(Engineering Drawing) Cecil Jensen, Jay D. Helsel, Dennis R. Short-Engineering Drawing and Design-McGraw-Hill (2008).pdf
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Contents Preface
Computer-Integrated Manufacturing (CIM)
xii
Acknowledgments
xiv
About the Authors
xv
Review and Assignments
1
PART
BASIC DRAWING AND DESIGN Chapter
1
Chapter
1
1-1 The Language of Industry Drawing Standards 3
1-3 The Drafting Office
2
2
1-2 Careers in Engineering Graphics 4 The Student 4 Places of Employment 4 Training, Qualifications, and Advancement Employment Outlook S
3 ""~11·.
--------·
3-1 Drawing Media and Format Drawing Media 32 Standard Drawing Sizes 32 Drawing Format 33 3-2 Filing and Storage Filing Systems 36 CAD 37
S
Review and Assignments
Chapter
15
4
42
!IBIIB·-----·
i';·--------
Basic Dimensioning
102
Holes Revolved to Show True Distance from Center
8
160 160
161
Review and Assignments 102
154
157
The Angle a Line Makes with a Plane
6-12 Materials of Construction
154
158
7-11 Angles between Lines and Planes
101
Repetitive Parts
153
154
Shortest Distance between Two Oblique Lines
Partial Views 99 Rear Views and Enlarged Views
Repetitive Details
152
Visibility of Oblique Lines by Testing 152 Visibility of Lines and Surfaces by Testing 152
98 99
Two-View Drawings
148
Locating the Piercing Point of a Line and a Plane-Auxiliary View Method 1SO
97
View Selection 98 One-View Drawings
148
148
Locating a Point on a Plane 149 Locating the Piercing Point of a Line and a Plane-Cutting-Plane Method 150
96
6-7 Oblique Surfaces
135
Dimensioning
177
177
Units of Measurement
181
Contents
Dual Dimensioning
9-2 Two or More Sectional Views on One Drawing 238
182
182
Angular Units
Reading Direction
183
9-3 Half-Sections 183
Basic Rules for Dimensioning Symmetrical Outlines 184 Reference Dimensions Operational Names
Threaded Assemblies
184
241
Section Lining on Assembly Drawings 241
184
184
Abbreviations
240 240
9-5 Assemblies in Section
184
Not-to-Scale Dimensions
239
9-4 Threads in Section
8-2 Dimensioning Circular Features Diameters 185 Radii 186
185
9-6 Offset Sections
243
8-3 Dimensioning Common Features
189 189
9-7 Ribs, Holes, and Lugs in Section Ribs in Sections 243 Holes in Sections 243 Lugs in Section 243 9-8 Revolved and Removed Sections Placement of Sectional Views 245
245
Repetitive Features and Dimensions Chamfers
189
Slopes and Tapers
190
191
Knurls
9-9 Spokes and Arms in Section
191 Undercuts 192 Limited Lengths and Areas 192 Wire, Sheet Metal, and Drill Rod 192 Formed Parts
8-4 Dimensioning Methods
9-11 Phantom or Hidden Sections 9-12 Sectional Drawing Review Review and Assignments
193 193 True-Position Dimensioning 193 Chain Dimensioning 193 Datum or Common-Point Dimensioning Polar Coordinate Dimensioning
PART
202 202 Basic Hole System 204 Basic Shaft System 205 Preferred Metric Limits and Fits 205 Standard Inch Fits
208
211
Review and Assignments
Chapter
Sections
9
209
209
211
Machined Surfaces
216
:~:B:!I:• • • • • • • • •
235
9-1 Sectional Views cutting-Plane Lines Full Sections Section Lining
237 237
235 235
FASTENERS, MATERIALS, AND FORMING PROCESSES 269
lQ
.,~:.;,gill_ _ _ _ __
Threaded Fasteners
Interchangeability of Parts
Surface Texture Symbol
2
Chapter
Surface Texture Characteristics
249
200
8-6 Fits and Allowances 201 Fits 201 Allowance 201 Description of Fits 201
8-7 Surface Texture
248
---------·.~· 195
195
Additional Rules for Dimensioning
248 248
193
Chordal Dimensioning
8-5 Limits and Tolerances Key Concepts 196 Tolerancing 197
247
9-10 Partial or Broken-Out Sections
192
Rectangular Coordinate Dimensioning
Application
242
270
10-1 Simplified Thread Representation 270 Screw Threads 271 Thread Forms 271 Thread Representation 271 Right- and Left-Hand Threads 272 Single and Multiple Threads 272 Simplified Thread Representation 273 Threaded Assemblies 273 Inch Threads 273 Metric Threads 276 Pipe Threads 278 10-2 Detailed and Schematic Thread Representation 278 Detailed Thread Representation 278 Threaded Assemblies 279 Schematic Thread Representation 279 10-3 Common Threaded Fasteners 280 Fastener Selection 280 Fastener Definitions 281 Fastener Configuration 281 Head Styles 281 Property Classes of Fasteners 282
v
vi
Contents
Drawing a Bolt and Nut Studs 285 Washers
284
Chapter
285
Terms Related to Threaded Fasteners 285 Specifying Fasteners
Setscrews
Ferrous Metals Cast Iron 341
287
287 287
Sealing Fasteners
290
290
291
Special Tapping Screws
SAE and AISI-Systems of Steel Identification High-Strength Low-Alloy Steels 348 Low- and Medium-Alloy Steels 348 Stainless Steels 348 Free-Machining Steels
291
Review and Assignments
12-3 Nonferrous Metals
295
11
·:JI.·- - - - - - - ·
Miscellaneous Types of Fasteners 11-1 Keys, Splines, and Serrations Keys
305
305
Splines and Serrations
11-2 Pin Fasteners
306
349
309
312
Spring Clips
11-5 Rivets
351 351
352 352
Machining 3S2 Material Selection
354
357
Material and Characteristics Kinds of Rubber 357
315
Assembly Methods
Standard Rivets 317 Large Rivets 317
Chapter
13-1 Metal Castings
323
Resistance-Welded Fasteners
323
323
11-7 Adhesive Fastenings Adhesion versus Stress Joint Design 325
364
364
Forming Processes Casting Processes Selection of Process
325
11-8 Fastener Review for Chapters 10 and 11 327 Review and Assignments
364 364 368
Design Considerations 369 Drafting Practices 371
325
328
359
13 .~Ill·,- - - - - - - ·
Forming Processes
318
Arc-Welded Studs
358
Review and Assignments
Rivets for Aerospace Equipment 317 Small Rivets 318
357
357
Design Considerations
11-6 Welded Fasteners
352
352
Forming Processes
12-5 Rubber 313 315
317
Blind Rivets
351
Thermosetting Plastics
313
Types of Springs Spring Drawings
351
Beryllium
Thermoplastics
Stamped Retaining Rings 312 Wire-Formed Retaining Rings 313 Spiral-Wound Retaining Rings 313
11-4 Springs
350
Titanium
12-4 Plastics
311
11-3 Retaining Rings
Magnesium Zinc 351
Precious Metals
Semipermanent Pins
349
Copper 350 Nickel 350
Refractory Metals
308
Quick-Release Pins
305
345
348
Manufacturing with Metals Aluminum 349
Chapter
343
Carbon Steels 343 Steel Specification 343
10-5 Fasteners for Light-Gage Metal, Plastic, and Wood 291 Tapping Screws
343
Carbon and Low-Alloy Cast Steels High-Alloy Cast Steels 343
Captive or Self-Retaining Nuts Inserts 290
341
341
12-2 Carbon Steel
Keeping Fasteners Tight Locknuts 288
341
12-1 Cast Irons and Ferrous Metals
286
10-4 Special Fasteners
12 :~.~:;·a,- - - - - •
Manufacturing Materials
Casting Datums 373 Machining Datums 374
13-2 Forgings
375
Closed-Die Forging
375
vii
Contents
General Design Rules Drafting Practices
13-3 Powder Metallurgy 13-4 Plastic Molded Parts Single Parts 380
380
15-2 Curved Surfaces in Isometric 464 Circles and Arcs in Isometric 464 Drawing Irregular Curves in Isometric
Review and Assignments
PART
387
3
WORKINCi DRAWINGS AND DESICiN Chapter
397
14
Detail and Assembly Drawings
14-2 Functional Drafting Procedural Shortcuts
403
405
Detail Drawing Requirements Drawing Checklist
405
Oblique Sectioning 472 Treatment of Conventional Features
14-5 Drawing Revisions
410
411
14-8 Detail Assembly Drawings 14-9 Subassembly Drawings
Image Generation 488 Data Extraction 489
491
412
413
415
Review and Assignments
416
Chapter
16 :~.~·····------·
Geometric Dimensioning and Tolerancing
15
Pictorial Drawings 457 15-1 Pictorial Drawings
484
Surface Modeling 486 Solid Modeling 486
Review and Assignments
411
14-7 Exploded Assembly Drawings
Chapter
484
Wire-Frame Modeling
Assembly Drawings for Catalogs
480
483
15-8 Solid Modeling
Design Assembly Drawings 410 Installation Assembly Drawings 411 Item List
402
15-6 Parallel, or One-Point, Perspective 474 Perspective Projection 474 Types of Perspective Drawings 475 Parallel, or One-Point, Perspective 476
CAD
407
409
14-6 Assembly Drawings
402
472
Basic Steps to Follow for Angular- Perspective Sketching (Fig. 15-58) 483
405 405
14-4 Multiple Detail Drawings
471
15.7 Angular, or Two-Point, Perspective Angular-Perspective Sketching 481
405
Qualifications of a Detailer Manufacturing Methods
470
Basic Steps to Follow for Parallel Perspective Sketching (Fig. 15-47) 477
404
14-3 Detail Drawings
15-4 Oblique-Projection 467 Inclined Surfaces 468 Oblique Sketching 468
15-5 Common Features in Oblique Circles and Arcs 471
Reducing the Number of Drawings Required Reproduction Shortcuts
15-3 Common Features in Isometric 465 Isometric Sectioning 465 Fillets and Rounds 467 Threads 467 Break Lines 467 Isometric Assembly Drawings 467
Dimensioning Oblique Drawings
400 400
Simplified Representations in Drawings
464
Basic Steps to Follow for Oblique Sketching (Fig. 15-29) 470
398
14-1 Drawing Quality Assurance 398 Review Considerations 398 Drawing Considerations 399 Fabrication Considerations 400 Assemble Considerations 400
Photodrawings
460
Isometric Sketching 461 Basic Steps to Follow for Isometric Sketching (Fig. 15-12) 462
383 386
Drawings
460
Dimensioning Isometric Drawings
380 380
Design Considerations
Assemblies
Nonisometric Lines
376
377
457 457 460
16-1 Modern Engineering Tolerancing Basic Concepts 511 Size of Dimensions 511
Axonometric Projection
Interpretation of Drawings and Dimensions 513
Isometric Drawings
Assumed Datums
513
510
510
viii
Contents
16-2 Geometric Tolerancing Feature Control Frame
S17
Profile Symbols
517
Placement of Feature Control Frame Form Tolerances 518 Straightness 519
16-3 Flatness
517
Coplanarity
S22
Concentricity
16-4 Straightness of a Feature of Size
522
16-16 Positional Tolerancing for Multiple Patterns of Features S84 Composite Positional Tolerancing
S29
529
16-6 Orientation Tolerancing of Flat Surfaces Reference to a Datum
587
Floating Fasteners 591 Calculating Clearance 592 Fixed Fasteners 592 Unequal Tolerances and Hole Sizes Coaxial Features 594
S3S
535
Angularity Tolerance 535 Perpendicularity Tolerance 535 Parallelism Tolerance 535 Examples of Orientation Tolerancing Control in Two Directions 536
Perpendicularity Errors
Review and Assignments
543
537
S42
Chapter
17 :~ ~ · - - - - - - - -
17-1 Two-Axis Control Systems
16-10 Projected Tolerance Zone
Review and Assignments
S6S
Chapter
636
18 ·~;g··.- - - - - - - -
Welding Drawings
641
18-1 Designing for Welding Welding Processes
18-2 Welding Symbols
641
641
643
The Design of Welded Joints
18-3 Fillet Welds S69
633 633
SS9
S61
Circularity 565 Cylindricity 567
629
Dimensioning and Tolerancing
Datum Target Symbol 562 Identification Targets 562 Targets Not in the Same Plane 563 Partial Surfaces as Datums 565 Dimensioning for Target Location 565
16-12 Circularity and Cylindricity
629
Computer Numerical Control (CNC) 629 Dimensioning for Numerical Control 630 Dimensioning for a Two-Axis Coordinate System 631
17-2 Three-Axis Control Systems
S49
Tolerancing Methods 549 Coordinate Tolerancing 550 Positional Tolerancing 553
S9S
595
S98
Drawings for Numerical Control
Control in Two Directions 543 Control on an MMC Basis 543 Internal Cylindrical Features 545 External Cylindrical Features 548
16-13 Profile Tolerancing
595
S37
16-8 Orientation Tolerancing for Features of Size
16-9 Positional Tolerancing
594
When to Use Geometric Tolerancing Basic Rules 595
535
Parts with Cylindrical Datum Features RFS and MMC Applications 538 Angularity Tolerance 543 Parallelism Tolerance 543 Perpendicularity Tolerance
S91
16-18 Summary of Rules for Geometric Tolerancing
16-7 Datum Features Subject to Size Variation
569
580
16-17 Formulas for Positional Tolerancing
Datums for Geometric Tolerancing Three-Plane System 531 Identification of Datums 532
Profiles
575
Noncircular Features at MMC
524
529
16-11 Datum Targets
574
16-1S Positional Tolerancing for Noncylindrical Features S80
Applicability of RFS, MMC, and LMC 525 Straightness of a Feature of Size 527
16-S Datums and the Three-Plane Concept
571
S74
Coaxiality 577 Symmetry 578 Runout 578
S23
Features of Size 523 Material Condition Symbols (Modifiers)
569
Profile-of-a-Surface Tolerance
16-14 Correlative Tolerances
Flatness of a Surface 522 Flatness per Unit Area 522 Two or More Flat Surfaces in One Plane
Datums
569
Profile-of-a-Line Tolerance
6SO
Fillet Weld Symbols 650 Size of Fillet Welds 653
648
ix
Contents
18-4 Groove Welds
654
Use of Break in Arrow of Bevel and J-Groove Welding Symbols 655 Groove Weld Symbols Groove Joint Design
18-5 Other Basic Welds Plug Welds 662 Slot Welds 663 Spot Welds 664 Seam Welds
Design of Roller Chain Drives
20-3 Gear Drives
660
Spur Gears
Flanged Welds
719
730 730
20-4 Power-Transmitting Capacity of Spur Gears 736 Selecting the Spur Gear Drive 736
668
Surfacing Welds Stud Welds
655 662
20-2 Chain Drives 717 Basic Types 717 Sprockets 719
20-5 Rack and Pinion
669 670
20-6 Bevel Gears
738
739
Working Drawings of Bevel Gears
671
Review and Assignments
20-7 Worm and Worm Gears
673
740
740
Working Drawings of Worm and Worm Gears
19 ,z~:•···~-------·
Chapter
Design Concepts
686
19-1 The Design Process 686 The Design Process 686
20-8 Comparison of Chain, Gear, and Belt Drives 744 Chains 744 Gears 744 Belts 744 Chain Drives Compared with Gear Drives Chain Drives Compared with Belt Drives
The Engineering Approach to Successful Design 687
Conclusion
Part Specifications
Review and Assignments
688
Do's and Don'ts for Designers
19-2 Assembly Considerations Cost of Assembly 690 Attachments 691 Design Checklist 697
690
Chapter
697
698
699
19-4 Project Management
699
699
702
703
21-2 Bearings
4
759
Shaft and Housing Fits Bearing Symbols
Chapter
707
767 769
21-6 Static Seals and Sealants 775 0-Ring Seals 775 Flat Nonmetallic Gaskets 776 Metallic Gaskets 777 Sealants 777 Exclusion Sea Is 777
708
20-1 Belt Drives Flat Belts 708 Conventional Flat Belts
709 710 How to Select a Light-Duty V-Belt Drive
763 763
21-S Lubricants and Radial Seals Lubricants 769 Grease and Oil Seals 770 Radial Seals 771
20
Belts, Chains, and Gears
760
766
21-4 Premounted Bearings
POWER TRANSMISSIONS
V-Belts
712
756
759
Bearing Classifications
PART
756
21-1 Couplings and Flexible Shafts Couplings 756 Flexible Shafts 758
21-3 Antifriction Bearings Bearing Loads 760 Ball Bearings 760 Roller Bearings 762 Bearing Selection 763
702
Review and Assignments
746
21 ';;,f~l!l~,·-------·
Plain Bearings
Online Project Management Assignments
745
Couplings, Bearings, and Seals
Concurrent Engineering through Computers Green Engineering
744 745
689
Design Approach to a Fabricated Structure
19-3 Concurrent Engineering
740
Review and Assignments
780
Contents
X
Chapter
22
23-11 Stampings
847
Design Considerations
Cams, Linkages, and Actuators 22-1 Cams, Linkages, and Actuators Cam Nomenclature
792
Review and Assignments
792
793
Chapter
Cam Followers 794 Cam Motions 794 Cam Displacement Diagrams
798
798
799
Conjugate Cams 800 Timing Diagrams 801 Dimensioning Cams Cam Size 804
808
22-6 Linkages
810
801
Pipe Drawings
867
Kinds of Pipes
867
871
Piping Drawings
24-2 Isometric Projection of Piping Drawings 80S
24-3 Supplementary Piping Information
Chapter 811
Systems Having Linkages and Cams
887
The Building Process
813
Review and Assignments
877
Structural Steel-Plain Material 888 Structural Drawing Practices 893
87S
2S-2 Beams
894
Assembly Clearances
5
2S-3 Standard Connections
SPECIAL FIELDS OF DRAFTING
Bolted Connections
823
2S-4 Sectioning
23
896
898
898
90S
Bottom Views
905
Elimination of Top and Bottom Views Right- and Left-Hand Details 906
Developments and Intersections 23-1 Surface Developments
895
Simple Square-Framed Beams
------------·t'' Chapter
877
------
25
2S-1 Structural Drafting
812
824
2S-S Seated Beam Connections
824
2S-6 Dimensioning
824
Bills of Material
Sheet-Metal Development Straight-Line Development
826
23-2 The Packaging Industry
827
912
828
Chapter
26
Jigs and Fixtures 919
23-S Radial Line Development of Conical Surfaces 834
26-1 Jig and Fixture Design
23-6 Development of Transition Pieces by Triangulation 836
Jigs 919 Drill Jigs 921
23-7 Development of a Sphere
Drill Bushings
839
Jig Body
843
919
921
26-2 Drill Jig Components
23-8 Intersection of Flat Surfaces-Lines Perpendicular 840
23-10 Intersecting Prisms · 844
909 910
Review and Assignments
23-4 Parallel Line Development of Cylindrical Surfaces 831
23-9 Intersection of Cylindrical Surfaces
907
Calculations of Weights (Masses)
23-3 Radial Line Development of Flat Surfaces
87S
880
Structural Drafting".'887
810
Straight-Line Mechanism
PART
868
869
Review and Assignments
Locus of a Point 810 Cams versus Linkages
22-7 Ratchet Wheels
24-1 Pipes
Pipe Joints and Fitting
806
22-S Indexing
24
Valves
22-3 Positive-Motion Cams 22-4 Drum Cams
8S3
Pipe Drawings 867
Simplified Method for Laying Out Cam Motion
22-2 Plate Cams
847
923
923
Cap Screws and Dowel Pins Locating Devices 924 Clamping Devices 926
923
911
905
xi
Contents
Locking Pins
927
Miscellaneous Standard Parts
27-2 Schematic Diagrams 942 Laying Out a Schematic Diagram
927
Design Examples 927
Graphic Symbols
26-3 Dimensioning Jig Drawings
27-3 Wiring (Connection) Diagrams 945 Basic Rules for Laying Out a Wiring Diagram
929
26-4 Fixtures 930 Milling Fixtures 930 Fixture Components 931 Fixture Design Considerations Review and Assignments
27-4 Printed Circuit Boards 947 CAD for Printed Circuit Boards 949 Basic Rules for Laying Out a Printed Circuit
932
Sequence in Laying Out a Fixture
942
942
935
936
27 \l'"lll'~-------· Electrical and Electronics Drawings 940
27-5 Block and Logic Diagrams Block Diagrams 951 Logic Diagrams 952 Graphic Symbols 952 Review and Assignments
947
951
951
956
Chapter
27-1 Electrical and Electronics Drawings Standardization 940 Using CAD for Electrical Drawings 941
940
Glossary
G-1
Appendix-Standard Parts and Technical Data Index
1-1
A-1
Preface Engineering Drawing and Design, Seventh Edition, prepares students for drafting careers in modem, technology-intensive industries. Technical drafting, like all technical areas, is constantly changing; the computer has revolutionized the way in which drawings and parts are made. This new edition translates the most current technical information available into the most useful for both instructor and student. The book covers graphic communication, CAD, functional drafting, material representation, shop processes, geometric tolerancing, true positioning, numerical control, electronic drafting, and metrication. The authors synthesize, simplify, and convert complex drafting standards and procedures into understandable instructional units. Like previous editions, this one is at the cutting edge of drafting and computer technologies. Because board-drafting skills are rapidly being replaced by computer-aided drafting (CAD), this edition provides an enhanced view of CAD while adhering to current ASME, ANSI, CSA, and ISO standards. Drafters must be knowledgeable about CAD and about international standards, for design files can now be electronically transmitted across borders, or around the world. The reader will find that this book helps build basic skills. It also supplies the technical knowledge required in today's marketplace.
TEXT FEATURES • Knowing and Applying Drawing Standards. A drawing made in the United States must meet the requirements set out in various ASME drawing standards publications. Also, if a firm is involved in international marketing and manufacturing, ISO guidelines (or other standards, such as Canadian drawing standards) must be strictly followed. Drafters will be pleased to see that this book not only covers these standards but also shows how to interpret and apply them. For example, the coverage of geometric tolerancing and true position is more comprehensive than in any other drafting text on the market today. • Knowing Manufacturing Materials and Their Processes. The authors bring together and explain the manufacturing materials that are available for engineering design. They describe the manufacturing processes that influence the shape, appearance, and design of the product. xii
• Knowing Fastening Methods. The correct fastening device plays a very important role in the cost, design, and appearance of a product. Readers can learn about various types of fasteners, both permanent and removable, that are currently available. • Providing All the Necessary Information to Complete the Design. The numerous assignments help the reader gain practice. These assignments can be completed with the help of a variety of Appendix tables reflecting realworld applications. • Unit Approach in Teaching the Subject Matter. The text's unit approach makes it possible for instructors to put together a customized program of instruction that suits the needs of their students and local industry.
KEY FEATURES OF THE SEVENTH EDITION Many users of the text were consulted before this new edition was undertaken. In response to their suggestions and recommendations, we have made major changes and added new features to this Seventh Edition, including: • The four-color format is easy to read. Color has been used as well to strengthen the important features in the 3000 line drawings and photographs. • Chapter 2 explains how drawings are produced by computers and peripherals. Computers and the Internet Web have become not only a laboratory but also a limit- less technical resource and design facility. • Solid modeling continues to play an important role in Chap. 15. The power of personal computers and workstations brings 3-D modeling into the classroom, home, CAD office, and on-site manufacturing centers. • Chapter 16 contains more information on geometric tolerancing and guidance on how to apply it to various drawings. The chapter is up to date with ASME standards and is more understandable to beginning students. • Chapter 19 covers concurrent engineering and project modeling. Today, engineers and technicians work side by side. All team members are responsible for coordinating efforts to deliver on-time and on-budget finished products.
Preface
• The section on stamping in Chap. 23 it covers the process of forming and cutting thicker-gage metals that are used in manufacturing. • Chapter 27, on electronic drafting, is consistent with solid-state, printed circuit board technology. • Many chapters include new CAD features. They give students and instructors a clear picture of how CAD can be used in the classroom while maintaining a focus on basic drafting principles. Many CAD features include assignments. • We have continued to provide the unit approach to teaching, which divides chapters into "mini" teaching units. Instructors find this approach to be a real bonus. By choosing the appropriate units, instructors can put together a customized program that suits the needs of their students and local industry. • Design concepts are covered in the text through drawing practice. Graduates find that these concepts give them an excellent background in drafting and design. Instructors can choose the units appropriate for their program. • This text continues to provide the latest drawing standards, indispensable to instructors. Current ANSI/ASME and ISO drawing practices are examined better here than in any other text. • Numerous Internet assignments appear throughout the book. The Websites, which relate directly to the topic of the unit, are of companies students might select to survey possible career opportunities. Instructors can ask students to describe what they found at the sites or to discuss sites that have the greatest regional career interest. Students can also view various technical product lines. Each chapter begins with objectives and ends with a chapter summary and list of key terms (both referenced to chapter units) and draftinvg assignments. A Glossary,
xiii
precedes the Appendix. The four-color design highlights the text's special features. Color is used to enhance the instructional value of the material. Thus, technical material is appealing visually and easy to follow and understand.
ADDITIONAL RESOURCES We have revised, improved, and added to the program's ancillary products. Here is what's new and updated:
Drawing Workbook The Workbook for Engineering Drawing and Design, Seventh Edition, covers all 27 chapters. It contains worksheets that provide a partially completed solution for assignments for each unit of the text. Each worksheet is referenced to a specific chapter and unit number in the text. Instructions are provided that give an overview for each assignment and references it to the appropriate text unit. The drawing problems contain both U.S. customary (decimal inch) and metric (millimeter) units of measurement. The worksheets are perforated for easy removal. Solutions are available to instructors at the book's website at www.mhhe.com/jensen.
Additional Chapters on Advanced Topics Three additional chapters, covering advanced topics, are provided on the book's website: Chapter 28-Applied Mechanics Chapter 29-Strength of Materials Chapter 30-Fluid Power Comments and suggestions concerning this and future editions of the text are most welcome. Visit the text website at: www.mhhe.com/jensen for various resources available to instructors and students.
Acknowledgments The authors are indebted to the members of ASME Y14.5M-1994 (R2004), Dimensioning and Tolerancing, and the members of the CAN/CSA-B78.2-M91, Dimensioning and Tolerancing of Technical Drawings, for the countless hours they have contributed to making successful standards. The authors and staff of McGraw-Hill wish to express their appreciation to the following individuals for their responses to questionnaires and their professional reviews of the new edition:
xiv
Fred Brasfield Tarrant County College Ralph Dirksen Western Illinois University James Freygang Ivy Tech Community College George Gibson Athens Technical College James Haick Columbus Technical College Richard Jerz St. Ambrose University Bisi Oluyemi Morehouse College Robert A. Osnes Everett Community College Douglas L. Ramers University of Evansville Jeff Raquet University of North Carolina-Charlotte Larry Shacklett Southeastern Community College Warner Smidt University of Wisconsin-Platteville James Stokes Ivy Tech Community College of Indiana Slobodan Urdarevik Western Michigan University Dean Zirwas Indian River Community College
About the Authors Cecil H. Jensen Cecil H. Jensen authored or coauthored many successful technical books, including Engineering Drawing and Design, Fundamentals of Engineering Drawing, FundamentaL~ of Engineering Graphics (formerly called Drafting Fundamentals), Interpreting Engineering Drawings, Geometric Dimensioning and Tolerancing for Engineering and Manufacturing Technology, Architectural Drawing and Design for Residential Construction, Home Planning and Design, and Interior Design. Some of these books
were printed in three languages and are popular in many countries. Mr. Jensen was a member of the Canadian Standards Committee (CSA) on Technical Drawings (which includes both mechanical and architectural drawing) and headed the Committee on Dimensioning and Tolerancing. He was Canada's ANSI representative. He represented Canada at two world ISO conferences in Oslo and Paris on the standardization of technical drawings. Cecil Jensen passed away in April, 2005.
Jay D. Helsel Jay D. Helsel is professor emeritus of applied engineering and technology at California University of Pennsylvania. He earned the master's degree from Pennsylvania State University and a doctoral degree in educational communications and technology from the University of Pittsburgh. He holds a certificate in airbrush techniques and technical illustration from the Pittsburgh Art Institute. He has worked in industry and has also taught drafting, metalworking, woodworking,
and a variety of laboratory and professional courses at both the secondary and the college levels. Dr. Helsel is now a full-time writer. He coauthored Engineering Drawing and Design, Fundamentals of Engineering Drawing, Programmed Blueprint Reading, the popular high school drafting textbook Mechanical Drawing: Board and CAD Techniques, now in its thirteenth edition, and Interpreting Engineering Drawings.
