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Research Papers

The Relationship Between Geometrical Complexity and Process Capability

[+] Author and Article Information
Marc Jr. Lépine

Department of Mechanical Engineering,
École de Technologie Supérieure,
1100 Notre-Dame West,
Montréal, QC H3C 1K3, Canada
e-mail: cc-marc-junior.lepine@etsmtl.ca

Antoine S. Tahan

Department of Mechanical Engineering,
École de Technologie Supérieure,
1100 Notre-Dame West,
Montréal, QC H3C 1K3, Canada
e-mail: antoine.tahan@etsmtl.ca

1Corresponding author.

Contributed by the Manufacturing Engineering Division of ASME for publication in the JOURNAL OF MANUFACTURING SCIENCE AND ENGINEERING. Manuscript received September 3, 2014; final manuscript received October 21, 2015; published online December 10, 2015. Assoc. Editor: Xiaoping Qian.

J. Manuf. Sci. Eng 138(5), 051009 (Dec 10, 2015) (13 pages) Paper No: MANU-14-1460; doi: 10.1115/1.4031900 History: Received September 03, 2014; Revised October 21, 2015

This paper proposes a new method to estimate the process capability for a profile geometric tolerance as defined by the ASME Y14.5 standard. The novelty of the method is that it uses the known process capability of a given geometry to predict, using the order statistics theorem, new capabilities for different geometries of higher or lower complexity. By considering the geometrical complexity of mechanical parts, a manufacturing process may be capable (e.g., Cpk > 1.5) for parts with simple geometry and incapable (e.g., Cpk < 1) for parts with complex geometry. In the proposed model, the process capability becomes a mathematical function of both the statistical behavior of the process (e.g., expectation and variance) and the geometric complexity of manufactured surfaces. Three experimental case studies are presented to illustrate the usefulness and the validity of the developed model.

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Figures

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Fig. 1

DFM process for simple geometry

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Fig. 2

Geometrical complexity of parts

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Fig. 3

Geometrical complexity of hole patterns

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Fig. 4

Example of geometric features (taken from ASME Y14.5 [3]): (a) example of position tolerance for a hole pattern and (b) example of profile tolerance for multiple surfaces

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Fig. 5

Schematic representation for a normalization operation on a geometrical complexity index

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Fig. 6

Representation of deviations normal to theoretical surface

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Fig. 7

Profile tolerancing according to ASME Y14.5 [3]

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Fig. 8

Representation of zTYPE1

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Fig. 9

PDF of f(zTYPE1,n) with f(δi) = N(0,1)

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Fig. 10

tolTYPE1 in relation to Cpk and for f(δi)=N(0,1)

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Fig. 11

Representation of zTYPE2

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Fig. 12

tolTYPE2 in relation to Cpk and n for f(δi)=N(0,1)

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Fig. 13

PDF of f(zTYPE2,n) with f(δi)=N(0,1)

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Fig. 14

Representation of zTYPE3

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Fig. 15

Probability density f(zTYPE3,n) function of with f(δi*)=N(0,1)

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Fig. 16

tolTYPE3 in relation to Cpk and for f(δi*)=N(0,1)

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Fig. 17

Bracket assembly capability index Cpk (continuous line is the prediction of the model and - - - - line indicates the confidence intervals 95%; interval plots are the in situ data measurements with 95% confidence intervals)

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Fig. 18

Wall structure capability index Cpk (continuous line is the prediction of the model and- - - -line indicates the confidence intervals 95%; interval plots are the in situ data measurements with 95% confidence intervals)

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Fig. 19

Freeform profile tolerance to achieve Cpk=1

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