fundamentals of dimensional...

FUNDAMENTALS OF DIMENSIONAL METROLOGY

I=OURTH EDITION

CONTENTS

..................................... .. x

MEASUREMENT AND METROLOGY ............ '1 1-1 Measurement as the Language of Science ............................ 1 1-2 The Uses of Measurement ......................................... 3 1-3 Communications about Measurement .............................. .5 1-4' Acts and Applications of Measurement ............................. 7 1-5 Codification of Measurement ...................................... 8 1-6 A Look Ahead .................................................. 9

Summary ..................................................... 10 End-of-Chapter Questions ....................................... 10

LANGUAGE AND SYSTEMS OF MEASUREMENT .. '12 2-1 How Big? ..................................................... 13 2-2 How Far Apart? ........................................... ' ..... 14 2-3 From End to End .............................................. :15 2-4 Accuracy, Precision, and Reliability ................................ 19 2-5 Accuracy versus Precision ....................................... 22 2-6 Evolution of Standards .......................................... 22 2-7 Origin of the Metric System ...................................... 24 2-8 Legality of the Metric System in the United States .................... 26 2-9 The International Inch ........................................... 26 2-10 Fundamental Criteria ........................................... 26 2-11 \ The Best System ................................................ 28 2-12 Practical Criteria .............................................. .28 2-13 The Decimal-Inch System ........................................ 29 2-14 Metrological Considerations ...................................... 29 2-15 Communications Considerations .................................. 30 2-16 Computational Considerations .................................... 30 2-17 Rounding off Numerical Values ................................... 31

Summary ...................................................... 37 End-of-Chapter Questions ...................................... .38

MEASUREMENT AND TOLERANCES .......... 42 3-1 Meaning of Tolerance .......................................... .42 3-2 Geometric Dimensioning and Tolerancing ......................... .43

v

VI • Fundamentals of Dimensional Metrology

~ 3-3 Tolerancing .................................................... 45


STATISTICS AND METROLOGY ............. . 5~ 4-1 Basic Statistics ................................................ .54 4-2 Probability .................................................... 58 4-3 Acceptance Sampling ........................................... 61


MEASUREMENT WITH GRADUATED SCALES AND SCALED INSTRUMENTS ............... 68 5-1 The Steel Rule ................................................. 70 5-2 The Role of Error ............................................... 73 5-3 Scaled Instruments ............................................. 78 5-4 Calipers: The Original Transfer I?struments ......................... 85

Summary .................. ~ .................................. 98 End-of-Chapter Questions ....... '.' ............................. 100

", \,t

VERNIER INSTRUMENTS '\'\

. ~ ............. .. t06 6-1 Vernier Instruments ............. : .. : ............................ 106 6-2 Vernier Caliper ...................•........................... 109 6-3 Vernier Depth Gage ............................................ 119 6-4 Vernier Height Gage ........................................... 120 6-5 Three Elements of Measurement ................................. 128

Summary .................................................... 128 End-of-Chapter Questions ...................................... 129

MICROMETER INSTRUMENTS ............. . 1~1 7-1 Micrometers .................................................. 131 7-2 Using the Micrometer .......................................... 144 7-3 Care of Micrometers ........................................... 150 7-4 Variations of Micrometers ....................................... 155


DEVELOPMENT AND USE OF GAGE BLOCKS ... 160 8-1 Development of Gage Blocks .................................... 160 8-2 Modern Gage Blocks ........................................... 166 8-3 Calibration of Gage Blocks ...................................... 172 8-4 Gage Block Applications ........................................ 174 8-5 Combining Gage Blocks ........................................ 181


Contents • VII

CHAPTER 9 MEASUREMENT BY COMPARISON .......... 204 9-1 The Dial Indicator ............................................. 208 9-2 Selection of a Dial Indicator ..................................... 228 9-3 Use of Dial Indicators .......................................... 230 9-4 Calibration of Dial Indicators .................................... 230 9-5 Accessories and Attachments .................................... 232 9-6 Constructive Use of Error ....................................... 240

Summary .................................................... 240 End-of-Chapter Questions ..................................... .243

HIGH-AMPLIII=ICATION COMPARATORS ....... 24'7 10-1 High-Amplification Comparators .................. , ............ .249 10-2 Electronic Measurement ........................................ 253 10-3 Applications Unique to Electronic Measurement ..................... 268 10-4; Metrological Advantages of Multiple Scales ....................... .270

Summary ................................................... .278 End-of-Chapter Questions ...................................... 280

PNEUMATIC MEASUREMENT .............. 28S 11-1 Background ................................................. .283 11-2 From History to Semantics ...................................... 284 11-3 Principles of Pneumatic Instruments .............................. 284 11-4 Application of Pneumatic Metrology ............................. .288 11-5 Metrological Advantages of Pneumatic Comparators ............... .294 11-6 Reading the Pneumatic Comparator ............................... 295


CALIBRATION ...........•............ .S04 12-1 The Role of Error .............................................. 305 12-2 Basic Calibration Procedure ..................................... 309 12-3 Record and Correct Calibration Readings ........................... 328

Summary ................................................... .331 End-of-Chapter Questions ...................................... 331