Dennis R. Short Dennis R. Short is professor of computer graphics technology at the School of Technology, Purdue University. He completed his undergraduate and graduate work at Purdue University and also studied at the University of Maryland, College Park. He enjoys teaching traditional engineering design and drafting, computer-aided drafting and design, computer-integrated manufacturing (CIM), and advanced modeling and animation. While at Purdue, he implemented
the first instructional CAD system for the School of Technology, as well as the first networked PC-based CAD laboratory. In addition to teaching undergraduates, he is on the graduate faculty. He codirects the Purdue International Center for Entertainment Technology (PICET), a university-level interdisciplinary research and development center. Dr. Short prepared the Instructor Wraparound Edition for Engineering Drawing and Design, Fifth and Sixth Editions.
XV
BASIC DRA:
Chapter 1 Engineering Chapter 2
Computer-
Chapter 3 Chapter 4 Chapter 5 Chapter 6 Theory of Shape Chapter 7
Auxiliary Views and
Chapter 8 Basic Dimensioning Chapter 9
Sections
235
Chapter
1
Engineering Graphics as a Language OBJECTIVES After studying this chapter, you will be able to:
• Define common terms used in drawing and design. ( 1-1) • Describe drawing standards and the standards organizations. (1-1) • Understand the training and qualifications needed for careers in drawing and design. (1-2) • Understand the uses of CAD in the drafting office. (1-3) • Describe drafting equipment such as drafting machines, slides, triangles, scales, and compasses. (1-4) • Use pencils and erasers in drafting. (1-4)
1-1
THE LANGUAGE OF INDUSTRY
Since earliest times people have used drawings to communicate and record ideas so that they would not be forgotten. Graphic representation means dealing with the expression of ideas by lines or marks impressed on a surface. A drawing is a graphic representation of a real thing. Drafting, therefore, is a graphic language, because it uses pictures to communicate thoughts and ideas. Because these pictures are understood by people of different nations, drafting is referred to as a universal language. Drawing has developed along two distinct lines, with each form having a different purpose. On the one hand artistic drawing is concerned mainly with the expression of real or imagined ideas of a cultural nature. Technical drawing, on the other hand, is concerned with the expression of technical ideas or ideas of a practical nature, and it is the communication method used in all branches of technical industry. Even highly developed word languages are inadequate for describing the size, shape, texture and relationship of physical objects. For every manufactured object there are drawings that describe its physical shape and size completely and accurately, communicating engineering concepts to manufacturing. For this reason, drafting is called the language of industry. Drafters translate the ideas, rough sketches, specifications, and calculations of engineers, architects, and designers into working plans that are used in making a product (Table 1-1). Drafters calculate the strength, reliability, and cost of materials. In their drawings and specifications, they describe exactly what materials workers are to use on a particular job. To prepare their drawings, drafters
CHAPTER 1
TABLE 1-1
Engineering Graphics as a Language
Various fields of drafting.
Mechanical
Designing Testing Manufacturing Maintenance Construction
Materials Machines Devices
Power generation Transportation Manufacturing Power services Atomic energy Marine vessels
Architectural
Planning Designing Supervising
Buildings Environment Landscape
Commercial buildings Residential buildings Institutional buildings Environmental space forms
Electrical
Designing Developing Supervising Programming
Computers Electronics Power Electrical
Power generation Power application Transportation Illumination Industrial electronics Communications Instrumentation Military electronics
Aerospace
Planning Designing Testing
Missiles Planes Satellites Rockets
Aerodynamics Structural design Instrumentation Propulsion systems Materials Reliability testing Production methods
Piping
Designing Testing Manufacturing Maintenance Construction
Buildings Hydraulics Pneumatics Pipe lines
Liquid transportation Manufacturing Power services Hydraulics Pneumatics
,J5 4
"
R, 100 n 20W
3
Structural designs :Buildings Planes Ships Automobiles Bridges
Planning Designing Manufacturing Construction
Technical illustration
Promotion Designing Illustrating
Catalogs Magazines Displays
New products Assembly instructions Presentations community projects Renewal programs
3
4
PART 1 Basic Drawing and Design
use either computer-aided drawing and design (CAD) systems or board drafting instruments, such as compasses, protractors, templates, and triangles, as well as drafting machines that combine the functions of several devices. They also may use engineering handbooks, tables, and calculators to assist in solving technical problems. Drafters are often classified according to their type of work or their level of responsibility. Senior drafters (designers) use the preliminary information provided by engineers and architects to prepare design layouts (drawings made to scale of the object to be built). Detailers Gunior drafters) make drawings of each part shown on the layout, giving dimensions, material, and any other information necessary to make the detailed drawing clear and complete. Checkers carefully examine drawings for errors in computing or recording sizes and specifications. Drafters may also specialize in a particular area, such as mechanical, electrical, electronic, aeronautic, structural, piping, or architectural drafting.
Drawing Standards Throughout the long history of drafting, many drawing conventions, terms, abbreviations, and practices have come into common use. It is essential that different drafters use the same practices if drafting is to serve as a reliable means of communicating technical theories and ideas. In the interest of worldwide communication, the International Organization of Standardization (ISO) was established in 1946. One of its committees, ISO TCIO, was formed to deal with the subject of technical drawings. Its goal was to develop a universally accepted set of drawing standards. Today most countries have adopted, either in full or with minor changes, the standards established by this committee, making drafting a truly universal language. The American Society of Mechanical Engineers (ASME) is the governing body that establishes the standards for the United States through its ASME Y14.5 committee (ANSI), made up of selected personnel from industry, technical organizations, and education. Members from the ASME Yl4.5 also serve on the ISO TCIO subcommittee. The standards used throughout this text reflect the current thinking of the ASME standards committee. These standards apply primarily to end-product drawings. End-product drawings usually consist of detail or part drawings and assembly or subassembly drawings, and are not intended to fully cover other supplementary drawings, such as checklists, item lists, schematic diagrams, electrical wiring diagrams, flowcharts, installation drawings, process drawings, architectural drawings, and pictorial drawings. The information and illustrations presented here have been revised to reflect current industrial practices in the preparation and handling of engineering documents. The increased use of reduced-size copies of engineering drawings made from microfilm and the reading of microfilm require the proper preparation of the original engineering
document regardless of whether the drawing was made manually or by computer (CAD). All future drawings should be prepared for eventual photographic reduction or reproduction. The observance of the drafting practices described in this text will contribute substantially to the improved quality of photographically reproduced engineering drawings.
INTERNET CONNECTION Visit this site and report on careers in drafting and related technical fields: www.bls.gov/bls/occupation
1-2
CAREERS IN ENGINEERING GRAPHICS
The Student While students are learning basic drafting skills, they will also be increasing their general technical knowledge, learning about some of the enginering and manufacturing processes involved in production. Not all students will choose a drafting career. However, an understanding of this graphic language is necessary for anyone who works in any of the fields of technology, and is essential for those who plan to enter the skilled trades or become a technician, technologist, or engineer. Because a drawing is a set of instructions that the worker will follow, it must be accurate, clean, correct, and complete. When drawings are made with the use of instruments, they are called instrument (or board) drawings. When they are developed with the use of a computer, they are known as computer-aided drawings. When made without instruments or the aid of a computer, drawings are referred to as sketches. The ability to sketch ideas and designs and to produce accurate drawings is a basic part of drafting skills. In everyday life, a knowledge of technical drawings is helpful in understanding house plans and assembly, maintenance, and operating instructions for many manufactured or hobby products.
Places of Employment There are well over 300,000 people working in CAD or drafting positions in the United States. A significant number of them are women. About 9 out of 10 drafters are employed in private industry. Manufacturing industries that employ a large number of drafters are those making machinery, electrical equipment, transportation equipment, and fabricated metal products. Nonmanufacturing industries employing a large number of drafters are engineering and architectural consulting firms, construction companies, and public utilities. Drafters also work for the government; the majority work for the armed services. Drafters employed by state and local governments work chiefly for highway and public works
CHAPTER 1 Engineering Graphics as a Language
departments. Several thousand drafters are employed by colleges and universities and by other nonprofit organizations.
Training, Qualifications, and Advancement Many design careers are available at different technical levels of performance. Most companies are in need of design and drafting services for growth in technical development, construction, or production. Any person interested in becoming a drafter can acquire the necessary training from a number of sources, including junior and community colleges, extension divisions of universities, vocational/technical schools, and correspondence schools. Others may qualify for drafting positions through on-the-job training programs combined with part-time schooling. The prospective drafter's training in post-high school drafting programs should include courses in mathematics and physical sciences, as well as in CAD and CADD. Studying fabrication practices and learning some trade skills are also helpful, since many higher-level drafting jobs require knowledge of manufacturing or construction methods. This is especially true in the mechanical discipline because of the implementation of CAD/CAM (computer-aided drawing/ computer-aided manufacturing). Many technical schools offer courses in structural design, strength of materials, physical metallurgy, CAM, and robotics. As drafters gain skill and experience, they may advance to higher-level positions such as checkers, senior drafters, designers, supervisors, and managers (Fig. 1-1). Drafters who take additional courses in engineering and mathematics are often able to qualify for engineering positions. Qualifications for success as a drafter include the ability to visualize objects in three dimensions and the development of problem-solving design techniques. Since the drafter is the one who finalizes the details on drawings, attentiveness to detail is a valuable asset.
Employment Outlook Employment opportunities for drafters are expected to remain stable as a result of the complex design problems of modern
Fig. 1-1
Positions within the drafting office.
5
products and processes. The need for drafters will, however, fluctuate with local and national economics. Since drafting is a part of manufacturing, job opportunities in this field will also rise or drop in accordance with various manufacturing industries. The demand for drafters will be high in some areas and low in others as a result of high-tech expansion or a slump in sales. In addition, computerization is creating many new products, and support and design occupations, including drafters, will continue to grow. On the other hand, photo-reproduction of drawings and expanding use of CAD have eliminated many routine tasks done by drafters. This development will probably reduce the need for some less skilled drafters. References and Source Materials 1. Charles Bruning Co. 2. Occupational Outlook Handbook.
INTERNET CONNECTION Visit this site to review information on drafting certification, specific job openings, and opportunities to post resumes: http://www.adda.org/
1-3
THE DRAFTING OFFICE
Drafting room technology has progressed at the same rapid pace as the economy of the country. Many changes have taken place in the modern drafting room compared to the typical drafting room scene before CAD, as shown in Fig. 1-2, p. 6. Not only is there far more equipment, but it is of much higher quality. Noteworthy progress has been and continues to be made. The drafting office is the starting point for all engineering work. Its product, the engineering drawing, is the main method of communication among all people concerned with the design and manufacture of parts. Therefore, the drafting office must provide accommodations and equipment for the drafters, from designer and checker to detailer or tracer; for the personnel who make copies of the drawings and file the originals; and for the secretarial staff who assist in the preparation of the drawings. Typical drafting workstations are shown in Figs. 1-3 and 1-4, p. 6. Fewer engineering departments now rely on board drafting methods. Computers are replacing drafting boards at a steady pace because of increased productivity. However, where a high volume of finished or repetitive work is not necessary, board drafting does the job adequately. CAD and board drafting can serve as full partners in the design process, enabling the designer to do jobs that are simply not possible or feasible with board equipment alone. Besides increasing the speed with which a job is done, a CAD system can perform many of the tedious and repetitive
6
PART 1
Basic Drawing and Design
(A) THE DRAFTING OFFICE AT THE TURN OF THE CENTURY.
Fig. 1-3
Board drafting office.
(B) BOARD DRAFTING OFFICE UP TO 1970.
Fig. 1-4 CAD drafting office.
(C) TODAY'S DRAFTING OFFICE.
Fig. 1-2
Evolution of the drafting office.
tasks ordinarily required of a drafter, such as lettering and differentiating line weights. CAD thus frees the drafter to be more creative while it quickly performs the mundane tasks of drafting. It is estimated that CAD has been responsible
for an improvement of at least 30 percent in production in terms of time spent on drawing. A CAD system by itself cannot create. A drafter must create the drawing, and thus a strong design and drafting background remains essential. It may not be practical to handle all the workload in a design or drafting office on a CAD system. Although most design and drafting work certainly can benefit from it, some functions will continue to be done by traditional means. Thus some companies use CAD for only a portion of the workload. Others use CAD almost exclusively. Whatever the percentage of CAD use, one fact is certain: It has had, and will continue to have, a dramatic effect on design and drafting careers. Once a CAD system has been installed, the required personnel must be hired or trained. Trained personnel generally originate from one of three popular sources: educational institutions, CAD equipment manufacturer training courses, and individual company programs.
CHAPTER 1
Engineering Graphics as a Language
7
INTERNET CONNECTION Visit the following site for information on computers and related accessories for the drafting office: http://www.ibm.com/ Examine this site and report on the typical furniture and equipment needed when planning a new drafting office: http://www.mayline.com/ Obtain information on the latest printers, scanners, and copiers: http://www.hewlett-packard.com/
1-4
BOARD DRAFTING
Over the years, the designer's chair and drafting table have evolved into a drafting station that provides a comfortable, integrated work area. Yet much of the equipment and supplies employed years ago are still in use today, although vastly improved.
Special tables and desks are manufactured for use in singlestation or multistation design offices. Typical are desks with attached drafting boards. The boards may be used by the occupant of the desk to which it is attached, in which case it may swing out of the way when not in use, or may be reversed for use by the person in the adjoining station. In addition to such special workstations, a variety of individual desks, chairs, tracing tables, filing cabinets, and special storage devices for equipment are available. The drawing sheet is attached directly to the surface of a drafting table (Fig. 1-5). Most professional drafting tables
STEEL DRAFTING TABLE
ELECTRIC DRAFTING TABLE
Fig. 1-5
Drafting tables.
Board drafting equipment.
have a special overlay drawing surface material that "recovers" from minor pinholes and dents.
Drafting Furniture
WOOD DRAFTING TABLE
Fig. 1-6
Drafting Equipment See Fig. 1-6 for a variety of drafting equipment.
Drafting Machines In a manually equipped drafting office, where the designer is expected to do accurate drafting, a drafting machine, or parallel slide, is used. A drafting machine, which is attached to the top of the table, combines the functions of a parallel slide, triangles, scale, and protractor and is estimated to save up to 50 percent of the user's time. All positioning is done with one hand, and the other hand is free to draw. Two types are currently available (Fig. 1-7, p. 8). In the track type, a vertical beam carrying the drafting instruments rides along a horizontal beam fastened to the top of the table. In the arm (or elbow) type, two arms pivot from the top of the machine and are relative to each other. The track-type machine has several advantages over the arm type. It is better suited for large drawings and is normally more stable and accurate. The track type also allows the drafting table to be positioned at a steeper angle and permits locking in the vertical and horizontal positions. Some track-type drafting machines provide a digital display of angles, the X- Y coordinates, and a memory function.
Parallel Slide The parallel slide, also called the parallel bar, is used in drawing horizontal lines and for supporting triangles when vertical and sloping lines are being drawn (Fig. 1-8, p. 8). It is fastened on each end to cords, which pass over pulleys. This arrangement permits movement up and down the
8
PART 1
Basic Drawing and Design
Fig. 1-8 Drafting table with parallel slide.
45° triangles. Singly or in combination, these triangles can be used to form angles in multiples of 15°. For other angles, the adjustable triangle (Fig. 1-11) is used (p. 10).
Scales Scale may refer to the measuring instrument or the size to which a drawing is to be made. (A) TRACK TYPE
(B)ARMTVPE
Fig. 1-7
Drafting machines.
board while maintaining the parallel slide in a horizontal position.
Triangles Triangles are used together with the parallel slide when you are drawing vertical and sloping lines (Fig. 1-9). The triangles most commonly used are the 30/60° and the
Shown in Fig. 1-10, p. 10, are the common shapes of scales used by drafters to make measurements on their drawings. Scales are used only for measuring and are not to be used as a straightedge for drawing lines. It is important that drafters draw accurately to scale. The scale to which the drawing is made must be given in the title block or strip that is part of the drawing. Measuring Instrument
Sizes to Which Drawings Are Made When an object is drawn at its actual size, the drawing is called full scale or scale 1:1. Many objects, however, such as buildings, ships, or airplanes, are too large to be drawn full scale, so they must be drawn to a reduced scale. An example would be the drawing of a house to a scale of 1,4 in. = 1 ft or 1:48. Frequently, objects such as small wristwatch parts are drawn larger than their actual size so that their shape can be seen clearly and dimensioned. Such a drawing has been drawn to an enlarged scale. The minute hand of a wristwatch, for example, could be drawn to a scale of 5:1. Many mechanical parts are drawn to half scale, 1:2, and quarter scale, 1:4, or nearest metric scale, 1:5. The scale to which the part is drawn and the actual size of the part are shown as an equation, the drawing scale shown first. With reference to the 1:5 scale, the left side of the equation represents a unit of the size drawn; the right side represents the equivalent 5 units of measurement of the actual object. Scales are made with a variety of combined scales marked on their surfaces. This combination of scales spares the drafter the necessity of calculating the sizes to be drawn when working to a scale other than full size.
CHAPTER 1
Engineering Graphics as a Language
9
(A) THE 45° TRIANGLE
(B) THE 60° TRIANGLE
(C) THE TRIANGLES IN COMBINATION
Fig. 1-9
Triangles.
Metric Scales The linear unit of measurement for mechanical drawings is the millimeter. Scale multipliers and divisors of 2 and 5 are recommended (Fig. 1-12, p. 10). The units of measurement for architectural drawings are the meter and millimeter. The same scale multipliers and divisors used for mechanical drawings are used for architectural drawings.
The divisions, or parts of an inch, can be used to represent feet, yards, rods, or miles. This scale is also useful in mechanical drawing when the drafter is dealing with decimal dimensions. On fractional inch scales, multipliers or divisors of 2, 4, 8, and 16 are used, offering such scales as full size, half size, and quarter size.
Inch (U.S. Customary) Scales
Foot Scales These scales are used mostly in architectural work (Fig. 1-14, p. 11). They differ from the inch scales in that each major division represents a foot, not an inch, and end units are subdivided into inches or parts of an inch. The more common scales are Ys in. = 1 ft, Y. in. = 1 ft, 1 in. = 1 ft, and 3 in. = 1 ft. The most commonly used inch and foot scales are shown in Table 1-2, p. 12.
There are three types of scales that show various values that are equal to 1 inch (in.) (Fig. 1-13, p. 11 ). They are the decimal inch scale, the fractional inch scale, and the scale that has divisions of 10, 20, 30, 40, 50, 60, and 80 parts to the inch. The last scale is known as the civil engineer's scale. It is used for making maps and charts. Inch Scales
10
PART 1
Basic Drawing and Design
REGULAR
em
RELIEVED FACET
1:1
DOUBLE
OPPOSITE
BEVEL
BEVEL
FLAT BEVEL
10
20
30
40
E
1:1 SCALE (1 mm DIVISIONS)
1'''''''''1 1111 11111 11111 11111 11111 11111 11111 11111
J;;~"''("~:>r~~~:·Y"'lc""'"~t"~~;"JC;;~;,;~'¥~"':'! (E) REVOLVING TOP VIEW
(F) REVOLVING ONLY LINE OA INTHETOPVIEW
Fig. 7-20 Typical true-length problems examined and solved.
A
B
(D) REVOLVING ONLY SURFACEOAB
(C) REVOLVING FRONTVIEW
A
(G) REVOLVING ONLY LINE OA IN THE FRONT VIEW
CHAPTER 7
auxiliary view in Fig. 7-20B, however, it does show its true length (TL), because the auxiliary plane is parallel to the surface OAB. Figure 7-20C shows another way to show the true length (TL) of line OA. In this case, revolve the object about an axis perpendicular to the vertical plane until surface OAB is parallel to the profile plane. The side view will then show the true size of surface OAB and also the true length of line OA. A shorter method of showing the true length of OA is to revolve only the surface OAB, as shown in Fig. 7-5-9D. In Fig. 7-20E the object is revolved in the top view until line OA in that view is horizontal. The front view now shows line OA in its true length because this line is now parallel to the vertical plane. In Fig. 7-20F still another method is shown. In this case, instead of the whole object being revolved, just line OA is turned in the top view until it is horizontal at OA. The point A 1 can then be projected to the front view. There, OA 1 will show line OA at its true length. You can revolve a line in any view to make it parallel to any one of the three principal planes. Projecting the line on the plane to which it is parallel will show its true length. In Fig. 7-20G the line has been revolved parallel to the horizontal plane. The true length of line OA then shows in the top view. Fig. 7-21 shows a simple part with one view revolved in each of the examples. Space 1 shows a three-view drawing of a block in its simplest position. In space 2 (upper right) the block is shown after being revolved from the position in space 1 through 45° about an axis perpendicular to the frontal plane. The front view was drawn first, copying the front view in space 1. The top view was obtained by projecting up from the front view and across from the top view of space 1.
Auxiliary Views and Revolutions
145
In space 3 (lower left) the block has been revolved from position 1 through 30° about an axis perpendicular to the horizontal plane. The top view was drawn first, copied from the top view of space 1. In space 4 the block has been tilted from position 2 about an axis perpendicular to the side plane 30°. The side view was drawn first, copied from the side view in space 2. The widths of the front and top views were projected from the front view of space 2.
See Assignment 6 for Unit 7-5 on page 170.
7-6
LOCATING POINTS AND LINES IN SPACE
Points in Space A point can be considered physically real and can be located by a small dot or a small cross. It is normally identified by two or more projections. In Fig. 7-22A (p. 146), points A and B are located on all three reference planes. Notice that the unfolding of the three planes forms a two-dimensional surface with the fold lines remaining. The fold lines are labeled as shown to indicate that F represents the front view, T represents the top view, and S represents the profile or right-side view. In Fig. 7-22B the planes are replaced with reference lines RL 1 and R~, which are placed in the same position as the fold lines in Fig. 7-22A.
Lines in Space Lines in descriptive geometry are grouped into three classes depending on how they are positioned in relation to the reference lines. Normal Lines A line that is perpendicular to the reference plane (a normal line) will project as a point on that plane. In Fig. 7-23A (p. 146), line AB is perpendicular to the front reference plane. As such, it is shown as a point (AFBF) in the front view and as a true-length line in the top and side views (lines ATBT and AsBs respectively).
3
Fig. 7-21
4
Revolving a view of a part.
Inclined lines appear inclined in one plane, as shown in Fig. 7-23B, and are parallel to the other two principal views, which will appear foreshortened in the other two views. The inclined line shown in the front view will be the true length of line AB. Inclined Lines
Oblique Lines A line that appears inclined in all three views is an oblique line. It is neither parallel nor perpendicular to any of the three planes. The true length of the line is not shown in any of these views (Fig. 7-23C).
PART 1
146
Basic Drawing and Design
r: f
TOPVIEW
A
•
B
B
FOLDING LINES
-1:
A
•
DEPTH
T/
REFERENCE LINES
DEPTH
T RL 1
F
t
F
HEIGHT
l.
A•
~
WIDTH
1---- DEPTH
FRONT VIEW
---1
~
A
•
• WIDTH
SIDE VIEW
DEPTH---I RL 2
IBI POINTS A AND B IDENTIFIED
(AI POINTS A AND B IDENTIFIED ON
BY REFERENCE LINES
UNFOLDED REFERENCE PLANES
Fig. 7-22
S
Points in space.
v L~
BT
mue
lENGTH
rDISTORTED
~~:GTH\
.
~
T
RLJ ------,T=-...LF
RLJ------::F:------
DISTORTED
rS
FS
AF-BF
F S As
loiNTVIEW OF LINE
~Bs
Bs
BF
RL2
(A) A NORMAL LINE
Fig. 7-23
As
AF
lENGTH
F S ~
~
T AT RL,-------,F=-------
REFERENCE LINES
AT
~.·DDIISSTTOORRTED LEN7TH
(B) INCLINED LINE
(C) OBLIQUE LINES
Lines in space.
True Length of an Oblique Line by Auxiliary View Projection Since a normal line and an inclined line have projections parallel to a principal plane, the true length of each can be seen in that projection. Since an oblique line is not parallel to any of the three principal reference planes, an auxiliary reference line RL3 can be placed parallel to any one of the oblique lines, as shown in Fig. 7-24. Transfer distances M and N shown in the regular views to the auxiliary view, locating points A 1 and B 1, respectively. Join points A 1 and B 1 with a line, obtaining the true length of line AB.
Point on a Line The line AFBF in the front view of Fig. 7-25A contains a point C. To place point C on the line in the other two views, it is necessary to project construction lines perpendicular to the reference lines RL 1 and RL 2, as shown in Fig. 7-25B. The construction lines are projected to line ArBr in the top view and to line AsBs in the side view, locating point C on the line in these views. If point C is to be located on the true length of line AB, another reference line, such as R~, is required, and the distances N and M in the front view are then used to locate the true length of line A 1B 1 in the auxiliary view. Position Cis
CHAPTER 7
PROBLEM-TO FIND THE TRUE LENGTH OF LINE A-B
147
Auxiliary Views and Revolutions
SOLUTION 2. REFERENCE LINE RL3 PLACED PARALLEL TO LINE A-8 IN SIDE VIEW
""'Bl
N/ .. ,
j
/TRUE LENGTH
AUXILIARY
BT~~ A. ~~I A
RL 3
RLI.
~
.....
UAT
T
M~.~A
l?AFFS F
I
- " ' -----Bg RL 2
SOLUTION 1. REFERENCE LINE RL2 PLACED PARALLEL TO LINEA-8 IN FRONTVIEW
Fig. 7-24
SOLUTION 3. REFERENCE LINE RL3 PLACED PARALLEL TO LINEA-8 INTHETOPVIEW
Finding the length of an oblique line by auxiliary view projection.
BT~AT
BT~AT RL
I
~~-'-'=cT ~~·~~
F
/AFFS\
BF
I
.
F
·
M
.!
-· M
:)_1
AUXILIARY ..• VIEW/.
.
Bs RL 2
(A) PROBLEM-TO LOCATE POINT C ON LINE A-8 IN OTHER VIEWS
Fig. 7-25
RL~T
Point on a line.
RL 2
(8) SOLUTION
N
PART 1
148
Basic Drawing and Design
then projected perpendicular to line AsBs in the side view to locate Con the true-length-line.
Point-on-Point View of a Line When the front and top views of line AB are given, as in Fig. 7-26A, and the point-on-point view of a line AB is required, the following procedure (Fig. 7-26B) may be used. Step 1 Add reference line RL 2 at any convenient distance, and parallel to line AFBF shown in the front view. This reference line is used to draw the primary auxiliary view. Step 2 To establish the true length of line A1B1 in the primary auxiliary view, project perpendicular lines from the end
\AT-~1°/AF i
Step 3 To draw the secondary auxiliary view, draw reference line RL 3 perpendicular to the true length of line A1B1 shown in the primary auxiliary view. Step 4 The secondary (next adjacent) auxiliary view A 2 B 2 will be a point-on-point view of line AB.
See Assignments 7 and 8 for Unit 7-6 on page 171.
7-7
-
BF
IAI PROBLEM -TO FIND THE POINT- ON - POINT OF A LINE
Br
points of line AFBF. Use distances M and N, taken from the top view, to establish the distances the end points are from reference line RL 2• Join points A1 and B1 with a line. This is the true length of line AB.
.
PLANES IN SPACE
Planes for practical studies are considered to be without thickness and can be extended without limit. A plane may be represented or determined by intersecting lines, two parallel lines, a line and a point, three points, or a triangle. The three basic planes, referred to as the normal plane, inclined plane, and oblique plane, are identified by their relationship to the three principal reference planes. Figure 7-27 illustrates the three basic planes, each plane being triangular in shape. Normal Plane A normal plane is one whose surface, in this case a triangular surface, appears in its true shape in the front view and as a line in the other two views. Inclined Plane An inclined plane results when the shape of the triangular plane appears distorted in two views and as a line in the other view.
An oblique plane is one whose shape appears distorted in all three views.
Oblique Plane
F /
/~' F
Locating a Line in a Plane
~~
The top and front views in Fig. 7-28A show a triangular plane ABC and lines RS and MN, each located in one of the views. To find their locations in the other views, the following procedures may be used.
To Locate Line RS in the Front View (Fig. 7-288)
SECO.LRY AUXILIARY VIEW
c.B:- RL, L
Step 2
Extend a line through points DF and EF.
POINT VIEW OF LINE
IBI SOLUTION Fig. 7-26
Step 1 Line RrSr crosses over lines ArB rand ArCr at points Dr and Er respectively. Project points Dr and Er down to the front view, locating points DF and EF.
Point-on-point view of a line.
Step 3 The length of the line can be found by projecting points Rr and Sr to the front view, locating the end points RF and SF.
CHAPTER 7
Auxiliary Views and Revolutions
EDGE VIEW
_tA
C
149
ALL THREE VIEWS DISTORTED
B
L
EDGE VIEW
'ic--M~IA
~--N-
IAI
NORMAL PLANE
Fig. 7-27
(8) INCLINED PLANE
ICI
OBLIQUE PLANE
Planes in space.
(AI PROBLEM -TO LOCATE A LINE IN THE OTHER VIEW
Fig. 7-28
(8) SOLUTION FOR LINE R-S
Locating a line on a plane.
