### 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 language | English (US) |
---|---|

Title of host publication | Proceedings of the ASME International Design Engineering Technical Conferences and Computers and Information in Engineering Conference - DETC2005 |

Pages | 509-520 |

Number of pages | 12 |

Volume | 2 A |

State | Published - 2005 |

Event | DETC2005: ASME International Design Engineering Technical Conferences and Computers and Information in Engineering Conference - Long Beach, CA, United States Duration: Sep 24 2005 → Sep 28 2005 |

### Other

Other | DETC2005: ASME International Design Engineering Technical Conferences and Computers and Information in Engineering Conference |
---|---|

Country | United States |

City | Long Beach, CA |

Period | 9/24/05 → 9/28/05 |

### Fingerprint

### ASJC Scopus subject areas

- Engineering(all)

### Cite this

*Proceedings of the ASME International Design Engineering Technical Conferences and Computers and Information in Engineering Conference - DETC2005*(Vol. 2 A, pp. 509-520)

**Allocating tolerances statistically with tolerance-maps and beta distributions : The target a planar face.** / Ameta, Gaurav; Davidson, Joseph K.; Shah, Jami J.

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

*Proceedings of the ASME International Design Engineering Technical Conferences and Computers and Information in Engineering Conference - DETC2005.*vol. 2 A, pp. 509-520, DETC2005: ASME International Design Engineering Technical Conferences and Computers and Information in Engineering Conference, Long Beach, CA, United States, 9/24/05.

}

TY - GEN

T1 - Allocating tolerances statistically with tolerance-maps and beta distributions

T2 - The target a planar face

AU - Ameta, Gaurav

AU - Davidson, Joseph K.

AU - Shah, Jami J.

PY - 2005

Y1 - 2005

N2 - 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.

AB - 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.

UR - http://www.scopus.com/inward/record.url?scp=33144457116&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=33144457116&partnerID=8YFLogxK

M3 - Conference contribution

SN - 079184739X

SN - 9780791847398

VL - 2 A

SP - 509

EP - 520

BT - Proceedings of the ASME International Design Engineering Technical Conferences and Computers and Information in Engineering Conference - DETC2005

ER -