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Research Papers: Design for Manufacturing

Semantic Tolerance Modeling With Generalized Intervals

[+] Author and Article Information
Yan Wang

Department of Industrial Engineering and Management Systems, University of Central Florida, 4000 Central Florida Boulevard, Orlando, FL 32816-2993wangyan@mail.ucf.edu

J. Mech. Des 130(8), 081701 (Jul 11, 2008) (7 pages) doi:10.1115/1.2936900 History: Received June 03, 2007; Revised February 28, 2008; Published July 11, 2008

A significant amount of research has been performed to explore the mathematical basis for dimensional and geometric tolerance representation, analysis, and synthesis. However, tolerancing semantics such as logical dependency among variations and sequence of specifications is not maintained in these models. Consequently, their numerical results are not interpretable. In this paper, a semantic tolerance modeling scheme based on generalized intervals is proposed to improve the interpretability of tolerance modeling. Under certain optimality conditions, semantic tolerance models allow for true variation range estimations with simple computations. With the theoretical support of semantic tolerance modeling, a new dimension and tolerance specification scheme for semantic tolerancing is also proposed to better capture design intents and manufacturing implications, including flexible material selection, rigidity of specifications and constraints, component sorting in selective assembly, and assembly sequences.

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Copyright © 2008 by American Society of Mechanical Engineers
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Figures

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Figure 1

The syntax tree of f1=∣x1+x2∣∕(x1−x2x3)

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Figure 2

Different types of semantics need to be captured, which are not differentiated in traditional modeling methods

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Figure 3

Variations of size and geometry, shape deformation, and kinematics from a closed loop in assembly

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Figure 4

An inf-sup diagram is also a rigidity diagram

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Figure 5

A priori and a posteriori tolerances in semantic tolerancing

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Figure 6

Semantic tolerancing implies assembly sequence

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Figure 7

Semantic tolerancing captures intent of material selection and selective assembly

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Figure 8

Modal intervals make complex algebraic relations with multi-incident variables interpretable; interpretations correspond to different value sets

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