2004-12-05 geometric dimension ing and tolerancing
TRANSCRIPT
-
7/31/2019 2004-12-05 Geometric Dimension Ing and Tolerancing
1/12
Tolerance Analysis
TQM - University of Michigan1
Pat Hammett
1
Geometric Dimensioningand Tolerancing (GD&T)
Tolerance Analysis Methods
2
Example: Joining Partsn Suppose you want to join the following two parts.
n They need to be properly aligned and dimensionallyacceptable to insure a good assembly.
weldAssembly
OK
Height
weld weld
PoorAlign
ExcessDeviation
NOK NOK
-
7/31/2019 2004-12-05 Geometric Dimension Ing and Tolerancing
2/12
Tolerance Analysis
TQM - University of Michigan2
Pat Hammett
3
What is GD&T?n Symbolized notation system to communicate
tolerances through the use of datums (references).
n GD&T is used whenever the location of a part is ascritical or more critical than its size. It insures thattwo parts can mate or join properly.
n Thus, GD&T communicates 2 key issues:
n Datum Reference System (how part is held).
n Tolerances for Part Characteristics.
4
Datums
n Datums define the reference system for a partto measure or assemble it.n reference systems may be absolute (XYZ) or relative (XY).
n Use pins ~ part holes or slots & clamps ~ part surfaces
Slot: B2
(2-way locator)
Hole:
(4-way locator)
A1 Clamp surface
to locator block
A2
A3Clamp
Clamp
-
7/31/2019 2004-12-05 Geometric Dimension Ing and Tolerancing
3/12
Tolerance Analysis
TQM - University of Michigan3
Pat Hammett
5
Symbols and Characteristics
Type of Tolerance Characteristic Symbol
Individual Feature Flatness
Diameter
Individual orRelated Features
Profile
Related Features Position
Parallelism
6
GD&T Drawing Examplen Dimension may deviate up to 1mm any direction draw
circle with a radius = 1 (profile = 2 -> tol.+/- 1)
(2mm total tolerance band relative to datums)
Geometric Tolerance
Allows deviation of
1mm in any direction
Square Tolerance
for T @45 = +/- 1
tX = 0.7; tY = 0.7
Dimension
-
7/31/2019 2004-12-05 Geometric Dimension Ing and Tolerancing
4/12
Tolerance Analysis
TQM - University of Michigan4
Pat Hammett
7
Interchangeability & Tolerancesn Interchangeability -- given the assembly of two
or more components, manufacturers mayrandomly select any sample for each componentand produce an acceptable assembly.
n To insure interchangeability, manufacturersassign tolerances to each component.
n
With interchangeability, a part dimension,d,may deviate from its nominal specification, N,
by some tolerance, t , and still produce anacceptable assembly.
8
Types of Tolerances
n Bi-lateral tolerance: Nominal +/- 1mm
n Most common in manufacturing
n Unilateral tolerance: Nominal + 1 mm
n Example: material thickness specification are oftenone-sided because the goal is to use the least
amount of material (lower cost).
-
7/31/2019 2004-12-05 Geometric Dimension Ing and Tolerancing
5/12
Tolerance Analysis
TQM - University of Michigan5
Pat Hammett
9
Tolerance Analysis Approaches
n Tolerance Allocation - (top-down)n assign tolerances of final assembly based on customer needs
n work backward from assembly to components
n Tolerance Synthesis - (bottom-up)n assign tolerances of components based on process capability.
n work forward from components to assembly
n Hybrid Systems (most common approach)n
Assign initial tolerances from bottom-up -- if final assemblytolerances are too large, - work top-down until componenttolerances are capable of meeting final assembly tolerances
10
Tolerance Analysis Methods
Linear Stack-Up Analysis:
1. Worst Case Stacking
2. Statistical Stacking - Root Mean Square Method
Non-Linear Stack-Up Analysis
3. Simulation
I n t his class, w e w ill focus on linear stack-upanalysis.
-
7/31/2019 2004-12-05 Geometric Dimension Ing and Tolerancing
6/12
Tolerance Analysis
TQM - University of Michigan6
Pat Hammett
11
1. Worst Case Stacking
Worst Case Stacking -- assumes assembly AB must joinextreme values for A & B.
Specification for Part A and B: 20 +/- 0.5mmBottom-Up: if tA= tB = 0.5, then
tAB = tA+ tB = 0.5 + 0.5 = 1 >> tAB +/- 1mm
==
+=N
i
iASMtAB
1
N
1i
iNominal
Part A Part BJoin A & B
ASM AB = overall length
12
Worst Case Top Down Example
Worst Case Stacking -- assumes assembly AB must joinextreme values for A & B.
Specification for AB: 40 +/- 1 mm
Top-Down: if tAB = 1 then
tAB/ 2 = 1/2 >> tA = tB = +/- 0.5 mm
==
+=N
i
iASM tAB1
N
1i
iNominal
Part A Part BJoin A & B
ASM AB = overall length
-
7/31/2019 2004-12-05 Geometric Dimension Ing and Tolerancing
7/12
Tolerance Analysis
TQM - University of Michigan7
Pat Hammett
13
Statistical Tolerance Analysisn If two parts follow a probabilistic distribution,
then worst case stacking may be inappropriate.
n For example, if the dimensions of part A and Bboth follow a normal distribution, then the jointprobability of selecting the extremes is quitesmall.
n So, rather than using worst case, statisticaltolerance analysis is used.
