A New Variational Association Process for the Verification of Geometrical Specifications

[+] Author and Article Information
Jean-Yves Choley

 LISMMA, SUPMECA, 93407 Saint-Ouen Cedex, Francejean-yves.choley@supmeca.fr

Alain Riviere, André Clement

 LISMMA, SUPMECA, 93407 Saint-Ouen Cedex, France

Pierre Bourdet

 LURPA, ENS Cachan, 94235 Cachan Cedex, France

J. Comput. Inf. Sci. Eng 7(1), 66-71 (Nov 22, 2006) (6 pages) doi:10.1115/1.2432900 History: Received September 30, 2005; Revised November 22, 2006

When this new association process of a datum is performed to verify a geometrical specification, measured points are considered as perturbations which generate modifications of the nominal geometry by variation of its location, orientation, and intrinsic dimensional characteristics, without requiring rotation and translation variables as the traditional methods usually do (Bourdet, , 1996, Advanced Mathematical Tools in Metrology II, World Scientific) with torsors or matrices. This new association process (Choley, 2005, Ph.D. thesis, Ecole Central, Paris; Choley, , 2006, Advanced Mathematical and Computational Tools in Metrology, VII, World Scientific) is based on both a reduced modeling of the geometry, taken out of the computer aided design system database, and a variational distance function. The whole measured points set influence is taken into account as an optimization criterion is applied (Bourdet and Clement, 1988, Ann. CIRP37(1), p. 503; Srinivasan, DIMACS Workshop on Computer Aided Design and Manufacturing, Rutgers University, NJ, October 7–9). Thus, the least squares optimization is achieved using the pseudo-inverse matrix, whereas the minimax optimization is treated with an algorithm developed by the Physikalisch-Technische Bundesanstalt and adapted for this purpose. In this paper, it is explained how this association process may be applied to planes and cylinders, used as single datum, datum systems, or common datum, with the least squares and minimax criteria.

Copyright © 2007 by American Society of Mechanical Engineers
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Figure 1

The association of a datum for the verification of a GPS specification

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Figure 2

The modeling of single datum

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Figure 3

The modeling of a common datum or datum system (three orthogonal planes)

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Figure 4

The modeling of a common datum or a datum system (a plane and two cylinders)

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Figure 5

CAD model and main casing design drawing of a gear unit

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Figure 6

The variational association process for the chosen location specification

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Figure 7

Distance function between the actual geometry and the ideal geometry

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Figure 8

The variational association process

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Figure 9

The “nonideal simulated” geometry

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Figure 10

The PTB combinatorial algorithm

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Figure 11

Matrix J for a common datum, three orthogonal planes, least squares criterion

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Figure 12

Matrix A for a datum system, three orthogonal planes, minimax criterion



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