Tolerances Design

Department of Mechanical Engineering, The Ohio State UniversitySl. #1

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Tolerance Design


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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


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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


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Affected Areas

Product Design Quality Control

Manufacturing

EngineeringTolerance


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Questions

“Can customer tolerances be accommodated by product?”

“Can product tolerances be accommodated by the process?”


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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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Tolerance Types

Size Form Location Orientation


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Size Tolerances


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Form Tolerances


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Location Tolerances


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Orientation Tolerances


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Tolerance Buildup


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Statistical Principles

Measurement of central tendency Mean Median mode

Measurement of variations Range Variance Standard deviation

USLLSL

tolerance 3

X


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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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Tolerance SPC Charting

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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Figure Source: Tolerance Design, p 93

Initial Tolerance Design

Initial Tolerance

Design


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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


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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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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


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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

∑


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Worst Case Scenario Example

Source: Tolerance Design, pp 109-111


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• Largest => 0.05 + 0.093 = 0.143

• Smallest => 0.05 - 0.093 = -0.043


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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


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Root Sum-of-Square

RSS Assumes normal distribution behavior


€

f (x) =1

σ 2πe−(1/ 2)[x−μ ) /σ ]2


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RSS method

Assembly tolerance stack equation

€

f (x) = T12 + T2

2 + T32 + ...Tn

2



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Pool Variance in RSS

€

adjusted =Tol

3Cp

€

gap =Te

3Cp

⎛

⎝ ⎜

⎞

⎠ ⎟

2

+Tpi

3Cpi

⎛

⎝ ⎜

⎞

⎠ ⎟

i=1

m

∑2



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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



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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

∑



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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

∑



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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



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RSS Example


• Largest => 0.05 + 0.051 = 0.101

• Smallest => 0.05 - 0.051 = -0.001


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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



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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



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Quality Loss Function

Identify customer costs for intolerable performance Quadratic quality loss function


€

L(y) = k(y − m)2 =Ao

Δo

(y − m)2


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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


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Manufacturing Tolerance

€

Δ =Ao

A

Δo

β

⎛

⎝ ⎜

⎞

⎠ ⎟


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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


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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.


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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.

Tolerances Design

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