Index Of: Mechanical Tolerance Stackup and Analysis

Accuracy and precision 8-9
Advanced Dimensional Management 14, 21, 78, 118, 208, 251, 286, 329-366
Ambiguity 4, 8-14
ASME B89 48
ASME Y14.5M-1994 5, 19, 22, 23, 54, 181, 187, 188, 207, 226, 271, 384
fundamental rules 54
rule #1 5
simultaneous requirements and 187, 188
Assembly shift 49, 68-74, 87-90, 93, 96-99, 102-103, 288, 293-296, 303-327, 378-383, 388
calculations 70-71
fastener diameters used in 70
chain of dimensions and tolerances and 70, 99-104
clearance and 68-69
definition of 68
dimension values and 70
direction of 70, 288, 293-296
labeling in the tolerance stackup 70
directional bias in 68
effect of assembly forces on 68, 303
effect of gravity 68, 87-90, 127-129, 378-383
effect of assembly process on 68-73, 233-234, 378-383, 388
adds to total predicted variation 68
default condition in this text 73
options for including in tolerance stackup 72-74
reduces total predicted variation 72
effect of mating features on 68
features of size 68
threaded fasteners 71-72, 74
fixed-fastener calculations and 70-72, 74, 161-164, 167, 168, 228
floating-fastener calculations and 70, 73, 100, 161-164, 167, 168, 228
including in the tolerance stackup 70, 73-74
rotational assembly shift 303-304, 304-327
formulas and calculations 313, 315, 323-324, 326
reporting in a tolerance stackup report 309, 311, 316, 322, 323, 327
rules for 74-75
sources of 68
worst-case 69-70
Assumptions 74-78, 99, 120, 393
default conditions in this text 77-78, 99
specified temperature(s) 77
static state 77
framing the problem 77-78, 99, 393
guesses and estimates 76
labeling 76
importance of stating 120
reasons for 74-76, 120
catalog and purchased parts 75-76
incomplete drawings 74-75
missing information 74-76
plus/minus 74-76
relying on manufacturing process tolerances 74-76
role of 74-76
Calculating part tolerances from a final assembly tolerance 367-372
adjusted RSS part allocation formula 370-372
in complex assemblies 367
iteration 367-369
spreadsheets and 369
RSS part allocation formula 371-372
what-if tolerancing 367-369
Central limit theorem 30-31
Gaussian distribution and 31, 106
Chain of dimensions and tolerances 53, 54, 57, 61, 63-64, 67, 78-104, 287-289
definition of 53, 104
moving from one interface to another in 99-104
reason for term 104
Complete Dimensioning and Tolerancing 4, 6, 8-14
Converting plus/minus dimensions and tolerances into equal bilateral format 33-37, 37-41, 65
limit dimensions 33-34
and mean shift 37-41
unequal bilateral 34-35
unilateral negative 36-37
unilateral positive 35-36
Coordinate measuring machine (CMM) 6, 386
Coordinates and coordinate systems 5, 137
Cartesian 5
and datum reference frames 137
and dimensions 5
polar 5
rectangular 5
Datum feature shift 48, 100-103, 147, 151, 180-187, 264, 270-286, 288, 293-296
calculations for 182-186
and datum feature simulation rules 181, 182-187
datum features of size simulated at MMC size 182-184
datum features of size simulated at MMC virtual condition size 184-187
and datum features of size 182
definition of 180
direction of 288, 293-296
geometric tolerances and 181
material condition modifiers and 181, 268, 270-271
rules for 190-192
separate requirements and 187, 192-195
similarity to assembly shift 183
simultaneous requirements and 147, 151, 187-192
sources of 180-181
Datum reference frames 107, 137, 139-140, 146-149, 160, 171-172, 394
coordinate systems defined by 107, 137
functional 137, 171-172, 394
more than one 137-138
Dimension
types of
angular (polar) 15-16
basic 18, 100-103, 141-145
chained 15-16
diametral 15-16
linear 15-16
math-data based, model-based 6, 10-12, 18-20
radial 15-16
rectangular coordinate 15, 17-18
Dimensioning and tolerancing philosophy 4-6, 8-14, 17-18, 57, 137, 154, 158-159, 171-172, 194, 201, 204, 216, 225-231, 330, 394
avoiding ambiguity 57, 216
functional dimensioning and tolerancing 17-18, 57, 137, 154, 158-159, 171-172, 194, 201, 204, 216, 225-231, 330, 394
