Research Papers

Capability Estimation of Geometrical Tolerance With a Material Modifier by a Hasofer–Lind Index

[+] Author and Article Information
Antoine S. Tahan

Department of Mechanical Engineering, École de technologie supérieure, Montreal, PQ H3C 1K3, Canadaantoine.tahan@etsmtl.ca

Jason Cauvier

Department of Mechanical Engineering, École de technologie supérieure, Montreal, PQ H3C 1K3, Canadajason.cauvier.1@ens.etsmtl.ca

J. Manuf. Sci. Eng 134(2), 021007 (Apr 04, 2012) (11 pages) doi:10.1115/1.4005797 History: Received October 31, 2010; Revised December 25, 2011; Published March 30, 2012; Online April 04, 2012

This paper considers a way of measuring a process capability index in order to obtain the geometric tolerance of a pattern of position elements according to the ASME Y14.5 standard. The number of elements present in the pattern, as well as its material condition (least LMC or maximum MMC), are taken into consideration during the analysis. An explicit mathematical model will be developed to identify the distribution functions (PDF and CDF) of defects on the location and diameter. Using these distributions and the Hasofer–Lind index, we will arrive at a new definition of process capability—meaning the value of tolerances that can meet the threshold of x% compliance. Finally, our method is validated using a variety of typical case studies.

Copyright © 2012 by American Society of Mechanical Engineers
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Figure 1

Example of statistical requirements

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Figure 2

Example of an MMC requirement

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Figure 3

Example of an erroneous requirement

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Figure 4

Example of PLTZF tolerance position

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Figure 5

Conformity and nonconformity domains

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Figure 6

Rosenblatt–Nataf transformation (s,r)→(z1,z2)

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Figure 7

Capability index Cp

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Figure 8

Hasofer–Lind index

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Figure 9

Hasofer–Lind index (2)

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Figure 10

Hasofer–Lind optimal index

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Figure 11

Example of positional tolerancing

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Figure 12

Illustration of a deviation vector for position tolerance

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Figure 13

Illustration of Pattern-Locating Tolerance Zone Framework (PLTZF)

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Figure 14

Probability density function kRi(x;(σr,μr)) of PLTZF for a single hole

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Figure 15

Probability density function fr(r;(σr,μr,n))

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Figure 16

Expected value and variance of rPLTZF

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Figure 17

Calculation methodology of capability index β

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Figure 18

Monte Carlo Simulation area in dimensional space



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