OPTICAL II=LATS AND OPTICAL ALIGNMENT ... SS6 13-1 Importance of Standards ........................................ 338 13-2 Light Waves as Standards ....................................... 338 13-3 Measurement with Optical Flats ................................. 345 13-4 Applications of Optical Flat Measurement ......................... 358 13-5 Principles of Optical Metrology .................................. 362 13-6 Alignment Telescope-Straightness Measurement ................... 365 13-7 Optical Squares-Squareness .................................... 380 13-8 Sight Level-Plumbness ........................................ 388 13-9 Optical Polygons-Angles ...................................... 393 13-10 Jig Transit-Planes ............................................. 399

viii • Fundamentals of Dimensional Metrology

~ 13-11 Theodolite-Angles and Planes ................................. .404 13-12 Beyond Vision ................................................ 407


REFERENCE PLANES ..................•. 418 14-1 Background ................................................. .418 14-2 Flatness ..................................................... .419 14-3 Perpendicularity ............................................. .423 14-4 Modern Reference Planes ...................................... .424 14-S How Flat Is Flat? ..................................... , ....... .432

Summary ................................................... .436 End-of-Chapter Questions ..................................... .437

ANGLE MEASUREMENT .....•............ 439 IS-1 IS-2 IS-3 IS-4 IS-S IS-6 IS-7 IS-8 IS-9 IS-10

Basic Geometry .............................................. .441 Angle Measurement ; ......................................... .444 The Level .................. r ....................... ' ......... 451 The Protractor ................................................ .462 Trigonometric Functions ....................................... .470 Sine Bars and Plates .............. \ ........................... .473 Mechanical Angle Measurement .... ~ ........................... .483 Measurements to Seconds of Arc .. : .. .' ........................... .487 Accuracy and Precision in Angle Measwement .................... .488 The Degree, Grad, and Gon ......... : .......................... .491 Summary .................................................... 493 End-of-Chapter Questions ..................................... .494

SURFACE MEASUREMENTS ............... 499 16-1 Background ................................................. .501 16-2 Surface Evaluation, Stylus Method .............................. .502 16-3 Numerical Values for Surface Assessment ........................ .510 16-4 Surface Texture Specimens ..................................... .514 16-S Surface Evaluation, Other Methods ............................... 516 16-6 Roundness ................................................... 517 16-7 Notation for Surface Assessment ................... -.............. 520


COORDINATE MEASURING MACHINES ....... 525 17-1 Background .................................................. 526 17-2 The Role of Coordinate Measuring Machines ....................... 527 17-3 Types of Coordinate Measuring Machines ......................... 527 17-4 Modes of Operation ............................................ 529 17-S Metrological Features ......................................... .539 17-6 Coordinate Systems ........................................... .540

Contents. IX

17-7 Future Expectations ............................................ 540 Summary .................................................... 540 End-of-Chapter Questions ...................................... 541

CHAPTER 1a: OPTICAL METROLOGY ................... 544 18-1 Principles of the Microscope ..................................... 545 18-2 Applications .................................................. 549 18-3 Comparison of Optical Comparators and Microscopes ............... 552 18-4 Optical Considerations ......................................... 553 18-5 Applications of the Optical Comparator ........................... 558 18-6 Accuracy of Optical Comparators ................................ 567 18-7 Machine Vision Systems ....................................... .571


Decimal Equivalents ................................................ .581 Conversion Tables .................................................. .583 Conversion Table: Inches toMillimeters ................................. 583 Conversion Table: Millimeters to Inches ................................ .585 Geometric Optics .................................................... 587

Geometric Optics .............................................. 587 Single Lens Magnifiers .................. , ...................... 593 Summary .................................................... 596 ,

Prefixes Used as Multipliers .......................................... .597 Recommended Pronunciation of Prefixes ................................ 597 Bibliography ...................................................... .598

............................ .. S99 . . . . • . . . . .1115

INDEX

Abbe, Ernest, 110 Abbe's Law, 110,204 Abstraction, 443

A

Acceptance sampling, 61-65, 62-67 Accessories, 84, 85 Accuracy, 5, 19-22, 101, 136-138, 204, 275

in angle measurement, 488-491, 488-491 of optical comparators, 568-571 versus precision, 22

Accuracy calibration, 323 of dial indicator, 324 of high-amplification comparators, 324-327,

326-327 Additive tolerances, 50 Air film, 178 Air gages, 248-249 Air-wedge configuration, 350, 350-351 Alidade, 400-401 Alignment bars, 403 Alignment collimator, 379, 379-380 Alignment target, 379, 380 Alignment telescope, 365, 365

auto collimation, 376, 378 auto-reflection, 370, 374-375

targets, 370, 373, 375-377 infinity, measuring, 379, 379-381 instrument calibration, 380 line of sight telescope, 365, 366, 367 optical limitations, 368-369, 369 projection, 376, 378-379, 379 targets, 369, 370-372

American National Standards Association (ANSI), 510

American Society of Mechanical Engineers (ASME), 510

American Standards Association (ASA), 29

Amplification, 206, 206-207, 207, 215, 216, 217 Amplitude density function, 514, 515 Analog instruments, 249 Angle measurement, 439-441, 440

accuracy and precision in, 488-491, 488-491 basic geometry, 441-443, 441-444 chapter summary, 493-494 the degree, grad, and gon, 491-492, 492 instruments for, 443-451, 445-451 the level, 451-452, 452-463, 454-461 measurements to seconds of arc, 487, 487-488 mechanical, 483-487, 484-486 the protractor, 462, 463-471, 464-469 sine bars and plates, 473-483, 473-483 trigonometric functions, 470-473, 471-473