Dimensioning strategy (see also Functional dimensioning and tolerancing) 17, 18, 57
and arrangement of dimensions 18
effect on Tolerance Stackups 17, 57
Direction of dimensions and tolerances in the tolerance stackup 58, 287-296, 302, 303-327
rules for including 295-296
tolerance stackup direction and 288, 295-296, 302
in tolerance stackups solved as a combination of translational and rotational variation 293-296, 303-327
in tolerance stackups solved as translational variation only 288-289, 293-296, 303-327
Drawings
history of 3-4
limited dimension 6, 15
math based, model based 6, 15, 267
Enclosure assembly
drawings 330-338
assembly 330, 337
cover 338
enclosure: option 1 331
enclosure: option 2 332
enclosure: option 3 333
ground plate: option 1 334
ground plate: option 2 335
ground plate: option 3 336
tolerance stackup examples
cover fit along X axis 339-345
cover fit along Y axis 342-349
ground plate to enclosure: option 1 353-356
ground plate to enclosure: option 2 356-360
ground plate to enclosure: option 3 360-365
screw head clearance 346-352
screw thread depth 337-341
Feature 5, 18, 22, 102
bounded 5
characteristics of 22
form 22, 23-24
location 22, 24-25
orientation 22, 24
size 22-23
complex 5, 102
"blending" the surface of 6
shape of 102
definition of 5
simple 5
Feature control frames 18, 146, 147, 148, 149, 159
Feature of size 5, 100-103
rule #1 and 5
Fit classifications 389-391
clearance fit 389, 390
interference fit 389, 391
transition fit 389, 390
Fixed fastener situation 383-388
assembly process and 388
assumptions 383, 384
assembly shift and 388
calculations 385, 387-388
datum features and 386
defined 373, 383
examples of 383
formula 384
distribution of tolerances in 384, 385
variables 384
interrelationship between part tolerances 384, 386
limitations of 388
positional tolerance and 384-388
projected tolerance zone and 384-386
virtual condition and 388
Fixtures 53-54
chain of dimensions and tolerances and 54
tolerances of 54-55
Floating fastener situation 373-383
assembly process and 378-383
assumptions 378, 382
assembly shift and 378-383
calculations 375, 377-378
datum features and 376
defined 373-374
effect of gravity and 379-380
examples of 374
formula 374, 375
variables 374
interrelationship between part tolerances 375-376
limitations of 378
positional tolerance and 374-378
virtual condition and 376, 378
Form tolerances in tolerance stackups 285-286, 393-428
assembly forces and 395, 402-412, 420-425
datum feature form tolerances 394-395
difference between inspection and assembly 394-402
effect on tolerance stackup 395-412
as rotational variation projected to a linear displacement 395, 402-412, 420-425
as translational variation only 395-402, 412, 417-420
examples of
as rotational variation projected to a linear displacement 402-412, 420-425
as translational variation only 395-402, 417-420
and idealization of the problem 393
how to include form tolerances in the tolerance stackup 412, 414-425
how to quantify the potential effect of the form tolerances 412, 425-427
whether form tolerances should be included in the tolerance stackup 395, 412, 413
whether variation allowed by form tolerances should be treated as translation or rotation 412, 413-414
mating surfaces and 394-402
mean shift and 417-424
other sources of form error 428
probability of occurrence 395, 401-402, 411-412, 425-427
step-by-step instructions for including 417-425
Format, plus/minus tolerances
conversion of +/- into equal bilateral 33-37, 65
conversion of GD&T into equal bilateral 138-139
position 154, 178-180
profile 139-145
dimensional limits and 30
effect on manufacturing process 29-31
effect on target value 29-31
equal bilateral 27
examples of 28
legal differences 29-31, 37
limit dimensions 27
rules for 28
leading zeroes 28
number of decimal places 28
trailing zeroes 28
SPC and 29-31
unequal bilateral 27
unilateral 27
