tolerance stack up statistics
DESCRIPTION
tolerance stack upTRANSCRIPT
Tolerance Stackup AnalysisTolerance Stackup AnalysisStatistics
ByDr N RamaniDr. N. Ramani
1
At the end of this Training, the participant should be able to:
1. Master basic Tolerance Types & Tolerance Concepts
2. To do basic Stack-up Analysis Techniques for 100% & 99.7% Interchangeability
3. Do a formal Tolerance stack-up analysis for Documenting d i C ditidesign Conditions
4. Determine if statistical Interchangeability will give a lower cost productcost product
5. Determine if larger tolerance zones can meet Design requirementsrequirements
6. Understand the Principle of ‘Robust Design’
2
Case of 100% infallible interchangeability no matter the cost :the cost :
Safety is of paramount importance
3
Why do we require to do Tolerance Analysis?y y
4
Why do we require to do Tolerance Analysis?
1.To determine whether the parts will assemble 100% of the time or only 99.7% of the time statistically?statistically?
2.To determine if the parts will function properly t t ditiat worst condition
3.To determine if the drawing tolerances could be larger
4.To complete the design processp g p
5.To provide a record of the dimensional design requirements that can be reviewed at a later
5
requirements that can be reviewed at a later date in case of a product problem
Assumptions while doing Tolerance Analysis:
1.All dimensions apply at 20oC
2 All f t d t t2.All manufactured parts meet dimensional requirements of drawing
3.All parts are rigid in free state & in assemblyasse b y
4.For , parts are manufactured ith th di i T t
STwith the mean dimension as Target
6
What are the Types of Tolerance Analysis?
7
What are the Types of Tolerance Analysis?
1.Radial Stack –
2 Linear Stack –2.Linear Stack –
3.Assembly Stack –
What do they do?
8
What are the Types of Tolerance Analysis?
1.Radial Stack – Involves diameters or radial directions
2.Linear Stack – Involves dimensions that are in X,Y or Z direction,
3.Assembly Stack – Involves radial or linear directions of several partsdirections of several parts
Give a pictorial example for each type
9
•Example of a Radial Stack
•R,Θ
10
,
X
Find the Dimension & Tolerance of ‘X’ for +/ 3 Sigma conformance100% I t h bilit
11Example of a Linear Stack
for +/-3 Sigma conformance100% Interchangeability
??
Assembly Stack
12
y
100 $ ? $100 $
COST
100% Interchangeability
99.7% Interchangeability
E ti t th t f 99 7% i t h bilit13
Estimate the cost for 99.7% interchangeability Please write down your answer
100 $ ? $100 $ ? $100 $
COST
100% Interchangeability
99.7% Interchangeability
14Estimate the cost for 99.7% interchangeability
1.Let us say that there is a possibility to reduce cost substantially, if you are prepared to accept 99.7% Interchangeability, in place of 100%
2.Let us say that cost saving will more than offset the loss of 0.3% Interchangeability (3 out of 1000
)assemblies)
3.Please answer the question, at what reduced cost, you will accept 99.7% Interchangeability
15
100 $100 $ Cost Saving
? $Cost Saving
COST
100% Interchangeability
99.7% Interchangeability
16At what reduced cost, you will accept 99.7% Interchangeability?
100 $
COST
< 20 $ !< 20 $ !
100% Interchangeability
99.7% Interchangeability
17Based on Statistical Principles!
100%100%Interchangeability
18
Assumption“Extreme assembly conditions
can and will be met in practice”
100%Interchangeability
19
Effect of component tolerancescomponent tolerances
upon the assembly
Assumption“Extreme assembly conditions
can and will be met in practice”
100%Interchangeability
20
Effect of component tolerances Functioning of component tolerances
upon the assembly
g
finished product
Assumption“Extreme assembly conditions
can and will be met in practice”
100%Interchangeability
21
Si f ‘B’ P t
Highest
Size of ‘B’ Part
Lowest
‘B’Lowest Highest
‘B’
Size of ‘A’ Part‘A’
22
C maxC min
B min B max
Assembly
AA i
yof 3 Parts
A maxA min
23
How does Insurance Business function?
24
Effect onEffect on Assembly
1 2 543 6 7 108 91 2 543 6 7 108 9Number of Parts / Feature Dimensions
25Affecting Assembly
26
27
•Assembly tolerance = Sum of all tolerances of the individual partsindividual parts
(OK for 2 or 3 parts…)
•One method is to provide the widest practicalOne method is to provide the widest practical component tolerances based upon the statistical fact that it is unlikely that all maximum-tolerance parts or all minimum-tolerance parts would ever be brought together in the same assembly.