Angles, 442-443, 442-444 Angular displacement, 441 ANSI! ASME B89.1.12M, 527 ANSI! ASQC Z1.4, 64-65, 65 ANSIj ASQC Z1.9, 65, 66-67 ANSI B46.1, 500, 501, 510-511, 514, 516 ANSI B89.31, 519 ANSI Y14.5, 519 ANSI Y14.36-1978, 503, 520 Aperture, 592 AQL plans, 62 Arithmetical progressions, 164, 166, 166 Arithmetic average roughness, 511, 511 ASA Z25.1, 33 ASAZ75.1,75 ASME Y14.5M, 43, 50 Asperities, 501, 505 Attribute gaging, 193, 195, 195-196 Attribute inspection, 559 Autocollimation, 376, 378, 411-412 Autocollimator, 444 Autocorrelation function, 514

615

616 • Fundamentals of Dimensional Metrology

Automatic mode, 538 Auto-reflection, 370, 374-375

targets, 370, 373, 375-377 Average outgoing quality limit, 62-63, 63 Average peak-to-valley roughness, 512, 513 Average spacing of roughness peaks, 512, 513 Average total inspection, 63, 63 Azimuth axis, 392

B Back-pressure comparators, 284, 284-285, 285 balanced systems, 285-286, 286-287 rate-of-flow systems, 286-288, 287-288

Balanced indicator dials, 222-223, 223 Beam trammel, 94, 94 Bearing length and bearing curve, 514, 515 Bearing length ratio, 512, 513 Bench micrometer, 156, 156 Best fit condition, 537-538 Best scale for measurement, 276 Bias, 76-78, 77-78, 152 Bifilar reticle, 549 Bilateral tolerancing, 45-48, 46-47 Binocular microscope, 549, 550 Binomial probability distribution, 59 Black granite, 427 Blade micrometer, 155, 155 Blades, 82-a4, 84 Bridge-type CMM, 527, 528, 530 Bridging, 185 Bubble instruments, 451

c Calibration, 304-305, 305

accuracy calibration, 323 of dial indicator, 324

basic procedure for, 309-310, 310 chapter summary, 331 of dial indicators, 319-323, 320-323 error

role of, 305-308, 307-309 visualizing by graphing, 311-313, 312

of gage blocks, 172-173, 173 high-amplification comparators, 324-327,

326-327 minimizing error with, 318, 319

"'.

~ internal instrument, 319, 320 of master standards and traceability, 327-328 of micrometers, 152-153, 153-154,316-317,317 observational variable in, 317-318 of polygon, 394, 398, 399, 399 rotary table, 394, 395-398 rounding off results, 329 variables to investigate, 313-315, 313-316 of vernier caliper, 310-311, 311 wear considerations, 329-331, 330 of working standards, 327, 328

Caliper principle, 490-491, 491 Calipers, 85-86, 85-87. See also Micrometers

dial, 117, 118 dividers, 87-89, 87-90 electronic digital, 117, 119, 119 gaging pressure importance, 93 inside and; outside, 89-90 layout insiruments, 94-95, 94-96 role of feel, 90-92, 91-92

\.

slide caliper, 95\'i-98, 96-97 use of, 92-93, 9a vernier, 109.:.110: 110

Cam measureme\t, 8 Cantilever-type CMM, 527, 528, 530 Cardinal numbers, 15 Casual contact, 321, 322 Center head, 81-82, 83 Centerline average, 511 Central tendency, 54-56 Chart-gage inspection, 570-571, 571 Cheese cutter, 357, 358 Chromatic aberration, 591, 591 Circle, 440-441 Clinometer, 460-461, 460-463 Coated surface, 346, 348 Collimator, 444 Collinear, 363 Column-type CMM, 527, 528, 530 Combination square, 79-80, 80 Commercial grade flats, 346 Comparators, 212, 213, 234. See also High-

amplification comparators; Optical comparator; Pneumatic comparators

accuracy of, 218-220, 219-221 resolution of, 217, 218

11 I

Comparison measurement, 204 Complementary angles, 442, 442 Complement of an angle, 477-479, 478-479 Compound angles, 480-482, 481-482 Compound sine angle plate, 482, 482-483, 483 Conclusion, 443 Conduction, 267 Conjugate points, 590 Consumer's risk, 62 Contact interference, 430 Contact points, 232, 233 Continuous indicator dials, 223-224, 225-226 Continuous probability distributions, 60 Convection, 266 Conversion table, 583-586 Coordinate measurement, 7 Coordinate measuring machines (CMM), 525, 526 bridge type, 527, 528, 530 cantilever type, 527, 528, 530 chapter summary, 544 column type, 527, 528, 530 coordinate systems, 541-542 direct computer control, 535-536 future expectations, 543-544 gantry type, 528, 529, 530 horizontal arm type, 528, 529, 530 metrological features, 540-543, 542-543 modes of operation, 529, 531 operational modes, 538-539 part programs, 536-538, 537-540 portable arm CMMs, 543, 543 probes

calibration of, 533-534, 534 noncontact-type, 534-535, 535-536 types of, 529, 531-533, 532-534

role of, 526-527, 527 software packages, 536

Coordinate systems, 541-542, 542-543 Correlated error, 308 Cosine error, 238, 239, 257-259, 258-260 Counterclockwise indicator dials, 225-226, 227 Cramping, 152 Critical angle, 588 Cross axis telescope, 400 Cross level, 389, 391 Crowned plate, 434, 434-435, 435

Cup mount, 367 Cutoff, 508-510, 509-510 Cylindrical gage head, 259-260, 262 Cylindrical square, 446-448, 447-448

