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Research Papers

Modeling of Geometric Variations for Line-Profiles

[+] Author and Article Information
Joseph K. Davidson

e-mail: j.davidson@asu.edu

Jami J. Shah

e-mail: jami.shah@asu.edu
Department of Mechanical and Aerospace Engineering,
Arizona State University, Tempe, AZ 85287-6106

Contributed by the Design Engineering Division of ASME for publication in the Journal of Computing and Information Science in Engineering. Manuscript received March 4, 2012; final manuscript received July 20, 2012; published online October 1, 2012. Assoc. Editor: Bahram Ravani.

J. Comput. Inf. Sci. Eng 12(4), 041004 (Oct 01, 2012) (10 pages) doi:10.1115/1.4007404 History: Received March 04, 2012; Revised July 20, 2012

The geometric variations in a tolerance-zone can be modeled with hypothetical point-spaces called Tolerance-Maps (T-Maps) for purposes of automating the assignment of tolerances during design. The objective of this paper is to extend this model to represent tolerances on line-profiles. Such tolerances limit geometric manufacturing variations to a specified two-dimensional tolerance-zone, i.e., an area, the boundaries to which are curves parallel to the true profile. The single profile tolerance may be used to control position, orientation, and form of the profile. In this paper, the Tolerance-Map (Patent No. 6963824) is a hypothetical volume of points that captures all the positions for the true profile, and those curves parallel to it, which can reside in the tolerance-zone. The model is compatible with the ASME/ANSI/ISO Standards for geometric tolerances. T-Maps have been generated for other classes of geometric tolerances in which the variations of the feature are represented with a plane, line or circle, and these have been incorporated into testbed software for aiding designers when assigning tolerances for assemblies. In this paper the T-Map for line-profiles is created and, for the first time in this model, features may be either symmetrical or nonsymmetrical simple planar curves, typically closed. To economize on length of the paper, and yet to introduce a method whereby T-Maps may be used to optimize the allocation of tolerances for line-profiles, the scope of the paper has been limited to square, rectangular, and triangular shapes. An example of tolerance accumulation is presented to illustrate this method.

Copyright © 2012 by ASME
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References

Figures

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Fig. 1

(a) Square and (b) rectangular bosses (external features) with their shapes controlled by the profile tolerance t-  =  0.5 mm relative to Datums A, B, and C

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Fig. 2

A plate containing a triangular cutout with radii at its vertices. The shape is controlled by the profile tolerance t-  =  0.2 mm relative to Datums A, B, and C.

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Fig. 3

The true profile and its tolerance-zone for a portion of a triangular profile with radii at its vertices. Both the true profile (to be manufactured) and the idealized profile have the same limit to angular displacements, i.e., t- /d.

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Fig. 4

(a) The middle-sized profile (dashed-lined square) in the (exaggerated) tolerance-zone that is specified with the profile tolerance t- ; the five basis profiles are labeled, three with dotted lines. (b) One 2D cross-section of the corresponding T-Map that is confined to all size variations and displacements ex only in the x-direction.

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Fig. 5

The T-Map for all the middle-sized squares in the sharp-cornered tolerance-zone of Fig. 4(a); it is one central hypersection of the 4D T-Map that represents the entire tolerance-zone.

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Fig. 6

The 4D T-Map for the square tolerance-zone in Fig. 4(a) and showing all five basis-points ψ1,…, ψ5. For clarity of the graphics, the scale in the direction of size (ψ1ψ2) is exaggerated.

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Fig. 7

The middle-sized profile (dashed-lined rectangle) in the (exaggerated) tolerance-zone that is specified with the profile tolerance t- , and two of its fully rotated variational possibilities (dotted lines)

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Fig. 8

That portion of the T-Map for a sharp-cornered rectangular profile which represents the middle-sized rectangles in the tolerance-zone of Fig. 7; it is one central hypersection of the 4D T-Map for the profile. The two vertices at the front (with dots) correspond to the two rotated profiles in Fig. 7.

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Fig. 9

A square profile and the exey-section of its T-Map. (a) and (b) all corners sharp, (c) and (d) one rounded corner, (e) and (f) two adjacent corners rounded.

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Fig. 10

(a) A diagonal displaced location (dotted line) for the middle-sized profile (dashed line) in the tolerance-zone of a blended square-and-semicircle profile. (b) An augmented solid model of the 3D hypersection of its T-Map, formed as a cylindrical truncation (diameter t-) of the T-Map hypersection for a square profile (Fig. 7).

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Fig. 11

The middle-sized profile (dashed-lined triangle) in the (exaggerated) tolerance-zone that is specified with the profile tolerance t- , and two of its fully translated variational possibilities (dotted lines)

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Fig. 12

That portion of the T-Map for a sharp-cornered right isosceles triangular profile which represents the middle-sized triangles in the tolerance-zone of Fig. 11; it is one central hypersection of the 4D T-Map for the profile. Edges intersect (heavy dots) the ex- and ey-axes at ±t-/2 and the θ′-axis at ±t- /2.

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Fig. 13

Two raised profiles on the base-plate of the engineering toy with an xy-frame of coordinates placed on each

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Fig. 14

(a) The coupling that would join the power and load modules of the engineering toy. (b) The functional map generated from assumed characteristics of the coupling.

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Fig. 15

Two central cross-sections of the accumulation map (solid lined boundary) obtained as the Minkowski sum of the 3D hypersection T-Maps in Figs. 5 and 12, each shown with dashed lines. Drawn for t-1  =  t-2.

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Fig. 16

One quadrant from each of the central cross-sections of the accumulation map in Fig. 15 shown superimposed on their counterparts from the functional map in Fig. 14. (a) Contact at point A. (b) Contact at point B. Drawn for t-1   = 0.08 mm and t-2 = 0.12 mm.

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