Tolerances Design
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Transcript Tolerances Design
GATEWAY
Tolerance Design
Department of Mechanical Engineering, The Ohio State University
Sl. #1
GATEWAY
Design Specifications and Tolerance
Develop from quest for production quality and
efficiency
Early tolerances support design’s basic
function
Mass production brought interchangeability
Integrate design and mfg tolerances
Department of Mechanical Engineering, The Ohio State University
Sl. #2
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Definition
“The total amount by which a given
dimension may vary, or the difference
between the limits”
- ANSI Y14.5M-1982(R1988) Standard [R1.4]
Department of Mechanical Engineering, The Ohio State University
Sl. #3
Source: Tolerance Design, p 10
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Affected Areas
Engineering
Tolerance
Product Design
Quality Control
Manufacturing
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Questions
“Can customer tolerances be
accommodated by product?”
“Can product tolerances be
accommodated by the process?”
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Sl. #5
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Tolerance vs. Manufacturing Process
Nominal tolerances for
steel
Tighter tolerances =>
increase cost $
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Geometric Dimensions
Accurately communicates the function of part
Provides uniform clarity in drawing delineation
and interpretation
Provides maximum production tolerance
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Sl. #7
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Tolerance Types
Size
Form
Location
Orientation
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Sl. #8
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Size Tolerances
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Sl. #9
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Form Tolerances
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Sl. #10
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Location Tolerances
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Orientation Tolerances
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Tolerance Buildup
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Sl. #13
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Statistical Principles
Measurement of central tendency
Mean
Median
mode
Measurement of variations
Range
Variance
Standard deviation
LSL
USL
X
3s
tolerance
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Probability
Probability
Likelihood of occurrence
Capability
Relate the mean and variability of the
process or machine to the permissible
range of dimensions allowed by the
specification or tolerance.
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Sl. #15
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Tolerance SPC Charting
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Sl. #16
Figure Source: Tolerance Design, p 125
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Tolerance Analysis Methods
Worst-Case analysis
Root Sum of Squares
Taguchi tolerance design
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Sl. #17
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Initial Tolerance Design
Initial
Tolerance
Design
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Sl. #18
Figure Source: Tolerance Design, p 93
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References
Handbook of Product Design for Manufacturing: A Practical Guide to
Low-Cost Production, James C. Bralla, Ed. in Chief; McGraw-Hill, 1986
Manufacturing Processes Reference Guide, R.H. Todd, D.K. Allen & L.
Alting; Industrial Press Inc., 1994
Standard tolerances for mfg processes
Machinery’s Handbook; Industrial Press
Standard Handbook of Machine Design; McGraw-Hill
Standard Handbook of Mechanical Engineers; McGraw-Hill
Design of Machine Elements; Spotts, Prentic Hall
Department of Mechanical Engineering, The Ohio State University
Sl. #19
Figure Source: Tolerance Design, p 92-93
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Worst-Case Methodology
Extreme or most liberal condition of tolerance
buildup
“…tolerances must be assigned to the
component parts of the mechanism in such a
manner that the probability that a mechanism
will not function is zero…”
- Evans (1974)
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Sl. #20
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Worst-Case Analysis
m
WC max N p i Tp i
i1
m
WC min N p i Tp i
i1
Ne + Te => Maximum assembly envelope
Ne - Te => Minimum assembly envelope
Department of Mechanical Engineering, The Ohio State University
Sl. #21
Source: “Six sigma mechanical design tolerancing”, p 13-14.
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Assembly gaps
m
Gmax N e Te N p i Tp i
i1
m
Gmin N e Te N p i Tp i
i1
m
Gnom N e N p i
i1
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Sl. #22
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Worst Case Scenario Example
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Sl. #23
Source: Tolerance Design, pp 109-111
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Worst Case Scenario Example
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Sl. #24
Source: Tolerance Design, pp 109-111
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Worst Case Scenario Example
• Largest => 0.05 + 0.093 = 0.143
• Smallest => 0.05 - 0.093 = -0.043
Department of Mechanical Engineering, The Ohio State University
Sl. #25
Source: Tolerance Design, pp 109-111
GATEWAY
Non-Linear Tolerances
y f (x1, x 2 , x 3,...x n )
f
f
f
f
Toly
tol1
tol2
tol3 ...
toln
x1
x 2
x 3
x n
f
f
f
f
Nomy
x1
x2
x 3 ...