D

Index • 617

Decimal equivalents, 581-582 Decimal-inch system, 29, 30-32 Degradation of workmanship, 420-421 Dependent error, 308 Depth gage, 78-79, 78-79

vernier, 119, 119-120, 120 Depth of focus, 368 Descriptive statistics, 54-58, 57-58 Determinate error, 305 Diabase, 427 Dial calipers, 117, 118 Dial index head, 484, 484-485, 485 Dial indicators, 208-209, 209-210

accessories and attachments for, 232-233, 233 accuracy calibration of, 324 calibration of, 230, 319-323, 320-323 dials of, 220, 221-222 balanced, 222-223, 223 continuous, 223-224, 225-226 counterclockwise, 225-226, 227

functional features, 210-211, 210-212 indicator range, 226-228, 227 metrological features, 211-213, 212-214, 242 resolution, 217, 218 scale discrimination, 209-210 selection of, 228-229, 229-230 sensitivity of, 215, 216, 217 use of, 230, 231-232

Diascopic projection, 558 Difference measurements, 268-269, 269-270 Differential comparator, 268 Differential measurement, 268 Digital instruments, 249, 276-278, 278 Digital micrometer, 139, 141-143,142-143 Dihedral angle, 480 Dimensional measurements, 14-15 Dimensional metrology, 3 Direct computer control, 535-536 Direct measurement, 204, 559-561, 560-562

accuracy of, 569-570, 570


chart-gage inspection, 570-571, 571 Dirt, 150 Disc micrometer, 155, 155 Discrepancy, 305 Discrete probability distributions, 59 Discrimination, 70, 72, 136-138 Dispersion, 56-57 Displacement method, 18-19, 111, 111-112, 112 Dispositive projection, 558 Dividers, 87-89, 87-90 Dividing engines, 490 Double sphere optical square, 384, 384 Dynamic measurement, 253

E Effective magnification, 548-549 Egyptians, 23 Einstein, Albert, 340, 408, 587 Electromagnetic spectrum, 347 Electronic amplifier and meter, 260-262, 263 Electronic digital calipers, 117, 119, 119 Electronic measurement, 252-253, 254

difference measurements, 268-269, 269-270 differential measurement, 268 electronic amplifier and meter, 260-262, 263 gage head, 256, 256-257

cylindrical, 259-260, 262 frictionlep.s, 259, 261 probe-type, 256-259, 257-258

generalized measurement system, 254-255, 255-256 power amplification for, 253-254 stands for electronic comparators, 263-267, 264-266 sum measurements, 269, 270

Ellstrom, Hjalmar, 161-162 End standards, 161, 189-190, 190-191 Episcopic projection, 558 Error, 5, 70, 73-75

accumulation of with dividers, 89, 89-90 avoidance in micrometers, 146-147 bias, 76-78, 77-78 in calibration, 305-308, 307-309 constructive use of, 240, 243 cosine, 238, 239, 257-259, 258-260 eccentricity, 489-490 of form, 501, 502

"".

,~

manipulative, 76, 77 observational, 75-76, 77

Face angles, 480 False triggers, 532 Feature, 17

F

Feel, 90-92, 91-92, 317-318 Field of view, 368, 549 Fixed arm-type CMM, 529 Fixed bridge-type CMM, 527 Flange cup, 367 Flatness, 419-423, 420-424, 432-435, 432-436 Flaw, 501, 502 Focal length, 590 Ford, Henry, 160 Form tolerance, 44 Four-way probes, 532 Frequency, 508-510,509-510 Frictionless gag/,: head, 259, 261 Fringe bands, 33~, 341-345, 342, 344-345

conversion tablt, 361 measurement of'parallelism, 354-355, 355-356 measurement offmall height differences,

356-358,357-359 patterns and surface inspection, 351-353,

351-353 which way should bands run?, 353, 353-354, 354

G Gage blocks:

angle measurement with, 487, 487-488 applications, 174, 174-176 arithmetical progressions, 164, 166, 166 attribute gaging with, 193, 195, 195-196 calibration of, 172-173, 173, 327 care of, 174-177, 177 chapter summary, 198-200 combining, 181-186, 183-185 development of, 160-162, 161 end standards, 189-190, 190-191 first inch sets, 162-163, 163 grades, 169-170, 170-171 holders for, 186-189, 187-190 Johansson's original standard, 162, 162

Ii ,

light waves to end standards, 163-164, 164-165 macrogeometry and micro geometry, 167-169,

167-169 materials for, 166-167 precalibrated indicator technique, 195-197,

197-199 setup, layout, assembly, 191-193, 192-194 sizes and shapes, 170, 172 using with sine instruments, 479, 479-480, 480 wear allowance, 172 wear blocks, 177 wringing, 177-181, 177-183

Gage head, 256, 256-257 cylindrical, 259-260, 262 frictionless, 259, 262 probe-type, 256-259, 257-258

Gagemaker's flats, 346 Gages, 7, 248, 248-249 Gaging element, 288-291, 290-292 Gaging force, 146,259 Gaging pressure, 93, 146 Gantry-type CMM, 528, 529, 530 Gaussian distribution, 60-61, 61 Gear tooth vernier caliper, 127-128, 128 Generalized measurement system, 254-255, 255-256 Geometric dimensioning and tolerancing, 43-44 Geometric optics:

aberrations, 590-592, 591 geometrical consideration, 587-588, 588-590,

590 optical magnification, 592, 592-594 single lens magnifiers, 593-595, 594-595 waves and rays, 587, 587

