Allocating tolerances statistically with tolerance-maps and beta distributions: The target a planar face

Gaurav Ameta, Joseph K. Davidson, Jami J. Shah

Research output: Chapter in Book/Report/Conference proceedingConference contribution

3 Scopus citations

Abstract

A new math model for geometric tolerances is used to build the frequency distribution for clearance in an assembly of parts, each of which is manufactured to a given set of size and orientation tolerances. The central element of the new math model is the Tolerance-Map® (T-Map®); it is the range of points resulting from a one-to-one mapping from all the variational possibilities of a feature, within its tolerance-zone, to a specially designed Euclidean point-space. A functional T-Map represents both the acceptable range of 1-D clearance and the acceptable limits to the 3-D variational possibilities of the target face consistent with it. An accumulation T-Map represents all the accumulated 3-D variational possibilities of the target which arise from allowable manufacturing variations on the individual parts in the assembly. The geometric shapes of the accumulation and functional maps are used to compute a measure of all variational possibilities of manufacture of the parts which will give each value of clearance. The measures are then arranged as a probability density function over the acceptable range of clearance, and a beta distribution is fitted to it. The method is applied to two examples.

Original languageEnglish (US)
Title of host publicationProceedings of the ASME International Design Engineering Technical Conferences and Computers and Information in Engineering Conferences - DETC2005
Subtitle of host publication31st Design Automation Conference
PublisherAmerican Society of Mechanical Engineers
Pages509-520
Number of pages12
ISBN (Print)079184739X, 9780791847398
DOIs
StatePublished - 2005
EventDETC2005: ASME International Design Engineering Technical Conferences and Computers and Information in Engineering Conference - Long Beach, CA, United States
Duration: Sep 24 2005Sep 28 2005

Publication series

NameProceedings of the ASME International Design Engineering Technical Conferences and Computers and Information in Engineering Conference - DETC2005
Volume2 A

Other

OtherDETC2005: ASME International Design Engineering Technical Conferences and Computers and Information in Engineering Conference
CountryUnited States
CityLong Beach, CA
Period9/24/059/28/05

ASJC Scopus subject areas

  • Engineering(all)

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    Ameta, G., Davidson, J. K., & Shah, J. J. (2005). Allocating tolerances statistically with tolerance-maps and beta distributions: The target a planar face. In Proceedings of the ASME International Design Engineering Technical Conferences and Computers and Information in Engineering Conferences - DETC2005: 31st Design Automation Conference (pp. 509-520). (Proceedings of the ASME International Design Engineering Technical Conferences and Computers and Information in Engineering Conference - DETC2005; Vol. 2 A). American Society of Mechanical Engineers. https://doi.org/10.1115/detc2005-85122