### Abstract

A new mathematical model for representing the geometric variations of lines is extended to include probabilistic representations of 1-D clearance which arise from multi-dimensional variations of an axis, a hole and a pin-hole assembly. The model is compatible with the ASME/ANSI/ISO Standards for geometric tolerances. Central to the new model is a Tolerance-Map ^{1} (T-Map), a hypothetical volume of points that models the 3-D variations in location and orientation for a segment of a line (the axis), which can arise from tolerances on size, position, orientation, and form. Here it is extended to model the increase in yield that occurs when maximum material condition (MMC) is specified. The frequency distribution of 1-D clearance is decomposed into manufacturing bias, i.e. toward certain regions of a Tolerance-Map, and into a geometric bias that can be computed from the geometry of multidimensional T-Maps. Although the probabilistic representation in this paper is focused on geometric bias and manufacturing bias is presumed to be uniform, the method is robust enough to include manufacturing bias in the future. Geometric bias alone shows a greater likelihood of small clearances than large clearances between an assembled pin and hole.

Original language | English (US) |
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Title of host publication | Proceedings of the ASME Design Engineering Technical Conference |

Volume | 2006 |

State | Published - 2006 |

Event | 2006 ASME International Design Engineering Technical Conferences and Computers and Information In Engineering Conference, DETC2006 - Philadelphia, PA, United States Duration: Sep 10 2006 → Sep 13 2006 |

### Other

Other | 2006 ASME International Design Engineering Technical Conferences and Computers and Information In Engineering Conference, DETC2006 |
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Country | United States |

City | Philadelphia, PA |

Period | 9/10/06 → 9/13/06 |

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### ASJC Scopus subject areas

- Engineering(all)

### Cite this

*Proceedings of the ASME Design Engineering Technical Conference*(Vol. 2006)

**Using tolerance-maps to generate frequency distributions of clearance for pin-hole assemblies.** / Ameta, Gaurav; Davidson, Joseph K.; Shah, Jami J.

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution

*Proceedings of the ASME Design Engineering Technical Conference.*vol. 2006, 2006 ASME International Design Engineering Technical Conferences and Computers and Information In Engineering Conference, DETC2006, Philadelphia, PA, United States, 9/10/06.

}

TY - GEN

T1 - Using tolerance-maps to generate frequency distributions of clearance for pin-hole assemblies

AU - Ameta, Gaurav

AU - Davidson, Joseph K.

AU - Shah, Jami J.

PY - 2006

Y1 - 2006

N2 - A new mathematical model for representing the geometric variations of lines is extended to include probabilistic representations of 1-D clearance which arise from multi-dimensional variations of an axis, a hole and a pin-hole assembly. The model is compatible with the ASME/ANSI/ISO Standards for geometric tolerances. Central to the new model is a Tolerance-Map 1 (T-Map), a hypothetical volume of points that models the 3-D variations in location and orientation for a segment of a line (the axis), which can arise from tolerances on size, position, orientation, and form. Here it is extended to model the increase in yield that occurs when maximum material condition (MMC) is specified. The frequency distribution of 1-D clearance is decomposed into manufacturing bias, i.e. toward certain regions of a Tolerance-Map, and into a geometric bias that can be computed from the geometry of multidimensional T-Maps. Although the probabilistic representation in this paper is focused on geometric bias and manufacturing bias is presumed to be uniform, the method is robust enough to include manufacturing bias in the future. Geometric bias alone shows a greater likelihood of small clearances than large clearances between an assembled pin and hole.

AB - A new mathematical model for representing the geometric variations of lines is extended to include probabilistic representations of 1-D clearance which arise from multi-dimensional variations of an axis, a hole and a pin-hole assembly. The model is compatible with the ASME/ANSI/ISO Standards for geometric tolerances. Central to the new model is a Tolerance-Map 1 (T-Map), a hypothetical volume of points that models the 3-D variations in location and orientation for a segment of a line (the axis), which can arise from tolerances on size, position, orientation, and form. Here it is extended to model the increase in yield that occurs when maximum material condition (MMC) is specified. The frequency distribution of 1-D clearance is decomposed into manufacturing bias, i.e. toward certain regions of a Tolerance-Map, and into a geometric bias that can be computed from the geometry of multidimensional T-Maps. Although the probabilistic representation in this paper is focused on geometric bias and manufacturing bias is presumed to be uniform, the method is robust enough to include manufacturing bias in the future. Geometric bias alone shows a greater likelihood of small clearances than large clearances between an assembled pin and hole.

UR - http://www.scopus.com/inward/record.url?scp=33751337380&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=33751337380&partnerID=8YFLogxK

M3 - Conference contribution

AN - SCOPUS:33751337380

SN - 079183784X

SN - 9780791837849

VL - 2006

BT - Proceedings of the ASME Design Engineering Technical Conference

ER -