Geometry, 441-443, 441-444 GGG-P-463,428 Glossary, 599-613 Gon,492 Go / no-go gage, 330 Graduated scales, 68-70 Graduated scales and scaled instruments:

accessories for, 84, 85 blades for, 82-84, 84 calipers, 85-98, 85-98 center head, 81-82, 83 chapter summary, 98-100

combination square, 79-80, 80 depth gage, 78-79, 78-79 error, 73-75, 76-78, 78 metrological data for, 100 protractor head, 81, 82 reliability check list for, 99 square head, 80-81, 80-82 steel rules, 70-73, 71, 73, 101-102

Grand master, 173

Index • 619

Granite surface plates, 424, 426-427, 428 classes and grades of, 428-429 functional considerations, 431, 431-432, 432 hardness of, 430, 430-431 plate selection, 428 production of, 429, 429-430, 430 stiffness, importance of, 427-428

Graphing errors, 311-313, 312

Hardness, 430, 430-431 Height gage:

setup, 263

H

vernier, 120-128, 121-128 Heisenberg's Uncertainty Principle, 305 Hermaphrodite calipers, 94-95, 94-95 High-amplification comparators, 247, 248, 250

accuracy calibration of, 324-327, 326-327 analog versus digital instruments, 249 chapter summary, 278-280 electronic, 252-262,254-263

applications unique to, 268-269, 269-270 stands for, 263-267, 264-266

gages versus measurement instruments, 248, 248-249

mechanical comparators, 249-251, 251 metrological data for, 279 minimizing observational errors with, 318, 319 multiple scales, advantages of, 270-278,

272-278 reed-type comparator, 251-252, 252-253

Hoke, William E., 162 Horizontal arm-type CMM, 528, 529, 530 Human error, 306 Hypotenuse, 477 Hysteresis, 288


Illegitimate error, 305 Image, 588

I

Inch sets, 162-163, 163 Independent error, 308 Indeterminate error, 305 Indicating micrometer, 156 Indicator head, 256 Indicator holder, 124 Indicator stands, 233-234, 236, 237-240, 238-239 Industrial Revolution, 419 Infinity, 379, 379-381 Initial line, 441 Inside calipers, 89-90 Inspection, 8, 559 Interchangeable manufacture, 160 Interchange method, 18, 110-111 Interferometer, 362, 407-408 Interferometry, 407-408, 408 Internal measurement instruments, calibrating,

319,320 .. International inch,· 26 ISO 10012, 309

Jig level, 399 J

Jig transit, 364-365, 399, 399-400 applicatiops, 401-402, 401-404 construction of, 400-401 cross-axis feature, 400, 401 leveling, 401

Jig transit telescope square, 400, 401 Johansson, Carl E., 161-164, 166, 487

K Kinematic mechanics, 234 Kurtosis, 514, 515

Lag, 285 Lamphouse, 370

L

Language and measurement, 12-13 accuracy, precision, reliability, 19-22 accuracy versus precision, 22 act of meflsurement, 17-19 best system of measurement, 28

~ chapter summary, 37-38 choosing best system, 28 communications considerations, 30 computational considerations, 30-31 decimal-inch system, 29 from end to end, 15, 17 evaluating measurement systems, 26-28 evolution of standards, 22-24 how big?, 13 how far apart?, 14-15 international inch, 26 legality of metric system in US., 26 metrological considerations, 29 origin of metric system, 24 rounding-off numerical values, 31-37 what is the real issue?, 34-35, 37

Laser alignment instrument, 409 Laser beam/inder screen, 411, 412 Lasers, 408i.412, 410-411 Lay, 502, 503

\'. Layout instrumerts, 94-95, 94-96 Lead, 316 .~

Least material:coftdition (LMC), 44 Ledges, 431, 431-'i2 Leonardo da VinCl, 501 Level,451

adjustment of, 455-456, 455-457 clinometer, 460-461, 460-463 error due to temperature, 454 micrometer water level, 459, 459-460 precision and sensitivity of, 452, 452-454,

454 reading, 455, 455 reversal technique for, 456-457, 457 use of, 457-459, 458

Level comparator, 457, 458 Leveling depth, 512, 513 Leveling head, 392, 401 Light waves, 163-164, 164-165,336,337

as standards, 338-345, 339-345, 439 Limit mode, 119 Line of collimation, 363 Line of measurement, 15 Line of sight, 363 Line of sight telescope, 364-365, 366, 367 Line standards, 161

Loading, 215, 254 Lobes, 517-518, 518 Location tolerance, 44 LTPD plans, 62 LURD convention, 369, 369 LVDT (linear-variable-differential transformer),

254,256

M Machine coordinate system, 542 Machine vision systems, 571-573, 572-574 Macrogeometry, 167-169 Macrometrology, 337 Magnification ratios, 506 Manipulative error, 76, 77, 115, 116 Manual computer-assisted mode, 529 Manual mode, 529,538 Master flats, 346 Master standards, accuracy calibration of,

327-328 Maximum material condition (MMC), 43, 44, 45 Maximum peak-valley roughness, 512, 513 Mean, 54

. Measured point, 72-73 Measurement:

acts and applications of, 7-8 angle, 443-451, 445-451 chapter summary, 10 codification of, 8-9 communications about, 5, 7 evaluating systems of, 26-31 with gage blocks, 160-200 with graduated scales and scaled instruments,

