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Department of Mechanical Engineering, The Ohio State UniversitySl. #1
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Tolerance Design
Department of Mechanical Engineering, The Ohio State UniversitySl. #2
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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 UniversitySl. #3
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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]
Source: Tolerance Design, p 10
Department of Mechanical Engineering, The Ohio State UniversitySl. #4
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Affected Areas
Product Design Quality Control
Manufacturing
EngineeringTolerance
Department of Mechanical Engineering, The Ohio State UniversitySl. #5
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Questions
“Can customer tolerances be accommodated by product?”
“Can product tolerances be accommodated by the process?”
Department of Mechanical Engineering, The Ohio State UniversitySl. #6
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Tolerance vs. Manufacturing Process
Nominal tolerances for
steel
Tighter tolerances =>
increase cost $
Department of Mechanical Engineering, The Ohio State UniversitySl. #7
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Geometric Dimensions
Accurately communicates the function of part
Provides uniform clarity in drawing delineation and interpretation
Provides maximum production tolerance
Department of Mechanical Engineering, The Ohio State UniversitySl. #8
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Tolerance Types
Size Form Location Orientation
Department of Mechanical Engineering, The Ohio State UniversitySl. #9
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Size Tolerances
Department of Mechanical Engineering, The Ohio State UniversitySl. #10
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Form Tolerances
Department of Mechanical Engineering, The Ohio State UniversitySl. #11
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Location Tolerances
Department of Mechanical Engineering, The Ohio State UniversitySl. #12
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Orientation Tolerances
Department of Mechanical Engineering, The Ohio State UniversitySl. #13
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Tolerance Buildup
Department of Mechanical Engineering, The Ohio State UniversitySl. #14
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Statistical Principles
Measurement of central tendency Mean Median mode
Measurement of variations Range Variance Standard deviation
USLLSL
tolerance 3
X
Department of Mechanical Engineering, The Ohio State UniversitySl. #15
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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.
Department of Mechanical Engineering, The Ohio State UniversitySl. #16
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Tolerance SPC Charting
Figure Source: Tolerance Design, p 125
Department of Mechanical Engineering, The Ohio State UniversitySl. #17
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Tolerance Analysis Methods
Worst-Case analysis Root Sum of Squares Taguchi tolerance design
Department of Mechanical Engineering, The Ohio State UniversitySl. #18
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Figure Source: Tolerance Design, p 93
Initial Tolerance Design
Initial Tolerance
Design
Department of Mechanical Engineering, The Ohio State UniversitySl. #19
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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
Figure Source: Tolerance Design, p 92-93
Department of Mechanical Engineering, The Ohio State UniversitySl. #20
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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)
Department of Mechanical Engineering, The Ohio State UniversitySl. #21
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Worst-Case Analysis
€
WCmax = N p i+ Tp i( )
i=1
m
∑
€
WCmin = N p i−Tp i( )
i=1
m
∑
Source: “Six sigma mechanical design tolerancing”, p 13-14.
Ne + Te => Maximum assembly envelope Ne - Te => Minimum assembly envelope
Department of Mechanical Engineering, The Ohio State UniversitySl. #22
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Assembly gaps
€
Gmax = Ne + Te − N p i−Tp i( )
i=1
m
∑
€
Gmin = Ne −Te − N p i+ Tp i( )
i=1
m
∑
€
Gnom = Ne − N p i( )i=1
m
∑
Department of Mechanical Engineering, The Ohio State UniversitySl. #23
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Worst Case Scenario Example
Source: Tolerance Design, pp 109-111
Department of Mechanical Engineering, The Ohio State UniversitySl. #24
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Worst Case Scenario Example
Source: Tolerance Design, pp 109-111
Department of Mechanical Engineering, The Ohio State UniversitySl. #25
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Worst Case Scenario Example
Source: Tolerance Design, pp 109-111
• Largest => 0.05 + 0.093 = 0.143
• Smallest => 0.05 - 0.093 = -0.043
Department of Mechanical Engineering, The Ohio State UniversitySl. #26
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Non-Linear Tolerances
€
y = f (x1,x2,x3,...xn )
€
Tol y =∂f
∂x1
tol1 +∂f
∂x2
tol2 +∂f
∂x3
tol3 + ...+∂f
∂xn
toln
€
Nomy ≈∂f
∂x1
x1 +∂f
∂x2
x2 +∂f
∂x3
x3 + ...+∂f
∂xn
xn
Wource: “Six sigma mechanical design tolerancing”, p 104
