wear, 23, 25, 59, 61, 62**

**abrasive wear constant, 62**

**adhesive wear, 23, 25, 59, 61, 62**

**Archard adhesive wear constant, 60**

**corrosion wear, 23, 25, 59**

**deformation wear, 23, 26, 59**

**fretting wear, 23, 26, 66, 68**

**impact wear, 23, 26**

**mean normal contact pressure, 60, 61**

**principle of conversion, 61**

**principle of diversion, 61**

**principle of protective layers, 61**

**surface fatigue wear, 23, 25, 59, 62**

**three-body wear, 61**

**two-body wear, 61**

**Weibull distribution, 76**

**Weldability, 526**

**Welded joints (see joints, welded)**

**Weld symbol, 524–526**

**Wide flange beam, section properties, 868,**

**869**

**Wire rope:**

**failure modes, 779–781**

**fatigue data, 785**

**materials, 782**

**selection procedure, 786–791**

**stresses, 782, 784–791**

**uses, 748, 749**

**Worm gears, 675–691 (also see gears)**

**Yielding, 23, 24, 32, 33**

**Yield strength (table), 95**

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