68-100 and language, 12-38 as language of science, 1-3 with micrometers, 131-157 milestones in, 25 movement in, 213-215,215 with optical flats, 345-358, 348-359 pneumatic, 283-300 power amplification for, 253-254 surface, 499-520 three elements of, 128, 205 and tolerances, 42-51 uses of, 3-5

Index • 621

with vernier instruments, -106-129 Measurement by comparison, 18,204-205, 205

angles, 564-565 chapter summary, 240-241, 243, 243 contours, 565-566 dial indicator, 208-228, 210-216, 218-227

accessories and attachments for, 232-233, 233-237

calibration of, 230 selection of, 228-229, 229-230 stands, 233-234, 236, 237-240, 238-239 use of, 230, 231-232

error, constructive use of, 240, 243 linear, 564, 565 role of amplification, 206, 206-207, 207 separation of the standard, 207-208, 208-209 with sine bars, 475-476, 476-477

Measurement by translation, 18-19,561-564, 562-564

accuracy of, 569 Measurement instruments, 248, 248 Measuring rolls, 470 Mechanical indexing, 483

dial index head, 484, 484-485, 485 metrology of, 486-487 plain index head, 485-486, 486

Median, 55 Menderlhall Act, 26 Mensuration, 3 Meter, 339 Methods divergence, 511 Metric system, 3, 3, 8, 26, 163

legality of in U.S., 26 origin of, 24

Metrology. See also Measurement coordinate measuring machines, 540-543,

542-543 defined, 1, 3 optical, 547-576, 548-574 optics applications, 336-337 pneumatic, 283-301 and statistics, 53-67 surface, 499-520

Michelson, AlbertA., 163, 338, 440 Microgeometry, 167-169 Micrometers, 131-133, 132-133

-


accuracy, precision, discrimination in, 136-138, 137

calibration of, 316-317, 317 care of, 150-152 chapter summary, 156-157 construction of, 138, 138, 140 controlled force feature, 144-146, 146 digital, 139, 141-143, 142-143 error avoidance, 146-147 holding, 144, 145 inspection of, 152-153, 153-154 measuring cylindrical parts with, 147-150,

149-151 measuring flat parts with, 147, 147-148 optical, 392-393 readings from, 134-136, 134-136 setting standards, 153, 153, 155 variations of, 155, 155-156, 156 vernier, 139, 141 what is measured by, 143-144, 144-145

Micrometer-water level, 459, 459-460 Microscope, 548, 548

applications, 552-554, 552-555 effective magnification, 548-549 measuring,549,551 micrometer eyepiece, 549, 551, 552 reticles, 549, 551 stage illu~ination, 551-552

Midrange, 55-56 Mils,491 MIL-STD-120, 120, 248, 317, 476 Mode, 55 Monochromatic light, 348, 348 Morley, Edward W., 163, 338 Mounting cup, 367 Multiple-sample measurements, 320 Multiple scale selection, 270-278, 272-278 Multipliers, 15 Multisensor systems, 572-573, 574

N N apier, John, 470 Napoleon Bonaparte I, 24 National Institute of Standards and Technology

(NIST), 22, 173, 179, 339 Normal probability distribution, 60-61, 61

.,.

o Observational error, 75-76, 77

minimizing with high-amplification comparators, 318, 319

Offset scriber, 122, 123 Operating characteristics curve, 62, 62 Optical alignment, 337

geometry of, 363-365, 363-365 Optical comparator, 547-548

accuracy of, 568-571 advantages over microscope, 555 basic optics system, 556-558, 556-558 direct measurement, 559-561 measurement by comparison

angles, 564-565 contours, 565-566 linear, 564, 565

measurel1)oent by translation, 561-564 profile prl9jection importance, 559 tracer techniqll,e, 566, 566-568, 568

Optical flats, 33i~-337, 337 air-wedge cqnfFsuration, 350, 350-351 measurement 345-346

applications 0.358, 360, 360-362, 361 comparative, 355-356, 356-357 parallelism, 354-355, 355-356 setup for, 346, 348, 348-349, 349 of small height differences, 356-358,.

357-359 parallel separation planes, 349, 349 surface inspection, 351-353, 351-353 which way should the bands run?, 353, 353-354,

354 Optical lever, 251 Optical magnification, 592, 592-594 Optical metrology, 547-548, 548 best inspection system, choosing, 575 chapter summary, 575-576 microscope

applications, 552-554, 552-555 principles, 548, 548-549, 550-552, 551-552

optical comparator, 556-558, 556-558 accuracy of, 568-571, 570-571 advantages over microscope, 555 applications, 559-566, 560-568, 568

primary applications of, 336-337

-

principles of, 362-365, 362-365 vision systems, 571-573, 572-574

Optical micrometer, 392-393 Optical polygons, 393

applications, 393-394 calibration of, 394, 398, 399, 399 construction of, 393, 393 rotary table calibration, 394, 395-398 two polygon calibration, 394

Optical square and adjustable table, 388, 390 Optical squares, 380-381, 381-382

attached,383,383-384,384 detached, 388, 390 scan prism, 384-385, 388-389 sweep optical square, 384, 386.-388 tooling bar, 384, 385

Optical tooling, 444 Optical tooling level, 391 Optical transit square, 399 Orientation tolerance, 44 Otho, Valentin, 470 Out of calibration, 152 Outside calipers, 89-90