Department of Mechanical Engineering, The Ohio State UniversitySl. #27
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Root Sum-of-Square
RSS Assumes normal distribution behavior
Wource: “Six sigma mechanical design tolerancing”, p 16
€
f (x) =1
σ 2πe−(1/ 2)[x−μ ) /σ ]2
Department of Mechanical Engineering, The Ohio State UniversitySl. #28
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RSS method
Assembly tolerance stack equation
€
f (x) = T12 + T2
2 + T32 + ...Tn
2
Wource: “Six sigma mechanical design tolerancing”, p 128
Department of Mechanical Engineering, The Ohio State UniversitySl. #29
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Pool Variance in RSS
€
adjusted =Tol
3Cp
€
gap =Te
3Cp
⎛
⎝ ⎜
⎞
⎠ ⎟
2
+Tpi
3Cpi
⎛
⎝ ⎜
⎞
⎠ ⎟
i=1
m
∑2
Wource: “Six sigma mechanical design tolerancing”, p 128
Department of Mechanical Engineering, The Ohio State UniversitySl. #30
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Probability
€
ZQ =Q−Gnom
σ gap
€
ZQ =
Q− Ne − N pi
i=1
m
∑ ⎛
⎝ ⎜
⎞
⎠ ⎟
Te
3Cp
⎛
⎝ ⎜
⎞
⎠ ⎟
2
+Tpi
3Cpi
⎛
⎝ ⎜
⎞
⎠ ⎟
i=1
m
∑2
Wource: “Six sigma mechanical design tolerancing”, p 128
Department of Mechanical Engineering, The Ohio State UniversitySl. #31
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Probability for Limits
€
ZG max =Gmax −Gnom
Te
3Cp
⎛
⎝ ⎜
⎞
⎠ ⎟
2
+Tpi
3Cpi
⎛
⎝ ⎜
⎞
⎠ ⎟
2
i=1
m
∑
€
ZG min =Gmin −Gnom
Te
3Cp
⎛
⎝ ⎜
⎞
⎠ ⎟
2
+Tpi
3Cpi
⎛
⎝ ⎜
⎞
⎠ ⎟
2
i=1
m
∑
Wource: “Six sigma mechanical design tolerancing”, p 128
Department of Mechanical Engineering, The Ohio State UniversitySl. #32
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Dynamic RSS
€
ZG max =Gmax −Gnom
Te
3Cpk
⎛
⎝ ⎜
⎞
⎠ ⎟
2
+Tpi
3Cpki
⎛
⎝ ⎜
⎞
⎠ ⎟
2
i=1
m
∑
€
ZG min =Gmin −Gnom
Te
3Cpk
⎛
⎝ ⎜
⎞
⎠ ⎟
2
+Tpi
3Cpki
⎛
⎝ ⎜
⎞
⎠ ⎟
2
i=1
m
∑
Wource: “Six sigma mechanical design tolerancing”, p 128
Department of Mechanical Engineering, The Ohio State UniversitySl. #33
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Nonlinear RSS
€
Tol y =∂f
∂x1
⎛
⎝ ⎜
⎞
⎠ ⎟
2
tol1
2 +∂f
∂x2
⎛
⎝ ⎜
⎞
⎠ ⎟
2
tol2
2 +∂f
∂x3
⎛
⎝ ⎜
⎞
⎠ ⎟
2
tol32 + ...+
∂f
∂xn
⎛
⎝ ⎜
⎞
⎠ ⎟
2
toln
€
adjusted =Tol i
3Cpki
Wource: “Six sigma mechanical design tolerancing”, p 128
Department of Mechanical Engineering, The Ohio State UniversitySl. #34
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RSS Example
Wource: “Six sigma mechanical design tolerancing”, p 128
• Largest => 0.05 + 0.051 = 0.101
• Smallest => 0.05 - 0.051 = -0.001
Department of Mechanical Engineering, The Ohio State UniversitySl. #35
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Taguchi MethodInput 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
Wource: “Six sigma mechanical design tolerancing”, p 21
Department of Mechanical Engineering, The Ohio State UniversitySl. #36
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Taguchi
Voice of customer Quality function deployment Inputs from parameter design
Optimum control-factor set points Tolerance estimates Initial material grades
Wource: “Six sigma mechanical design tolerancing”, p 22
Department of Mechanical Engineering, The Ohio State UniversitySl. #37
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Quality Loss Function
Identify customer costs for intolerable performance Quadratic quality loss function
Wource: “Six sigma mechanical design tolerancing”, p 208
€
L(y) = k(y − m)2 =Ao
Δo
(y − m)2
Department of Mechanical Engineering, The Ohio State UniversitySl. #38
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Cost of Off Target and Sensitivity
Cost to business to adjust off target performance
Sensitivity,
Wource: “Six sigma mechanical design tolerancing”, p 226-227
€
φ=Ao
A
€
A =Ao
Δ[β (x − m)]2
Department of Mechanical Engineering, The Ohio State UniversitySl. #39
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Manufacturing Tolerance
€
Δ =Ao
A
Δo
β
⎛
⎝ ⎜
⎞
⎠ ⎟
Department of Mechanical Engineering, The Ohio State UniversitySl. #40
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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 UniversitySl. #41
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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
Credits
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 UniversitySl. #42
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Disclaimer
This information is provided “as is” for general educational purposes; it can change over time and should be interpreted with regards to this particular circumstance. While much effort is made to provide complete information, Ohio State University and Gateway do not guarantee the accuracy and reliability of any information contained or displayed in the presentation. We disclaim any warranty, expressed or implied, including the warranties of fitness for a particular purpose. We do not assume any legal liability or responsibility for the accuracy, completeness, reliability, timeliness or usefulness of any information, or processes disclosed. Nor will Ohio State University or Gateway be held liable for any improper or incorrect use of the information described and/or contain herein and assumes no responsibility for anyone’s use of the information. Reference to any specific commercial product, process, or service by trade name, trademark, manufacture, or otherwise does not necessarily constitute or imply its endorsement.
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