Functional dimensioning and tolerancing 17-18, 57, 137, 154, 158-159, 171-172, 194, 201, 204, 216, 225-231, 330, 394
justifications for 57
tolerance stackups and 57
GD&T 5, 13-14, 16, 18-21, 22-25, 45, 48, 54, 74-75, 100-104, 137-200, 245-247, 264-266, 268-286
basic dimensions 18, 100-103, 141-145
measuring in CAD 142
benefits of 4, 13-14, 17-21, 75, 107-108
bonus tolerance 48, 102-103, 154, 158-159, 169, 171, 180, 227, 229-231, 264, 268, 270-286
and material condition modifiers 154, 158-159, 169
comparison with +/- 4, 13-14, 74, 75, 107-108, 138
concentricity, limitations of 215
converting +/- to positional tolerances 178, 201-207
Pythagorean theorem 201-206
right angle solution 205-206
datum feature 100-103, 137, 353-365
affect on tolerance stackups 100-103, 353-366
complex 102
feature of size 102-103
planar 100-101
datum feature shift 48, 100-103, 180-188, 264, 270-286
calculations for 182-186
and datum feature simulation rules 181
and datum features of size 182-183
datum features of size simulated at MMC size 182-184
datum features of size simulated at MMC virtual condition size 184-188
definition of 180
geometric tolerances and 181
material condition modifiers and 181, 268, 270-271
rules for 190-192
separate requirements and 187, 192-195
similarity to assembly shift 183
simultaneous requirements and 147, 151, 188-192
sources of 180-181
tolerance stackup direction and 293-296
datum reference frames 137, 139-140, 146-149, 160
coordinate systems defined by 107, 137
functional 137, 171-172, 394
more than one 137-138
feature control frames 18, 146, 147, 148, 149, 159-163, 189, 207
projected tolerance zones in 207, 384-386
feature of size 5, 100-103
form tolerances 101, 285-286, 393-428
fundamental rules 54
interfaces in the tolerance stackup and 99-104, 137
functional datum features 137, 171-172, 394
material condition modifiers 48, 69-71, 97, 153-154, 225-231, 268, 270-271
alignment and 158-159
bonus tolerance and 154, 158-159, 169, 227, 229-231, 264, 268, 270-286
effect on tolerance zones 154, 158-159
LMC 48, 69-71, 97, 153-154, 157, 158
MMC 48, 153-154, 156, 158-159
part cost and 159
RFS 154, 155, 158
symbols for 154, 226
tolerance charts 155-157
variation and 158-159
orientation tolerances 101, 102, 104, 282-285
positional tolerances 102-103, 153-180
assembly shift, misalignment and 154, 158-165
bonus tolerance and 48, 102-103, 169, 171, 180
circumscribing a cylindrical zone for converting +/- to position 178, 201-207
composite position 104, 160-173
converting +/- to positional tolerances 178, 201-207
converting to equal bilateral +/- 154, 178-180
datum reference frames and 160, 267, 268, 270-286
features of size and 153-154
in fixed- and floating-fastener formulas 161-164, 167, 168, 373-388
including upper and lower segment tolerances in the tolerance stackup 160-173
inner and outer boundaries and 155
material condition modifiers and 153-154
projected tolerance zones 207-213, 384-386
reporting in a tolerance stackup report 160, 178-180, 275-283
simultaneous requirements and 161, 167
tolerance zone 153-160, 201-207
virtual and resultant condition and 156-157
profile tolerances 100-101, 139-153, 271-277
benefits of 139-140
complex surfaces 141-142
composite profile 101, 146-153
converting to equal bilateral +/- 140-145
datum reference frames and 139-140
equal bilateral 140-142
including upper and lower segment tolerances in the tolerance stackup 145-153
planar surfaces 141
reporting in a tolerance stackup report 141, 143, 145, 147, 149-152, 271-277
similarities to +/- 139-140
simultaneous requirements and 147, 151
tolerance zone 139-147
unequal bilateral 142-144
unilateral 144-145
universal applicability 140
projected tolerance zones 207-213, 384-386
automated tools for calculating 208
and CMMs 208, 386
effect inside and outside the part 210
examples of 209-210
in fixed fastener calculations 213, 384-386
formulas to calculate equivalent tolerance when projected tolerance is not specified 211-213