To Locate Line MN in the Top View (Fig. 7-28C) Step 1 Extend line MFNF to the front view, locating points HF and GF on lines AFBF and AFCF respectively.
Project points HF and GF to the top view, locating points HT and GT. Step 2
Step 3
(C) SOLUTION FOR LINE M-N
Draw a line through points HT and GT.
Step 4 Project points MF and NF to the top view, locating points MT and NT on line HTNT.
Locating a Point on a Plane The top and front views shown in Fig. 7-29A (p. 150) show a triangular plane ABC and points R and S each located in one of the views. To find their location in
the other views, refer to Fig. 7-29B and the following procedures. To locate point R in the front view (Fig. 7-29B): • Draw a line from AT passing through point RT to a point MT on line B TCT. • Project point MT to front view, locating point MF. • Join points AF and MF with a line. • Project point RT to front view, locating point RF. To locate pointS in the top view (Fig. 7-29C): • Draw a line between points BF and SF• locating point NF on line AFCF. • Project point NF to top view, locating point NT. • Draw a line through points BT and NT. • Project point SF to top view, locating point ST.
150
PART 1
Basic Drawing and Design
T - - - - - = - F - - - RLI AF
(AI PROBLEM-TO LOCATE A POINT INTHE OTHER VIEW
Fig. 7-29
ICI TO LOCATE POINT S
(B) TO LOCATE POINT R IN THE FRONTVIEW
INTHETOPVIEW
Locating a point on a plane.
CT
____T~---------------------------~ Rl
c
---;_----+-+---+-------
RL1
VF
(AI PROBLEM-TO LOCATE THE PIERCING
IBI SOLUTION
POINT OF A LINE AND A PLANE
Fig. 7-30
Locating the piercing point of a line and a plane, cutting-plane method.
Locating the Piercing Point of a Line and a Plane-Cutting-Plane Method The top and front views in Fig. 7-30A show a line UV passing somewhere through plane ABC. The piercing point of the line through the plane is found as follows (see Fig. 7-30B). • Locate points Dr and Er in the top view. • Project points Dr and Er to the front view, locating points DF and EF. • Connect points DF and EF with a line.
• The intersection of lines DFEF and UFVF is the piercing point, labeled Op. • Project point OF to top view, locating point Or.
Locating the Piercing Point of a Line and a Plane-Auxiliary View Method The top and front views in Fig. 7 -31A show a line UV passing somewhere through plane ABC. The piercing point of the line through the plane is found as described on page 152.
CHAPTER 7
PROBLEM-TO FINDTHE PIERCING POINT OF A LINE AND A PLANE
Auxiliary Views and Revolutions
STEP I. ESTABLISHING REFERENCE LINE RL 2
AUXILIARY VIEW
PIERCING POINT
STEP 2. ESTABLISHING THE AUXILIARY VIEW AUXILIARY VIEW
STEP 3. LOCATING THE PIERCING POINT ON THE FRONT AND TOP VIEWS
Fig. 7-31
Locating the piercing point of a line and a plane, auxiliary view method.
151
152
PART 1
Basic Drawing and Design
Step 1 Establishing Reference Line RL 2 • Draw line ArDr in the top view parallel to reference line RL1• • Project point Dr to front view, locating point Dp. • Draw reference line R~ perpendicular to a line intersecting points Ap and Dp in the front view.
Step 2
T
ALI--~------------~F~-----
Establishing the Auxiliary View
• Project lines from the front view perpendicular to reference line R~. From distances such as R and S shown in the top view, complete the auxiliary view. • The intersection of the line and plane is the piercing point.
Step 3
(A) PROBLEM-TO DETERMINE VISIBILITY OF LINES
Locating the Piercing Point in the Front and Top Views
• Project a line from the piercing point 0~> to line UpVp in the front view. This locates the piercing point Op in the front view. • Project a line up from Op to line UrVr in the top view. This locates the piercing point Or in the top view.
CT
AT T F
ALl
DF AF
See Assignments 9 and 10 for Unit 7-7 on page 172.
(8) ESTABLISHING LINES WHICH ARE CLOSER TO OBSERVER
7-8
ESTABLISHING VISIBILITY OF LINES IN SPACE
Visibility of Oblique Lines by Testing In the example of the two nonintersecting pipes shown in Fig. 7-32A, it is not apparent which pipe is nearest the viewer at the crossing points in the two views. To establish which of the pipes lies in front of the other, the following procedure is used. To establish the visible pipe at the crossing shown in the top view (Fig. 7-32B): • Label the crossing of lines ArB r and CrDr as CD, Q). • Project the crossing point to the front view, establishing point CD on line ApBp and point Q) on CpDp. • Point CD on lineApBpis closer to reference line RL1, than point Q) on line CpDp, which means that line ArBr is nearer when the top view is being observed and thus is visible. To establish the visible pipe at the crossing shown in the front view (Fig. 7-32C): • Label the crossing of lines AFBF and CpDp as CD, @.
(C) SOLUTION
Fig. 7-32
Visibility of oblique lines by testing.
• Project the crossing point to top view, establishing points Q) on line ArBr and @ on line CrDr. • Point @ is closer to reference line RL1, which means that line CpDp is nearer when the front view is being observed and thus is visible. Figure 7-32C shows the correct crossings of the pipes.
CHAPTER 7
CT
DT
RL1
T
Bf
DT
T
Bf
Af
RL1
F
T
F
AF
Cf
Cf
Cf
DF
Of
Fig. 7-33
DT
BF
AF
(A) PROBLEM: TO DETERMINE VISIBILITY OF LINES
CT AT
RL1
F
153
CT AT
AT
Auxiliary Views and Revolutions
(B) ESTABLISH LINES WHICH ARE CLOSER TO OBSERVER
(C) SOLUTION
Establishing visibility of lines and surfaces by testing.
Visibility of Lines and Surfaces by Testing When points or lines are approximately the same distance away from the viewer, it may be necessary to graphically check the visibility of lines and points, as in Fig. 7-33, which shows a part having four triangular-shaped sides. To check visibility of lines ArCr and BrDr in the top view, refer to Fig. 7-33B. • Label the intersection of lines ArC r and BrDr as CD, ~• Project the point of intersection to front view, establishing point which means that line ArC r is nearer when the top view is being observed and thus is visible. • Point @ on line B pDp is farther away from reference line RLI> which means that line B rD r would not be seen when one is viewing from the top. To check visibility of lines A PCP and BPDP in the front view, refer to Fig. 7-33B. • Label the intersection of lines ApCp and BpDp as®,@. • Project the point of intersection to top view, establishing point Q) on line ArCr and point@ on line BrDr. • Point Q) is closer to reference line RL1, which means that line A F C p is nearer when the front view is being observed and thus is visible. • Point @ in the top view is farther away from reference line RL1, which means that line BpDF would not be seen when one is viewing from the front. Figure 7-33C shows the completed top and front views of the part.
Visibility of Lines and Surfaces by Observation In order to fully understand the shape of an object, it is neces-
sary to know which lines and surfaces are visible in each of the views. Determining their visibility can, in most cases, be done by inspection. With reference to Fig. 7-34A (p. 154), the outline of the part is obviously visible. However, the visibility of lines and surfaces within the outline must be determined. This is accomplished by determining the position of Or in the front view. Since position OF is the closest point to the reference line RL1 in the front view, it must be the point that is closest to the when viewing the top view. Thus it can lines converging to point Or are visible. ref1~rel11ce to determining the visibility of the lines see the top view. Plane OrCrDr is closest to reference RL 1• Therefore, it must be the closest surface when the observer is looking at the front view, and it must be · Since point Br in the top view is farthest ref,~reJnce line RL~> it is the point that is farthest observer is looking at the front view. Since OpCpDp, it cannot be seen. cAi:U111Jlc it may be stated that lines or points hJ...,,,.,.,.,,.r will be visible, and lines and points the viewer but lying within the outline of hidden. 1
154
PART 1
Basic Drawing and Design
RLI----------~T~-----------F
RLI----------T=-------------F
DF (A) PROBLEM-TO DETERMINE VISIBILITY OF LINES
Fig. 7-34
7-9
Visibility of lines and surface by observation.
DISTANCES BETWEEN LINES AND POINTS
Distance from a Point to a Line When the front and side views are given, as in Fig. 7-35A, and the shortest distance between line AB and point P is required, the procedure is as follows: Step 1
Draw the Primary Auxiliary View
• Draw reference line R~ at any convenient distance and parallel to line AsBs shown in the side view. • Transfer distances designated as R, S, and U in the front view to the primary auxiliary view. The resulting line A1B 1 in the auxiliary view is the true length of line AB. Step 2
Draw the Secondary Auxiliary View
• Next draw reference line RL3 at any convenient distance and perpendicular to line A 1B 1• • Transfer distances designated as V and W in the side view to the secondary auxiliary view, establishing points P 2 and A 2 B 2 , the latter being the point view of line AB. • The shortest distance between point P and line AB is shown in the secondary auxiliary view. Figure 7-36 illustrates the application of the point-on-point view of a line to determine the clearance between a hydraulic cylinder and a clip on the wheel housing. The procedure is as follows: Design Application
Step 1
(B) SOLUTION
Draw the Primary Auxiliary View
• Draw reference line R~ at any convenient distance and parallel to line A sB s shown in the side view.
• Transfer distances R, S, and T in the front view to the primary auxiliary view. The resulting line A 1B 1 in the primary auxiliary view is the true length of line AB. Step 2
Draw the Secondary Auxiliary View
• Next draw the reference line~ at any convenient distance and perpendicular to line A1B1 in the auxiliary view. • Transfer distances designated as V and W in the side view to the secondary auxiliary view, establishing points P2 and A 2 B 2, the latter being the point view of line AB. • The minimum clearance between point P and line AB is shown in the secondary auxiliary view.
Shortest Distance between Two Oblique Lines When the front and top views are given, as in Fig. 7-37A on page 156, and the shortest distance between the two lines AB and CD is required, the procedure is as follows: Step 1
Draw the Primary Auxiliary View
• Draw reference line R~ at any convenient distance and parallel to line AFBF shown in the front view. • Transfer distances R, S, U, and V in the top view to the primary auxiliary view to establish lines A 1B 1 and C1D 1 • The resultant line A1B1 is the true length of line AB. Step 2
Draw the Secondary Auxiliary View
• Next draw the reference line at any convenient distance and perpendicular to line A 1B 1 shown in the primary auxiliary view. • Transfer distances L, M, and N from the front view to the secondary auxiliary view, establishing line C2D 2 and the point view of line A2B2 • The shortest distance between these two lines is shown in the secondary auxiliary view.
CHAPTER 7
Auxiliary Views and Revolutions
155
CLIP
F S
'_/
WHEEL HOUSING
!Al PROBLEM - TO DETERMINE THE DISTANCE FROM A POINTTO A LINE
(A) PROBLEM-TO FINDTHE DISTANCE FROM A POINTTO A LINE
PRIMARY AUXILIARY VIEW
STEP I. DRAWTHE PRIMARYAUXILIARYVIEW STEP 1. DRAWTHE PRIMARYAUXILIARYVIEW
PRIMARY AUXILIARY VIEW
RL 1
STEP 2. DRAWTHE SECONDARY AUXILIARY VIEW
Fig. 7-35
Distance from a point to a line.
STEP 2. DRAWTHE SECONDARYAUXILIARYVIEW
Fig. 7-36 to a line.
Design application of distance from a point
156
PART 1
Basic Drawing and Design
(A) PROBLEM-TO FIND THE DISTANCE BETWEEN TWO LINES
SHORTEST DISTANCE
_,. . - A2B2/ s~cos
M
AUXILIARY VIEW
STEP 2. DRAW THE SECONDARY AUXILIARY VIEW
7-9 ASSIGNMENTS See Assignments 13 and 14 for Unit 7-9 on page 174. PRIMARY AUXILIARY VIEW
STEP I. DRAWTHE PRIMARY AUXILIARY VIEW
Fig. 7-37
Shortest distance between oblique lines.
};J;J~~
CHAPTER 7
7-10
EDGE AND TRUE VIEW OF PLANES
The three primary planes of projection are horizontal, vertical (or frontal), and profile. A plane that is not parallel to a primary plane is not shown in its true shape. To show a plane in true view, it must be revolved until it is parallel to a projection plane. Figure 7-38A shows an oblique plane ABC in the top and front views. The object is to find the true view of this plane. When the top and front views are examined carefully, no line is parallel to the reference line in either view. To find the edge and true views of these planes, the following steps are used:
Auxiliary Views and Revolutions
157
Step 1 Establish Point D on the Plane and Draw the Primary Auxiliary View • Draw line CrDr on the top view. This establishes a line parallel to reference line RL 1• • Project point Dr to the front view, locating point DF. The line DFCF is shown in its true length. • Draw reference line RL 2 perpendicular to line DFCF in the front view. • Project lines perpendicular to RL 2 from points AF, BF> CF, and DF to the primary auxiliary view area. • Transfer distances R, S, and U shown in the top view to the primary auxiliary view area, establishing points AI> B~> and C1. • Join these points with lines to establish the primary auxiliary view. The resulting line A 1B 1 is the edge view of the plane. Step 2
Draw the Secondary Auxiliary View
• Draw reference line RL3 at any convenient distance and parallel to line A1B1. • Draw reference line RL2 at any convenient distance and perpendicular to reference line RL3 from points A I> B I> C1, and D 1 to the secondary auxiliary view area. • Transfer distances L, M, and N shown in the front view to the secondary auxiliary view area, establishing points Az, B 2 , C2 , and D 2• • Join points A 2 , Bz, and C2 with lines. The true shape of plane ABC is shown in this view.
PROBLEM- TO FINDTHETRUE VIEW OF A PLANE
t
R
T
F
l RL,
\ L
TRUE SHAPE OF PLANE ABC
STEP I. DRAW THE PRIMARY AUXILIARY VIEW
Fig. 7-38
Finding the true view of a plane.
STEP 2. DRAW THE SECONDARY AUXILIARY VIEW
158
PART 1
Basic Drawing and Design
PROBLEM-TO SHOW THE LENGTH OF PIPE FROM A TO C IN ITS TRUE SHAPE
STEP I. ESTABLISH POINT DON PIPE
G
L
STEP 2. DRAWTHE PRIMARY AUXILIARY VIEW
Fig. 7-39
Design application of true view of a plane
STEP 3. DRAW THE SECONDARY AUXILIARY VIEW
for Fig. 7-38. Design Application Figure 7-39 shows the application of the procedure followed for Fig. 7-38. Points A, B, C, and D correspond in both drawings, but line AC is omitted in Fig. 7-39 since it serves no practical purpose in the design.
Planes in Combination Figure 7-40, demonstrates a solution in which a combination of planes is involved. Note that ArBrCr and AFBFCF form one plane and BrCrDr and BFCFDF form another. Also, line BC is common to both planes. The objective in the problem is to find the true bends at the angles ABC and BCD. The procedure is as follows.
P'IUI .. ILI,.,IIT-w'VTI:IL;-.rov-O- -
Step 1
Draw the Primary Auxiliary View
• Draw reference line RL 2 parallel to line BFCF shown in the front view. • Project lines perpendicular to line BFCF from points Ap, Bp, Cp, and DF shown in the front view to the auxiliary view. • Transfer distances E, F, G, and H shown in the top view to the primary auxiliary view, establishing points A1, B1, C~o and D 1• • Join these points with lines to establish the primary auxiliary view. The true length of line BC is shown in this view.
CHAPTER 7
Auxiliary Views and Revolutions
159
CF
PROBLEM-TO FIND THE TRUE LENGTHS AND ANGLES OF PIPE ABCD
T
RLs _.......--+--TRUE LENGTH
SECONDARY AUXILIARY VIEW 3
STEP 4. DRAW THE SECONDARY AUXILIARY VIEW 3
SECONDARY AUXILIARY VIEW I
STEP 3. DRAW THE SECONDARY AUXILIARY VIEW 2
Fig. 7-40
Use of planes in combination.
RL4
160
PART 1
Basic Drawing and Design
Step 2 Draw the Secondary Auxiliary View 1 • Draw reference line RL3 at any convenient distance and perpendicular to line B1C1 shown in the primary auxiliary view. • Project lines parallel to line B1C1 from points AI> Bl> C1, and D 1 to the secondary auxiliary view 1 area. • Transfer distances J, K, and L, shown in the front view of the secondary auxiliary view 1 area, establishing points A 2 , B 2 , C2 , and D 2 • • Join these points with lines to establish secondary auxiliary view 1. This view shows line BC as a point-onpoint view. The result is the edge view of both planes ABC and BCD shown in this view.
Step 3 Draw the Secondary Auxiliary View 2 • Draw reference line RL4 at any convenient distance and parallel to line A 2B2 shown in the secondary auxiliary view 1. • Project lines perpendicular to line A 2B 2 from points A 2 , Bz, Cz, and D 2 to the secondary view 2 area. • Transfer distances M, N, R, and S shown in the primary auxiliary view to the secondary auxiliary view area, establishing points A 3 , B 3 , C3, and D 3 • • Join these points with lines to establish secondary auxiliary view 2. • Since any view adjacent to a point-on-point view of a line must show the line in its true length, line BC is shown in its true length in this view. Therefore, projecting perpendicularly from the edge view in secondary auxiliary view 1 to the secondary auxiliary view 2 shows not only the true length of lines BC and AB but also the true angle of ABC.
Step 4 Draw the Secondary Auxiliary View 3 • Draw reference line RL5 parallel to line C2D 2 shown in the secondary auxiliary view 1. • Project lines perpendicular to line C2D 2 from points A 2 , B 2 , C2, and D 2 to the secondary view 3 area. • Transfer distances M, N, R, and S shown in the primary auxiliary view to the secondary auxiliary 3 area, establishing points A 3 , B3 , C3, and D3. • Join these points with lines to establish secondary auxiliary view 3. • Since any view adjacent to a point-on-point view of a line must show the line in its true length, line BC will be shown in its true length in secondary auxiliary view 3. Therefore, projecting perpendicularly from the edge views in secondary auxiliary view 1 to the secondary auxiliary view 3 shows not only the true length of line BC but also the true angle BCD.
See Assignments 15 and 16 for Unit 7-10 on pages 174-175.
7-11
ANGLES BETWEEN LINES AND PLANES
The Angle a Line Makes with a Plane The top and front views in Fig. 7-41 show a line UV passing somewhere through plane ABC. The true angle between the line and the plane will be shown in the view that shows the edge view of the plane and the true length of the line. This view is found as follows:
Step 1 Draw a Line Parallel to Reference Plane RL, • Draw line ATDT in the top view parallel to reference line RL1• • Project point DT to the front view, locating point DF.
Step 2 Draw the Primary Auxiliary View • Draw reference line RLz at any convenient distance and perpendicular to a line intersecting points AF and DF in the front view. • Project lines perpendicular to reference line RLz from points AF, BF, CF, UF, and VF, shown in the front view, to the primary auxiliary view area. • Transfer distances G, H, R, S, and T, shown in the top view, to the primary auxiliary view area, establishing points Ul> Vl> At> B1o and C1• • Join points U1 to V1, and points A1 to B1 to C1, to establish the primary auxiliary view 1. • The point of intersection between the line and the edge view of the plane is established. Project this point back to the front view and then up to the top view to establish the point of intersection of these two views.
Step 3 Draw the Secondary Auxiliary View 1 • Draw reference line ~ at any convenient distance and parallel to line C1B1 shown in the primary auxiliary view. • Project lines perpendicular to reference line R~ from points At> B1, C1o Ul> and V1, shown in the primary auxiliary view, to the secondary auxiliary view 1 area. • Transfer distances D, E, L, M, and N from the front view to the secondary auxiliary view 1 area, establishing points A 2 , B2 , C2, U2 , and V2 • • Join points A 2 , Bz, and C2 to form the plane and join points U2 to V2 to form the line. • This view shows the true view of the plane and location of the piercing point.
Step 4 Draw the Secondary Auxiliary View 2 • Draw reference line RL4 at any convenient distance and parallel to line V2 U2 shown in the secondary auxiliary view 2. • Project lines perpendicular from reference line RL4 from points A 2 , B 2 , C2 , V2 , and U2 shown in the secondary auxiliary view 1 to the secondary auxiliary view 2 area. • Transfer distances W, X, and Y shown in the primary auxiliary view to the secondary auxiliary view 2 area,
CHAPTER 7
161
Auxiliary Views and Revolutions
POINT OF INTERSECTION
fT
T
R
vT
RL 1
T
vT
RL 1
F
T
F
VF
-·""'='---
_j_ T
RL 1
CF---J_ -~ {;__ j v
VF
CF
---
CF
AF
1 -
I
0~-- ~~~~
AF
-z
POINT OF
~-
EDGE VIEW OF PLANE
--
J'------R
UF
'1
-1 :~·~~·. ~-=---. ___ ----·------·--
PROBLEM-TO FINDTHEANGLE A LINE MAKES WITH A PLANE
r------~--~-
STEP I. DRAW A LINE PARALLEL TO REFERENCE PLANE RL 1
R~-------H 2
PRIMARY AUXILIARY VIEW
STEP 2. DRAW THE PRIMARY AUXILIARY VIEW
j- x--iv VT
V
T
RLI ~c~-~~---~~=---~~~~~~~~~-
VT
1----------
D
~1'1---
I
M
# _/\
CF
fl
AF
3 TRUE LENGTH OF LINE
X C
,/
I
IL - BF~"~,f
EDGE VIEW OF PLANE
1
------------ L
N ---......./-
~PRIMARY Rlz
AUXILIARYVIEW
STEP 3. DRAW SECONDARY AUXILIARY VIEW I
Fig. 7-41
STEP 4. DRAW SECONDARY AUXILIARY VIEW 2
The angle a line makes with a plane.
establishing line U 3V3 and the edge view of plane ABC. This view shows the true length of line UV and the true angle between the line and edge view of the plane.
Edge lines of Two Planes Figure 7-42 on page 162, shows a line of intersection AB made by two planes, triangles ABC and ABD. When the top and
front views are given, the point-on-point view of line AB and the true angle between the planes are found as follows: Step 1 Draw the Primary Auxiliary View
• Draw reference line RLz at any convenient distance and parallel to line AFBF shown in the front view. • Project lines perpendicular to reference line RLz from points AF, BF, CF, and DF shown in the front view to the primary auxiliary view area.
162
PART 1
j
Basic Drawing and Design
1
-----1------=F-.....CT
T
RLI
I
I
I
'
PRIMARY AUXILIARY VIEW
I
D(\ ,\ '\ '\
\
....
\
\
£------',_,
PROBLEM-TO FIND THE EDGE LINE OFTWO PLANES
RL2
R f Cl
___
'A'A~ ~~
I'
I
·. ·
BT
1
1!
~T
VIEW
U
\
--C2
~·
l
,
2
2
SECONDARYl AUXILIARY L
r
AI
RL3
,
02
POINTVIEW
TRUE ANGLE OF LINE A B BETWEEN PLANES
STEP 2. DRAW THE SECONDARY AUXILIARY VIEW
- - , - - - -.......-~~-.....__.....__ RL 1
Step 2
PRIMARY AUXILIARY VIEW
STEP I. DRAWTHE PRIMARY AUXILIARY VIEW
Fig. 7-42
Draw the Secondary Auxiliary View
• Draw reference line RL3 at any convenient distance and perpendicular to line A 1B1• • Project lines parallel to line A 1B 1, from points A, C, and D shown in the primary auxiliary view, to the secondary auxiliary view area. • Transfer distances L, M, and N, shown in the front view, to the secondary auxiliary view, establishing points A2, B2, C2, and D 2 • • Join these points with lines as shown. • Point A 2B 2 is a point-on-point view of line AB. The true angle between the two planes is seen in this view.
Edge lines of two planes.
• Transfer distances R, S, and U, shown in the top view, to the primary auxiliary view area, establishing points A1, B~o C1, and D 1• • Join these points to establish the primary auxiliary view. The resulting line A 1B 1, is the true length of line AB.
See Assignments 17 through 19 for Unit 7-11 on pages 175-176.
SUMMARY 1. Auxiliary views are used to replace orthographic views
2. 3.
4.
5. 6. 7.
8.
when surfaces are not perpendicular to the plane of projection. Such surfaces are called sloping or inclined surfaces. Auxiliary views show the surface clearly and without distortion. (7 -1) The recommended dimensioning method for engineering drawings is the unidirectional system. (7 -1) Circular features (including cylinders) may appear elliptical in auxiliary projection. A series of points on a line is used to draw the true-shape projection of a curved surface. (7-2) When more than one surface is not perpendicular to the plane of projection, it may be necessary to use a multiauxiliary view to show the true shape. (7-3) Sometimes a secondary auxiliary view is needed to show the true shape of a surface. (7 -4) The drafter uses descriptive geometry to think through problems of space relationships. (7-5) One way to show the true size and shape of an inclined surface is to use an auxiliary view. Another way is to mentally revolve the object. Imagining that an axis has been passed through the object is an aid to this approach. (7-5) The rule of revolution states that a view that is perpendicular to the axis of revolution stays the same except in position, and that distances parallel to the axis of revolution stay the same. (7-5)
9. The true shape of an oblique surface is found by successive revolutions. The true size of an inclined surface or the true length of a line is found by either an auxiliary view or a revolved view. (7-5) 10. Points in space can be located by dots or crosses. Points are usually identified by two or more projections. (7 -6) 11. Lines are grouped into three categories: normal lines, inclined lines, and oblique lines. (7 -6) 12. The three basic planes in space are the normal plane, the inclined plane, and the oblique plane. (7-7) 13. The visibility of lines and surfaces in space can be determined by testing or by observation. (7 -8) 14. Different procedures are needed to find the distance from a point to a line and the shortest distance between two oblique lines. (7-9) 15. The three primary planes of projection are horizontal, vertical (or frontal), and profile. To show a plane in true view, it must be revolved until it is parallel to a projection plane. (7 -10) 16. The true angle between a line and a plane will be shown in the view that shows the edge view of the plane and the true length of the line. (7 -11) 17. The true angle of two planes is found by determining the point-on-point view of the line of intersection made by the two planes. (7-11)
t(EV TERMS Descriptive geometry (7-5) Inclined line (7 -6) Inclined plane (7-7)
Multi-auxiliary view (7-3) Normal line (7-7) Normal plane (7-7)
Oblique line (7-6) Oblique plane (7-7) Revolutions (7-5)
163
164
PART 1
Basic Drawing and Design
ASSIGNMENTS Assignment for Unit 7-1, Primary Auxiliary Views
1. Make a working drawing of one of the parts shown in Figs. 7-43 through 7-47. For Fig. 7-43 draw the front, side, and auxiliary view. For all others draw the top, front, and auxiliary view. Partial views are to be used unless you are otherwise directed by your instructor. Hidden lines may be added for clarity. Scale 1: 1.
2.38
SURFACES 3~UNLESS OTHERWISE SPECIFIED ROUNDS AND FILLETS R.l2 MATL- MALLEABLE IRON
Fig. 7-43
Angle bracket.
MATL- GRAY IRON
Fig. 7-44
Angle plate.
Fig. 7-45
Truncated prisms.
(AI METRIC
(B) INCH
(CI INCH
CHAPTER 7
165
Auxiliary Views and Revolutions
3 HIGH X 25 WIDE BOSS
90 O.llj SURFACES \7 UNLESS OTHERWISE SPECIFIED ROUNDS AND Fl LLETS R 5 MATL- MALLEABLE IRON
Fig. 7-46
Cross-slide bracket.
T 50
HEXAGON- 50 ACRFLT
S?
OCTAGON- 50 ACRFLT
C>::(NTER LINE VERTEX
50
50
Fig. 7-47
Statue bases. .125 IPS, ASME 81.20.1
Assignment for Unit 7-2, Circular Features in Auxiliary Projection
DRAWING SET-UP
2. Make a working drawing of one of the parts shown in Figs. 7-48 through 7-51 (p. 166). Refer to the drawing for setup of views. Draw complete top and front views and a partial auxiliary view. Hidden lines may be added for clarity.
0.531 L.J 0.94
+"
.04
RI.OO
ROUNDS AND FILLETS R .10
Fig. 7-48
Shaft support.
166
PART 1
Basic Drawing and Design
I
I
/
I
I
•
~"
/'\/
BOTH ARMS
t
70
,
DRAWING SET-UP
0
25
1.6/
SURFACES 2VUNLESS OTHERWISE SPECIFIED MATL- Gl
Fig. 7-49
Link.
DRAWING SET-UP
.60 SQUARE HOLE,
0 LIO C BORE X 1.20 DEEP
DOVETAIL BOTH ENDS ROUNDS AND FILLETS R .12 MATL- Gl 32 DOVETAIL FINISH 3 SIDES 63 ALL OTHER FINISHES
V
DRAWING SET-UP
VI 4X 0.406
Fig. 7-50
Control block.
EOL SPABOUT RIBS ON 0 2.40
ROUNDS & FILLETS R .10
Fig. 7-51
Pedestal.
