Feature cluster algebra for geometric tolerancing

Yadong Shen, Jami J. Shah, Joseph K. Davidson

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

3 Citations (Scopus)

Abstract

The ASME Y14.5.1 companion to the Geometric Dimensioning and Tolerancing (GD&T) standard gives an exhaustive tabulation of active and invariant degrees of freedom (DOF) for Datum Reference Frames (DRF). These DRFs are entity clusters of points, lines, and planes with different geometric relations to each other (coincident, parallel, perpendicular etc.). This paper investigates the systematic derivation of DRF & target clusters' DOFs and associates them with tolerance classes. A vector representation of geometric entities and Boolean operations are proposed. This algebra was validated by applying it to all cases in the Y14.5.1 tabulation; the results were identical to those in the standard. Only translational and rotational DOFs were considered since size dimensions are independent of this analysis. Of course, only a handful of DRF cases in the standard have practical use. Based on the algebraic calculation of DOF in each DRF cluster, the general rules regarding how target entities are constrained by diverse DRF clusters are discussed in this paper. Target entities are associated with specific DRF and tolerance or composite tolerances.

Original languageEnglish (US)
Title of host publicationProceedings of the ASME Design Engineering Technical Conference
Pages709-722
Number of pages14
Volume2
EditionPARTS A AND B
DOIs
StatePublished - 2011
EventASME 2011 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference, IDETC/CIE 2011 - Washington, DC, United States
Duration: Aug 28 2011Aug 31 2011

Other

OtherASME 2011 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference, IDETC/CIE 2011
CountryUnited States
CityWashington, DC
Period8/28/118/31/11

Fingerprint

Tolerancing
Cluster Algebra
Algebra
Tolerance
Target
Degree of freedom
Boolean Operation
Dimensioning
Coincident
Composite materials
Perpendicular
Composite
Invariant
Line
Standards

ASJC Scopus subject areas

  • Mechanical Engineering
  • Computer Graphics and Computer-Aided Design
  • Computer Science Applications
  • Modeling and Simulation

Cite this

Shen, Y., Shah, J. J., & Davidson, J. K. (2011). Feature cluster algebra for geometric tolerancing. In Proceedings of the ASME Design Engineering Technical Conference (PARTS A AND B ed., Vol. 2, pp. 709-722) https://doi.org/10.1115/DETC2011-47937

Feature cluster algebra for geometric tolerancing. / Shen, Yadong; Shah, Jami J.; Davidson, Joseph K.

Proceedings of the ASME Design Engineering Technical Conference. Vol. 2 PARTS A AND B. ed. 2011. p. 709-722.

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

Shen, Y, Shah, JJ & Davidson, JK 2011, Feature cluster algebra for geometric tolerancing. in Proceedings of the ASME Design Engineering Technical Conference. PARTS A AND B edn, vol. 2, pp. 709-722, ASME 2011 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference, IDETC/CIE 2011, Washington, DC, United States, 8/28/11. https://doi.org/10.1115/DETC2011-47937
Shen Y, Shah JJ, Davidson JK. Feature cluster algebra for geometric tolerancing. In Proceedings of the ASME Design Engineering Technical Conference. PARTS A AND B ed. Vol. 2. 2011. p. 709-722 https://doi.org/10.1115/DETC2011-47937
Shen, Yadong ; Shah, Jami J. ; Davidson, Joseph K. / Feature cluster algebra for geometric tolerancing. Proceedings of the ASME Design Engineering Technical Conference. Vol. 2 PARTS A AND B. ed. 2011. pp. 709-722
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