methods of specifying 207-209
reasons for 207-208
reluctance of companies to use 208
in tolerance stackups 208
rule #1 5
runout tolerances 286
separate requirements 187, 192-195
compared with simultaneous requirements 192, 195-199
and datum feature shift
and datum reference frames 192
examples of 195-199
and feature control frames 192
and functional dimensioning and tolerancing 194
and inspection 192
rules for including datum feature shift in the tolerance stackup 192
simultaneous requirements 147, 151, 188-192
and the chain of dimensions and tolerances 190-192
and datum feature shift 187, 189-192
and datum reference frames 188-192
default condition per ASME Y14.5M-1994 187-188
examples of 195-199
and feature control frames 188
and inspection 188-192
overriding 187, 193
and patterns 189-190
rules for including datum feature shift in the tolerance stackup 190-192
use of +/- on drawings based on 138
Geometric characteristic symbols 21
History 3-4
of design & manufacturing practices 3-4
of engineering drawings 3-4
of tolerance analysis 1-4
Interchangeability 2
Justification for GD&T 4, 137-138
Loop (see Chain of dimensions and tolerances)
Manufacturing processes 7-8, 43-48
Material condition modifiers 48, 69-71, 97, 153-154, 155, 156, 158-159, 169, 225-231
bonus tolerance and 154, 158-159, 169, 227, 229-231
choosing the correct modifier 225, 227-231
alignment 229-230
combination of factors 230-231
edge distance or wall thickness 229
fit or clearance 228
selection criteria 227-231
difference between the material condition modifiers 226-227
effect on datum feature shift 225
effect on tolerance stackup 225
effect on tolerance zone 153-154
entering into the tolerance stackup report 225
LMC 48, 69-71, 97, 153-154, 157, 158, 225, 227
definition of 227
effect on tolerance zones 154, 158-159
and internal and external features 227
MMC 48, 153-154, 156, 158-159, 226-227
definition of 226-227
effect on tolerance zones 154, 158-159
and internal and external features 226-227
part cost and 159
positional tolerance and 153-154
RFS 154, 155, 158, 225-226
ANSI Y14.5M-1982 226
definition of 226
effect on tolerance zones 154, 158-159
as a subset of MMC and LMC 227
symbols for 154, 226
tolerance charts 155-157
variation and 158-159
Mean 39-40
definition of 40
Mean shift 37-41, 150, 417-424
calculation of 38-41
limit dimensions 38
unequal bilateral tolerances 38
unilateral tolerances 38-39
definition of 37
effect on Tolerance Stackup 38-40
form tolerances and 417-424
with and without dimensions 38-39
form and orientation tolerances and 150, 417-424
and manufacturing 40
sign and direction of 39
Mean, Arithmetic
definition of 40
Moving from one part to another in a tolerance stackup 99-104
complex-curved interfaces 102
disclaimer 104
feature-of-size interface
for +/- dimensions and tolerances 102
for GD&T - if it is a referenced datum feature 102-103
for GD&T - if it is not a referenced datum feature 103-104
guidelines for 99-104
planar interface
for +/- dimensions and tolerances 100
for GD&T - if it is a referenced datum feature 100-101
for GD&T - if it is not a referenced datum feature 101
Nominal 4, 6, 15, 16, 27, 29, 37-41, 44, 102, 105, 107, 139
dimension value and 4, 15, 16, 27, 29
manufacturing nominal 30-31
math-data/model-data and 6, 12, 44
mean shift of 37-41
statistical tolerance stackups and 105, 107
Orientation tolerances in tolerance stackups 393, 395
(see also form tolerances in tolerance stackups) 393-428
Probability 30, 105-108
Rule #1 5
Separate requirements 187, 192-195
compared with simultaneous requirements 192, 195-199
and datum feature shift
and datum reference frames 192
examples of 195-199
and feature control frames 192
and functional dimensioning and tolerancing 194
and inspection 192
rules for including datum feature shift in the tolerance stackup 192
Simultaneous requirements 147, 151, 187-192
chain of dimensions and tolerances and 190-192