CHAPTER 7
Auxiliary Views and Revolutions
167
Assignments for Unit 7-3, Multi-Auxiliary-View Drawings
3. Make a working drawing of one of the parts shown in Figs. 7-52 through 7-54. Refer to the drawings for setup of views. Draw complete top and front views and partial auxiliary views.
MATL-.12 ALUMINUM
DRAWING SET-UP
3X 0.25 EQL SP ON 0 2.50
R.60
.,.._'•
HEX .80 ACRFLT
,(
(
''yj.
l
',~, ~T-:!:i
'"\._ L__ j 1.00
0.75 SLOT
DRAWING SET-UP
Fig. 7-52
Mounting plate.
el
ALL SIDES
fll20 SLOT
SURFACES MARKED .fTo BE ROUNDS AND FILLETS RS MATL- Gl
Fig. 7-53
Connecting bar.
MATERIAL·GRAY IRON 16 SURFACES MARKED v TO BE .06 ·~ ROUNDS AND FILLETS R.l2
Fig. 7-54
Angle slide.
DRAWING SET-UP
~-----4.00 SQ-~!..---...j
2%'
PART 1
168
Basic Drawing and Design
4. Make a working drawing of one of the parts shown in Figs. 7-55 through 7-57. Draw partial auxiliary views for Fig. 7-55; partial auxiliary and side views for Fig. 7-56; and full top and front views, and partial auxiliary views for Fig. 7-57.
DRAW PARTIAL AUXILIARY VIEW HERE
0 6 X 3 KEYS EAT DRAW BOTTOM VIEW HERE
R25
2X 010.3 L...J020
2X 020
~3
ROUNDS & FILLETS R4
Fig. 7-55
Dovetail bracket.
Fig. 7-56
Offset guide.
SURFACES MARKED
V TO BE .066~
MATL- Ml ROUNDS AND Fl LLETS R .10
Fig. 7-57
Inclined stop.
CHAPTER 7
169
Auxiliary Views and Revolutions
Assignment for Unit 7-4, Secondary Auxiliary Views
5. Make a working drawing of one of the parts shown in Figs. 7-58 through 7-60. The selection and placement of views are shown with the drawing. Only partial auxiliary views need be drawn, and hidden lines may be added to improve clarity. HEX 26 ACRFLT
010.3 L...J 020
10
<
4Eo/
25>-Y ..... LOCATION OF 020 HOLE ON AUXILIARY VIEW
ROUNDS & FILLETS R3
DRAWING SET-UP
Fig. 7-58
DRAWING SET-UP
Hexagon slot support.
Fig. 7-60
2.75\~
I
Q
o
12.00
3rog Lc:•====~
Pivot arm.
HEX .75 ACRFLT PERPENDICULAR TO SURFACE ./6 SIDES
DRAWING SET-UP
SURFACES MARKED \?"To
BE~
ROUNDS AND FILLETS R .12
Fig. 7-59
Dovetail bracket.
MATL- GRAY IRON
170
PART 1
Basic Drawing and Design
Assignment for Unit 7-5, Revolutions
6. Select one of the parts shown in Fig. 7-61 and draw the views as positioned in the example given.
DRAW TOP AND SIDE VIEWS
/\_ /\_ REVOLVE FRONT VIEW
2
3
4
REVOLVE TOP VIEW SIDE VIEW FROM SPACE 2 REVOLVED 30°
-
DRAW FRONT AND SIDE VIEW
DRAW TOP AND FRONT VIEW
DlDTariCD!~~ D-!T'·" 1- --1 f-t '
l-1.5o-j
j--1.20--l
A
B
.1o
t
.10
.10
+.1o
_i_
OJ ITJI
l--1.5o
o~.t2J D II'=l!-1\l~.t j_LJ ~j_ [OI _t _l .70
T
c
D
F
E
:ftJ~~~CJI~I'\IZ1ITJI
01~ ~~
QlLS±ffi±LS± fCTifG J--z.oo--j
J--z.oo--! --j1.oo f 1.00
G
Fig. 7-61
Revolution assignments.
H
J
1--
f--z.oo--j K
L
M
CHAPTER 7
Assignments for Unit 7-6, Locating Points and Lines in Space
7. With the use of a grid and reference lines, locate the points and/or lines in the third view for the drawings shown in Fig. 7-62. Scale to suit.
171
Auxiliary Views and Revolutions
8. With the use of a grid and reference lines, locate the lines in the other views for the drawings shown in Fig. 7-63. Scale to suit.
,::~t:.~t~~~L~,~~~~=""~--~~~~_:,,_F...s:.,.'_-..._c--L-~~!1! LOCATE POINTS IN THE TOP VIEW
·-
-ii
-i>
· - .. &
-- i .
- --1[ -·--·
(2) LOCATE POINTS IN THE SIDE VIEW
'------------ --------..,--,,-----~,
c· [
EFEAliNCE
f
LINE
F
(3) LOCATE INCLINED LINES IN THE OTHER VIEW
-
...
l~~~----.;-= ~--"-'~~~..r:.__,..~ ·-~=-~· .,,._~--=·~'·' "--~~, ~"yO
(3) DRAW SIDE AND AUXILIARY VIEWS
---~----~------------,
--~1~-4 ------+
---------;
Af:~' I.•:,' FS ·-- ·.:
ir'.
--
''-~:.:.-_.:_::~~-..;_)~~-,:_~. -~ ~ ··"~ ---i"""'" -~
'.
(4) LOCATE NORMAL AND INCLINED LINES IN THE OTHER VIEW
Fig. 7-62
Assignment 7.
Fig. 7-63
Assignment 8.
,
-·J
r
-
.-~"'
172
PART 1
Basic Drawing and Design
Assignments for Unit 7-7, Planes in Space
9. Locating a Plane or a Line in Space. With the use of a grid and reference lines, complete the three drawings shown in Fig. 7-64. Scale to suit. 10. Locating a Point in Space and the Piercing Point of a Line and a Plane. With the use of a grid and reference lines, complete the drawings shown in Fig. 7-65. Scale to suit.
Assignments for Unit 7-8, Establishing Visibility of Lines in Space
11. Visibility of Lines and Suifaces by Observation and Testing. With the use of a grid and reference lines, lay out the drawings shown in Fig. 7-66. By observation, sketch the circular pipes (drawings 1 and 2) in a manner similar to that shown in Fig. 7-32 (on page 152), showing the direction in which the pipes are sloping and which pipe is closer to the observer in the two views. By testing in a manner similar to that
(I) DRAW THE SIDE VIEW OF TRIANGLE ABC
(I) LOCATE THE POINTS IN SPACE
(2) DRAW THE FRONT VIEW OF TRIANGLE ABC
1--Hl.
'
i
I
... ! ./
l_
~
.....:..
!- ~--·,_,_::~
.CL
'
...L
;
....,
..
:A
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--
--rt·
--r--.•
.i
1/'
,_
·•-
I
. Ll--
....
IlL +--: ______
i ~- I
•
·'·
r--
L{
'/; i/i
·r-~-+--:· __ ,
,,,J
1/....,ir'
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;r r-:·
i •
-r:~ j 1--. ~ 01 -~:. :j
:
20: _/(
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i
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j .•
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;.,...,......_
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\;·r~f:- i-.;( --;--r·' '-\
\
,_
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(2) LOCATE THE PIERCING POINT OF THE LINE AND PLANE AND COMPLETE LINE UV.
(3) LOCATING A LINE IN THE OTHER VIEW
Fig. 7-64
Assignment 9.
Fig. 7-65
Assignment 10.
CHAPTER 7
Auxiliary Views and Revolutions
the four parts shown in Fig. 7-67. By testing in the manner shown in Fig. 7-33 (on page 153), complete the two-view drawings, showing the visible and hidden lines. Scale to suit.
shown in Fig. 7-33 (on page 153), establish the visibility of lines and surfaces of drawings 3 and 4. Scale to suit.
12. Establishing Visibility of Lines and Surfaces by Testing. With the use of a grid and reference lines, draw
L
,,' ~-~~~~~-·~~~~~,-!~ ~·,. ~ -r'" (A) RADII THAT NEED NOT HAVE THEIR CENTERS LOCATED
R9
15
1__~-------t---'
1---28.2 (B) LOCATING RADIUS CENTER
Fig. 8-18
Dimensioning radii.
~
,.,
l--uo (C) RADII WITH COMMON TANGENT POINTS
(D) FORESHORTENED RADII
(E) RADII LOCATED BY TANGENTS
CHAPTER 8
~''~===b
2X R
2X
r:;=:=;n
R.SO
(A) FULLY ROUNDED ENDS
Fig. 8-20
(B) PARTIALLY ROUNDED ENDS
187
W'~9n
(R.40)
(C) WITH HOLE LOCATIONS THAT ARE MORE CRITICAL
Dimensioning external surfaces with rounded ends.
(AI CHORD
Fig. 8-21
Basic Dimensioning
(BI ARC
(CI ANGLE
Dimensioning chords, arcs, and angles.
Dimensioning Chords, Arcs, and Angles The difference in dimensioning chords, arcs, and angles is shown in Fig. 8-21.
taken to avoid placing the hole size and quantity values together without adequate spacing. It may be better to show the note on two or more lines than to use a single line note that might be misread (Fig. 8-23D).
Spherical Features Spherical surfaces may be dimensioned as diameters or radii, but the dimension should be used with the abbreviations SR or S0 (Fig. 8-22).
Cylindrical Holes Plain, round holes are dimensioned in various ways, depending upon design and manufacturing requirements (Fig. 8-23). However, the leader is the method most commonly used. When a leader is used to specify diameter sizes, as with small holes, the dimension is identified as a diameter by placing the diameter symbol 0 in front of the numerical value. The size, quantity, and depth may be shown on a single line, or on several lines if preferable. For through holes, the abbreviation THRU should follow the dimension if the drawing does not make this clear. The depth dimension of a blind hole is the depth of the full diameter and is normally included as part of the dimensioning note. When more than one hole of a size is required, the number of holes should be specified. However, care must be
(B) ADDING THE WORD "THRU" WHEN IT IS NOT CLEAR THE HOLE GOES THROUGH (A) DIMENSIONING ONE HOLE
~0.75
l___!_j ' '""
TOP VIEW NOT SHOWN
OR
(C) DIMENSIONING A BLIND HOLE 6X 0.50 EOL SP
NOTE: SEE UNIT 8-3 FOR DIMENSIONING REPETITIVE FEATURES
(B)
Fig. 8-22
Dimensioning spherical surfaces.
(D) DIMENSIONING A GROUP OF HOLES
(C)
Fig. 8-23
Dimensioning cylindrical holes.
188
PART 1
Basic Drawing and Design
Minimizing Leaders If too many leaders would impair the legibility of a drawing, letters or symbols as shown in Fig. 8-24 should be used to identify the features.
Slotted Holes Elongated holes and slots are used to compensate for inaccuracies in manufacturing and to provide for adjustment. See Fig. 8-25. The method selected to locate the slot depends on how the slot was made. The method shown in Fig. 8-25B is used when the slot is punched out and the location of the punch is given. Figure 8-25A shows the dimensioning method used when the slot is machined out.
Countersinks, Counterbores, and Spotfaces
Fig. 8-24
Counterbores, spotfaces, and countersinks are specified on drawings by means of dimension symbols or abbreviations, the symbol being preferred. The symbols or abbreviations indicate the form of the surface only and do not restrict the methods used to produce that form. The dimensions for them are usually given as a note, preceded by the size of the through hole (Figs. 8-26 and 8-27). A countersink is an angular-sided recess that accommodates the head of flathead screws, rivets, and similar items. The diameter at the surface and the included angle are given. When the depth of the tapered section of the
Minimizing leaders.
(A)
Fig. 8-25
(B)
(C)
Slotted holes.
~COUNTERBORE
\SPOTFACU::l
0.38/
0.38
0.38
0.38
LJ 0.75
0.75 CBORE .25 DEEP
0.75 CBORE
0.75 SFACE
R .06
COUNTERBORE
SPOTFACE
(A) USING SYMBOLS
Fig. 8-26
Counterbored and spotfaced holes.
COUNTER BORE
COUNTER BORE (B) USING WORDS
SPOTFACE
CHAPTER 8
Basic Dimensioning
(]).40 (]).80 X 1200 CDR ILL .25 DEEP
0.40 (]) .80 X 820 CSK
COUNTERSINK
COUNTERDRILL
~ COUNTERSINK
(A) USING SYMBOLS
Fig. 8-27
189
COUNTERDRILL
(B) USING WORDS
Countersunk and counterdrilled holes.
countersink is critical, it is specified in the note or by a dimension. For counterdrilled holes, the diameter, depth, and included angle of the counterdrill are given. A counterbore is a flat-bottomed, cylindrical recess that permits the head of a fastening device, such as a bolt, to lie recessed into the part. The diameter, depth, and corner radius are specified in a note. In some cases, the thickness of the remaining stock may be dimensioned rather than the depth of the counterbore. A spotface is an area in which the surface is machined just enough to provide smooth, level seating for a bolt head, nut, or washer. The diameter of the faced area and either the depth or the remaining thickness are given. A spotface may be specified by a general note and not delineated on the drawing. If no depth or remaining thickness is specified, it is implied that the spotfacing is the minimum depth necessary to clean up the surface to the specified diameter. The symbols for counterbore or spotface, countersink, and depth are shown in Figs. 8-26 and 8-27. In each case the symbol precedes the dimension. Reference and Source Material 1. ASME Yl4.5M-1994 (R 2004), Dimensioning and Tolerancing. 2. CAN/CSA B78.2-M91 (R 2002), Dimensioning and Tolerancing of Technical Drawings. 3. ASME Y14.38M-1999 (A 2004), Abbreviations and Acronyms.
See Assignments 4 through 6 for Unit 8-2 on pages 220-222.
INTERNET CONNECTION Explain the benefits of being a member of American Society of Mechanical Engineers: http://www.asme.org/
8-3
DIMENSIONING COMMON FEATURES
Repetitive Features and Dimensions Repetitive features and dimensions may be specified on a drawing by the use of an X in conjunction with the numeral to indicate the "number of times" or "places" they are required. A space is shown between the X and the dimension. An X that means "by" is often used between coordinate dimensions specified in note form. Where both are used on a drawing, care must be taken to ensure that each is clear (Fig. 8-28, p. 190).
Chamfers The process of chamfering, that is, cutting away the inside or outside piece, is done to facilitate assembly. Chamfers are normally dimensioned by giving their angle and linear length (Fig. 8-29, p. 190). When the chamfer is 45°, it may be specified as a note. When a very small chamfer is permissible, primarily to break a sharp corner, it may be dimensioned but not drawn, as in Fig. 8-29C. If not otherwise specified, an angle of 45° is understood. Internal chamfers may be dimensioned in the same manner, but it is often desirable to give the diameter over the chamfer. The angle may also be given as the included angle if this is a design requirement. This type of dimensioning is generally necessary for larger diameters, especially those over 2 in. (50 mm), whereas chamfers on small holes are usually expressed as countersinks. Chamfers are never measured along the angular surface.
190
PART 1
Basic Drawing and Design
17X Ql.258
,
•
ax
Ql.2BI EQL SP ON Ql2.34
(A) USING "NUMBER OF TIMES" SYMBOL .16
0.281 8 HOLES EQL SP ON Ql2.34
(B) USING DESCRIPTIVE NOTES
Fig. 8-28
0.25 8 HOLES EQL SP ON (1)1.60
Dimensioning repetitive detail.
.10 X .10
MAX .015 CHAMFER7
OR
a
b
I
(C) SMALL CHAMFERS
sol\~
(A) FOR 45° CHAMFERS ONLY
(/L_j ·~.10~
(Fig. 8-30). Figure 8-30D is the preferred method of dimensioning slopes on architectural and structural drawings. The following dimensions and symbol may be used, in different combinations, to define the slope of a line or flat surface: • The slope specified as a ratio combined with the slope symbol (Fig. 8-30A). • The slope specified by an angle (Fig. 8-30B). • The dimensions showing the difference in the heights of two points from the base line and the distance between them (Fig. 8-30C).
Taper
(B) FOR ALL CHAMFERS
Fig. 8-29
(D) CHAMFERS BETWEEN SURFACES AT OTHER THAN goo
Dimensioning chamfers.
Slopes and Tapers Slope A slope is the slant of a line representing an inclined surface. It is expressed as a ratio of the difference in the heights at
right angles to the base line, at a specified distat?-ce apart
A taper is the ratio of the difference in the diameters of two sections (perpendicular to the axis of a cone to the distance between these two sections), as shown in Fig. 8-31. When the taper symbol is used, the vertical leg is always shown to the left and precedes the ratio figures. The following dimensions may be used, in suitable combinations, to define the size and form of tapered features: • • • • • • •
The diameter (or width) at one end of the tapered feature The length of the tapered feature The rate of taper The included angle The taper ratio The diameter at a selected cross section The dimension locating the cross section
CHAPTER 8
riOO
1
[[:]
30
1_'----~ ~50~
(8)~50~
(AI
rD. L '0
Basic Dimensioning
or millimeter and may be the straight pitch, circular pitch, or diametral pitch. For cylindrical surfaces, the diametral pitch is preferred. The knurling symbol is optional and is used only to improve clarity on working drawings.
Formed Parts In dimensioning formed parts, the inside radius is usually specified, rather than the outside radius, but all forming dimensions should be shown on the same side if possible. Dimensions apply to the side on which the dimensions are shown unless otherwise specified (Fig. 8-33).
30
_j__
(C)
~50~
L
(D)
~50~
PREFERRED METHOD FOR ARCHITECTURAL AND STRUCTURAL DRAWINGS
Fig. 8-30
(A)
96 DP RAISED DIAMOND KNURL
:1.251 t
~Joe...~=·===-----' -1---.__._:rs
--1
Dimensioning slopes.
(B)
.50
~FULL
OR
KNURL
(A) DIAMOND KNURL
~0.3:1
Fig. 8-31
Dimensioning tapers. (B) STRAIGHT KNURL
Fig. 8-32
Dimensioning knurls.
Knurls Knurling is specified in terms of type, pitch, and diameter before and after knurling (Fig. 8-32). The letter P precedes the pitch number. When control is not required, the diameter after knurling is omitted. When only portions of a feature require knurling, axial dimensions must be provided. When required to provide a press fit between parts, knurling is specified by a note on the drawing that includes the type of knurl required, the pitch, the toleranced diameter of the feature prior to knurling, and the minimum acceptable diameter after knurling. Commonly used types are straight, diagonal, spiral, convex, raised diamond, depressed diamond, and radial. The pitch is usually expressed in terms of teeth per inch
191
11.25---t-o-.62 R .10
Fig. 8-33
Dimensioning theoretical points of intersection.
192
PART 1
Basic Drawing and Design
Undercuts
Wire, Sheet Metal, and Drill Rod
The operation of undercutting or necking, that is, cutting a recess in a diameter, is done to permit two parts to come together, as illustrated in Fig. 8-34A. It is indicated on the drawing by a note listing the width first and then the diameter. If the radius is shown at the bottom of the undercut, it will be assumed that the radius is equal to one-half the width unless otherwise specified, and the diameter will apply to the center of the undercut. When the size of the undercut is unimportant, the dimension may be left off the drawing.
Wire, sheet metal, and drill rod, which are manufactured to gage or code sizes, should be shown by their decimal dimensions; but gage numbers, drill letters, and so on, may be shown in parentheses following those dimensions.
Sheet -.141 (NO. 10 USS GA) -.081 (NO. 12 B & S GA)
Limited Lengths and Areas Sometimes it is necessary to dimension a limited length or area of a surface to indicate a special condition. In such instances, the area or length is indicated by a chain line (Fig. 8-35A). When a length of surface is indicated, the chain line is drawn parallel and adjacent to the surface. When an area of surface is indicated, the area is crosshatched within the chain line boundary (Fig. 8-35B).
References and Source Material 1. ASME Y14.5M-1994 (R 2004), Dimensioning and Tolerancing. 2. CAN/CSA B78.2-M91 (R 2002), Dimensioning and Tolerancing of Technical Drawings.
See Assignments 7 through 12 for Unit 8-3 on pages 223-224.
INTERNET CONNECTION Describe the Web links available through the Canadian Standards Association:
http://www.csa.ca/
CHAMFER ADDED TO HOLE TO ACCEPT SHOULDER OF PART
PART CANNOT FIT FLUSH IN HOLE BECAUSE OF SHOULDEf'l
SAME PART WITH UNDERCUT ADDED PERMITS PART TO FIT FLUSH
(A) CHAMFER AND UNDERCUT APPLICATION
(8) PLAIN UNDERCUT
Fig. 8-34
(C) UNDERCUT WITH RADIUS
Dimensioning undercuts.
--+---+B++--r-___~--·r
8-4
DIMENSIONING METHODS
The choice of the most suitable dimensions and dimensioning methods will depend, to some extent, on how the part will be produced and whether the drawings are intended for unit or mass production. Unit production refers to cases when each part is to be made separately, using generalpurpose tools and machines. Mass production refers to parts produced in quantity, where special tools and gages are usually provided. Either linear or angular dimensions may locate features with respect to one another (point-to-point) or from a datum.
2.50
(A) LENGTH OF SURFACE
2.00
.75b_
~----~~------~-------+--,
.90 1.00
1.50
1_~-+------------~
~1.50
Fig. 8-35
(B) LIMITED AREA
Dimensioning limited lengths and areas.
Fig. 8-36
Rectangular coordinate dimensioning.
CHAPTER 8
Point-to-point dimensions may be adequate for describing simple parts. Dimensions from a datum may be necessary if a part with more than one critical dimension must mate with another part. The following systems of dimensioning are used more commonly for engineering drawings.
193
Basic Dimensioning
It may be advantageous to have a part dimensioned symmetrically about its center, as shown in Fig. 8-41 (p. 194). When the center lines are designated as the base (zero) lines, positive and negative values will occur. These values are shown with the dimensions locating the holes.
Polar Coordinate Dimensioning Rectangular Coordinate Dimensioning This is a method for indicating distance, location, and size by means of linear dimensions measured parallel or perpendicular to reference axes or datum planes that are perpendicular to one another. Coordinate dimensioning with dimension lines must clearly identify the datum features from which the dimensions originate (Fig. 8-36).
Polar coordinate dimensioning is commonly used in circular planes or circular configurations of features. This method indicates the position of a point, line, or surface by means of a linear dimension and an angle, other than 90°, that is implied by the vertical and horizontal center lines (Fig. 8-42A, p. 194).
Chordal Dimensioning
Rectangular Coordinates for Arbitrary Points Coordinates for arbitrary points of reference without a grid appear adjacent to each point (Fig. 8-37) or in tabular form (Fig. 8-38). CAD systems will automatically display any point coordinate when it is picked.
The chordal dimensioning system may also be used for the spacing of points on the circumference of a circle relative to a datum, when manufacturing methods indicate that this will be convenient (Fig. 8-42B).
Rectangular Coordinate Dimensioning without Dimension Lines Dimensions may be shown on extension lines
True-Position Dimensioning
without the use of dimension lines or arrowheads. The base lines may be zero coordinates, or they may be labeled as X, Y, and Z (Fig. 8-39).
True-position dimensioning has many advantages over the coordinate dimensioning system (Fig. 8-43, p. 195). Because of its scope, it is covered as a complete topic in Chap. 16.
Tabular dimensioning is a type of coordinate dimensioning in which dimensions from mutually perpendicular planes are listed in a table on the drawing rather than on the pictorial delineation. This method is used on drawings that require the location of a large number of similarly shaped features when parts for numerical control are dimensioned (Fig. 8-40, p. 194).
Tabular Dimensioning
Chain Dimensioning When a series of dimensions is applied on a point-to-point basis, it is called chain dimensioning (Fig. 8-44, p. 195). A possible disadvantage of this system is that it may result in an undesirable accumulation of tolerances between individual features. See Unit 8-5.
X= 70 y =80
A
.246
B
.189
c
.154
D
.125
1.20
1.90
X= 80 Y=40 .30
.70
X= 10 y =20
Fig. 8-37
3.00 3.60 3.20
Coordinates for arbitrary points.
10
Fig. 8-38
2.40
20
2
80
40
3
70
80
4
20
60
Coordinates for arbitrary points in tabular form.
0
2BASELINES
Fig. 8-39 Rectangular coordinate dimensioning without dimension lines (arrowless dimensioning).
I
194
PART 1 Basic Drawing and Design
r
42~1
~'4' ~3
50
ll
4-4 -~.
~~ 6. DRIVEN KEY
B. SLIP FIT WITH KEY
10. SETSCREW
3. KNURLED JOINT
a (J ~~
I
Fig. 11-1
we
2. PRESS FIT
II. PINS
cd~
£6Qr:o.~
12. SPLIT HUB
ac:n. ~
Miscellaneous types of fasteners.
approximately one-quarter the diameter of the shaft, and its diameter should approximate the diameter of the shaft. Half the width of the key extends above the shaft and into the hub. (Refer to the Appendix for exact sizes.) Woodruff keys are identified by a number that gives the nominal dimensions of the key. The numbering system, which originated many years ago, is identified with the fractional-inch system of measurement. The last two digits of the number give the normal diameter in eighths of an inch, and the digits preceding the last two give the nominal width in thirty-seconds of an inch. For example, a No. 1210 Woodruff key describes a key 1Y32 X IJlls in., or a :Ys X 1Y4 in. key. However, in most industries fractions are now converted to decimal-inch sizes as shown in Fig. 11-2. When keys are to be specified, only the information shown in the callout in Fig. 11-2 need be given.
Dimensioning of Keyseats Keyseats and keyways are dimensioned by width, depth, location, and, if required, length. The depth of the keyway is dimensioned from the opposite side of the shaft or hole (Fig. 11-3). The depth of tapered keyways in hubs, which is shown on the drawing, is the nominal depth H/2 minus an allowance. This is always the depth at the large end of the tapered keyway and is indicated on the drawing by the abbreviation LE. The radii of fillets, when required, must be dimensioned on the drawing. Since standard milling cutters for Woodruff keys have the same number as the key, it is possible to call for a Woodruff keyway by the number only. When detailing Woodruff keyways on a drawing, all dimensions are given in the form of a note in the following order: width, depth, and radius of
Tapered Keyways
cutter. Alternatively, Woodruff keyways may be dimensioned in the same manner as for square and flat keys, with the width and then the depth specified (Fig. 11-4).
Splines and Serrations A splined shaft is a shaft having multiple grooves, or keyseats, cut around its circumference for a portion of its length, in order that a sliding engagement may be made with corresponding internal grooves of a mating part. Splines are capable of carrying heavier loads than keys, permit lateral movement of a part, parallel to the axis of the shaft, while maintaining positive rotation, and allow the attached part to be indexed or changed to another angular position. Splines have either straight-sided teeth or curved-sided teeth. The latter type is known as an involute spline. Involute Splines These splines are similar in shape to involute gear teeth but have pressure angles of 30°, 37.5°, or 45°. There are two types of fits, the side fit and the majordiameter fit (Fig. 11-5). Straight-Side Splines The most popular are the SAE straightside splines, as shown in Fig. 11-6. They have been used in many applications in the automotive and machine industries. Serrations Serrations are shallow, involute splines with 45° pressure angles. They are primarily used for holding parts, such as plastic knobs, on steel shafts.
Drawing Data It is essential that a uniform system of drawing and specifying splines and serrations be used on drawings. The conventional method of showing and calling out splines on a drawing is shown in Fig. 11-7, p. 308. Distance L does not include the cutter runout. The drawing callout shows the symbol
CHAPTER 11
Miscellaneous Types of Fasteners
D
307
R
.25 X .313 X .50 WOODRUFF KEYSEAT
SQUARE
.25 SQUARE KEY, 1.25 LG OR . 25 SQUARE TAPERED KEY, 1.25 LG
Fig. 11-4
Alternate method of detailing a Woodruff keyseat .
FLAT
.188 X .125 FLAT KEY, 1.00 LG OR .188 X .125 FLAT TAPERED KEY, 1.00 LG GIB-HEAD
(A) SIDE FIT .375 SQUARE GIB-HEAD KEY, 2.00 LG
NO. 15 PRATT AND WHITNEY KEY
(B) MAJOR DIAMETER FIT
Fig. 11-5
Involute splines.
NO. 1210 WOODRUFF KEY
Fig. 11-2
Common keys. H
l
r-.253 .250
I
01.250 1.247 KEYSEAT
Fig. 11-3
Dimensioning keyseats.
10-SPLINE
6-SPLINE
4-SPLINE
4
0.241 D
o.075
o· 0.85 D
0.125 D
0.75 D
6
0.250 D 0.050 D
0.90 D
0.075 D
0.85 D
0.100 D
0.80 D
10
0.156 D
0.045 D
0.91 D
0.070 D
0.86 D
0.095 D
0.81 D
16
0.098 D 0.045 D
0.91 D
0.070 D
0.86 D
0.095 D
0.81 D
Fig. 11-6
Sizes of SAE parallel-side splines.
