Research Papers

Comparison of Analysis Line and Polytopes Methods to Determine the Result of a Tolerance Chain

[+] Author and Article Information
Laurent Pierre

ENS Cachan,
University of Paris-Sud,
61, av. du Président Wilson,
Cachan Cedex 94235, France
e-mail: laurent.pierre@lurpa.ens-cachan.fr

Bernard Anselmetti

ENS Cachan,
University of Paris-Sud,
61, av. du Président Wilson,
Cachan Cedex 94235, France
e-mail: Bernard.anselmetti@lurpa.ens-cachan.fr

1Corresponding author.

Contributed by the Computers and Information Division of ASME for publication in the JOURNAL OF COMPUTING AND INFORMATION SCIENCE IN ENGINEERING. Manuscript received October 6, 2014; final manuscript received October 29, 2014; published online April 8, 2015. Editor: Bahram Ravani.

J. Comput. Inf. Sci. Eng 15(2), 021007 (Jun 01, 2015) (9 pages) Paper No: JCISE-14-1317; doi: 10.1115/1.4029049 History: Received October 06, 2014; Revised October 29, 2014; Online April 08, 2015

Functional tolerancing must ensure the assembly and the functioning of a mechanism. This paper compares two methods of tolerance analysis of a mechanical system: the method of “analysis lines” and the method of “polytopes.” The first method needs a discretization of the ending functional surface according to various analysis lines placed on the outer-bound of the face and oriented along the normal of the surface. The second method uses polytopes. The polytopes are defined from the acceptable limits of the geometric deviations of parts and possible displacements between two parts. Minkowski sums and intersections polytopes are then carried out to take into account all geometric variations of a mechanism.

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Fig. 2

Setting-up table of the cover on the housing

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Fig. 4

ISO tolerancing of both parts

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Fig. 5

Assembling requirement of the shaft

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Fig. 6

Main specifications

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Fig. 7

Discretization in eight analysis directions

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Fig. 8

Straightness between two different parts

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Fig. 9

Influence of the cover

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Fig. 10

Influence of junction housing/cover

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Fig. 11

Geometric polytope D1,1/ABg

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Fig. 12

Geometric polytope D1,1/Ag

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Fig. 13

Global geometric polytope D1,1/ABg

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Fig. 14

Geometric polytope D2,1/CDg

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Fig. 15

Polytope of contact DAB/CDC

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Fig. 16

Inclusion of the calculated polytope D1,1/2,1 in the functional polytope D1,1/2,1f




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