and datum feature shift 187, 189-192
and datum reference frames 188-192
default condition per ASME Y14.5M-1994 187, 188
examples of 195-199
and feature control frames 188
and inspection 188-192
overriding 193
and patterns 189-190
rules for including datum feature shift in the tolerance stackup 190-192
Statistical Process Control (SPC) 13, 29-31, 105-107
Statistical tolerance stackup 99, 105-136
adjusted statistical tolerance stackup 107-109, 120-136
appropriateness of 105-106
number of dimensions and tolerances and 105-106
assembly tolerance and 108
chain of dimensions and tolerances in 110-111, 120-136
comparison with worst-case result 120-136
conditional assumptions 99, 106
examples using Advanced Dimensional Management method 119, 149, 150, 151, 152, 169, 170, 172, 173, 176, 196, 197, 198, 237-240, 241, 242, 244, 252, 253, 261, 290, 291, 308, 311, 319, 322, 329-366
examples using GD&T - simplified
complex bolted assembly 168-178
examples using plus/minus - simplified 120-136
assembly with effect of gravity 127-129
complex bolted assembly 133-136
complex welded assembly 130-133
simple assembly 125-127
single part 121-125
manufacturing process controls and 106
Monte-Carlo 107
probability and 105-108
results 105-136
root-sum-square (RSS) and 107-108, 114-117, 120-136
definition of 107
formula for 107
process related assumptions and 108
standards deviations (σ) and 108
spreadsheets and 116-120
benefits of 116-119
preformatted tolerance stackup report format 116-119, 120
statistical process control (SPC) and 106-109
Cp & Cpk 107
step-by-step procedure 109-118
adjusted statistical result 116, 118
converting the dimensions and tolerances into equal bilateral format 112-113
determining the nominal distance being studied 115, 117
determining the positive and negative directions 110-113
determining the upper and lower limits 116-118
entering data into the tolerance stackup report form 100-104, 114-118
labeling positive and negative direction dimensions 110-113
labeling the distance being studied 109-110
root-sum-square (RSS) and 114-117
tolerance distribution and 106
Tolerance
conversion of +/- 33-37, 65
conversion of GD&T
position 154, 178-180
profile 140-145
definition of 7
effects of not specifying 8-14
format of 27-30
effect on manufacturing process 29-31
effect on target value 29-31
equal bilateral 27
examples of 28
legal differences 29-31
limit dimensions 27
rules for 28
SPC and 29-31
unequal bilateral 27
unilateral 27
importance of 4, 6
range 39
types of 20-25
+/- 16-20
angular 20
form 22, 24
general note - default 20
geometric 14, 16-21
local 20
location 22, 24-25
orientation 22, 24
size 22-23
statistical 105-136
title block - default 20
worst-case 58
Tolerance analysis 2, 51-60
assumptions in 74-78, 99, 120
computer modeled 59
of cumulative variation 51-52
definition of 51
design complexity and 2
at different stages in a project
before and after production 52
importance of specifications in 51
of individual tolerances 51
manually modeled 58
methods and types of 58-59
reasons for 51-53, 55-56, 58
clearance and interference 53
statistical 58, 105-136
root-sum-square (RSS) 59, 107
steps of performing 51-52
three-dimensional 59, 62, 107
Monte-Carlo 107
worst-case (arithmetic) 58
Tolerance stackup
Advanced Dimensional Management method 119, 149, 150, 151, 152, 169, 170, 172, 173, 176, 196, 197, 198, 237-240, 241, 242, 244, 252, 253, 261, 290, 291, 308, 311, 319, 322, 329-366
assumptions in 74-78, 107, 99, 120
calculating part tolerances from a final assembly tolerance 367-372
adjusted RSS part allocation formula 370-372
RSS part allocation formula 371-372
chain of dimensions and tolerances in 53, 54, 57, 61, 63, 99-104, 165
including dimensions and tolerances in 56, 58, 287-288, 293-296
and decision making 53, 303
at different stages in a project
before and after production 52
definition of 51, 53