308
PART 2
Fasteners, Materials, and Forming Processes
DIA
! (AI EXTERNAL SPLINE
(A) EXTERNAL SPLINE
ROOT DIA (THIN LINE)
(B) INTERNAL SPLINE
(B) INTERNAL SPLINE
(C) ASSEMBLY DRAWING
(C) ASSEMBLY DRAWING
INVOLUTE SPLINES
STRAIGHT-SIDED SPLINES
Fig. 11-7 Callout and representation of splines. indicating the type of spline followed by the type of fit, the pitch diameter, number of teeth and pitch for involute splines, and number of teeth and outside diameter fort straight-sided teeth.
References and Source Material 1. ASME Bl8.25.1M-1996 (R 2003), Square and Rectangular Keys and Keyways. 2. ASME Bl8.25.2M-1996 (R 2003), Woodruff Keys and Keyways. 3. ASME Bl?.l-1967 (R 2003), Keys and Keyseats. 4. ASME Bl7.2-1967 (R 2003), Woodruff Keys and Keyseats.
See Assignments 1 and 2 for Unit 11-1 on pages 329-331. INTERNET CONNECTION Visit this site and report on keys, splines, and serrations: http://www.machinedesign.com/
11-2
PIN FASTENERS
Pin fasteners are an inexpensive and effective method of assembly when loading is primarily in shear. They can be separated into two groups: semipermanent and quick-release.
CHAPTER 11
Standardized in nominal diam· eters ranging from .12 to .88 (3 to 22mm). I. Holding laminated sections together with surfaces either drawn up tight or separated in some fixed relationship. 2. Fastening machine parts where accuracy of alignment is a primary consideration. 3. Locking components on shafts, in the form of transverse pin key.
Standard pins have a taper of 1:48 measured on the diameter. Basic dimension is the diameter of the large end. Used for lightduty service in the attachment of wheels, levers, and similar components to shafts. Torque capacity is determined on the basis of double shear, using the average diameter along the tapered section in the shaft for area calculations.
Miscellaneous Types of Fasteners
Standard nominal diameters for clevis pins range from .19 to 1.00 (5 to 25mm). Basic function of the clevis pin is to connect mating yoke, or fork, and eye members in knuckle-joint assemblies. Held in place by a small cotter pin or other fastening means, it provides a mobile joint construction, which can be readily disconnected for adjustment or maintenance.
309
Sizes have been standardized in nominal diameters ranging from .03 to .75 (I to 20mm). Locking device for other fasteners. Used with a castle or slotted nut on bolts, screws, or studs, it provides a convenient, low-cost locknut assembly. Hold standard clevis pins in place. Can be used with or without a plain washer as an artificial shoulder to lock parts in position on shafts.
Fig. 11-8 Machine pins.
Semipermanent Pins Semipermanent pin fasteners require application of pressure or the aid of tools for installation or removal. The two basic types are machine pins and radial locking pins. The following general design rules apply to all types of semipermanent pins: • Avoid conditions in which the direction of vibration parallels the axis of the pin. • Keep the shear plane of the pin a minimum distance of one diameter from the end of the pin. • In applications in which engaged length is at a minimum and appearance is not critical, allow pins to protrude the
TABLE 11-1
Recommended cotter pin sizes.
.250 (6)
.062
(1.5)
.078
(1.9)
.11 (3)
.312 (8)
.078
(2)
.094 (2.4)
.11 (3)
.375 (10)
.094
(2.5)
.109 (2.8)
.14 (4)
.500 (12)
.125
(3)
.141
(3.4)
.17 (6)
.625 (14)
.156
(3)
.172 (3.4)
.23 (5)
.750 (20)
.156
(4)
.172 (4.5)
.27 (7)
1.000 (24)
.188
(5)
.203
(5.6)
.31 (8)
1.125 (27)
.188
(5)
.203 (5.6)
.39 (8)
1.250 (30)
.219
(6)
.234 (6.3)
.41 (10)
1.375 (36)
.219
(6)
.234 (6.3)
.44 (ll)
1.500 (42)
.250
(6)
.266 (6.3)
.48 (12)
1.750 (48)
.312 (8)
.328 (8.5)
.55 (14)
*Distance from extreme point of bolt or screw to center of cotter pin hole. Note: Inch (mm)
length of the chamfer at each end for maximum locking effect.
Machine Pins Four types are generally considered to be most commonly used: hardened and ground dowel pins and commercial straight pins, taper pins, clevis pins, and standard cotter pins. Descriptive data and recommended assembly practices for these four traditional types of machine pins are presented in Fig. 11-8. For proper size selection of cotter pins, refer to Table 11-1.
Radial Locking Pins Two basic pin forms are employed: solid with grooved surfaces and hollow spring pins, which may be either slotted or spiral-wrapped as shown in Fig. 11-9 on page 310. Grooved Straight Pins Locking action of the grooved pin is provided by parallel, longitudinal grooves uniformly spaced around the pin surface. Rolled or pressed into solid pin stock, the grooves expand the effective pin diameter. When the pin is driven into a drilled hole corresponding in size to nominal pin diameter, elastic deformation of the raised groove edges produces a secure force-fit with the hole wall. On page 310, Figure 11-9 shows six types of the grooved-pins that have been standardized. For typical grooved pin applications and size selection, refer to Table 11-2 and Fig. 11-10 (p. 310). Hollow Spring Pins Resilience of hollow cylinder walls under radial compression forces is the principle under which spiral-wrapped and slotted tubular pins function (Fig. 11-9). Both pin forms are made to controlled diameters greater than the holes into which they are pressed. Compressed when driven into the hole, the pins exert spring pressure against the hole wall along their entire engaged length to produce a locking action. For added strong standard slotted tubular pins are designed so that several sizes can be used inside one another. In such combinations, shear strength of the individual pins is cumulative. For spring pin applications, refer to Fig. 11-11 (p. 311 ).
310
PART 2
Fasteners, Materials, and Forming Processes
TABLE 11-2
TYPE A
TYPE A3
Full-length grooves. Used for general purpose fastening.
TYPE B
Full-length grooves with pilot section at one end to facilitate assembly. Expanded dimension of this pin is held to a maximum over the full grooved length to provide uniform locking action. It is recommended for applications subject to severe vibration or shock loads where maximum locking effect is required.
Grooves extend half length of the pin. Used as a hinge or linkage "bolt" but also can be employed for other functions in through-drilled holes where a locking fit over only part of the pin length is required.
D
9 TYPED
Reverse tapered grooves extend half the pin length. It is the counterpart of the Type B pin for assembly in blind holes. TYPE E Half-length groove section centered along the pin surface. Used as a cotter pin or in similar functions where an artificial shoulder or a locking fit over the center portion of the pin is required.
.500
(14)
.156
(5)
0
.562
(16)
.188
(5)
2
.625
(18)
.188
(6)
2
.750 (20)
.250
(6)
4
.875
(22)
.250
(6)
1.000
(24)
.312
(8)
1.062
(26)
.312
(8)
(28)
.375
(lO)
(30)
.375
(10)
(32)
:315
(10)
(34)
.438
{36)
.438
(38)
.500
TYPE U Full-length grooves with pilot section at both ends for hopper feeding. Same as Type C.
liT SPIRAL-WRAPPED
Fig. 11-9
Recommended groove pin sizes.
. ;e
1.500
(12)
.125
(4)
.156
(5)
4
.219
(6)
6
.25Q
8
.438
SLOTTED TUBULAR
Grooved radial locking pins.
LOCKING COLLAR TO SHAFT
KEYING GEAR TO SHAFT ROLLER PINS
LOCKING GEAR TO SHAFT
LEVER AND SHAFT ASSEMBLY
HINGE PINS
TYPE A
TVPEB
TYPEA3
T HANDLE FOR VALVE
ATTACHING KNOB TO SHAFT
TYPED
PINNING V PULLEY TO SHAFT
TYPE E
Fig. 11-10
Groove pin applications.
TYPEU
(11)
CHAPTER 11
Miscellaneous Types of Fasteners
311
Quick-Release Pins
Positive-Locking Pins
Commercially available quick-release pins vary widely in head styles, types of locking and release mechanisms, and range of pin lengths (Fig. 11-12). Quick-release pins can be divided into two basic types: push-pull and positive-locking pins. The positive-locking pins can be further divided into three categories: heavy-duty cotter pins, single-acting pins, and double-acting pins.
For some quick-release fasteners, the locking action is independent of insertion and removal forces. As in the case of push-pull pins, these pins are primarily suited for shear-load applications. However, some degree of tension loading usually can be tolerated without affecting the pin function.
Push-Pull Pins These pins are made with either a solid or a hollow shank, containing a detent assembly in the form of a locking lug, button, or ball, backed up by some type of resilient core, plug, or spring. The detent member projects from the surface of the pin body until sufficient force is applied in assembly or removal to cause it to retract against the spring action of the resilient core and release the pin for movement.
USED AS A SPACER
1. Machine Design, Fastening and joining reference issue. 2. ASME Bl8.8.1-1994 (R 2000), Clevis Pins and Cotter Pins. 3. ASME Bl8.8.2-1995 (R 2000), Taper Pins, Dowel Pins, Straight Pins, Grooved Pins and Spring Pins (Inch Series). 4. ASME Bl8.8.100M-2000, Spring Pins: Coiled and Slotted, Machine Dowel Pins: Hardened Ground, and Grooved Pins (Metric Series).
, ·''~'"'c ~~
11-2 ASSIGNMENTS
See Assignments 3 through 5 for Unit 11-2 on pages 331-332.
KEYING PULLEY TO SHAFT
HINGE IN LIGHT-GAGE METAL
Fig. 11-11
References and Source Material
INTERNET CONNECTION Describe what you find about pin fasteners at this site: http://www.machinedesign.com/
COTTER PIN
TO PREVENT SHAFT ROTATION
DOWEL APPLICATION
T HANDLE
STOP PIN
Spring pin applications.
c=:;J (A) COMMON TYPES
CLEVIS-SHACKLE PIN
DRAW-BAR HITCH PIN RIGID COUPLING PIN
TUBING LOCKPIN
(B) APPLICATIONS
Fig. 11-12
Quick-release pins.
ADJUSTMENT PIN
SWIVEL HINGE PIN
312
PART 2
11-3
Fasteners, Materials, and Forming Processes
RETAINING RINGS
devices can be placed into three categories, which describe the type and method of fabrication: stamped retaining rings, wire-formed rings, and spiral-wound retaining rings.
Retaining rings, or snap rings, are used to provide a removable shoulder to accurately locate, retain, or lock components on shafts and in bores of housings (see Fig. 11-13 and Appendix Tables 35 and 36). They are easily installed and removed, and since they are usually made of spring steel, retaining rings have a high shear strength and impact capacity. In addition to fastening and positioning, a number of rings are designed for taking up end play caused by accumulated tolerances or wear in the parts being retained. In general, these
Stamped Retaining Rings Stamped retaining rings, in contrast to wire-formed rings with their uniform cross-sectional area, have a tapered radial width that decreases symmetrically from the center section to the free ends. The tapered construction permits the rings to remain circular when they are expanded for assembly over a shaft or contracted for insertion into a bored hole or
EXTERNAL
INTERNAL
(A) AXIAL AND RADIAL ASSEMBLY
EXTERNAL
(B) AXIAL ASSEMBLY
EXTERNAL
INTERNAL BOWED
EXTERNAL
(C) END-PLAY TAKE-UP
Fig. 11-13
EXTERNAL GRIP RING
(D) SELF-LOCKING
Retaining ring applications. AX,~t ~SSEMBL V
0
0
INTERNAL
EXTERNAL
0
INTERNAL
BASIC TYPES
RJI\IGS
0
EXTERNAL
0
INTERNAL
0
EXTERNAL
0
INTERNAL
SElF-lOCK~NG
0
0
CIRCULAR EXTERNAL RINGS
n
EXTERNAL CRESCENT RING
Stamped retaining rings.
0
EXTERNAL
RINGS
c
c
EXTERNAL
c
EXTERNAL
RINGS
0
CIRCULAR INTERNAL
0
EXTERNAL
LOCKING-PRONG RADIAL RINGS
BEVELED RINGS
BOWED RINGS
0
EXTERNAL
HEAVY-DUTY RINGS
INVERTED RINGS
END !'lAY RINGS
Fig. 11-14
INTERNAL
BEVELED
0 GRIP EXTERNAL RINGS
c
6
6
TRIANGULAR RETAINER
RAD!Al ASSEMBLY RINGS
EXTERNAL
EXTERNAL
E·RING
REINFORCED E-RING
0
EXTERNAL INTERLOCKING RING
CHAPTER 11
housing. This constant circularity ensures maximum contact surface with the bottom of the groove. Stamped retaining rings can be classified into three groups: axially assembled rings, radially assembled rings, and self-locking rings which do not require grooves. Axially assembled rings slip over the ends of shafts or down into bores; radially assembled rings have side openings that permit the rings to be snapped directly into grooves on a shaft. Commonly used types of stamped retaining rings are illustrated and compared in Fig. 11-14.
Wire-Formed Retaining Rings The wire-formed retaining ring is a split ring formed and cut from spring wire of uniform cross-sectional size and shape. The wire is cold-drawn or rolled into shape from a continuous coil or bar. Then the gap ends are cut into various configurations for ease of application and removal. Rings are available in many cross-sectional shapes, but the most commonly used are the rectangular and circular cross sections.
Spiral-Wound Retaining Rings Spiral-wound retaining rings consist of two or more turns of rectangular material, wound on edge to provide a continuous crimped or uncrimped coil.
11-4
Miscellaneous Types of Fasteners
SPRINGS
Springs may be classified into three general groups according to their application. Controlled action springs have a well-defined function, or a constant range of action for each cycle of operation. Examples are valve, die, and switch springs. Controlled Action Springs
Variable-Action Springs Variable-action springs have a changing range of action because of the variable conditions imposed upon them. Examples are suspension, clutch, and cushion springs. Static Springs Static springs exert a comparatively constant pressure or tension between parts. Examples are packing or bearing pressure, antirattle, and seal springs.
Types of Springs The type or name of a spring is determined by characteristics such as function, shape of material, application, or design. Figure 11-15 illustrates common springs in use. Figure 11-16 provides spring nomenclature.
Compression Springs A compression spring is an open-coiled helical spring that offers resistance to a compressive force (see Fig. ll-15A).
References and Source Material 1. Machine Design, Fastening and joining reference issue. 2. ASME B27.7-1977 (R 1999), General-Purpose Tapered and Reduced Cross-Section Retaining Rings. 3. ASME B 18.27-1999, Tapered and Reduced Cross-Section Retaining Rings (Inch Series).
See Assignments 6 through 8 for Unit 11-3 on pages 333-334.
INTERNET CONNECTION
Discuss the data on retaining rings that you find on this site:
~ ~SIZE OF MATERIAL
http://www.machinedesign.com/ Fig. 11-16
Spring nomenclature .
. . DIRECTION OF FORCE (TYP) COIL BAR
VOLUTE
(B) TORSION SPRINGS
(A) COMPRESSION SPRINGS
COIL SPRING
t
~
FLAT COIL (C) POWER SPRING
Fig. 11-15
COIL (D) EXTENSION SPRING
Types of springs.
313
..· .
LEAF (E) FLAT SPRINGS
BELLEVILLE
314
PART 2
Fasteners, Materials, and Forming Processes
$-BPLAIN ENDS
$·~ MACHINE HALF-LOOP OPEN
G-flfllPLAIN ENDS GROUND
G-MSQUARED AND GROUND ENDS
$-B SQUARED OR CLOSED ENDS NOT GROUND (A) END STYLES FOR COMPRESSION SPRINGS
Fig. 11-17
$8-
RECTANGULAR HOOK
$~ V-HOOK
·~
SHORT TWISTED LOOP
~
-$·~--· THREADED PLUG TO FIT PLAIN-END SPRING
RAISED HOOK
FULL TWISTED LOOP
{D}-1 SHORT HOOK END
-~-~
~
REDUCED SIDE LOOP
DOUBLE-TWISTED LOOP
)
!-
.
.
SPECIAL ENDS
•• d-W HINGE ENDS
MACHINE CUTOFF
~·~
+.:
\
-$---~
-t--~
STRAIGHT TORSI ON
(B) END STYLES FOR EXTENSION SPRINGS
DOUBLE TORSION
-$+ STRAIGHT OFFSET
(C) END STYLES FOR TORSION SPRINGS
End styles for helical springs.
Figure 11-17A shows the ends commonly used on compression springs. Plain open ends are produced by straight cutoff with no reduction of helix angle (Fig. 11-18). The spring should be guided on a rod or in a hole to operate satisfactorily. Ground open ends are produced by parallel grinding of open-end coil springs. Advantages of this type of end are improved stability and a larger number of total coils. Plain closed ends are produced with a straight cutoff and with reduction of helix angle to obtain closed-end coils, resulting in a more stable spring. Ground closed ends are produced by parallel grinding of closed-end coil springs, resulting in maximum stability. Compression Spring Ends
Extension Springs
Extension Spring Ends The end of an extension spring is usually the most highly stressed part. Thus, proper consideration
Torsion Springs Springs exerting pressure along a path that is a circular arc, or in other words, providing a torque (turning action), are called torsion springs, motor springs, power springs, and so on. The term torsion spring is usually applied to a helical spring of round, square, or rectangular wire, loaded by torque. The variation in ends used is almost limitless, but a few of the more common types are illustrated in Fig. 11-17C. A torsion bar spring is a relatively straight bar anchored at one end, on which a torque may be exerted at the other end, thus tending to twist or rotate it about its axis.
A fiat coil spring, also known as a clock or motor spring, consists of a strip of tempered steel wound on an arbor and usually confined in a case or drum.
COilS-l
~-I
i
I
I
I
4 ACT!V':_j
r-
6
Flat Springs Flat springs are made of flat material formed in such a manner as to apply force in the desired direction when deflected in the opposite direction.
COILS-"'1
'--CLOSED-END PiLAH\l
NOTE-LEFT-HAND HELIX SHOWN
Power Springs Clock or Motor Type
6 TOl AL
Coil definitions.
should be given to its selection. The types of ends shown in Fig. 11-17B are most commonly used on extension springs. Different types of ends can be used on the same type of spring.
Torsion Bar Springs
An extension spring is a close-coiled, helical spring that offers resistance to a pulling force. It is made from round or square wire (see Figs. 11-15D and ll-17B).
Fig. 11-18
'\;/ I
FULL LOOP AT SIDE
-$8-
~~4
A leaf spring is composed of a series of flat springs nested together and arranged to provide approximately uniform distribution of stress throughout its length. Springs may be used in multiple arrangements, as shown in Fig. ll-19A. Leaf Springs
CHAPTER 11
Belleville Springs
"ll . are washer-shaped, Bellevz e sprmgs
h rt truncated cone. made in the form of a s o ' . eries to acBelleville washers may be assembled m s . commodate greater deflections, in parallel to reslst greater forces, or in combination of series and parallel, as shown
315
M'lscellaneous Types of Fasteners
d d depending on the or solid black shading is rec~mmen e ' size of the wire's diameter (Flg. 11-21).
Dimensioning Springs
.
f
The following information should be given on a drawmg 0 a spring. . h and kind of material used in the spring • S1ze, s ape, • Diameter (outside or inside)
in Fig. ll-19B.
Spring Drawings On working drawings, a schematic drawing of a helical spring is recommended to save drafting time (Fig. 11-2~). As in screw-thread representation, straight lines are used m place of the helical curves. On assembly drawings, springs are normally shown in section, and either crosshatching lines
• Pitch or number of coils • Shape of ends • Length • Load and rate (not covered in this text)
~".".
EXAMPLE
,;&
ONE HELICAL TENSION SPRING 3.00 LG (OR )..l.~IBER OF COILS), .50 ID, PITCH .25. 18 B & S GA SPRIXG BRASS WIRE
SERIES
(A) LEAF SPRING
rh LtJ I
I
Spring Clips Spring clips perform multiple functions and eliminate the handling of several small parts; thus they reduce assembly costs (Fig. 11-23, p. 316). The spring clip is generally self-retaining. requiring cnly a flange, panel edge, or mounting hole to clip to. Basi.::~y.
I
-:===~~".: ':.~~-~ ~__; '\,Q l
(A) PLAIN ENDS
Fig. 11-20
(B) BELLEVILLE SPRING
Spring arrangements.
Fig. 11-19
When single-line representation is used, the dimensions should state the applicable size of material required to ensure correct interpretation on such features as inside diameter. outside diameter, and end loops (fig. 11-:!21.
(B) PLAIN-END GROUND
I
(C) SQUARED ENDS OR SQUARE-END GROUND
Schematic drawing of springs.
(A) COMPRESSION
(B) EXTENSION
(A) LARGE SPRINGS
TYPE OF END
(B) SMALL SPRINGS
Fig. 11-21
J__ _
~ '~"""'"
Showing helical springs on assembly drawings.
(C) TORSIONAL
Fig. 11-22
Dimensioning springs.
316
PART 2
Fasteners, Materials, and Forming Processes
(A) DART-TYPE SPRING CLIPS
(B) STUD RECEIVER CLIPS
(C) CABLE, WIRE, AND TUBE CLIPS
MOLDING
(E) U.SHAPED, S-SHAPED, AND C·SHAPED CLIPS
(D) SPRING MOLDING CLIPS
Fig. 11-23
Spring clips.
spring clips are light-duty fasteners and serve the same function as small bolts and nuts, self-tapping screws, clamps, spot welding, and formed retaining plates. Dart-shaped panel retaining elements have hips to engage within panel or component holes. The top of arms of the fastener can be formed in any shape to perform unlimited fastening functions. Dart-Type Spring Clips
Stud Receiver Clips There are three basic types of stud receivers: push-ons, tubular types, and self-threading fasteners. All are designed to make attachments to unthreaded studs, rivets, pins, or rods of metal or plastic.
These fasteners incorporate self-retaining elements for engaging panel holes or mounting on panel edges and flanges. Spring-clip cable, wire, and tubing fasteners are frontmounting devices, requiring no access to the back of the panel. Cable, Wire, and Tube Clips
Molding retaining clips are formed with legs that hold the clips to a panel and arms that positively engage the flanges of various sizes and shapes Spring Molding Clips
of trim molding and pull the molding tightly to the attaching panel. U-, 5-, and C-Shaped Spring Clips These spring clips get their names from their shapes. The fastening function is accomplished by using inward compressive spring force to secure assembly components or provide self-retrntion after installation. References and Source Material 1. 2. 3. 4.
General Motors Corp. The Wallace Barnes Co. Ltd. Machine Design, Fastening and joining reference issue. ASME Y14.13M-1981 (R 2003), Mechanical Spring Representation.
See Assignments 9 through 11 for Unit 11-4 on pages 334-336.
INTERNET CONNECTION Report on what you find out about springs on this site: http://www.machinedesign.com/
CHAPTER 11
11-5
RIVETS
Standard Rivets Riveting is a popular method of fastening and joining, primarily because of its simplicity, dependability, and low cost. A myriad of manufactured products and structures, both small and large, are held together by these fasteners. Rivets are classified as permanent fastenings, as distinguished from removable fasteners, such as bolts and screws. Basically, a rivet is a ductile metal pin that is inserted through holes in two or more parts, and having the ends formed over to securely hold the parts. Another important reason for riveting is versatility, with respect to both the properties of rivets as fasteners and the method of clinching. • Part materials: Rivets can be used to join dissimilar materials, metallic or nonmetallic, in various thicknesses. • Multiple functions: Rivets can serve as fasteners, pivot shafts, spacers, electric contacts, stops, or inserts. • Fastening finished parts: Rivets can be used to fasten parts that have already received a final painting or other finishing.
Riveted joints are neither watertight nor airtight, although such a joint may be attained at some added cost by using a sealing compound. The riveted parts cannot be disassembled for maintenance or replacement without knocking the rivet out and installing a new one in place for reassembly. Common riveted joints are shown in Fig. 11-24.
Miscellaneous Types of Fasteners
types: butt and lapped. The more common types of large rivets are shown in Fig. 11-25. In order to show the difference between shop rivets (rivets that are installed at the shop) andfield rivets (rivets that are installed on the site), two types of symbols are used. When shop rivets are drawn, the diameter of the rivet head is shown on the drawings. For field rivets, the shaft diameter is used. Figure 11-26 (p. 318) shows the conventional rivet symbols adopted by the American and Canadian Institutes of Steel Construction.
Rivets for Aerospace Equipment The following representation of rivets on drawings for aerospace equipment is also recommended for other fields of work involving rivets.
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SINGLE-RIVETED LAP JOINT
(A) LAP JOINTS
Fig. 11-24
Common riveted joints.
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Large rivets are used in structural work of buildings and bridges. Today, however, high-strength bolts have almost completely replaced rivets in field connections because of cost, strength, and the noise factor. Rivet joints are of two
---1
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I
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Large Rivets
317
FLAT -TOP COUNTERSUNK HEAD
-i D ~ROUND-TOP COUNTERSUNK HEAD
Fig. 11-25 Approximate sizes and types of large rivets .50 in. (12 mm) and up.
DOUBLE-RIVETED BUTT JOINT
SINGLE-RIVETED BUTT JOINT
(B) BUTT JOINTS
318
PART 2
Fasteners, Materials, and Forming Processes
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Fig. 14-68 Drill jig.
@ BUSHING PLATE MATL Cl I REOD @SHOULDER SCREW .375-16UNC x 1.25 LG THREAD, SHOULDER 0 .438 x .641
(j) SETSCREW SO HD .500-13UNC x 2.00 LG, FLAT POINT, I REQD @ LINER BUSHING 1.75 ID x 2.12 OD x 1.25 LG I REOD
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0
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SECTION A-A THREAD CONTROLLING ORGANIZATION AND STANDARD-ASME 81.1-2003
Fig. 14-86
Winch. (continued on opposite page.)
CHAPTER 14
Detail and Assembly Drawings
449
R.70 PARTIAL SIDE VIEW OF FRAME
.12
,
EXTENSION SPRING .26 OD WIRE 0.026 FREE LENGTH - .50 .
~-~>J...---1- PINION
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SEE ENLARGED DETAIL
SECTION 8-8 0.38
Fig._ 14-86
Winch.
PAWL
MATL .375 STEEL 1 REQD
450
PART 3
Working Drawings and Design
39. On a C (A2) size sheet make a two-view assembly drawing (front and side) of the grinder shown in Fig. 14-87 Show the front view in half section. Include on the drawing an item list and identification part numbers. Scale 1: I. 40. Make detail drawings of parts 1 and 4 shown in Fig. 14-87, replacing the descriptive fit terms with appropriate dimensions.
MATL-.0575 (#17 G S GA) STL PT 2 GUARD AS SHOWN I REOD PT 3 GUARD OPPOSITE HAND I REQD
PT 9 BEARING SKF 600Z-2Z (SEE APPENDIX) 2 REOD PT 10 GRINDING WHEEL-FINE 6.00 OD
x 1.00 THK x 0
PT II GRINDING WHEEL-MED. 6.00 OD
x 1.00 THK X 0 .501 BORE, I REOD
PT 12 CARRIAGE BOLT .250-20 UNC
.501 BORE, I REQD
x 1.00 LG, 4 REQD
PT 13 WASHER PLAIN TYPE A .2811D
x
.625 OD
x
.065, 4 REOD
PT 14 SETSCREW-SLOTTED HEAD CUP POINT .250-20UNC X .31 LG, I REOD
.500-13 UNC-2A LH .500-13 UNC-2A 2X LN3 FIT WITH PT 9 0 .625 LC4 FIT WITH PT 7
PT 15 WING NUT .250-20 UNC, 4 REOD
.40~ b2.10~ ~-~
PT 16 NUT-REG HEX .500 UNC, I REQD PT 17 NUT-REG HEX .500 UNC-LH, I REQD
10.70, _ _ _ __:_..:..__ _ PT 4 SHAFT MATL-CRS I REQD
.250-20 UNC-2B
MATL-0934 (#13 G S GA) STL PT 5 GUIDE AS SHOWN I REOD PT 6 GUIDE OPPOSITE HAND I REOD ROUNDS & FILLETS
PT 7 PULLEY MATL-STL I REOD
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THREAD CONTROLLING ORGANIZATION AND STANDARD-ASME B1.1-2003
ta:
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PTS SPACER MATL-.0934 (#13 G S GA) 4REOD PT I BASE MATERIAL-Gil REQD
Fig. 14-87
Bench grinder.
CHAPTER 14
Assignments for Unit 14-7, Exploded Assembly Drawings
41. Make an exploded isometric assembly drawing of one of the assemblies shown in Figs. 14-28 (p. 420), 14-88,
Detail and Assembly Drawings
and 14-89. Use center lines to align parts. Include on the drawing an item list and identification part numbers. Scale 1:1.
.50
SEE APPENDIX FOR KEYWAY SIZE.