Parallax, 75-76, 77

p

Parallelism, 354-355, 355-356 Parallel separation planes, 349, 349 Part coordinate system, 542 Part programs, 536-538, 537-540 Path equation, 45, 47, 47 Peak mode, 119 Pentaprism, 381, 382-383 Percentiles, 57-58, 58 Perpendicularity, 423-424, 425-426, 444 Phase shift, 342-343 Photoelectric instruments, 408, 409 Pilot specimens, 516 Pitch,316 Pitch line, 292 Plain index head, 485-486, 486 Plane angles, 480, 492 Planer, 419, 420 Plumbness, 388-393, 390-392 Pneumatic comparators, 248-249 back-pressure, 284, 284-285, 285

Index • 623

balanced systems, 285-286, 286-287 rate-of-flow systems, 286-288, 287-288

chapter summary, 299-300, 300-301 gaging elements, 288-291, 290-292 "mastering," 293-294 metrological advantages of, 294-295, 294-296 reading, 295, 296, 297, 297

scale selection, 297-298, 298 top zero spindle technique, 298-299, 299

surface finish considerations, 291-292, 292-294

Pneumatic metrology, 283 background, 283-284

Pocket comparator, 595, 595 Pocket slide caliper rule, 95-98, 96-97 Point contact, 322 Pointing interferometer, 407, 444 Poisson distribution, 59 Polar chart method, 518, 518-519, 519 Portable arm CMMs, 543, 543 Position, 57, 57-58, 58 Positional tolerancing, 48-50, 49-50 Power amplification, 253-254 Precalibrated indicator technique, 195-197,

197-199 Precision, 5, 19-22, 136-138,452

versus accuracy, 22 in angle measurement, 488-491, 488-491

Precision reference specimens, 514 Premise, 443 Primary focus, 590 Probability, 58, 58-61, 60-61-Probes, 529, 531-533, 532-534

calibration of, 533-534, 534 noncontact-type, 534-535, 535-536

Probe-type gage head, 256-259, 257-258 Producer's risk, 62 Profile projection, 547-548

limitations of, 556-558, 557-558 Profile tolerance, 44 Profiljup Method, 512, 513 Programming mode, 539 Projection, 376, 378-379, 379 Projection screen, 556 Proof,443 Protractor, 444, 462, 464


universal bevel, 462, 464, 465, 466-471, 467, 469 vernier, applications fo;' 464-465, 465-466

Protractor head, 81, 82

Quad cell target, 410 Quality assurance, 9, 53 Quality control, 53 Quartiles, 57, 57-58

Rad,492 Radian, 441 Radiation, 266-267 Random error, 305 Range, 56 Ray, 340, 587 Ray tracing, 340, 587 Real image, 590,590

o

R

Reason, R.E., 501 , Rectangular·gage block holders, 187-189, 188-190 Reed-type comparator, 251-252, 252-253 Reference flats, 346 Reference planes, 418 background, 418-419 chapter summary, 436 flatness controver~y defining, 432-435, 432-436

modern, 424, 426-432, 427-432 perpendicularity, 423-424, 425-426

Reference point, 71-72 References, 15 Reference surfaces, 264-265, 265-267 Refraction index, 588 Regardless of feature size, 44 Reliability, 19-22 Repeatability, 218, 320 Repeat error, 271 Resolution, 210, 217, 218 Reticle, 549, 551, 595, 595 Reticle-gage follower, 566, 568 Reticle pattern, 400, 400 Reversal technique, 421, 450, 450-451, 451,

456-457, 457 Rheticus, Joachim, 470 Right angle, 442, 442

"".

~ Roberts, Richard, 419 Root-mean-square roughness, 512 Rotary tables, 488-489, 488-490 Roughness, 501, 502 Roughness average, 511 Roughness comparison specimens, 516 Rounding-off numerical values, 31-37, 33-37, 329 Roundness, 7,440, 516-519, 518-519 Rule of ten-to-one, 270-271,273,274-278,275

, Rulers, 70-78 Runout tolerance, 44

Sampling, 61 Sampling length, 511 Sampling plans, 61-65

5

Scaled instruments, 78-85, 78-85 Scales, 392 Scan prism!J84-385, 388-389 Schmaltz method, 516

\. Scriber, 95 it

offset, 122, 123·~ Seconds, 487, 487~488 See-through targ~ 411, 411 Sensitivity, 215, 216, 217, 452, 454 Serial measurements, 89 Shewhart, Walter A, Dr., 54 Side adjacent, 443, 444 Side opposite, 443, 444 Sight level, 388-389, 391, 391-392, 392 Sigma 3,271 SI (International System of Units). See Metric

system Sine,444,472,472-473,473 Sine bars, 473, 473-474, 474

calculations for 5-inch, 474, 474-476 comparison measurement with, 475-476, 476-477

Sine blocks, 476-477, 477-478 Sine plates, 476-477, 477-478 Sine tables, 476-477, 477-478 Sine waves, 340-341, 341 Single lens magnifiers, 593-595, 594-595 Sizes, visualizing, 13 Skewness, 514, 515 Skidless instruments, 505 Skid-type instruments, 507

Slide caliper, 95-98, 96-97 Society of Automotive Engineers (SAE), 29 Society of Manufacturing Engineers (SME), 29 Solid angles, 492 Spherical aberration, 591 Spindles, 289 Spirit level, 451 Square gage block holders, 186-187, 188 Square head, 80-81, 81-82 Square level, 452, 454 Squareness, 380-388, 381-390

degree of, 448-449, 449-450 Squares, 439, 440, 444-446, 445-447 Standard deviation, 57 Standard of length, 164 Standards, 204

evolution of, 22-24 importance of, 338, 338 light wave as, 338-345, 339-345, 439 master, calibrating, 327-328 separating from measuring instrument, 207-208,