14
2. Statistical Tolerance Analysis
If assume A & B follow probabilistic distributions such thattAB = f(variation of A & B).
1.7.722
22
=+=
+=
AB
BAAB
t
ttt
==
=N
ii
tX1
2N
1iiNominal
Part A Part BJoin A & B
ASM AB = overall length
Bottom-upTolerancing
So if tA= tB = +/- 0.7
-
7/31/2019 2004-12-05 Geometric Dimension Ing and Tolerancing
8/12
Tolerance Analysis
TQM - University of Michigan8
Pat Hammett
15
Additive Theorem of Variance
n Statistical tolerance: based on additive theorem of2.
222
AASM
BAASM
XXX
XXX
BAASM
B
+=
+=
+=
Part A Part BJoin A & B
ASM AB = overall length
Linear Stack-Up:
Mean Stack-Up:
Variance Stack-Up:
16
Example: Statistical Stacking
If Part A ~N(21, 0.202) and Part B ~N(19, 0.152)What is the predicted assembly mean?
What is the predicted assembly sigma?
What are necessary tolerances for Part A and B to achieve 6?(Hint: Suppose you need to achieve a Cp = 2.0.)
Part A Part BJoin A & B
ASM AB = overall length
-
7/31/2019 2004-12-05 Geometric Dimension Ing and Tolerancing
9/12
Tolerance Analysis
TQM - University of Michigan9
Pat Hammett
17
Tolerances and Six Sigma
n Suppose specification for ASM AB is 40 +/- 1 mm
n What sigma must be achieved for each component toinsure the assembly achieves a Cp = 2.0, Cpk > 1.5?
Part APart BJoin A & B
ASM AB = overall length
18
Worst Case Vs. Statisticaln Suppose ASM tolerance +/1 mm
n Worst Case Top Down: tA= tB = +/- 0.5 mm
n Statistical Top-Down: tA= tB = +/- 0.7 mm
n
For the same assembly tolerance, statisticalstatistical allows greater variation in thecomponents.
-
7/31/2019 2004-12-05 Geometric Dimension Ing and Tolerancing
10/12
Tolerance Analysis
TQM - University of Michigan10
Pat Hammett
19
3. Tolerance Simulation Modelsn The prior statistical stack-up analysis is based on root-
mean-squared method (additive variance theorem).
n Alternatively, we could write a simulation model andrandomly generate combinations of components fromtheir distributions (e.g., normal, uniform, etc).
n Then, compute the expected variance of the assembly.
Typically, you would then assign tolerances of say +/-4assy or 6assy
20
Bender Correction - Statistical
n if more than 2 components are assembledwith statistical, we sometimes use correctionfactors because components may becomeunnecessarily wide.
n Bender Factor, B = 1.5
==22
5.1 iiassy ttBt
-
7/31/2019 2004-12-05 Geometric Dimension Ing and Tolerancing
11/12
Tolerance Analysis
TQM - University of Michigan11
Pat Hammett
21
Gilson Correction Worst Casen If using worst case stacking, the Gilson
correction factor allows loosening ofcomponent tolerances.
N 2 3 4 5
K 1* 0.92 0.80 0.72
if N=2; K (Gilson = 1.0)
NK 6.1=
=
=N
iiassy tKt
1
22
Tolerance Analysis Examples
n Bottom-Up Tolerance Stack-Upn If each block can be held to 20 +/- 0.5 mm, what is the
expected tolerance for the assembly?
n Worst Case - Linear Stackn No Correction:
n tABC = +/- (.5+.5+.5+.5) = +/- 2.0 mm
n With Correction:
n tABC = +/- K(4*0.5) = .80(2.0) = +/- 1.6 mm
A B C
overall length: ABCD = tolerance??
D
-
7/31/2019 2004-12-05 Geometric Dimension Ing and Tolerancing
12/12
Tolerance Analysis
TQM - University of Michigan12
Pat Hammett
23
Non-Traditional Methodsn Both worst case and statistical tolerance models
assume rigid parts and additive theorem of variance.(often resulting in unnecessarily tight tolerances forcomponents within assembly)
n Tolerance Adjustments:n Additional Factors: some models include assembly processing
variation in addition to the variation of joining components.
n Weighted Tolerance Models: some models assign contributionfactors if one variable dominates the assembly.
24
Example: Non-Rigid to Rigid Part
n A 2 mm thick center pillar is attached to an 0.7 mm thickbody side is 0.7mm thick with the following results:
Why might you assign a tightertolerance to the center pillar and a
looser tolerance for body side?
VariablePart A -
Body Side
Part B - Center
Pillar
Predicted
Stack-Up
Actual
Assembly
Mean -0.70 0.20 -0.50 0.30
Std Deviation 0.33 0.11 0.35 0.12
222
AASM
XXX
BAASM
B
+=
+=
Predicted Stack-Up