~~.20 DETAIL OF CONNECTOR
.375-16 UNC-2 B, ASME B1.1 .50 FROM END
Fig. 14-88
Coupling.
PT3- STUD
01.75
PT2- RING
Fig. 14-89
Universal joint.
451
PT I - FORK
452
PART 3
Working Drawings and Design
42. Make an exploded assembly drawing in orthographic projection of one of the assemblies shown in Figs. 14-89 (previous page) and 14-90. Use center lines to align the parts. Include on the drawing an item list and identification part numbers.
450 X I CHAMFER
PT I - POST MATL- SAE 1112 I REQD
018
PT 2 - BRACKET MA TL - 13 GA (2.38) USS STL I REQD
(2116
450 X 1.5 CHAMFER PT 3- SHAFT MATL- SAE 1112 I REQO
PT 6- RETAINING RING EXT SERIES 5133
A1i') I REQD ""MATL- STEEL
PT 5- BUSHING MATL- BRASS I REQD
PT 4- WHEEL MATL- HARD RUBBER I REQD
Fig. 14-90
Caster.
CHAPTER 14
Assignment for Unit 14-8, Detail Assembly Drawings
43. Make a three-view detail assembly drawing of any one of the assemblies shown in Figs. 14-91, 14-93, and 14-94. For Fig. 14-92 only a partial assembly drawing is required. Include on the drawing the method of assembly (i.e., nails, wood screws, dowels) and an item list and identification part numbers. Include in the item list
Detail and Assembly Drawings
453
the assembly parts. The student is to select scale and drawing paper size. For Fig. 14-93 the basic sizes are given. Design a table of your choice. Show on the drawing how the sides and feet are designed and fastened.
1.50
DETAIL OF LEG
OVERALL HEIGHT~ 18
Fig. 14-93
Night table.
2X
GLUE AND DOWEL PT 3
MATL- CONSTRUCTION GRADE SPRUCE NOTE: WOOD SIZES (THICKNESS AND WIDTH) ARE NOMINAL INCH SIZES.
Fig. 14-91
R 25
Sawhorse. MATL- #I WHITE PINE
Fig. 14-94 ENLARGED VIEW SHOWING NAILING ARRANGEMENT OF GUSSETS
UPPER CHORD (RAFTER)
Roof truss.
Book rack.
NOTE: -ALL GUSSETS ARE .50 PLYWOOD AND ARE NAILED ON BOTH SIDES. -ALL LUMBER SIZES ARE NOMINAL SIZES IN INCHES. EXCEPT LUMBER LENGTHS, WHICH ARE IN FEET AND INCHES.
454
PART 3
Working Drawings and Design
Assignments for Unit 14-9, Subassembly Drawings
44. For Fig. 14-95 make a two-view subassembly drawing of die set B1-36l with dimensions, identification part numbers, and an item list. K = 7.50. Select a plain (journal) bearing from the Appendix. Convert to decimal inch dimensions. Scale 1:2. Identify the hole and shaft sizes for the fits shown. 45. For Fig. 14-96 make a one-view subassembly drawing of the wheel. A broken-out or partial section view is recommended to show the interior features. Include on the drawing pertinent dimensions, identification part numbers, and an item list. Four 010-mm bolts fasten the wheel to an 8-mm plate. Scale l: 1.
RC4 FIT BETWEEN BUSHING AND SHAFT J LN2 FIT BETWEEN BUSHING AND PUNCH HOLDER LN2 FIT BETWEEN SHAFT AND DIE SHOE
Fig. 14-95
Die sets.
PT I - TOP PLATE MATL- MALLEABLE IRON
018 PT 3 - AXLE SUPPORT MATL- MALLEABLE IRON
ROUNDS AND FILLETS R5 ALL-,j SHOWN TO BE .
PT 2- WHEEL MATL- MALLEABLE IRON
Fig. 14-96
Wheel assembly.
-,j
CHAPTER 14
46. On a B (A3) size sheet make a partial-section assembly drawing of the idler pulley shown in Fig. 14-97. Place on the drawing dimensions suitable for a catalog. Add to the drawing an item list and identification part numbers. Scale 1: 1.
Detail and Assembly Drawings
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OBJECT DRAWN UPRIGHT
Fig. 15-4
459
Pictorial Drawings
60
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Ellipse and line reduction sizes for axonometric projection.
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(C) TRIMETRIC
460
PART 3
Working Drawings and Design
projection and the 11 S and 30° angles for trimetric projection are shown because these angles are used widely by industry.
Fig. 15-7. In one method, the object is divided mentally into a number of sections and the sections are created one at a time in their proper relationship to one another. In the second method, a box is created with the maximum height, width, and depth of the object; then the parts of the box that are not part of the object are removed, leaving the pieces that form the total object.
Isometric Drawings This method is based on a procedure of revolving the object at an angle of 45° to the horizontal, so that the front comer is toward the viewer, and then tipping the object up or down at an angle of 35° 16' (Fig. 15-6). When this is done to a cube, the three faces visible to the viewer appear equal in shape and size, and the side faces are at an angle of 30° to the horizontal. If the isometric view were actually projected from a view of the object in the tipped position, the lines in the isometric view would be foreshortened and would, therefore, not be seen in their true length. To simplify the drawing of an isometric view, the actual measurements of the object are used. Although the object appears slightly larger without the allowance for shortening, the proportions are not affected. All isometric drawings are started by constructing the isometric axes, which are a vertical line for height and isometric lines to left and right, at an angle of 30° from the horizontal, for length and width. The three faces seen in the isometric view are the same faces that would be seen in the normal orthographic views: top, front, and side. Figure 15-6B illustrates the selection of the front comer (A), the construction of the isometric axes, and the completed isometric view. Note that all lines are drawn to their true length, measured along the isometric axes, and that hidden lines are usually omitted. Vertical edges are represented by vertical lines, and horizontal edges by lines at 30° to the horizontal. Two techniques can be used for making an isometric drawing of an irregularly shaped object, as illustrated in
Nonisometric lines Many objects have sloping surfaces that are represented by sloping lines in the orthographic views. In isometric drawing, sloping surfaces appear as nonisometric lines. To create them, locate their endpoints, found on the ends of isometric lines, and join them with a straight line. Figures 15-8 and 15-9 (p. 462) show the construction of nonisometric lines.
Dimensioning Isometric Drawings At times, an isometric drawing of a simple object may serve as a working drawing. In such cases, the necessary dimensions and specifications are placed on the drawing. Dimension lines, extension lines, and the line being dimensioned are shown in the same plane. Unidirectional dimensioning is the preferred method of dimensioning isometric drawings. The letters and numbers are vertical and read from the bottom of the sheet. An example of this type of dimensioning is shown in Fig. 15-10 (p. 462). Since the isometric is a one-view drawing, it is not usually possible to avoid placing dimensions on the view or across dimension lines. However, this practice should be avoided whenever possible.
~
. f
~M>vv
[]]] (I) REVOLVING THE OBJECT
(2) TIPPING THE OBJECT
(3) ISOMETRIC
PROJECTION
(4) ISOMETRIC DRAWING
(A) ISOMETRIC PROJECTION
. ( 1 2•.0-. o' \ . . 1200
~ .
1200
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LJToilJ []][I] A
FRONT
SIDE
~OP
FRONT~SIDE ISOMETRIC AXES
(B) ISOMETRIC AXES
Fig. 15-6
~~c
\
Isometric axes and projection.
CHAPTER 15
Pictorial Drawings
461
~~1l
b
,..
l
(A) DEVELOPMENT BY SECTIONS
4.00
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ti2.00-i
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4~,..--j Fig. 15-7
(B) BOX CONSTRUCTION
Developing an isometric drawing.
and easy means of communicating technical ideas. Isometric sketching, one of several types of pictorial drawing, is the most frequently used. With the use of isometric grid sheets and an isometric ellipse template, pictorial drawings can be sketched quickly and accurately.
Isometric Sketching The basic techniques for sketching were covered in Unit 4-4. Pictorial sketching is widely used in industry because this type of drawing is easy to read and understand It is also a quick
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.25
.38
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(A)
Fig. 15-8
(B)
Examples in the construction of nonisometric lines.
(C)
462
PART 3 Working Drawings and Design
(A) PART
(B) BLOCK IN FEATURES
(C) DARKEN ISOMETRIC LINES
(D) COMPLETE NONISOMETRIC LINES
Sequence in drawing an object having nonisometric lines.
Fig. 15-9
2X
Fig. 15-10
Isometric dimensioning.
Isometric sketching paper has evenly spaced lines running in three directions. Two sets of lines are sloped at a 30° angle with the horizon. The third set of lines are vertical and pass through the intersection of the sloping lines (see Fig. 15-11). The most commonly used grids are the inch, which is further subdivided into smaller evenly spaced grids, and the centimeter, which is further subdivided into 10 equal grids of 1 mm. No units of measure are shown on these sheets; therefore the spaces could represent any convenient unit of size. To save time and to make a more accurate and neaterlooking sketch, use an isometric ellipse template for drawing arcs and circles, and a straightedge for drawing long lines.
Fig. 15-11
Isometric grid paper.
Block in the Overall Sizes for Each Detail. These subblocks or frames enclose each detail. They are drawn using very light thin lines. Step 2.
Add the Details. Lightly sketch the shapes of the details in each of their frames. These details are drawn using light thin lines. For circles, which are covered in Unit 15-2, draw squares equal to the size of the diameter. Also sketch in lines to represent the center lines of the circle.
Step 3.
Step 4. Darken the Lines. Using a soft lead pencil, first darken all the isometric lines. Next darken the nonisometric lines. Last, darken the arcs and circles. References and Source Material
Basic Steps to Follow for Isometric Sketching (Fig. 15-12) Step 1. Build a Frame. The frame (or box) is the overall border size of the part to be drawn. It is drawn with light thin lines.
1. ASME Yl4.4M-1989 (R2004), Pictorial Drawings 2. General Motors Corp.
See Assignments 1 through 6 for Unit 15-1 on pages 492-495.
CHAPTER 15
STEP 1. BUILDTHE FRAME
Pictorial Drawings
STEP 3. ADD THE DETAILS
t
STEP 2. BLOCK INTHE DETAILS
Fig. 15-12
Isometric sketching.
STEP 4. DARKEN THE LINES
463
464
PART 3 Working Drawings and Design
15-2
CURVED SURFACES IN ISOMETRIC
Circles and Arcs in Isometric A circle on any of the three faces of an object drawn in isometric has the shape of an ellipse (Fig. 15-13). Practically all circles and arcs shown on manually prepared isometric
drawings are made with the use of an isometric ellipse template. A wide variety of elliptical templates are available. The template shown in Fig. 15-14 combines ellipses, scales, and angles. Markings on the ellipses coincide with the center lines of the holes, speeding up the drawing of circles and arcs. Figure 15-15 shows a part having the holes and arcs constructed with a template.
Drawing Irregular Curves in Isometric To manually draw curves other than circles or arcs, the plotting method shown in Fig. 15-16 is used.
D lA) A SQUARE DRAWN IN THE THREE ISOMETRIC POSITIONS
1. Draw an orthographic view, and divide the area enclosing the curved line into equal squares. 2. Produce an equivalent area on the isometric drawing, showing the offset squares. 3. Take positions relative to the squares from the orthographic view, and plot them on the corresponding squares on the isometric view. 4. Draw a smooth curve through the established points with the aid of an irregular curve.
See Assignments 7 through 9 for Unit 15-2 on pages 495-496.
IBI A CIRCLE PLACED INSIDE A SQUARE AND DRAWN
IN THE
THREE ISOMETRIC POSITIONS
Fig. 15-13
Circles in isometric.
Fig. 15-14
Positioning of the isometric ellipse template for the three planes of projection.
CHAPTER 15
Pictorial Drawings
465
THEPARTNOTETHE POSITION OFTHETEMPLATE FOR DRAWING THE CIRCLES A AND D, AND THE ARCS BAND C.
Fig. 15-15
Application of the isometric ellipse template.
15-3
COMMON FEATURES IN ISOMETRIC
Isometric Sectioning (A) CURVED LINE TO BE DRAWN
(B)
(C)
(D)
(E)
Fig. 15-16 Curves drawn in isometric by means of offset measurements.
Isometric drawings are usually made showing exterior views, but sometimes a sectional view is needed. The section is taken on an isometric plane, that is, on a plane parallel to one of the faces of the cube. Figure 15-17 (p. 466) shows isometric full sections taken on a different plane for each of three objects. Note the construction lines representing the part that has been cut away. Isometric half sections are illustrated in Fig. 15-18 on page 466. When an isometric drawing is sectioned, the section lines are shown at an angle of 60° with the horizontal or in a horizontal position, depending on where the cutting-plane line is located. In half sections, the section lines are sloped in opposite directions, as shown in Fig. 15-18.
466
PART 3
Fig. 15-17
Working Drawings and Design
Examples of isometric full sections.
~CUTTING PLANE
OUTLINE OF CUT SURFACE
FINISHED DRAWING INITIAL CONSTRUCTION
(AI
PART 1
CONSTRUCTION LINES . .
,.--CUTTING PLANE
. '
. '~
,'
OUTLINE OF CUT SURFACE FINISHED DRAWING INITIAL CONSTRUCTION
IBI PART2 Fig. 15-18
Examples of isometric half sections.
CHAPTER 15
Pictorial Drawings
467
Fillets and Rounds For most isometric drawings of parts having small fillets and rounds, the adopted practice is to draw the corners as sharp features. However, when it is desirable to represent the part, normally a casting, as having a more realistic appearance, either of the methods shown in Fig. 15-19 may be used.
Threads The conventional method for showing threads in isometric is shown in Fig. 15-20. The threads are represented by a series of ellipses uniformly spaced along the center line of the thread. The spacing of the ellipses need not be the spacing of the actual pitch.
Break Lines For long parts, break lines should be used to shorten the length of the drawing. Freehand breaks are preferred, as shown in Fig. 15-21.
ACCEPTABLE
Isometric Assembly Drawings Regular or exploded assembly drawings are frequently used in catalogs and sales literature (Fig. 15-22, p. 468).
Fig 15-21
Conventional breaks in isometric.
See Assignments 10 through 16 for Unit 15-3 on pages
496-499.
15-4 (AI CURVED LINE
(B) STRAIGHT LINE
Fig. 15-19
Representation of fillets and rounds in isometric.
Fig. 15-20
Representation of threads in isometric.
OBLIQUE PROJECTION
This method of pictorial drawing is based on the procedure of placing the object with one face parallel to the frontal plane and placing the other two faces on oblique (or receding) planes, to left or right, top or bottom, at a convenient angle. The three axes of projection are vertical, horizontal, and re.ceding. Figure 15-23 (p. 468) illustrates a cube drawn in typical positions with the receding axis at 60°, 45°, and 30°. This form of projection has the advantage of showing one face of the object without distortion. The face with the greatest irregularity of outline or contour, or the face with the greatest number of circular features, or the face with the longest dimension faces the front (Fig. 15-24, p. 469). Two types of oblique projection are used extensively. In cavalier oblique, all lines are made to their true length, measured on the axes of the projection. In cabinet oblique, the lines on the receding axis are shortened by one-half their true length to compensate for distortion and to approximate more closely what the human eye would see. For this reason, and because of the simplicity of projection, cabinet oblique is a
468
PART 3
Working Drawings and Design
927 REGULATING SCREW ASSEMBLY {2
REQD)~
929 REGULATING SCREW PACKING {2 REQD) 4X Ql.221
,a::~:E\Jil~
701·N SHELL INCLUDING BEARING
D
J (A) ISOMETRIC ASSEMBLY
Fig. 15-22
Isometric assembly drawings.
Fig. 15-23
Typical positions of receding axes for oblique projection.
commonly used form of pictorial representation, especially when circles and arcs are to be drawn. Figure 15-25 shows a comparison of cavalier and cabinet oblique. Note that hidden lines are omitted unless required for clarity. Many of the drawing techniques for isometric projection apply to oblique projection. Figure 15-26 illustrates the construction of an irregularly shaped object by the box method.
Inclined Surfaces Angles that are parallel to the picture plane are drawn as their true size. Other angles can be laid off by locating the ends of the inclined line. A part with notched comers is shown in Fig. 15-27A (p. 470). An oblique drawing with the angles parallel to the picture plane is shown in Fig. 15-27B. In Fig. 15-27C the angles are parallel to the profile plane. In each case the angle is laid off by measurement parallel to the oblique axes, as
(B) EXPLODED ISOMETRIC ASSEMBLY
shown by the construction lines. Since the part, in each case, is drawn in cabinet oblique, the receding lines are shortened by one-half their true length.
Oblique Sketching Oblique sketching is another type of pictorial sketching. Oblique sketching paper is similar to two-dimensional sketching paper except that 45° lines, which pass through the intersecting horizontal and vertical lines, are: added in either one or both directions. The most commonly used oblique grids are the inch, which is subdivided into smaller evenly spaced grids, and the centimeter. There are no units of measurements shown on these sheets; therefore the spaces could represent any convenient unit of size (Fig. 15-28, p. 470). To save time and make a more accurate and neater-looking sketch, use a circular or elliptical template for drawing circles or arcs, and a straightedge when drawing long lines.
CHAPTER 15
Pictorial Drawings
469
THIS! B
THIS!
Fig. 15-24 1\vo general rules for oblique drawings.
I!
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J CABINET PROJECTION
CAVALIER PROJECTION
Fig. 15-25 Types of oblique projection.
-+--+--+-
(A)
IBI
Fig. 15-26 Oblique construction by the box method.
(C)
(D)
470
PART 3 Working Drawings and Design
I l
(AI
Fig. 15-27
(B)
(C)
(D)
Drawing inclined surfaces.
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Oblique sketching paper.
Basic Steps to Follow for Oblique Sketching (Fig. 15-29) Step 1. Build a Frame. The frame or box is the overall border size of the part to be drawn. It is drawn with light thin lines. Step 2. Block in the Overall Size of Each Detail. These subblocks or frames enclose each detail. They are drawn using light thin lines.
Dimensioning Oblique Drawings Dimension lines are drawn parallel to the axes of projection. Extension lines are projected from the horizontal and vertical object lines whenever possible. The dimensioning of an oblique drawing is similar to that of an isometric drawing. The recommended method is uni-directional dimensioning, which is shown in Fig. 15-30. As in isometric dimensioning, some dimensions must be placed directly on the view.
Step 3. Add the Details. Lightly sketch the shape of the details in each of their frames. These details are drawn using light thin lines. For circles, draw squares equal to the diameter size. Also sketch the center lines. Step 4.
Darken the Lines.
darken the lines.
Use a soft lead pencil to
See Assignments 17 through 21 for Unit 15-4 on pages 499-501.
CHAPTER 15
it
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471
Pictorial Drawings
Oblique sketching.
15-5
COMMON FEATURES IN OBLIQUE
Circles and Arcs Whenever possible, the face of the object having circles or arcs should be selected as the front face, so that such circles or arcs can be easily drawn in their true shape (Fig. 15-31, p. 472). When circles or arcs must be drawn on one of the oblique faces, the offset measurement method in Fig. 15-32 (p. 472) may be used. Fig. 15-30
Dimensioning an oblique drawing.
1. Draw an oblique square about the center lines, with sides equal to the diameter.
472
PART 3
Working Drawings and Design
SCHEMATIC OF A COMPLETELY AUTOMATIC REGISTRATION CONTROL SYSTEM MAINTAINING THE LOCATION OF CUTOFF ON A CONTINUOUS PRINTED WEB. CONTROLLER
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Fig. 15·31
Application of an oblique drawing.
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2 I 0 FOR CAVALIER
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method. In Fig. 15-33 a circle is shown as it would be drawn on a front plane, a side plane, and a top plane. Circles not parallel to the picture plane when drawn by the approximate method are not pleasing but are satisfactory for some purposes. Ellipse templates, when available, should be used because they reduce drawing time and give much better results. If a template is used, the oblique circle should first be blocked in as an oblique square in order to locate the proper position of the circle. Blocking in the circle first also helps the drafter select the proper size and shape of the ellipse. The construction and dimensioning of an oblique part are shown in Fig. 15-34.
CABON
'·
Fig. 15-53
Horizon lines.
(D) OBJECT BELOW HORIZON
~R
CHAPTER 15
Pictorial Drawings
483
HORIZON \\~)
(':7
TO LEFT VANISHING POINT
TO RIGHT VANISHING POINT
HORIZON
(A) BIRD'S-EYE VIEW
0
Fig. 15-54
Fig. 15-56
(B) WORM'S-EYE VIEW
Grid variations.
Angular-perspective grid.
viewing grids. The sketches made on this type of grid provide a more realistic view and thus are gaining in popularity. Exterior Grid When the three adjacent exterior planes of the cube are developed, the resultant image is referred to as an exterior grid. When this grid is used, the points are projected from the top plane downward and from the picture planes away from the observer (see Figs. 15-54 and 15-55). Interior Grid When the three adjacent interior planes of the cube are exposed and developed, the resultant image is called an interior grid. When this grid is used, the points are projected from the base plane upward and from the picture planes toward the observer. Each produces the same results. Two further variations of both the exterior and the interior grids are known as the bird's-eye and worm's-eye grids. These effects are achieved by rotating the vertical plane of the grid about the horizon line. Objects drawn in the bird's-eye grid appear as if they were being viewed from above the horizon line, as seen in Fig. 15-56. Objects drawn in the worm's-eye grid appear as if they were being viewed from below the horizon line.
Grid Increments I The three surfaces or planes of the grid are subdivided into multiple vertical and horizontal increm9nts. Each increment is proportionately foreshortened as it r~cedes from the picture plane and thus creates the perspective illusion. The grid increments can be any size desired (Fig[ 15-57, p. 484).
Basic Steps to Follow for Ang~lar-Perspective Sketching (Fig. 15-58 on page 1485) Step 1. Build a Frame. The frame or pox is the overall border size of the part to be drawn. It is drawn with light thin lines.
~ach
Step 2. Block in the Overall Size of Detail. These subblocks or frames enclose each detail. They are drawn using light thin lines. I Step 3. Add the Details. Lightly sketch the shape of the details in each of their frames. These details are drawn using light thin lines. For circles, draw squares equal to the size of the diameter. Also sketch the center lines. Step 4.
Darken the Lines.
Use a soft lead pencil to
darken the lines.
(A) EXTERIOR GRID
Fig. 15-55
(B) INTERIOR GRID
Types of angular-perspective grids.
CAD systems that support 3-D modeling usually support the generation of perspective drawings. In the construction of the perspective drawing, the position of the "camera" represents the person viewing the object. Several parameters such as zoom, distance, and view clip are then manipulated to create the required perspective view of the object. Only the view is manipulated, for the original model of the object remains unaffected.
484
PART 3
Working Drawings and Design
Fig. 15-57 Angular-perspective grid applications.
References and Source Material 1. General Motors Corp.
See Assignment 29 for Unit 15-7 on page 507.
15-8
SOLID MODELING
Geometric models in three dimensions provide accurate information on the shape of a part or assembly for use in CAE (computer-aided engineering) or CAM (computer-aided manufacturing) applications. In CAD, three-dimensional (3-D) geometric models may be made in three ways: wire-frame models, surface models, and -solid models. No matter which method is used, all models are achieved using basic, underlying 2-D and 3-D geometric elements.
Important for an engineering designer, CAD allows additional information such as volume and surface area to be easily determined, even for very complex objects. CAD allows easy construction of orthographic views and pictorial images or drawings, including axonometric and perspective views. Such 3-D geometric models are essential to developing and extracting the data required for CAM, including the calculation of tool paths for complex CNC operations.
Wire-Frame Modeling Wire-frame models are simple, using just edges and vertices (Fig. 15-59). Although they were the first (and easiest) type, they are the least suitable models for manufacturing and engineering, for they cannot represent complex surfaces or interior volumes and details. Wire models also can be difficult to interpret based on the user's viewpoint (Fig. 15-60). Thus, this type of model is used just as a starting point from which the designer can proceed to more complex drawings with other model types.
CHAPTER 15
Pictorial Drawings
STEP 1. BUILD THE FRAME
STEP 3. ADD THE DETAILS
STEP 2. BLOCK IN THE DETAILS
STEP 4. DARKEN THE LINES
Fig. 15-58 Angular-perspective sketching.
Fig. 15·59 A simple wire frame model.
Fig. 15-60 The orientation of a wire-frame model can confuse the viewer.
485
486
PART 3
Working Drawings and Design
Fig. 15-61
A simple surface model.
Fig. 15-62
A simple NURBS model.
Surface Modeling Surface models allow the surfaces of a part (or object) to be accurately represented as geometric meshes (Fig. 15-61). The accuracy of surface meshes depends on two factors: the complexity of the curves used to define the edges of the surface area, and the mathematical complexity of the equation used to describe the surface. The best system is NURBS (nonuniform rational B-splines) (Fig. 15-62). Such models may be blended and trimmed to produce highly sculpted surfaces such as cars and other consumer items (Fig. 15-63). Both the automotive industry and the aerospace industry rely heavily on this method. This method also allows the generation of tool paths for CNC machining operations.
Fig. 15-63
An example of a surface model.
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Solid Modeling Solid modeling creates 3-D geometric models whose interior details are unambiguously defined. Such models produce parts that can be manufactured. Two main ways are used to make solid models: CSG (constructive solid geometry) and BREP (boundary representation). CSG models are based on geometric principles and are created using basic Boolean operations (union, subtraction, and intersection). (See Fig. 15-64.) In contrast, BREP models make use of surfaces that can be "stitched" or joined to produce the 3-D "solid" (Fig. 15-65). BREP models are made by the use of extrusion (Fig. 15-66) or by revolution or sweeping about an axis (Fig. 15-67).
A-B
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Fig. 15-64
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The three Boolean operations.
\ J
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CHAPTER 15
Fig. 15-65
A schematic example of a BREP model.
Fig. 15-66
Pictorial Drawings
487
Shape generation by extrusion.
When CSG and BREP are used together, the result is a highly complex model. For example, extruded profiles can be intersected to produce complex shapes (Fig. 15-68). The resulting models have geometries that are unambiguous and can be used as geometric data for more complex CAE and CAM functions.
Image Generation
Fig. 15-67
Shape generation by sweeping about an axis.
(A) MODEL PROFILES
Fig. 15-68
It is possible to extract or produce 2-D images from 3-D models, including standard orthographic views, axonometric views (isometric, dimetric, and trimetric ), and pictorial views (perspective). Simple line drawings, such as isometric drawings, can be produced from 3-D models by removing the hidden or obstructed lines from the displayed view (Fig. 15-69, p. 488).
(B) INTERSECTING EXTRUSIONS
Generating a model from intersecting extrusions.
(C) RESULT OF BOOLEAN INTERSECT OF THE THREE EXTRUSIONS
488
PART 3
Working Drawings and Design
Fig. 15-70
(A) BEFORE
Simple shaded model.
Because these images, or drawings, are generated through true projection, the representation of shapes and surfaces may not follow usual drafting practice. Basic shaded drawings are created by first assuming a light source and location and then determining how much light each surface is receiving (Fig. 15-70). More complex renderings may include "materials" or textures; a part may be made up of metal, glass, paint, or plastic (Fig. 15-71). These images can make use of the interaction of lights, showing the many surfaces of the model
(B) AFTER
Fig. 15-69
Hidden line removal.
Fig. 15-71
A rendered surface model.
CHAPTER 15
through the reflection, refraction, and transmission of light and color (Fig. 15-72). These highly realistic images are referred to as photorealistic images, for they appear to be a photograph of a real object.
Pictorial Drawings
489
Data Extraction Geometric models can determine mass properties (Fig. 15-73) or simulate the mechanical or thermal behavior of a part, for example, through an application such as finite element analy-
--------------· SOLIDS --------------· Mass: 9.4301 Volume: 9.4301 Bounding box: X: 0.0000 -- 3.7800 Y: 0.0000 -- 2.2400 Z: 0.0000 -- 2.0000 Centroid: X: 1.8940 Y: 1.4381 Z:0.7355 Moments of inertia: X: 29.2541 Y: 51.4933 Z:66.2404 Products of inertia: XV: 26.4346 YZ: 10.7126 ZX: 13.8483 Radii of gyration: X: 1.7613 Y: 2.3368 Z: 2.6503 Principal moments and X-Y-Z directions about centroid: 1:4.5080 along [0.9906 0.1007 0.09261 J: 12.1190 along [-0.1363 0.7820.6078] K: 13.4946 along [-Q.0113 -0.610.7886] Fig. 15-72
A complex rendering.
Fig. 15-73 A sample mass properties output from AutoCAD 2000 for Fig. 15-68C on page 487.
490
PART 3 Working Drawings and Design
sis, or FEA (Fig. 15-74). Demonstrating how a part will function in the real world is called simulation and is obviously critical to design and manufacturing.
See Assignments 30 through 32 for Unit 15-8 on pages 508-509.