xn
x1
x 2
x 3
x n
Department of Mechanical Engineering, The Ohio State University
Sl. #26
Wource: “Six sigma mechanical design tolerancing”, p 104
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Root Sum-of-Square
RSS
Assumes normal distribution behavior
1
(1/ 2)[x )/s ]2
f (x)
e
s 2
Department of Mechanical Engineering, The Ohio State University
Sl. #27
Wource: “Six sigma mechanical design tolerancing”, p 16
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RSS method
Assembly tolerance stack equation
f (x) T T T ...T
2
1
2
2
2
3
2
n
Department of Mechanical Engineering, The Ohio State University
Sl. #28
Wource: “Six sigma mechanical design tolerancing”, p 128
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Pool Variance in RSS
s adjusted
s
Tol
3Cp
gap
2
Tpi
Te
3Cp i1 3Cpi
2
m
Department of Mechanical Engineering, The Ohio State University
Sl. #29
Wource: “Six sigma mechanical design tolerancing”, p 128
GATEWAY
Probability
ZQ
ZQ
Q Gnom
s gap
m
Q N e N pi
i1
2
Te
Tpi
3Cp i1 3Cpi
2
m
Department of Mechanical Engineering, The Ohio State University
Sl. #30
Wource: “Six sigma mechanical design tolerancing”, p 128
GATEWAY
Probability for Limits
ZG min
ZG max
Gmin Gnom
2
Te 2 m Tpi
3Cp i1 3Cpi
Gmax Gnom
2
Te 2 m Tpi
3Cp i1 3Cpi
Department of Mechanical Engineering, The Ohio State University
Sl. #31
Wource: “Six sigma mechanical design tolerancing”, p 128
GATEWAY
Dynamic RSS
ZG min
ZG max
Gmin Gnom
2
Te 2 m Tpi
3Cpk i1 3Cpki
Gmax Gnom
2
Te 2 m Tpi
3Cpk i1 3Cpki
Department of Mechanical Engineering, The Ohio State University
Sl. #32
Wource: “Six sigma mechanical design tolerancing”, p 128
GATEWAY
Nonlinear RSS
2
2
2
2
f 2 f 2 f 2
f
Toly tol1 tol2 tol3 ... toln
x1
x 2
x 3
x n
s adjusted
Toli
3Cpki
Department of Mechanical Engineering, The Ohio State University
Sl. #33
Wource: “Six sigma mechanical design tolerancing”, p 128
GATEWAY
RSS Example
• Largest => 0.05 + 0.051 = 0.101
• Smallest => 0.05 - 0.051 = -0.001
Department of Mechanical Engineering, The Ohio State University
Sl. #34
Wource: “Six sigma mechanical design tolerancing”, p 128
GATEWAY
Taguchi Method
Input from the voice of the customer and QFD processes
Select proper quality-loss function for the design
Determine customer tolerance values for terms
in Quality Loss Function
Determine cost to business to adjust
Calculate Manufacturing Tolerance
Proceed to tolerance design
Department of Mechanical Engineering, The Ohio State University
Sl. #35
Wource: “Six sigma mechanical design tolerancing”, p 21
GATEWAY
Taguchi
Voice of customer
Quality function deployment
Inputs from parameter design
Optimum control-factor set points
Tolerance estimates
Initial material grades
Department of Mechanical Engineering, The Ohio State University
Sl. #36
Wource: “Six sigma mechanical design tolerancing”, p 22
GATEWAY
Quality Loss Function
Identify customer costs for intolerable performance
Quadratic quality loss function
Ao
L(y) k(y m)
(y m) 2
o
2
Department of Mechanical Engineering, The Ohio State University
Sl. #37
Wource: “Six sigma mechanical design tolerancing”, p 208
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Cost of Off Target and Sensitivity
Cost to business to adjust off target
performance
Sensitivity, b
Ao
A
Ao
2
A [b (x m)]
Department of Mechanical Engineering, The Ohio State University
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Wource: “Six sigma mechanical design tolerancing”, p 226-227
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Manufacturing Tolerance
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Ao o
A b
Department of Mechanical Engineering, The Ohio State University
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Summary
Importance of effective tolerances
Tolerance Design Approaches
Worst-Case analysis
Root Sum of Squares
Taguchi tolerance method
Continual process
Involvement of multi-disciplines
Department of Mechanical Engineering, The Ohio State University
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GATEWAY
Credits
This module is intended as a supplement to design classes in
mechanical engineering. It was developed at The Ohio State
University under the NSF sponsored Gateway Coalition (grant
EEC-9109794). Contributing members include:
Gary Kinzel…………………………………. Project supervisor
Phuong Pham.……………. ………………... Primary author
Reference:
“Six Sigma Mechanical Design Tolerancing”, Harry, Mikel J. and Reigle
Stewart, Motorola Inc. , 1988.
Creveling, C.M., Tolerance Design, Addison-Wesley, Reading, 1997.
Wade, Oliver R., Tolerance Control in Design and Manufacturing,
Industrial Press Inc., New York, 1967.
Department of Mechanical Engineering, The Ohio State University
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Department of Mechanical Engineering, The Ohio State University
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