Research Papers

Comparison of Two Similar Mathematical Models for Tolerance Analysis: T-Map and Deviation Domain

[+] Author and Article Information
Max Giordano

e-mail: Max.Giordano@univ-savoie.fr
Laboratoire S.Y.M.M.E.,
5 chemin de Bellevue,
Annecy-le-vieux 74 940, France

Joseph K. Davidson

Department of Mechanical and
Aerospace Engineering,
Arizona State University,
Tempe, AZ 85287
e-mail: j.davidson@asu.edu

Contributed by the Design for Manufacturing Committee of ASME for publication in the JOURNAL OF MECHANICAL DESIGN. Manuscript received January 4, 2013; final manuscript received July 5, 2013; published online September 5, 2013. Assoc. Editor: Rikard Söderberg.

J. Mech. Des 135(10), 101008 (Sep 05, 2013) (7 pages) Paper No: MD-13-1004; doi: 10.1115/1.4024980 History: Received January 04, 2013; Revised July 05, 2013

The major part of production cost of a manufacturing product is set during the design stage and especially by the tolerancing choice. Therefore, a lot of work involves trying to simulate the impact of these choices and provide an automatic optimization. For integrating this modeling in computer aided design (cad) software, the tolerancing must be modeled by a mathematical tool. Numerous models have been developed but few of them are really efficient. Two advanced models are “T-map” model developed by Joseph K. Davidson and “deviation domain” developed by Max Giordano. Despite the graphical representation of these two models seems to be similar, they have significant differences in their construction and their resolution method. These similarities and differences highlight the needs of tolerancing modeling tool in each kind of problems, especially in case of assembly with parallel links.

Copyright © 2013 by ASME
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Fig. 1

Size and position tolerances specified for a round boss [7] according to the ASME representation

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Fig. 2

Limiting configurations of the axis in its tolerance zone in the case of MMC. The circles have diameter t [7].

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Fig. 3

T-map model of the axis localization tolerancing in the case of MMC. The circles have diameter t, which is the position tolerance [7].

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Fig. 4

Projection of the T-map modeling the maximal material specification tolerancing [7]

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Fig. 5

Illustration of the deviation domain in the (P; Q; L′) space

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Fig. 6

Self-aligned coupling assembly [7] according to the ASME representation

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Fig. 7

Positional variation for one pin-slot assembly (adapted from [7])

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Fig. 8

Geometry to determine the variations in the position of the point P (adapted from [7])

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Fig. 9

Application of the Minkowski sum to obtain the accumulation T-map [7]

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Fig. 10

Accumulation T-map included in the functional T-map [7]

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Fig. 11

Deviation domain of the #1 engaged pin-slot

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Fig. 12

Accumulation deviation domain for the 3pin-slot assembly




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