INTERNET CONNECTION Investigate and report on the 3-D solid modeling design capabilities of SolidWorks software: www.proe-design.com/ Describe the information you find on software for computer-aided drawing and design (CADD} at this site: http://www3.autodesk.com/
Fig. 15-74
An example of an FEA false-color map showing stress areas.
SUMMARY 1. The three types of pictorial drawings are the axonomet-
13. Specially designed oblique lines or grids are available
ric, oblique, and perspective. (15-1) Axonometric projection is a projected view in which the lines of sight are perpendicular to the plane of projection, but in which the three faces of a rectangular object are all inclined to the plane of projection. Axonometric drawings are grouped into three types: isometric, dimetric, and trimetric; isometric is the most commonly used. (15-1) Isometric drawing is based on revolving an object at an angle of 458 to the horizontal, so that the front corner is toward the viewer, and then tipping the object up or down at an angle of 358 169. (15-1) In isometric drawing, sloping surfaces appear as nonisometric lines. (15-1) The preferred method of dimensioning isometric drawings is unidirectional dimensioning. (15-1) Isometric grid sheets, isometric ellipse templates, and a straightedge are useful in isometric sketching. (15-1, 15-2) Every CAD system provides an ISOMETRIC GRID option. (15-1) In isometric, a circle on any of the three faces of an object has the shape of an ellipse. (15-2) In CAD, the ELLIPSE command provides two methods for constructing an ellipse. (15-2) When a sectional view is needed in an isometric drawing, the section is taken on an isometric plane (on a plane parallel to one of the faces of the cube). Conventional methods are used in isometric drawings and oblique drawings to show fillets and rounds, threads, and break lines. Isometric assembly drawings can also be made. (15-3, 15-4) With oblique projection, the object is placed with one face parallel to the frontal plane and the other two faces on oblique planes, to left or right, top or bottom, at a convenient angle. Cavalier oblique and cabinet oblique projection are the most commonly used. (15-4) Oblique sketching is similar to two-dimensional sketching paper except that 458 lines, which pass through the intersecting horizontal and vertical lines, are added in either one or both directions. The dimensioning of oblique drawings is similar to that of isometric drawings; unidirectional dimensioning is recommended. (15-4)
on some CAD systems, but oblique modeling is not a CAD option. (15-4) When circles or arcs must be drawn on an oblique face, the offset measurement method or the four-center method is used. (15-5) In CAD, the CIRCLE, ARC, and FILLET commands are used to create circles and arcs on the front face of an oblique drawing. For oblique faces, the ELLIPSE command is used. CAD systems provide a modeling option known as 3-D modeling that permits automatic generation of a model from a drawing. (15-5) Perspective is a method of drawing that depicts a threedimensional object on a flat plane as it appears to the eye. The main elements of a perspective drawing are the picture plane, the station point, the horizon, the vanishing point or points, and the ground line. (15-6) The three types of perspective drawings are the parallel, angular, and oblique. (15-6) In a parallel-perspective drawing, all lines converge at one point on the horizon. This type of drawing is often used to represent the interior of a building. (15-6) The cube grid is most commonly used in producing perspective drawings. (15-6) In angular-perspective drawings (two-point perspective drawings) the receding lines converge at two vanishing points located on the horizon. (15-7) Angular-perspective grids include two-and three-point perspective sheets designed for bird's- and worm's-eye views, as well as interior and exterior viewing grids. ( 15-7) In CAD, 3-D geometric models may be made using wireframe models, surface models, and solid models. (15-8) It is possible to produce 3-D models from 2-D images using CAD. Some highly realistic images produced this way are called photorealistic images. (15-8) Geometric models can determine mass properties or simulate the mechanical or thermal behavior of a part and thus can demonstrate how a part will function; this significant ability is called simulation. (15-8)
2.
3.
4. 5. 6.
7. 8. 9. 10.
11.
12.
14.
15.
16.
17. 18.
19. 20.
21.
22.
23.
23.
KEY TERMS Axonometric projection (15-1) Dimetric drawing (15-1) Isometric drawing (15-1)
Nonisometric lines (15-1) Oblique projection (15-6) Perspective (15-6)
Solid modeling (15-8) Trimetric drawing (15-1) Unidirectional dimensioning (15-5)
491
492
PART 3 Working Drawings and Design
ASSIGNMENTS 2. On isometric grid paper or using the CAD isometric grid, draw the parts shown in Fig. 15-76. Do not show hidden lines. Each square shown on the drawing represents one isometric square on the grid. 3. On isometric grid paper or using the CAD isometric grid, sketch the parts shown in Fig. 15-77. Do not show hidden lines.
Assignments for Unit 15-1, Pictorial Drawings
1. On isometric grid paper or using the CAD isometric grid, draw the parts shown in Fig. 15-75. Do not show hidden lines. Each square shown on the drawing represents one isometric square on the grid.
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Isometric flat-surface assignments.
Isometric flat-surface assignments.
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Sketching assignments.
12
13
14
15
CHAPTER 15
Pictorial Drawings
493
4. On isometric grid paper or using the CAD isometric grid, make an isometric drawing of one of the parts shown in Figs. 15-78 through 15-80. A partial starting layout is provided for each of the parts shown. Start at the comer indicated by thick lines. Scale 1: 1. 5. On isometric grid paper or using the CAD isometric grid, make an isometric drawing of one of the parts shown in Figs. 15-81 through 15-83. For Fig. 15-81 use the layout shown in Fig. 15-79; for Fig. 15-82 use the layout shown in Fig. 15-80; and for Fig. 15-83 (p. 494) use the layout shown in Fig. 15-78. Scale 1:1.
Fig. 15-78
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Brace.
Fig. 15-82
Ratchet.
494
PART 3
Working Drawings and Design
MATL-SAE 1050 -
.75 -
-
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fo
Fig. 15-86
Step block.
1--3.25--1
Fig. 15-83
Stop.
6. Make an isometric drawing, complete with dimensions, of one of the parts shown in Figs. 15-84 through 15-89. Scale 1:1.
MATL-SAE 1020
Fig. 15-87
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MATL-GI
Fig. 15-88
Stand.
CHAPTER 15
Fig. 15-91
Pictorial Drawings
Isometric curved-surface assignments.
MATL-SAE 1050 (1)60
Fig. 15-89
Base plate.
ROUNDS AND FILLETS R5 MATL-GI
019 KEYSEAT FOR SQUARE KEY
Assignments for Unit 15-2, Curved Surfaces in Isometric
7. On isometric grid paper or using the CAD isometric grid, draw the parts shown in Fig. 15-90. Each square shown on the figure represents one square on the isometric grid. Hidden lines may be omitted for clarity. 8. On isometric grid paper or using the CAD isometric grid, draw the parts shown in Fig. 15-91. Each square shown on the figure represents one square on the isometric grid. Hidden lines may be omitted for clarity. 9. Make an isometric drawing, complete with dimensions, of one of the parts shown in Figs. 15-92 through 15-95. Scale 1:2 for Fig. 15-95 (p. 496). For all others the scale is 1:1.
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Fig. 15-92
Link.
Fig. 15-93
T-guide.
Fig. 15-94
Cradle bracket.
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495
496
PART 3
Working Drawings and Design
2X
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Fig. 15-95
Base.
Assignments for Unit 15-3, Common Features in Isometric
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Fig. 15-97
Base.
CHAPTER 15
Pictorial Drawings
11. Make an isometric full-section drawing, complete with dimensions, of one of the parts shown in Figs. 15-98 through 15-100. Scale 1:1. 12. Make an isometric drawing, complete with dimensions, of one of the parts shown in Figs. 15-101 and 15-102. Use a conventional break to shorten the length for Fig. 15-101. Scale 1:1.
Fig. 15-100
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Fig. 15-99 Pencil holder.
Fig 15-102 Assignment 12.
497
498
PART 3
Working Drawings and Design
13. Make an isometric assembly drawing of the two-post die set, Model 302, shown in Fig. 15-103. Allow 2 in. between the top and base. Scale 1:2. Do not dimension. Include on the drawing an item list. Using part numbers, identify the parts on the assembly.
14. Make an isometric exploded assembly drawing of the book rack model #1 shown in Fig. 15-104. Use a B (A3) sheet. Scale 1:2. Do not dimension. Include on the drawing an item list. Using part numbers, identify the parts on the assembly.
A 11.12 14.00
B 6.00 7.50 6.50 8.00 D 1.62 1.75
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110
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200
250
300
B
320
370
420
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GLUE AND DOWEL
Fig. 15-104
Book rack.
CHAPTER 15
15. Make an isometric assembly drawing of the gear clamp shown in Fig. 15-105. Add dimensions, identification part numbers, and an item list. Scale 1: 1.
Pictorial Drawings
499
16. Make an isometric exploded assembly drawing of the universal joint shown in Fig. 15-106. Scale 1:1. Do not dimension. Include on the drawing an item list. Using part numbers, identify the parts on the assembly. Assignments for Unit 15-4, Oblique Projection
10-24 UNC SOCKET HD CAP SCREW
Fig. 15-105
17. On coordinate grid paper or using the CAD grid, make oblique drawings of the three parts shown in Fig. 15-107. Each square shown on the figure represents one square on the grid. Hidden lines may be omitted to improve clarity.
Gear clamp.
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Fig. 15-106
Universal joint.
Fig. 15-107
Oblique flat-surface assignments.
500
PART 3
Working Drawings and Design
18. On coordinate grid paper or using the CAD grid, make oblique drawings of the three parts shown in Fig. 15-108. Each square shown on the figure represents one square on the grid. Hidden lines may be omitted to improve clarity. 19. On oblique grid paper or using the CAD grid, sketch the parts shown in Fig. 15-109. Do not dimension or show hidden lines. 20. Make an oblique drawing of one of the parts shown in Figs. 15-110 and 15-111. A partial starting layout is provided for each of the parts shown. Start at the comer indicated by thick lines. Scale 1: 1.
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I Fig. 15-108
Oblique flat-surface assignments.
Fig. 15-111
V-block.
CHAPTER 15
Pictorial Drawings
501
21. Make an oblique drawing, complete with dimensions, of one of the parts shown in Figs. 15-112 through 15-115. Scale 1:1.
1.10
T Fig. 15-112
Control arm.
Fig. 15·115
Dovetail guide.
Assignments for Unit 15-5, Common Features in Oblique
22. Make an oblique drawing of one of the parts shown in Figs. 15-116 and 15-117 (p. 502). A partial starting layout is provided for each of the parts shown. Add dimensions. Scale 1: 1.
•
--1'5
I
--1
•
70
20
1--
35 I
I•
IOO-----:\l
(B) INTERPRETATION
Applying both an angularity and a flatness tolerance to a flat surface.
DATUM FEATURES SUBJECT TO SIZE VARIATION
In Unit 16-5, single features, such as fiat surfaces or line elements of a surface, were used to establish datums for measuring purposes. When a feature of size, such as diameter or width, is specified as a datum feature, it differs from singular fiat surfaces in that it is subject to variations in size as well as form. The datum has to be established from the full surface of a cylindrical feature or from two opposing surfaces of other features of size. However, the datum is a datum axis, median line, or median plane of the feature. The datum identifying symbol is directed to the datum feature of size by the methods shown in Fig. 16-52 on page 532.
Parts with Cylindrical Datum Features Figure 16-63 iiJustrates a part having a cylindrical datum feature. Primary datum feature A relates the part to the first datum plane. Since secondary datum feature B is cylindrical, it is associated with two theoretical planes-the secondary and tertiary planes in the three-plane relationship. These two theoretical planes are represented on the drawing by center lines crossing at right angles. The intersection of these planes creates the datum axis. Once established, the datum axis becomes the origin for related dimensions and the two planes X and Y indicate the direction of measurements. In such cases, only two datum features are referenced in the feature control frame. Figure 16-64 (p. 538) is another example in which the cylindrical feature is used as the secondary datum. The primary datum is then a perfect plane on which the part would normally rest. The secondary datum is still the axis of an
SECONDARY DATUM AXIS B
02.500
2.496
4X 0 .3 I 0 - .3 12
(A) DRAWING CALLOUT
Fig. 16-63
Part
wif~ylindrical
',
datum feature.
(B) INTERPRETATION
538
PART 3
Working Drawings and Design
4X
9.6 0 9 •5
I-Eitl
00.2
.ill "'Il!
®I I ®I A
076.4 SECONDARY DATUM CYLINDER B
B
T
-
t
-
,.---
AXIS OF DATUM
76.4 0 76.2
CENTER LINE OF DATUM FEATURE
....._
~
~
(A) DRAWING CALLOUT
Fig. 16-64
PRIMARY DATUM PLANE A
(B) INTERPRETATION
Cylindrical feature as secondary datum.
-+
~ ---ro.,., ___ffi__+ C~T .749
~
.750 (j) .746
(A) DRAWING
(A) DRAWING CALLOUT
DATUM AXIS A
SIMULATED DATUM A- SMALLEST CIRCUMSCRIBED CYLINDER (MAY VARY WITH EACH PART) _ _ _ _....j
(B) DATUM FEATURE SIMULATOR
I I (C) PRIMARY DATUM CALLOUT IN FEATURE CONTROL FRAME
Fig. 16-65
SIMULATED DATUM A- LARGEST INSCRIBED CYLINDER (MAY VARY WITH EACH PART)
(B) DATUM FEATURE SIMULATOR
I I
External primary datum cylinder-RFS.
imaginary perfect cylinder, but also one that is perpendicular to the primary datum. This cylinder would theoretically touch the feature at only two points. The part has been purposely drawn out of square to show the effect of such deviations.
(C) PRIMARY DATUM CALLOUT IN FEATURECONTROLFRAME
Fig. 16-66
Internal primary datum cylinder-RFS.
Datum Features-RFS RFS and MMC Applications Because variations are allowed by the size dimension, it becomes necessary to determine whether RFS or MMC applies in each case.
When a datum feature of size is applied on an RFS basis, the datum is established by physical contact between the feature surface, or surfaces, and surfaces of the measuring equipment.
CHAPTER 16
Primary Datum Feature-Cylindrical If an external feature, such as the shaft shown in Fig. 16-65, is specified as a primary datum feature, the datum is the axis of the smallest circumscribed cylinder that contacts the feature surface. If an internal cylindrical feature, such as the hole shown in Fig. 16-66, is specified as a datum feature, the datum is the axis of the largest inscribed cylinder that contacts the feature surface.
Primary Datum Feature-Parallel Surfaces The simulated datum features consist of two flat surfaces, such as two opposite faces of a rectangular part or two sides of a slot. For an internal feature, the datum is the center plane between two simulated parallel planes that, at maximum separation, contact the corresponding surfaces of the feature. For an external feature, the datum is the center plane between two simulated parallel planes that, at minimum separation, contact the corresponding surfaces of the feature (Fig. 16-67).
Geometric Dimensioning and Tolerancing
Datum Features-MMC When a datum feature of size is applied on an MMC basis, machine and gaging elements in the measuring equipment, which remain constant in size, may be used to simulate a true geometric counterpart of the feature and to establish the datum. In this case, the size of the simulated datum is established by the specified MMC limit of size of the datum feature or its virtual condition, where applicable. In Fig. 16-68 (p. 540), because no form tolerance is specified, the simulated datum is made to the specified MMC limit of size of .565 in. When a datum feature of size is controlled by a straightness tolerance, as shown in Fig. 16-69 (p. 540), the size of the simulated datum is the virtual condition of the datum feature. Figure 16-70 on page 540 shows a flatness tolerance that applies to both datum surfaces. The simulated datum consists of two parallel planes separated by a distance equal to the maximum material condition, since the flatness tolerances must lie within the specified limits of size. It should be noted that the gage does not check the flatness requirement.
t
1.500
i-
(A) DRAWING CALLOUT
SIMULATED DATUM ATWO PARALLEL PLANES AT MINIMUM SEPARATION (VARIES FOR EACH PART)
SIMULATED DATUM ATWO PARALLEL PLANES AT MAXIMUM SEPARATION (VARIES FOR EACH PART)
DATUM CENTER PLANE A
DATUM CENTER PLANE A (B) INTERPRETATION
Fig. 16-67 Width as primary datum-RFS.
539
540
PART 3
Working Drawings and Design
When secondary or tertiary datum features of size in the same datum reference frame are controlled by a specified tolerance of location or orientation with respect to one another, the size of the simulated datum is the virtual condition of the datum feature. Figure 16-71 illustrates both secondary and tertiary datums specified at MMC but simulated at virtual condition. When design requirements disallow a virtual condition, or if no form or orientation tolerance is specified, it is
t
(AI DRAWING CALLOUT
Fig. 16-68
assumed, for datum reference purposes, that the tolerance is zero at MMC. The fact that a datum applies on an MMC basis is given in the feature control frame by the addition of the MMC symbol @ immediately following the datum reference (Fig. 16-71 C). When there is more than one datum reference, the MMC symbol must be added for each datum where the modification is required.
0.565 .561
i
(C) DATUM CALLOUT IN THE FEATURE CONTROL FRAME
(B) INTERPRETATION
External primary datum without form tolerances-MMC.
-+ 0.567
_1 (A) DRAWING CALLOUT
Fig. 16-69
(B) DATUM FEATURE SIMULATOR
SIMULATED DATUM A= MAXIMUM MATERIAL SIZE PLUS STRAIGHTNESS TOLERANCE = .565 + .002 = 0.567
A@l (C) DATUM CALLOUT IN THE FEATURE CONTROL FRAME
External primary datum with straightness tolerance-MMC. DATUM CENTER PLANE A
SIMULATED DATUM A-CENTER PLANE OF TWO PARALLEL PLANES NOTE: FLATNESS TOLERANCE MUST BE CHECKED SEPARATELY AND MUST LIE WITHIN THE LIMITS OF SIZE. (A) DRAWING CALLOUT
Fig. 16-70
External primary datum-MMC.
(B) INTERPRETATION
(C) DATUM CALLOUT IN THE FEATURE CONTROL FRAME
CHAPTER 16
4X
Geometric Dimensioning and Tolerancing
0 .25 I - .253
1•1
0.004
el AI Bel c el
(AI DRAWING CALLOUT
SIMULATED DATUM C- VIRTUAL CONDITION WIDTH PERPENDICULAR TO DATUM PLANE A
DATUM CENTER PLANE C ALIGNED WITH DATUM AXIS B
I----0.748~SIMULATED DATUM B- VIRTUAL CONDITION
I
I
CYLINDER PERPENDICULAR TO DATUM PLANE A
SIMULATED DATUM PLANE A
(B) DATUM FEATURE SIMULATORS
1cRTIARV
Dt~TUM-
MMC...J.
(C) SECONDARY AND TERTIARY DATUM CALLOUTS IN FEATURE CONTROL FRAME
Fig. 16-71
Secondary and tertiary datum features-MMC.
541
542
PART 3
Working Drawings and Design
References and Source Material 1. ASME Y14.5M-1994 (R2004), Dimensioning and Tolerancing. 2. CAN/CSA B78.2-M91, Dimensioning and Tolerancing of Technical Drawings. 3. ISO drawing standards.
See Assignment 19 for Unit 16-7 on page 607.
16·8
ORIENTATION TOLERANCING FOR FEATURES OF SIZE
Unit 16-6 outlined how to apply orientation tolerances to fiat surfaces. In these instances the feature control frames were directed to the surfaces requiring orientation. When orienta-
"""'""'~'""'"""~""'-Lf
( / ) i
tion tolerances apply to the axis of cylindrical features or to the datum planes of two fiat surfaces, the feature control frame is associated with the size dimension of the feature requiring control (Fig. 16-72). Tolerances intended to control orientation of the axis of a feature are applied to drawings as shown in Fig. 16-73. Although this unit deals mostly with cylindrical features, methods similar to those given here can be applied to noncircular features, such as square and hexagonal shapes. The axis of the cylindrical feature must be contained within a tolerance zone consisting of the space between two parallel planes separated by the specified tolerance. The parallel planes are related to the datum by the basic angles of 45°, 90°, or 0° in Fig. 16-73. The absence of a modifying symbol in the tolerance compartment of the feature control frame indicates that RFS applies.
10.022 10.000 ( IOHB)
I;; I (/)
0.05
el
A
---+ l-r"'1'"7..,...,~'1""7"7'"'7'"'1'"7-:l
(B) ATTACHED TO THE EXTENSION OF THE DIMENSION LINE
(A) ATTACHED TO A DIMENSION
Fig. 16-72
Feature control frame associated with size dimension.
INTERNAL FEATURES
20.00 019.94-----r 0.15
EXTERNAL FEATURES
DRAWING CALLOUTS
Fig. 16-73
Orientation tolerances for cylindrical features-RFS.
A
CHAPTER 16
Angularity Tolerance The tolerance zone is defined by two parallel planes at the specified basic angle from a datum plane or axis within which the axis of the considered feature must lie. Figure 16-74 illustrates the angularity tolerance zone for the part shown in Fig. 16-73.
Parallelism Tolerance Parallelism is the condition of a surface equidistant at all points from a datum plane or an axis equidistant along its length from a datum axis or plane. A parallelism tolerance specifies a tolerance zone defined by two planes or lines parallel to a datum plane or axis within which the axis of the considered feature must lie (Fig. 16-75), or a cylindrical tolerance zone, the axis of which is parallel to the datum axis within which the axis of the considered feature must lie (see Fig. 16-82, p. 546).
Perpendicularity Tolerance A perpendicularity tolerance specifies one of the following:
1. A cylindrical tolerance zone perpendicular to a datum plane or axis within which the center line of the considered feature must lie (Fig. 16-73). TOLERANCE ZONE- TWO PARALLEL PLANES 0.15 APART
Geometric Dimensioning and Tolerancing
543
2. A tolerance zone defined by two parallel planes perpendicular to a datum axis within which the axis of the considered feature must lie (Fig. 16-85, p. 547). When the tolerance is one of perpendicularity, the tolerance zone planes can be revolved around the feature axis without affecting the angle. The tolerance zone therefore becomes a cylinder. This cylindrical zone is perpendicular to the datum and has a diameter equal to the specified tolerance (Fig. 16-76, p. 544). A diameter symbol precedes the perpendicularity tolerance.
Control in Two Directions The feature control frames shown in Fig. 16-73 control angularity and parallelism with the base (datum A) only. If control with a side is also required, the side should be designated as the secondary datum (Fig. 16-77, p. 544). The center line of the hole must lie within the two parallel planes.
Control on an MMC Basis
As a hole is a feature of size, any of the tolerances shown in Fig. 16-73 can be modified on an MMC basis. This is specified by adding the symbol @) after the tolerance. Figure 16-78 (p. 545) shows an example.
DATUM PLANE A
POSSIBLE ORIENTATION OF FEATURE AXIS (A) INTERNAL FEATURE TOLERANCE ZONE- TWO PARALLEL PLANES 0.15 APARTl BLE ORIENTATION FEATURE AXIS POSSIBLE ORIENTATION OF FEATURE AXIS TOLERANCE ZONE- TWO PARALLEL PLANES 0.15 APART WHICH ARE PARALLEL TO DATUM PLANE
(8) EXTERNAL FEATURE
(B) EXTERNAL FEATURE
Fig. 16-74
Tolerance zones for angularity shown in Fig. 16-73.
Fig. 16-75
Tolerance zones for parallelism shown in Fig. 16-73.
544
PART 3
Working Drawings and Design
PARALLEL PLANES CAN BE REVOLVED, THUS
TOL,RANC' ZON' B'COM"' A C Y U 7
0.15 TOLERANCE ZONE
TUM PLANE A
(B) EXTERNAL FEATURE
(A) INTERNAL FEATURE
Fig, 16-76
Tolerance zones for perpendicularity shown in Fig. 16-73 (p. 542). •005-WIDE TOLERANCE ZO
0.188 - - - - - - , .186
CENTER LINE OF HOLE MUST LIE BETWEEN THE TWO PARALLEL PLANES
DRAWING CALLOUT
TOLERANCE ZONE (A) ANGULARITY TOLERANCE
DATUM PLANE
~~~
1:~~~~~-- ~ r)---~--t ~ DRAWING CALLOUT
~
PARALLEL
DATUM PLANE TOLERANCE ZONE (B) PARALLELISM TOLERANCE
Fig. 16-77
ER LINE OF HOLE MUST LIE BETWEEN THE TWO PARALLEL PLANES
Orientation tolerances referenced to two datums.
CHAPTER 16
::=:=:1 r-j_L ,0.006~~ II
Perpendicularity tolerance for a hole on an
MMCbasis.
Because the cylindrical features represent features of size, orientation tolerances may be applied on an MMC basis. This is specified by adding the modifying symbol after the tolerance, as shown in Figs. 16-79 and 16-80.
Internal Cylindrical Features Figure 16-73 (p. 542) shows parts in which the axis or center line of a hole is related by an orientation tolerance to a flat surface. The flat surface is designated as the datum feature.
l I
545
The axis of each hole must be contained within a tolerance zone consisting of the space between two parallel planes. These planes are separated by a specified tolerance of 0.15 mm for the part shown in Fig. 16-73.
0 .250 ±.002
Fig. 16-78
Geometric Dimensioning and Tolerancing
Specifying Parallelism for an Axis Regardless of feature size, the feature axis shown in Fig. 16-81 must lie between two parallel planes, .005 in. apart, that are parallel to datum plane A. In addition, the feature axis must be within any specified tolerance of location. Figure 16-82 (p. 546) specifies parallelism for an axis when both the feature and the datum feature are shown on an RFS basis. Regardless of feature size, the feature axis must lie within a cylindrical tolerance zone of .002 in. diameter whose axis is parallel to datum axis A. Moreover, the feature axis must be within any specified tolerance of location. Figure 16-83 (p. 546) specifies parallelism for an axis when the feature is shown on an MMC basis and the datum feature is shown on an RFS basis. When the feature is at the maximum material condition (.392 in.), the maximum parallelism tolerance is .002 in. diameter. When the feature departs from its MMC size, an increase in the parallelism tolerance is allowed equal to the amount of such departure. Also, the feature axis must be within any specified tolerance of location.
+.000 0.750-.002
lj_l
0.004
el I A
I"""" I--
r Fig. 16-79
Perpendicularity tolerance for a shaft on an
(A) DRAWING CALLOUT
MMCbasis.
.005-WIDE TOLERANCE ZONE 0.875 .872
1111
.006
el 1 A
DATUM PLANE A '-POSSIBLE ORIENTATION OF FEATURE AXIS
Fig. 16-80
MMC basis.
(B) INTERPRETATION
Parallelism tolerance for a shaft on an Fig. 16-81
Specifying parallelism for an axis (feature RFS).
546
PART 3
Working Drawings and Design
0.395 .392
0.002 TOLERANCE ZONE
(A) DRAWING CALLOUT
Fig. 16-82
(B) INTERPRETATION
Specifying parallelism for an axis (both feature and datum feature RFS).
0.395 .392
1!110.002
®I A I
SIMULATED CYLINDRICAL DATUM FEATURE A
.004
.395
.005
(B) INTERPRETATION
(A) DRAWING CALLOUT
Fig. 16-83
.393 .394
Specifying parallelism for an axis (feature at MMC and datum feature RFS).
Perpendicularity for a Median Plane Regardless of feature size, the median plane of the feature shown in Fig. 16-84 must lie between two parallel planes, .005 in. apart, that are perpendicular to datum plane A. In addition, the feature center plane must be within the specified tolerance of location.
perpendicularity tolerance, equal to the amount of such departure, is allowed. Moreover, the feature axis must be within the specified tolerance of location.
Perpendicularity for an Axis (Both Feature and Datum RFS) Regardless of feature size, the feature axis shown in
Fig. 16-85 must lie between two parallel planes, .005 in. apart, that are perpendicular to datum axis A. In addition, the feature axis must be within the specified tolerance of location.
the MMC (0SO.OO), its axis must be perpendicular to datum plane A. When the feature departs from MMC, an increase in the perpendicularity tolerance is allowed equal to the amount of such departure. Also, the feature axis must be within any specified tolerance of location.
Perpendicularity for an Axis (Tolerance at MMC) When the feature shown in Fig. 16-86 is at the MMC (0 2.000), its axis must be perpendicular within .002 in. to datum plane A. When the feature departs from MMC, an increase in the
When the feature shown in Fig. 16-88 (p. 548) is at MMC (050.00), its axis must be perpendicular to datum plane A. When the feature departs from MMC, an increase in the
Perpendicularity for an Axis (Zero Tolerance at MMC) When the feature shown in Fig. 16-87 (p. 548) is at
Perpendicularity with a Maximum Tolerance Specified
CHAPTER 16
1
Geometric Dimensioning and Tolerancing
.005-WIDE TOLERANCE ZONE REGARDLESS OF FEATURE SIZE
.804 .801
I..LI.oo5 I I A
DATUM PLANE A TWO PARALLEL PLANESl"-
t
T (A) DRAWING CALLOUT
Fig. 16-84
POSSIBLE ORIENTATION OF THE FEATURE MEDIAN PLANES
(B) INTERPRETATION
Specifying perpendicularity for a median plane (feature RFS).
