A New Mathematical Model for Geometric Tolerances as Applied to Round Faces-Reference-Cited by-同舟云学术

A New Mathematical Model for Geometric Tolerances as Applied to Round Faces

Published:2002-11-26 Issue:4 Volume:124 Page:609-622
ISSN:1050-0472
Container-title:Journal of Mechanical Design
language:en
Short-container-title:

Author:

Davidson J. K.¹,Mujezinovic´ A.²,Shah J. J.³

Affiliation:

1. Department of Mechanical and Aerospace Engineering, Arizona State University, Tempe, AZ 85287-6106

2. Power Systems Division, General Electric Co., Schenectady, NY

3. Arizona State University, Tempe, AZ 85287-6106

Abstract

A new mathematical model is presented for representing the tolerances of planar surfaces. The model is compatible with the ASME Standard for geometric tolerances. Central to the new model is a Tolerance-Map®,1 a hypothetical volume of points which corresponds to all possible locations and variations of a segment of a plane which can arise from tolerances on size, form, and orientation. Every Tolerance-Map is a convex set. This model is one part of a bi-level model that we are developing for geometric tolerances. The new model makes stackup relations apparent in an assembly, and these can be used to allocate size and orientational tolerances; the same relations also can be used to identify sensitivities for these tolerances. Stackup relations are developed for parts where the centers of faces are offset laterally. All stackup relations can be met for 100% interchangeability or for a specified probability. Methods are introduced whereby designers can identify trade-offs and optimize the allocation of tolerances. Examples are presented that illustrate important features of the new model.

Publisher

ASME International

Subject

Computer Graphics and Computer-Aided Design,Computer Science Applications,Mechanical Engineering,Mechanics of Materials

Link

http://asmedigitalcollection.asme.org/mechanicaldesign/article-pdf/124/4/609/5798064/609_1.pdf

Reference42 articles.

1. American National Standard ASME Y14.5M, 1994, Dimensioning and Tolerancing, The American Society of Mechanical Engineers, NY.

2. Gossard, D. C., Zuffante, R. P., and Sakurai, H., 1988, “Representing Dimensions, Tolerances, and Features in MCAE Systems,” IEEE Comput. Graphics Appl., 8(2), pp. 51–59.

3. Hillyard, R. C., and Braid, I. C., 1978, “Analysis of Dimensions and Tolerances in Computer-Aided Mechanical Design,” Comput.-Aided Des., 10(3), pp. 161–166.

4. Light, R. A., and Gossard, D. C., 1982, “Modification of Geometric Models through Variational Geometry,” Comput.-Aided Des., 14(4), pp. 209–214.

5. Lin, V. C., Gossard, D. C., and Light, R. A., 1981, “Variational Geometry in Computer-Aided Design,” Proc. of Siggraph ’81, Comput. Graph., 15(3), pp. 171–177.

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