28
Objectives of this presentation:
1
Preferred Worst case
1
component tolerances
Worst case assembly variation for 100% & 99 7%
(Based on Cp & Cpk)
for 100% & 99.7% Interchangeability
p p )
229
2
?*?*
* For 100% Interchangeability
30
31
32
X
Find the Dimension & Tolerance of ‘X’
33for +/-3 Sigma conformance100% Interchangeability
Stage 1. Covert all Dimensions to be Median values
34
Stage 1. Covert all Dimensions to be Median values & Tolerances into Bilateral ones
Start End
234 34
1
35
Plus Direction Distance
Minus Direction Distance
+/-Tolerance
A #Distance
'B'Distance
'C'Tolerance
'D'1 0.2175 0.00252 2.62 0.013 0.42 0.01
Stage3:
Tabulate4 1.8985 0.0025
2.62 2.536 0.025
Tabulate Analysis
360.084 0.025
Introduction to Normal Distribution
37
38
100% Successful Interchangeability X σ?
39
40Please remember the value of tolerance!
6
41100% Success 6σ (?)
6σ
2.63 / 2.61
42
43
44
45
Cf 100% Vs 99.7% Interchangeability
46
Comparison bet een 6 &3 LimitsComparison between 6σ &3σ Limits# Sigma Value Toleranceg1 6 (100%
I t h bilit )+/-0.0250
Interchangeability)2 3 (99.7% +/-0.0146(
Interchangeability)
Which is better from Assembly point of view? Lesson?
47
Lesson?
Compare the two drawingsg
AA
B48
B
BX
Calculate the Dimension & Tolerance for the Circlip Groove @ 100% & 99 7%
49
Circlip Groove @ 100% & 99.7% Interchangeability
50Cf between 100% & 99.7% Interchangeability
Comparison bet een 6 &3 LimitsComparison between 6σ &3σ Limits# Sigma Value Toleranceg1 6 (100%
I t h bilit )+/-0.0500
Interchangeability)2 3 (99.7% +/-0.0250(
Interchangeability)
Which is better from Assembly point of view? Cf Cost also
51
# Sigma Value Tolerance1 6 (100%
Interchangeability)+/-0.0500
Interchangeability)2 3 (99.7% +/-0.0250
Interchangeability)Determine the relationship betweenDetermine the relationship between Assembly (resultant) tolerance of +/-0.025 & four tolerances of part viz.0.0125four tolerances of part viz.0.0125
52
(Assembly Tolerance)2
{ Number of Parts * (Part Tolerance)2 }Part Tolerance = Assembly Tolerance / Sq.Rt of N,Part Tolerance Assembly Tolerance / Sq.Rt of N,
where N is the number of parts or dimensions involved
Very Important to note:
Assembly Variance = Arithmetic sum of Variances ofAssembly Variance = Arithmetic sum of Variances of Parts
2 A bl ( * 2) f P id CLTσ2 Assembly =Σ (n1 * σ12) of Parts vide CLT
∴ Assembly Tol = Part Tolerance *√n
53
# Sigma Value Tolerance1 6 (100%
Interchangeability)+/-0.0500
Interchangeability)2 3 (99.7% +/-0.0250
Interchangeability)
(√
Assembly tolerance of +/-0.025 = 2 * 0.0125
= 4 * 0 0125)(√= 4 * 0.0125)
54
55
TSA Vs STA
56
ST?ST?
STSuper Structure
ST
? Foundation
57
?
Assigning of Tolerances to related components of an p
assembly
STSuper Structure
STAssembly Tolerance
= Foundation
58RMS value of Individual Tolerances
Process Control:
1.Must be maintained on any statistical tolerance vide ASME Y14.5 standard
2.Symbol drawn next to dimension
3 Not shown in our drawings3.Not shown in our drawings
4.Operations / QC will maintain Statistical t l fcontrol of process
59
What are the benefits of Statistical Tolerancing?
60
Benefits of ST:
1.Reduced costs
2.Closer average Fits2.Closer average Fits
3. Improved Quality / Performance of Product
• Sony USA Vs Sony Japan Story
61
When should we apply ST?
62
When should we apply ST?
1.Limited Space requires a close assembly tolerance
2.Fits with a narrow range of Clearance required
3 100% Interchangeability not possible3.100% Interchangeability not possible
4.Means of reducing manufacturing cost
5. To reduce Tolerance Accumulation
• Selective assembly requiredSelective assembly required
• Adjustments / complex designs required
63• Tighter tolerances on components required
When should we apply ST?
•What if Analysis?
•You want to know what will be the condition•You want to know what will be the condition for 99.7% of parts if manufactured around the mean of dimensions
TSA Vs STA
64
When will ST succeed?When will ST succeed?
65
When will ST succeed?
1.Manufacturing is done to the middle of the dimension
2.Use of proper controls to produce parts to a near normal distribution within drawing specification
66
Responsibility for achieving ST:
1.Engineers understand that parts are to be produced with the ‘Target on the mean’
2.Tools are designed & produced to achieve the above target*
3.Necessary inspection equipment are available (In process gauging..) to determine ( p g g g )Cp & Cpk
*Reamer Design Example
67
Normal Distribution:
1.Formed where manufacturing processes produce in a random manner about the mean with a majority of the dimensions close to the mean & a decreasing number occurring away from the meanfrom the mean
2. If dimensions from a stable process are measured & recorded according to size, a plot of resulting frequency distribution will approximate the Gaussian curveapproximate the Gaussian curve
68
0.084+/-0.05 0.084+/-0.025 @ 100%
Interchangeability@ 99.7%
Interchangeability
69CLT?You cant have something…….
Conclusion?
70
• Four tolerance zones can be increased & still• Four tolerance zones can be increased & still meet original design requirements of 0.084+/-0.025 using 99.7% probabilityg p y
71
1 Four tolerance zones can be increased & still1.Four tolerance zones can be increased & still meet original design requirements of 0.084+/-0.025 using 99.7% probabilityg p y
2.How did we get to suggest +/-0.0125 tolerance?
72
1 Four tolerance zones can be increased & still1.Four tolerance zones can be increased & still meet original design requirements of 0.084+/-0.025 using 99.7% probabilityg p y
2.How did we get to suggest +/-0.0125 tolerance?
3.From CLT formula:
4.Tol of parts / features = Tol of Assy / (Sq.rt of p y ( qnumber of parts or features)
73
74
75
100%
99 7%99.7%
76
Is it possible to relax manufacturing tolerances on all 5 di i * & till hi bl t t f5 dimensions* & still achieve assembly target of 0.034 +/-0.022, thereby reducing cost
77* +/- 2,3,4,5 & 8 thous
1.We have relaxed original tolerances of +/- 2,3,4,5 & 8 thous to +/ 0 0108 thous to +/- 0.010
2.Check correctness of Calculations
783.How did we get proposed tolerance of 0.010?
Dim.Tolerance = (assembly Tolerance / Sq.rt of b f di i i l d)number of dimensions involved)
= 0.022 / √ 5
= 0.010
Very ImportantVery Important
79
Part 3
P t 1Part 1Part 2
•You are the designer of this assembly
•The top surface of part 1 is to be proud of the top surface of part 3 by 0.0005 – 0.018
•Determine the Unknown Length & fix tolerances of the di i f t 2 & 3 t hi th bj ti f 100%
80
dimensions of parts 2 & 3 to achieve the objective for 100% interchangeability
1. Average Axial Clearance = (0.0005+0.018) / 2 = 0.00925 Nominal
2. Total Tolerance = (0.018 - 0.0005) = 0.0175 = +/- 0.00875
3. Target Clearance = 0.00925 +/- 0.00875 (Check max & min values)
4. Nominal Unknown Length = (0.250+0.125+0.00925) = 0.384(approx)
5. Tolerance of Dimensions 0.384, 0.250 & 0.125 = +/- 0.00875 / 3 = +/- 0.0029
81
Part 3
P t 1Part 1Part 2
•You are the designer of this assembly
•The top surface of part 1 is to be proud of the top surface of part 3 by 0.0005 – 0.018
•Determine the Unknown Length & fix tolerances of the di i f t 2 & 3 t hi th bj ti f 99 7%
82
dimensions of parts 2 & 3 to achieve the objective for 99.7% interchangeability
Part Tolerance = Assembly tolerance / √ n
= 0.0175 / √3
= 0 010= 0.010
= +/- 0.005
Rechecking:
83
84
85
Determine Assembly Gap for 100% of cases
86
87
T iti b tTransition between
Max Clearance 0.0275
Max Interference 0.0035
88
Determine Assembly Gap for 99.7% of cases
89
90
91
Thank You
92