SIMULATED CYLINDRICAL DATUM FEATURE A - - --.005-WIDE TOLERANCE ZONE L > - T W O PARALLEL PLANES
DATUM AXIS A
(A) DRAWING CALLOUT
Fig. 16-85
(B) TOLERANCE ZONE
Specifying perpendicularity for an axis (both feature and datum feature RFS).
DATUM PLANE A POSSIBLE ORIENTATION OF THE FEATURE AXIS
2.000 (AI DRAWING CALLOUT
lliG
.003
2.002
.004
2.003
.005
2.004
""~·~c
(B) TOLERANCE ZONE
Fig. 16-86 Specifying perpendicularity for an axis (tolerance at MMC).
.002
2.001
.006
547
548
PART 3
Working Drawings and Design
lj_l (A) DRAWING CALLOUT
A
DATUM PLANE A
POSSIBLE ORIENTATION OF THE FEATURE AXIS
"~
I I
(AI DRAWING CALLOUT
DATUM PLANE A
' 2
00 @100.1 MAX
POSSIBLE ORIENTATION OF THE FEATURE AXIS
50.00
0
50.01
0.01
50.01
0.01
50.02
0.02
50.02
0.02
t
t
t 50.10 t
0.1
0
50.15
0.15
50.16
0.16 LP;fi~.
(B) INTERPRETATION
50.16
t t
0.1
(B) INTERPRETATION
Fig. 16-87 Specifying perpendicularity for an axis (zero tolerance at MMC).
Fig. 16-88 Specifying perpendicularity for an axis (zero tolerance at MMC with a maximum specified).
perpendicularity tolerance, equal to the amount of such departure up to the 0.1 mm maximum, is allowed. Also, the feature axis must be within any specified tolerance of location.
When the feature departs from its MMC size, an increase in the perpendicularity tolerance, equal to the amount of such departure, is allowed. Also, the feature axis must be within the specified tolerance of location.
External Cylindrical Features Regardless of feature size, the feature axis shown in Fig. 16-89 must lie within a cylindrical zone (0 0.4 mm) that is perpendicular to, and projects from, datum plane A for the feature height. Also, the feature axis must be within the specified tolerance of location. Perpendicularity for an Axis (Pin or Boss RFS)
Perpendicularity for an Axis (Pin or Boss at MMC) When the feature shown in Fig. 16-90 is at MMC (0 15.984 mm), the maximum perpendicularity tolerance is 0 0.05 mm.
References and Source Material 1. ASME Y14.5M-1994 (R2004), Dimensioning and Tolerancing. 2. CAN/CSA B78.2-M91, Dimensioning and Tolerancing of Technical Drawings. 3. ISO drawing standards.
See Assignments 20 through 22 for Unit 16-8 on pagec 607-608.
o-
CHAPTER 16
549
Geometric Dimensioning and Tolerancing
015.984 (16f7) 15.966
(A) DRAWING CALLOUT
(AI DRAWING CALLOUT
~~ VPOSSIBLE 0 ORIENTATION
\'~fc-"\7
\;/
\I I
OF FEATURE AXIS 0.4 DIAMETER TOLERANCE ZONE
!
FEATURE HEIGHT PLANE A
MMC 15.984
(B) INTERPRETATION
Fig. 16·89 boss RFS).
Specifying perpendicularity for an axis (pin or
,/(;
/~~"--)
\~
0.05
15.983
0.051
15.982
0.052
t
t
15.967
0.067
LMC 15.966
0.068
(B) INTERPRETATION
Fig. 16-90 Specifying perpendicularity for an axis (pin or boss at MMC).
16-9
POSITIONAL TOLERANCING
The location of features is one of the most frequently used applications of dimensions on technical drawings. Tolerancing may be accomplished either by coordinate tolerances applied to the dimensions or by geometric (positional) tolerancing. Positional tolerancing is especially useful when it is applied on an MMC basis to groups or patterns of holes or other small features in the mass production of parts. This method meets functional requirements in most cases and permits assessment with simple gaging procedures. Most examples in this unit are devoted to the principles involved in the location of round holes bec~use they represent the most commonly used applications. The same principles apply, however, to the location of other features, such as slots, tabs, bosses, and noncircular holes.
Tolerancing Methods A single hole is usually located by means of basic rectangular coordinate dimensions, extending from suitable edges or other features of the part to the axis of the hole. Other dimensioning methods, such as basic polar coordinates, may be used when circumstances warrant.
There are two standard methods of tolerancing the location of holes as illustrated in Fig. 16-91 (p. 550).
1. Coordinate tolerancing refers to tolerances applied directly to the coordinate dimensions or to applicable tolerances specified in a general tolerance note. 2. Positional tolerancing refers to a tolerance zone within which the center line of the hole or shaft is permitted to vary from its true position. Positional tolerancing can be further classified according to the type of modifying symbol associated with the tolerance. These are: • Positional tolerancing, regardless of feature size (RFS) • Positional tolerancing, maximum material condition basis (MMC) • Positional tolerancing, least material condition basis (LMC) These positional tolerancing methods are part of the system of geometric tolerancing. Any of these tolerancing methods can be substituted one for the other, although with differing results. It is necessary, however, to first analyze the widely used method of coordinate tolerancing in order to explain and understand the advantages and disadvantages of the positional tolerancing methods.
550
PART 3
Working Drawings and Design
NO MODIFYING SYMBOL USED
.700 ±.005
I
~
.90?/.005
(A) COORDINATE TOLERANCING
(B) POSITIONAL TOLERANCING- RFS 0 .625
± .003
1$10.010
(C) POSITIONAL TOLERANCING- MMC
Fig. 16-91
-
GIA I
(D) POSITIONAL TOLERANCING- LMC
Comparison of tolerancing methods.
Coordinate Tolerancing Coordinate dimensions and tolerances may be applied to the location of a single hole, as shown in Fig. 16-92. They locate the hole axis and result in either a rectangular or a wedge-shaped tolerance zone within which the axis of the hole must lie. If the two coordinate tolerances are equal, the tolerance zone formed will be a square. Unequal tolerances result in a rectangular tolerance zone. When one of the locating dimensions is a radius, polar dimensioning gives a circular ring section tolerance zone. For simplicity, square tolerance zones are used in the analysis of most of the examples in this section. It should be noted that the tolerance zone extends for the full depth of the hole, that is, the whole length of the axis. This is illustrated in Fig. 16-93 and explained in more detail in a later unit. In most of the illustrations, tolerances will be analyzed as they apply at the surface of the part, where the axis is represented by a point.
Maximum Permissible Error The actual position of the feature axis may be anywhere within the tolerance zone. For square tolerance zones, the maximum allowable variation from the desired position occurs in a direction of 45° from the direction of the coordinate dimensions (Fig. 16-94).
For rectangular tolerance zones, this maximum tolerance is the square root of the sum of the squares of the individual tolerances or, expressed mathematically: X2 + Y 2• For the examples shown in Fig. 16-92, the tolerance zones are shown in Fig. 16-95, and the maximum tolerance values are as shown in the following examples.
V
V.Ol0 2 + .020 2
=
.0224
For polar coordinates the extreme variation is
VA2 + T2 where A T R
=
R tan a
= tolerance on radius =
mean radius
a = angular tolerance
CHAPTER 16
Geometric Dimensioning and Tolerancing
551
SQUARE TOLERANCE ZONE
.620
_j_,___-+--+-'
~.745 DRAWING CALLOUT
TOLERANCE ZONE AT SURFACE
(A) EQUAL TOLERANCES XTREME PERMISSIBLE VARIATION IN POSITION OF AXIS
Fig. 16-93
Tolerance zone extending through part.
.620
l_._____...~l--l
~.740
DRAWING CALLOUT
TOLERANCE ZONE AT SURFACE
(B) UNEQUAL TOLERANCES
MAXIMUM PERMISSIBLE LOCATION FOR POSITIONING CENTER OF HOLE
DRAWING CALLOUT
TOLERANCE ZONE AT SURFACE
(C) POLAR TOLERANCES
Fig. 16-94
Fig. 16-92 Tolerance zones for coordinate tolerancing. (See also below.)
J
.o1o2 + .0102
= .014
EXAMPLE A
Fig. 16-95
J
.o1o2 + .o2o2
= .o224
EXAMPLE B
Tolerance zones for parts shown above in Fig. 16-92.
Square tolerance zone.
EXAMPLE C
552
PART 3
Working Drawings and Design
Thus, the extreme variation in example C is
V(1.25 X 0.17 45)
2
+ .0202
=
1. It results in a square or rectangular tolerance zone .030
Note: Mathematically, A in the above formula should be 2R tan a/2, instead of R tan a, and T should beT cos A/2, but the difference in results is quite insignificant for the tolerances normally used.
Use of Charts A quick and easy method of finding the maximum positional error permitted with coordinate tolerancing, without having to calculate squares and square roots, is by use of a chart like that shown in Fig. 16-96. In the example shown on the previous page in Fig. 16-92A, the tolerance in both directions is .010 in. The extensions of the horizontal and vertical lines of .010 in the chart intersect at point A, which lies between the radii of .013 and .014 in. When these dimensions are interpolated and rounded to three decimal places, the maximum permissible variation of position is .014 in. In the example shown in Fig. 16-92B, the tolerances are .010 in. in one direction and .020 in. in the other. The extensions of the vertical and horizontal lines at .010 and .020 in., respectively, in the chart intersect at point B, which lies between the radii of .022 and .023 in. When these dimensions are interpolated and rounded to three decimal places, the maximum variation of position is .022 in. Figure 19-96 also shows a chart for use with tolerances in millimeters.
Disadvantages of Coordinate Tolerancing The direct tolerancing method has a number of disadvantages, as listed next.
.000 .002 .004
.006
.008
.010
.012
.014
.016
.018 .020
within which the axis must lie. For a square zone this permits a variation in a 45° direction of approximately 1.4 times the specified tolerance. This amount of variation may necessitate the specification of tolerances that are only 70 percent of those that are functionally acceptable. 2. It may result in an undesirable accumulation of tolerances when several features are involved, especially when chain dimensioning is used. 3. It is more difficult to assess clearances between mating features and components than when positional tolerancing is used, especially when a group or a pattern of features is involved. 4. It does not correspond to the control exercised by fixed functional "go" gages, often desirable in mass production of parts. This becomes particularly important in dealing with a group of holes. With direct coordinate tolerancing, the location of each hole has to be measured separately in two directions, whereas with positional tolerancing on an MMC basis, one functional gage checks all holes in one operation.
Advantages of Coordinate Tolerancing The advantages claimed for direct coordinate tolerancing are as follows: 1. It is simple and easily understood and, therefore, it is commonly used. 2. It permits direct measurements to be made with standard instruments and does not require the use of specialpurpose functional gages or other calculations.
0.0
0.05
HORIZONTAL TOLERANCE DIMENSIONS IN INCHES
Fig. 16-96
Chart for calculating maximum tolerance using coordinate tolerancing.
0.1
0.15
0.2
0.25
0.3
0.35
HORIZONTAL TOLERANCE DIMENSIONS IN MILLIMETERS
0.4
0.45
0.5
CHAPTER 16
Geometric Dimensioning and Tolerancing
553
Positional Tolerancing
Material Condition Basis
Positional tolerancing is part of the system of geometric tolerancing. It defines a zone within which the center, axis, or center plane of a feature of size is permitted to vary from true (theoretically exact) position. It ensures achievement of design requirements, offers greater production tolerances, and allows the use of functional gages. A positional tolerance is indicated by the position symbol, a tolerance, and appropriate datum references placed in a feature control frame. Basic dimensions represent the exact values to which geometrical positional tolerances are applied elsewhere by symbols or notes on the drawing. They are enclosed in a rectangular frame (basic dimension symbol) as shown in Fig. 16-97. When the dimension represents a diameter or a radius, the symbol 0 or R is included in the rectangular frame. General tolerance notes shown on the drawing do not apply to basic dimensions. The frame size need not be any larger than that necessary to enclose the dimension. Permissible deviations from the basic dimension are then given by a positional tolerance as described in this unit.
Positional tolerancing is applied on an MMC, RFS, or LMC basis. The appropriate symbol for MMC and LMC follows the specified geometric tolerance and where applicable is placed after the datum reference in the feature control frame. As positional tolerance controls the position of the center, axis, or center plane of a feature, the feature control frame is normally attached to the size of the feature, as shown in Fig. 16-99.
Symbol for Position The geometric characteristic symbol for position is a circle with two solid center lines, as shown in Fig. 16-98. This symbol is used in the feature control frame in the same manner as for other geometric tolerances.
Positional Tolerancing for Circular Features The positional tolerance represents the diameter of a cylindrical tolerance zone, located at true position as determined by the basic dimensions on the drawing, within which the axis or center line of the feature must lie. Except for the fact that the tolerance zone is circular instead of square, a positional tolerance on this basis has exactly the same meaning as direct coordinate tolerancing but with equal tolerances in all directions. It has already been shown that with rectangular coordinate tolerancing the maximum permissible error in location is not the value indicated by the horizontal and vertical tolerances but, rather, is equivalent to the length of the diagonal between the two tolerances. For square tolerance zones this
0
ax
l'$'1 ON.£\
Fig. 16-97
\"
SY'M,[3{()'~
·1,s
!~~-~~1C,.if>----~/ 0
G
8
/,....---~<
M
DESIRED WELD
ROLL)>---~~ FLAT
IO
~ R
Surfacing Welds 7. When the pitch or length of seam is not parallel to the axis of the weld, it must be shown on the drawing (see figure at top of next column).
1. The surfacing weld symbol is used to indicate surfaces built up by welding. Surfaces built up by welding, whether by single- or multiple-pass surfacing welds, are
670
PART 3
Working Drawings and Design
shown by the surfacing weld symbol. The surfacing weld symbol does not indicate the welding of a joint, and hence has no arrow- or other-side significance. This symbol is drawn below the reference line, and the arrow must point clearly to the surface on which the weld is to be deposited.
I
4. Multiple-layer surfacing welds may be specified by using multiple reference lines with the required size (thickness) of each layer placed to the left of the weld symbol.
"
"':"""'--.:-: 12C"C"CA:/-x--r----~·of o~ tqOth aruf. the top .of'·tne mating tooth
Root diameter-RD
The diameter at the bottom of the tooth
14S or zoo RD = PD= PD zoo stub RD = PD= PD-
ZDED Z.314 MDL ZDED ZMDL
14.5° or zoo RD = PD- ZDED + DP zoo stub RD = PD- ZDED = (N- Z) + DP
TO FIND RADII RAND r, SEE TABLE BELOW
(A) APPROXIMATE REPRESENTATION OF INVOLUTE SPUR GEAR TEETH
Fig. 20-21
Methods of drawing involute spur gear teeth.
(B) GRANT'S ODONTOGRAPH REPRESENTATION
Chapter 20
TABLE 20-16
Values for drawing involute spur
gear teeth.
2.51 2.62 2.72 2.82
0.96 1.09 1.22 1.34
12 13 14 15
2.51 2.62 2.72 2.82
0.96 1.09 1.22 1.34
2.92 3.02 3.12 3.22
1.46 1.58 1.69 1.79
16 17 18 19
2.92 3.02 3.12 3.22
1.46 1.58 1.69 1.79
3.32 3.41 3.49 3.57
1.89 1.98 2.06 2.15
20 21 22 23
3.32 3.41 3.49 3.57
1.89 1.98 2.06 2.15
3.64 3.71 3.78 3.85
2.24 2.33 2.42 2.50
24 25 26 27
3.64 3.71 3.78 3.85
2.24 2.33 2.42 2.50
3.92 3.99 4.06 4.13
2.59 2.67 2.76 2.85
28 29 30 31
3.92 3.99 4.06 4.13
2.59 2.67 2.76 2.85
4.20 4.27 4.33 4.39
2.93 3.01 3.09 3.16
32 33 34 35
4.20 4.27 4.33 4.39
2.93 3.01 3.09 3.16
4.20 4.45 4.63 5.06
3.23 4.20 4.63 5.06
36 37-40 41-45 46-51
4.20 4.45 4.63 5.06
3.23 4.20 4.63 5.06
5.74 6.52 7.72 9.78
5.74 6.52 7.72 9.78
52-60 61-70 71-90 91-120
5.74 6.52 7.72 9.78
5.74 6.52 7.72 9.78
13.38 21.62
13.38 21.62
121-180 181-360
13.38 21.62
13.38 21.62
passing through the circular thickness points established on the pitch diameter, starting at the base circle and ending at the top of the teeth. The part of the tooth profile below the base circle is drawn as a radial line ending in a small fillet at the root circle. For a closer approximation of the involute tooth profile, the Grant's odontograph method is used. Lay out the outside, pitch, root, and base circles and circular thickness in the same manner as used in the approximation method. The top portion of the tooth profile from point A to point B is drawn
Belts, Chains, and Gears
733
with the radius R, and the portion of the tooth profile from point B to point C is drawn with the radius r. The values of the radii R and r are found by dividing the numbers found in Table 20-16 by the diametral pitch for inch-size gears or by multiplying the numbers in Table 20-16 by the module for metric-size gears. The lower portion of the tooth from points C to D is drawn as a radial line ending in a small fillet at the root circle. If CAD is used, one tooth is drawn, and the remainder of the teeth may be created using the COPY/REPEAT or ARRAY command.
Working Drawings of Spur Gears The working drawings of gears, which are normally cut from blanks, are not complicated. A sectional view is sufficient unless a front view is required to show web or arm details. Since the teeth are cut to shape by cutters, they need not be shown in the front view (Figs. 20-22 and 20-23 on the next page). ANSI recommends the use of phantom lines for the outside and root circles and a center line for the pitch circle. In the section view, the root and outside circles are shown as solid lines. The dimensioning for the gear is divided into two groups, because the finishing of the gear blank and the cutting of the teeth are separate operations in the shop. The gear-blank dimensions are shown on the drawing, and the gear tooth information is given in a table. The only differences in terminology between inch-size and metric-size gear drawings are the terms diametral pitch and module. For inch-size gears, diametral pitch is used instead of module. The diametral pitch is a ratio of the number of teeth to a unit length of pitch diameter. Diametral pitch
= DP =
.:6
Module is the term used on metric gears. It is the length of pitch diameter per tooth measured in millimeters.
Module
= MDL = -PD N
From these definitions it can be seen that the module is equal to the reciprocal of the diametral pitch and thus is not its metric dimensional equivalent. If the diametral pitch is known, the module can be obtained. Module = 25.4 ..;- diametral pitch Gears currently used in North America are designed in the inch system and have a standard diametral pitch instead of a preferred standard module. Therefore, it is recommended that the diametral pitch be referenced beneath the module when gears designed with standard inch pitches are used. For gears designed with standard modules, the diametral pitch need not be referenced on the gear drawing. The standard modules for metric gears are 0.8, 1, 1.25, 1.5, 2.25, 3, 4, 6, 7, 8, 9, 10, 12, and 16.
734
Part 4
Power Transmissions
fAJ PLAIN STYLE (B) WEBBED STYLE
(C) WEBBED WITH CORED HOLES (D) SPOKED STYLE
Fig. 20-22
Stock spur gear styles.
ROUNDS AND FILLETS R.IO
Fig. 20-23
Working drawing of a spur gear.
For metric gear calculations, we have soft-converted the diametral pitch of the inch-size gears to modules in Table 20-14 (p. 731). This conversion was done for comparison purposes and for use in assignments.
Spur Gear Calculations The center distance between the two shaft centers is determined by adding the pitch diameter of the two gears and dividing the sum by 2.
Center Distance
A 12-DP, 36-tooth pinion mates with a 90-tooth gear. Find the center distance. Pitch diameter
number of teeth + diametral pitch = 36 + 12 = 3.00 in. (pinion) = 90 + 12 = 7.50 in. (gear) =
Chapter 20
Sum of the two pitch diameters = 3.00 in. + 7.50 in. = 10.50 in. Center distance
=
. Ratlo
Belts, Chains, and Gears
=
735
PD of gear PD of pm10n ..
= 8.500 = 4
1/2 sum of the two pitch diameters
2.125 - -10.50 - 5 .25 m. . 2--
or Ratio = 4:1
A 3.18-module, 24-tooth pinion mates with a 96-tooth gear. Find the center distance. Pitch diameter (PD) = number of teeth X module = 24 X 3.18 = 076.3 (pinion) = 96 X 3.18 = 0305.2 (gear) Sum of the two pitch diameters = 76.3 + 305.2 = 381.5 mm
Determining the Pitch Diameter and Outside Diameter The pitch diameter of a gear can readily be found if the number of teeth and the diametral pitch or module are known. The outside diameter (OD) is equal to the pitch diameter plus two addendums. The addendum for a gear tooth other than a 20° stub tooth is equal to 1 -;- DP (U.S. customary) or the module (metric).
A 25° spur gear has a diametral pitch of 5 and 40 teeth. Pitch diameter = N -;- DP =4075 = 8.00 in.
Center distance = 1/2 sum of the two pitch diameters
= 38 1. 5 = 190.75 mm 2
Ratio
OD = PD
+ 2ADD
=
8.00
+ 2 ~p
= 8.00 + 52
The ratio of gears is a relationship between any of
the following:
=
1. Revolutions per minute of the gears 2. Number of teeth on the gears 3. Pitch diameter of the gears
The ratio is obtained by dividing the larger value of any of the three by the corresponding smaller value.
8.40 in.
A 20° spur gear has a module of 6.35 and 34 teeth. Pitch diameter
=N
X MDL
= 34 X 6.35 = 216 mm A gear rotates at 90 r/min and the pinion at 360 r/min.
g
Ratio = 396
= 4 or ratio = 4:1
OD
= PD +
2 ADD = 216 + 2(6.35) = 228.7 mm
References and Source Material 1. ASME Y14.7.1-1971 (R2003), Gear Drawing Standards-Part 1.
A gear has 72 teeth, the pinion 18 teeth. Ratio =
i~ = 4
or ratio
= 4:1
See Assignments 9 through 13 for Unit 20-3 on pages 749-751.
INTERNET CONNECTION Visit this site for information on gear drives (with links to related sites, products, and services) and summarize your findings: http://www.deltadynamics.com/ Report on the information on gears and gear drives given at these sites: http://www.bostgear.com/
A gear with a pitch diameter of 8.500 in. meshes with a pinion having a pitch diameter of 2.125 in.
http://lwww.science.howstuffworks.com/
736
20-4
Part 4
Power Transmissions
POWER-TRANSMITTING CAPACITY OF SPUR GEARS
Selecting the Spur Gear Drive
Gear drives are required to operated under such a wide variety of conditions that it is very difficult and expensive to determine the best gear set for a particular application. The most economical procedure is to select standard stock gears with an adequate load rating for the application. Approximate horsepower (kilowatt) ratings for spur gears of various sizes (numbers of teeth), at several operating speeds (revolutions per minute), are given in catalogs with the spur gear listings. Ratings for gear sizes and/or speeds not listed may be estimated from the values shown in Fig. 20-24 Pitch-line velocities exceeding 1000 ft/min. (5 m/s) for 14.SO PA (pressure angle), or 1200 ft/min (6 m/s) for 20° PA, are not recommended for metallic spur gears. Ratings are listed for speeds below these limits. The ratings given (or calculated) should be satisfactory for gears used under normal operating conditions, that is, when they are properly mounted and lubricated, carrying a smooth load (without shock) for 8 to 10 hours a day. The charts shown in Fig. 20-24 indicate the approximate horsepower (kilowatt) ratings of 16- and 20-tooth steel spur gears of several tooth sizes operating at various speeds. They may be used to determine the approximate diametral pitch or module of a 16- or 20-tooth steel pinion that will carry the horsepower (kilowatts) required at the desired speed. The intersection of the lines representing values of revolutions per minute and horsepower (kilowatts) indicates the approximate gear diametral pitch (module) required. The number of teeth normally should not be less than 16 to 20 in a 14.SO pinion, or less than 13 in a 20° pinion. Ratings shown for spur gears in catalogs normally are for class 1 service. For other classes of service, the service factors in Table 20-17 should be used.
TABLE 20·17
Service class and factor for spur gears.
1. Determine the class of service. 2. Multiply the horsepower (kilowatts) required for the application by the service factor. 3. Select spur gear pinion with a catalog rating equal to or greater than the horsepower (kilowatts) determined in step 2. 4. Select driven spur gear with a catalog rating equal to or greater than the horsepower (kilowatts) determined in step 2.
Select a pair of 20° spur gears that will drive a machine at 150 r/min. Size of driving motor= 25 hp, 600 r/min. Service factor = 1. SOLUTION
Since the service factor is 1, we do not need to increase or decrease the design horsepower. Refer to the charts in Fig. 20-24A, which show design data for 20° spur gears having 16 and 20 teeth. Selecting a pinion having 16 teeth and reading vertically on the column showing 600 r/min to horsepower rating of 25, we find that the required DP is 4. (Select the DP equal to or greater than the horsepower required.) • Pinion: N= 16, DP = 4, PD = 16 + 4 = 4.000 in. • Ratio 4:1 • Gear: N = 16 X 4 5 64, DP = 4, PD = 64 + 4 = 16.000 in.
A 5-hp, 1200-r/min motor is used to drive a machine that runs 8 hours a day under moderate shock. If the machine is to run at 200 r/min and at the capacity of the motor, what spur gears would you select? SOLUTION
The operating conditions of the machine are such that the machine fits into the service class 2 and requires a service factor of 1.2. Therefore: Horsepower required for design purposes = 5 hp X 1.2
= Class III
Continuous 24-hr duty with moderate shock load
1.3
Intmmttent
0.7
per· hr, witl;t
Class V
not over 30-min lQad (Qn shQCk)
Hand operation, limited duty, with smooth load (on shock)
6 hp
The pinion will be mounted on the motor and will run at 1200 r/min. Selecting a 20° pinion having 16 teeth, refer to Fig. 20-24A to find the required DP. Reading vertically on the 1200-r/min line and horizontally at 6 hp, we find that the required DP is 8. • Pinion: N = 16, DP = 8, PD = 16 + 8 = 2.000 in.
0.5
*Heavy shock loads and/or severe conditions require the use of higher service factors. Such conditions may require factors of 1.5 to 2.0 or greater than required for Class I service.
• Gear: N = 16 X
~O~O
= 96, DP = 8,
PD = 96 + 8 = 12.000 in.
Chapter 20
16- AND 20-TOOTH STEEL SPUR GEARS
14.50
200 70
16- AND 20-TOOTH STEEL SPUR GEARS
20
50 40 30
16
L ~v~ v -_,.,
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737
Belts, Chains, and Gears
I.OOlnOOO Ll)0 -NNM'¢1ll"Q
00
000000000000
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g~~g:eg~~g~gg -
REVOLUTIONS PER MINUTE 14.50 PRESSURE ANGLE
--NMM
REVOLUTIONS PER MINUTE 200 PRESSURE ANGLE (A) DIAMETRAL PITCH SELECTION CHART
50 40 30 20
..1~
15 10
s U'l
~...J
1.5 II
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0.8
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0.5 0.3
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200 PRESSURE ANGLE (B) MODULE SELECTION CHART
Service class and factor for spur gears.
./
~
REVOLUTIONS PER MINUTE
14.50 PRESSURE ANGLE
Fig. 20-24
v
~~{ 1/t/.... [I '~I
1--
v
IL /1. l ..a--1.6v/
.6 v
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REVOLUTIONS PER MINUTE
~
~vv ~.'-!o/ .
5 4 3
f-
n=---.:1,-- A DJ US TABlE TRUNNION WORKPIECE
?)/??7/?J?h
(A) SHAPER SHOWING QUICK-RETURN MECHANISM
.J
w
>
u 2.00f7 I 1.00[711
~-~4~0~~--------~P~O~S~IT~I~O~N~O~F~T~R~U~N~N~IO~N~----------.J (B) MOTION DISPLACEMENT DIAGRAM
Fig. 22-43
Shaper using Whitworth quick-return mechanism stroke.
821
822
PART 4
Power Transmissions
Assignments for Unit 22-7, Ratchet Wheels
18. Lay out a ratchet assembly using a U-shaped pawl with a ratchet wheel. The ratchet wheel is to have 24 teeth; OD of 0146 mm; hub 048 mm; shaft 032.5 mm; keyseat to suit; width of teeth 12 mm; depth of teeth 10 mm; and the hub is to extend 16 mm on one side. Scale 1: 1. Show two views. 19. Ratchet and Crank Mechanism. Lay out a one-view drawing of the ratchet design shown in Fig. 22-44. Two
pawls are used, a drive pawl as shown and a holding pawl held in position by a spring. Using crank rotation positions every 22-5°, plot the path of the end of the drive pawl. Use your judgment for dimensions not shown. Scale 1: 1. 20. Lay out the pinion and pawl shown in Fig. 14.36 (p. 422), but show the assembly in the reverse locking position. Scale 2:1.
25
HOLDING PAWL---.... (DROPS IN AND
RATCHETJUSTBEFOIRE'~
DRIVE PAWL)
SPRI
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