determining which dimensions and tolerances to include 56, 58, 287-288, 293-296, 303
diametral and radial tolerance stackups 215-224
calculating coaxiality error / misalignment in 216, 218-224
coaxiality versus concentricity 215
controlling coaxiality with GD&T 216
datum feature shift and 219
examples of 217-224
formula with variables 218-218
material condition modifiers and 216-224
direction of 58, 287-289, 293-296
dimensions, tolerances and other variables 293-296
linear one-dimensional stackups 58, 77
effect of assembly process on 57-58, 108, 233-234, 353-366
effect of dimensioning and tolerancing schemes on 56-57, 236, 353-365
effect of part and assembly geometry on 56, 287-327, 367-368
effect of changing part and assembly geometry 367-368
locating features closer together 316-327
locating features farther apart 305-316
rotation of parts in an assembly 303-327
elimination of ambiguity in 107-108
fixed fastener 383-388
and fixtures 53-55
floating fastener 373-383
form tolerances in 285-286, 393-428
importance of GD&T in 107-108
iteration in 367-369
moving from one part to another in 99-104
purpose of 51-52, 55-56, 58, 303
rotation of parts within a linear tolerance stackup 293, 303-327
affect on the tolerance stackup 305
comparisons of translational variation versus rotational variation in a linear tolerance stackup 293, 303-327
importance of 305
locating features closer together 316-327
locating features farther apart 305-316
reporting in a tolerance stackup report 309, 311, 316, 322, 323, 327
separate requirements and 192-195, 196-199
simultaneous requirements and 187-192, 195-199
statistical 58, 105-136
examples of 120-136
root-sum-square (RSS) 59, 107
steps of, general 55
subjects of a 51-52, 303
clearance and interference 53
examples of 52
as a subset of tolerance analysis 52
units 302-303
determining which units to report in a tolerance stackup 303
without dimensions 142
worst-case (arithmetic) 58, 61-104
examples of 58, 61-104
Tolerance stackup report 62, 66-67, 80, 83, 86, 89, 93, 97, 100-104,  116-120, 169, 249-286, 329-366
Advanced Dimensional Management tolerance stackup report form 119, 253, 261, 329-365
as a communication tool 250-251
consistency and 117-118, 250-251
data entry in 62, 100-104, 111-118
data fields in 120, 251-260
decision making and 249-250
examples of
Advanced Dimensional Management method 119, 150, 152, 170, 173, 196, 197, 241, 244, 252, 253, 261, 291, 308, 311, 319, 322, 329-366, 398, 419, 421, 424, 426
simplified 67, 80, 83, 86, 89, 93, 97, 117, 118, 122, 124, 126, 129, 131, 135, 177
format of 251
general guidelines for description, part number and revision information 260-262
guidelines for entering dimension and tolerance data 262-268
+/- dimensions and tolerances 262-264
basic dimensions 266-268
bonus tolerance 264, 268, 270-286
datum feature shift 264, 270-286
datum reference frames 160, 267, 268, 270-286
form tolerances 285-286, 393-428
GD&T 264-266, 268-286
material condition modifiers 268, 270-271
orientation tolerances 282-285
positional tolerances 160, 178-180, 275-283
profile tolerances 141, 143, 145, 147, 149-152, 271-277
runout tolerances 286
importance of preformatted tolerance stackup report format 116-120, 250-251
purpose of 249-251
reasons for 249-250
simplified examples for +/- 80, 83, 86, 89, 93, 97
step-by-step instructions for completing a simplified tolerance stackup form 65-67
step-by-step instructions for filling out the Advanced Dimensional Management tolerance stackup report form 251-260
assumptions block 260
data entry block 254-258
notes block 259-260
results block 258-259
suggested action block 260
tracking and title block data 253-254
step-by-step simplified introduction for worst-case +/- 66-67
tolerance stackup report form 116-120, 249-286
Tolerance stackup sketch 62-67, 80, 83, 86, 88, 92, 96, 169, 233-247, 287-288
annotation in 238-247
assembly shift 238-240, 243, 245, 246
contributing dimensions and tolerances 238-239, 243, 246