208-209 setting, 153, 153, 155 surface texture, 510-512, 511, 513, 514, 515 working, calibrating, 327, 328

Station plane, 401 Statistical analysis mode, 539 Statistical Process Control (SPC), 54, 275 Statistical quality control (SQC), 7, 54 Statistical tolerancing, 50, 50 Statistics, 53-54

acceptance sampling, 61-65, 62-67 chapter summary, 65, 67 descriptive statistics, 54-58, 57-58 probability, 58, 58-61, 60-61

Steel rule, 70-73, 71, 73, 206 Stereoscopic microscope, 549, 550 Stiffness, 427-428 Straight angle, 423 Straightness, 365-380, 366-380 Striding level, 389, 390 Stylus instruments, 505, 507-508, 507-509 Stylus method, 502-510, 504-510 Sum measurements, 269, 270 Supplementary angles, 442, 442 Supports, for optical instruments, 403, 405-406

Surface-datum, 505, 507 Surface finish, 291-292, 292-294 Surface gage, 95, 95 Surface inspecton, 351-353, 351-353 Surface measurement, 499, 501 background, 501 chapter summary, 520 definitions, 501-502, 502-503 notation for, 520, 520

Index • 625

numerical values for assessment, 510-512, 511, 513,514,515

roundness, 516-519, 518-519 surface evaluation

other methods, 516 stylus method, 502-510, 504-510

surface texture specimens, 514, 516 Surface topography, 167-169, 167-169 Swedish height of irregularities, 512, 513 Sweep optical square, 384, 386-388 Symbols, 6 Systematic error, 305

T Tangent, 470, 471, 472 Targets, 251, 369, 370-372 Telescope, 363-365 Telescope axle mirror, 400 Telltale, 211 Temperature, effect on error, 265-267, 267-268, 454 Ten-point height, 512, 513 Terminal line, 441 Test indicator, 212 Test stand, 233, 237 Theodolite, 364-365, 404, 406, 407, 407 Thread micrometer, 143, 155 Three-plate method, 421-423, 421-424 Three-point anvil, 322, 322 Three-point saddle, 322, 323 Tilting level, 391 Tilt target, 379, 380 Tolerances, 42 bilateral, 45-48 chapter summary, 51 geometric dimensioning and tolerancing, 43-44 of location, 45 meaning of tolerance, 42-43


positionat 48-50 statistical tolerancing, 50

Tooling bar, 384, 385 Toolmaker's flats, 346 Toolmaker's microscope, 549, 551 Topical error, 313 Torque, 145, 146 Torque band, 261 Total Quality Management (TQM), 4, 275 Tracer technique, 566, 566-568, 568 Transit square, 399 Translation, 561 Traversing length, 511 Triangles, 443, 443, 444 Trigonometric functions, 470-473, 471-473 True-datum instruments, 505, 507 Type A sampling plan, 61-62 Type B sampling plan, 61-62

Uncertaintyr 305, 323 Unit of length, 164

u

Universal bevel protractor, 462, 464 measuring acute angles using, 465, 466, 467, 467 precautions for using, 467, 468-469 reliability with, 469, 470-471

Universal measuring machine, 527

Variance, 56-57 V-blocks, 517-518, 518

v

Vernier caliper, 109-110, 110, 113, 113, 114 calibration of, 310-311, 311

Vernier depth gage, 119, 119-120, 120 Vernier height gage, 120-122, 121-122

checking, 125 dial,122 electronic, 122, 124 problem with, 125, 126-128, 127-128 using, 124-125, 125

Vernier instruments, 106-109, 107-109 Abbe's Law, 110 chapter summary, 128-129 clamping screw importance, 112 dial calipers, 117, 118

tf displacement method, 111, 111~ 112, 112 electronic digital calipers, 117, 119, 119 flat surfaces, 115, 115 inside diameter measurement, 114 interchange method, 110-111 jaw wear, 115-116, 116 . outside diameter measurement, 113-114, 115 repeatability tests, 116, 116 three elements of measurement, 128 vernier caliper

accuracy checks for, 115, 116 alignment consideration, 113; 114 measurement with, 113, 113

vernier calipers, 109-110, 110 vernier depth gage, 119, 119-120, 120 vernier height gage, 120-128, 121-128 zero setting check, 117, 118

Vernier micrometer, 139, 141 Vernier proJractor, 444 Virtual image, 590, 590 Vision systems,~~71-573, 572-574

~

Wall effect, 557 Watt, J ames, 3 ~

w

Wave front, 339, 339-340, 587, 587 Wavelength, 508-510, 509-510 Waviness, 501, 502. See also Lobes Waviness height, 512, 513 Wavy plate, 434, 434-435, 435 Wear, 329-331, 330 Wear blocks, 167, 177 White light, 346 Whitney, Eli, 160 Whitworth, Joseph, Sir, 418-419, 424 Wilkinson, John, 3 Work envelope, 527 Working flats, 346 Working standards, accuracy calibration of, 327,

328 Wringing gage blocks, 177

techniques for, 179-181, 180-183 theory of, 177-179, 178-179

Wringing interval, 178 Wrung contact, 321, 322

z Zenith sights, 399 Zero offset optical square, 383, 383-384,384 Zero of ignorance, 15 Zero setting check, 219-220, 316

Index • 627

fundamentals of dimensional...

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