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Tolerance Analysis
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Sheet music for piano arrangement of Temple of Tolerance, Guild Wars Prophecies soundtrack by Jeremy Soule, reused in Kryta areas of Guild Wars 2.Full description
Statistics By . .
Att t h e end A en d o f t h i s Tr ai ain n i n g , th t h e par p artt i c i p an antt s h o u l d b e abl ab l e to to:
1. Mas Master bas basic ic Tolerance Tolerance Types Types & Tolerance olerance Concep C onceptts 2. To do bas basic St S tack-up Analys nalysis Techniq echnique ues s for 100 100% %& 99.7% Interchangeability 3. Do a formal formal Tolerance Tolerance st stack-up analys analysis for Document Documenting ing es gn on ons 4. Determ Determine if statis statisttical ical Int Interchang erchangeabili eabilitty will give a lower 5. Determ Determine ine if larger tolerance zones can meet meet Design Design 6. Underst nderstan and d the the P rinciple rinciple of ‘Robust obust Design Design’’
Att t h e end A en d o f t h i s Tr ai ain n i n g , th t h e par p artt i c i p an antt s h o u l d b e abl ab l e to to:
1. Mas Master bas basic ic Tolerance Tolerance Types Types & Tolerance olerance Concep C onceptts 2. To do bas basic St S tack-up Analys nalysis Techniq echnique ues s for 100 100% %& 99.7% Interchangeability 3. Do a formal formal Tolerance Tolerance st stack-up analys analysis for Document Documenting ing es gn on ons 4. Determ Determine if statis statisttical ical Int Interchang erchangeabili eabilitty will give a lower 5. Determ Determine ine if larger tolerance zones can meet meet Design Design 6. Underst nderstan and d the the P rinciple rinciple of ‘Robust obust Design Design’’
Case of 100% infallible interchangeability no matter Safety is of paramount importance
Why do we require to do Tolerance Analysis?
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 2.To determine if the parts will function properly at worst con t on 3.To determine if the drawing tolerances could be larger 4.To com lete the desi n rocess 5.To provide a record of the dimensional design date in case of a product problem
Assumptions while doing Tolerance Analysis: 1.All dimensions apply at 20o C . manu ac ure par s mee dimensional requirements of drawing 3.All parts are rigid in free state & in assembl 4.For w
, parts are manufactured e mean mens on as arge ST
What are the Types of Tolerance Analysis?
What are the Types of Tolerance Analysis? 1.Radial Stack – .
–
3.Assembly Stack – What do they do?
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 Give a pictorial example for each type
•Example of a Radial Stack •R,Θ
X
Find the Dimension & Tolerance of ‘X’ n erc angea y
Assembl Stack
100 $
100 $
?$
COST
100% Interchangeability
99.7% Interchangeability
s ma e e cos or . n erc angea Please write down your answer
y
100 $
?
COST
100% Interchangeability
99.7% Interchangeability
Estimate 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
100 $
100 $ ?$
COST
100% Interchangeability
99.7% Interchangeability
At what reduced cost, you will accept 99.7% Interchangeability?
100 $
COST
100% Interchangeability
99.7% Interchangeability
Based on Statistical Principles!
Interchangeability
Assumption “Extreme assembly conditions can and will be met in practice”
100% Interchangeability
Effect of upon the assembly Assumption “Extreme assembly conditions can and will be met in practice”
100% Interchangeability
Effect of
Functionin of
upon the assembly
finished product
Assumption “Extreme assembly conditions can and will be met in practice”
100% Interchangeability
Highest
ze o
ar Lowest Lowest
‘A’
Highest
Size of ‘A’ Part
C min
C max
B min
B max
mn
max
Assembl of 3 Parts
How does Insurance Business function?
Assembly
Number of Parts / Feature Dimensions Affecting Assembly
•Assembly tolerance = Sum of all tolerances of the (OK for 2 or 3 parts…)
• 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.
Objectives of this presentation:
assembly variation . Interchangeability
Preferred component tolerances (Based on C &C k
* For 100% Interchangeability
X
Find the Dimension & Tolerance of ‘X’ for +/-3 Sigma conformance 100% Interchangeability
Sta e 1. Covert all Dimensions to be Median values & Tolerances into Bilateral ones
Start End 2
1
Plus Minus Direction Direction Distance Distance A # 'B' 'C'
0.2175
1
Stage3: Analysis
2
+/Tolerance 'D'
0.0025 0.01
2.62
3
0.42
0.01
4
1.8985
0.0025
2.536
0.025
2.62
Introduction to Normal Distribution
100% Successful Interchangeability
X σ?