datum feature shift 238-240 ,246
dimension direction labels 238-240, 243, 246
identification of the distance or gap being studied 238-239, 243, 245
item numbers 238-240, 245, 246-247
part identification 238-239, 243, 245
title and reference information 238-239, 245, 247
tolerance stackup direction 238-240, 243, 245-246
chain of dimensions and tolerances and 233, 236, 240, 243, 246-247
as a communication tool 233, 247
content of 236-237
correlating with the tolerance stackup report 239, 241-243, 245, 247
dimensioning and tolerancing schemes and 236
examples of
Advanced Dimensional Management method 119, 149, 151, 169, 172, 176, 198, 237-240, 242, 290, 329-366, 397, 418, 420, 423, 425
for drawings based on +/- 240
for drawings based on GD&T 242
simplified 67, 80, 83, 86, 88, 92, 96, 117, 118, 122, 124, 126, 129, 131, 135
form tolerances in 393-428
importance of 233-236, 287-288
part and assembly geometry in 237-239
clarity and 238-239
scale of 238-239
sources of 238
purpose of 236-237, 247
reason for 233, 234-236, 247, 287-288
required information 233-236
assembly drawings 233, 236
catalog and purchased item drawings 233, 235
manufactured component drawings 233-234
part and assembly model(s) 233
simplified examples for +/- 80, 83, 86, 88, 92, 96
step-by-step directions for completing 243-247
for drawings based on +/- 243-245
for drawings based on GD&T 245-247
simplified 61-67
step-by-step simplified introduction for worst-case +/- 62-67
timing of 233
visualization of the problem and 233, 236, 247, 287-288
Trigonometry 99-100, 141-142, 201, 287-327, 343-345, 347-349
converting +/- to positional tolerance zone 201-207
Pythagorean theorem 201-206
right angle solution 205-206
converting angular dimensions and tolerances into linear units 296-302
+/- example 297-299
GD&T example 300-302
like triangles 304-305, 407-408, 422, 423
projection into the tolerance stackup direction 99-100, 141-142, 287-302
rotation of parts within a linear tolerance stackup 303-327
tolerance stackup units and 302-303
linear units 302
polar units 302
Units 302-303
determining which units to report in a tolerance stackup 303
Variation 43-49, 53-54, 58, 108, 233-234, 287, 293
of actual parts versus models 44
defining allowable 43-44
definition of 43
from a design point of view 43
from a manufacturing point of view 43
from a measurement point of view 43
from a tolerance analysis point of view 44
prediction of
by a tolerance stackup 53, 58
reducing predicted 53-54
fixturing 53-54
sources of 45-49
ambient conditions 46-47
assembly process 48-49, 108, 233-234
difference in process 47
difference in processing equipment 47
inspection process 48
manufacturing process capability 45
operator error and bias 46
poor maintenance 47-48
tool wear 46
variations in material 46
tolerances and 44
Worst-case tolerance stackup 61-104
chain of dimensions and tolerances in 61, 63-64, 67, 78-104
conditional assumptions 61, 77-78, 99
examples using Advanced Dimensional Management method 119, 149, 150, 151, 152, 169, 170, 172, 173, 176, 196, 197, 198, 237-240, 241, 242, 244, 252, 253, 261, 290, 291, 308, 311, 319, 322, 329-366
examples using GD&T - simplified
complex bolted assembly 168-178
examples using plus/minus - simplified 78-99
assembly with effect of gravity 87-90
complex bolted assembly 93-99
complex welded assembly 90-93
simple assembly 84-87
single part 79-84
results 61
step-by-step procedure 61-68
converting the dimensions and tolerances into equal bilateral format 33-37, 65
determining the nominal distance being studied 65-66
determining the positive and negative directions 62-64
determining the upper and lower limits 66, 67
entering data into the tolerance stackup report form 65, 100-104
labeling positive and negative direction dimensions 62-65, 68
labeling the distance being studied 61-62
summation of values 65

Mechanical Tolerance Stackup, Tolerance Analysis Book, Tolerance  Analysis Terms