6 100% Success
6σ (?)
6σ
2.63 / 2.61
Cf 100% Vs 99.7% Interchangeability
w
σ
σ
#
Si m a Val u e
To l er an c e
1
6 (100% n er erc angea y 3 99.7% Interchangeability)
+/-0.0250
2
+/-0.0146
Which is better from Assembly point of view?
Compare the two drawin s
X
Calculate the Dimension & Tolerance for the . Interchangeability
B
Cf between 100% & 99.7% Interchangeability
w
σ
σ
#
Si ma Value
Tolerance
1
6 (100% n erc angea y 3 99.7% Interchangeability)
+/-0.0500
2
+/-0.0250
Which is better from Assembly point of view? Cf Cost also
#
Sigma Value
Tolerance
1
6 (100%
+/-0.0500
2
3 (99.7% Interchangeability)
+/-0.0250
Assembly (resultant) tolerance of +/-0.025 &
(Assembly Tolerance)2 {Number of Parts * (Part Tolerance)2 } = where N is the number of parts or dimensions involved Very Important to note: = Parts σ
ssem y
∴ Assembly Tol
=Σ n1 σ1 o
arts v e
=Part Tolerance *√n
#
Sigma Value
Tolerance
1
6 (100%
+/-0.0500
2
3 (99.7% Interchangeability)
+/-0.0250
Assembly tolerance of +/-0.025 =2 * 0.0125 .
TSA Vs STA
Super Structure
Foundation
Assigning of Tolerances to related com onents of an assembly Super Structure
Assembly Tolerance = RMS value of Individual Tolerances
Foundation
Process Control:
1.Must be maintained on any statistical tolerance vide ASME Y14.5 standard 2.Symbol drawn next to dimension . 4.Operations / QC will maintain Statistical con ro o process
What are the benefits of Statistical Tolerancing?
Benefits of ST:
1.Reduced costs
3.Improved Quality / Performance of Product • Sony USA Vs Sony J apan Story
When should we apply ST?
When should we apply ST?
1.Limited Space requires a close assembly tolerance 2.Fits with a narrow range of Clearance required . 4.Means of reducing manufacturing cost 5. To reduce Tolerance Accumulation • • Adjustments / complex designs required • Tighter tolerances on components required
When should we apply ST?
•What if Analysis? for 99.7% of parts if manufactured around the mean of dimensions
TSA Vs STA
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
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 rocess au in .. to determine Cp & Cpk *Reamer Design Example
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 2.If dimensions from a stable process are measured & recorded according to size, a plot of resulting frequency distribution will
0.084+-0.05 @ 100% Interchangeability
You cant have something…….
0.084+-0.025 @ 99.7% Interchangeability
Conclusion?
meet original design requirements of 0.08 0.084+/-0.025 /-0.025 usin 99 99.7% .7% roba robabilit bilit
. meet original design requirements of 0.08 0.084+/-0.025 /-0.025 usin 99 99.7% .7% roba robabilit bilit 2.H 2. How did we get to sugg sugges estt +/-0.0125 /-0.0125 tole tolerance? rance?
. meet original design requirements of 0.08 0.084+/-0.025 /-0.025 usin 99 99.7% .7% roba robabilit bilit 2.H 2. How did we get to sugg sugges estt +/-0.0125 /-0.0125 tole tolerance? rance? 3.F 3. F rom CLT form formula: 4.T 4. Tol of parts parts / featur features es =Tol of Assy / (Sq.rt (S q.rt of number of parts or features)
100%
.
Is it possible to relax manufacturing tolerances on all mens ons s ac eve assem y arge o 0.034 +/-0.022, thereby reducing cost * +/- 2,3,4,5 & 8 thous
1.We have relaxed original tolerances of +/- 2,3,4,5 & - . 2.Check correctness of Calculations 3.How did we get proposed tolerance of 0.010?
Dim.Tolerance =(assembly Tolerance / Sq.rt of num er o mens ons nvo ve = 0.022 / √ 5 = 0.010
Part 3
ar Part 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 mens ons o parts to ac eve t e o ect ve or interchangeability
ar Part 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 mens ons o parts to ac eve t e o ect ve or . interchangeability
Part Tolerance =Assembly tolerance / √ n = 0.0175 / √3 = . =+/- 0.005 Rechecking:
