NDLI: Introducing a Projection-Based Method to Compare Three Approaches Computing the Accumulation of Geometric Variations

Content Provider	The American Society of Mechanical Engineers (ASME) Digital Collection
Author	Delos, Vincent Arroyave-Tobón, Santiago Teissandier, Denis
Copyright Year	2018
Abstract	In mechanical design, tolerance zones and contact gaps can be represented by sets of geometric constraints. For computing the accumulation of possible manufacturing defects, these sets have to be summed and/or intersected according to the assembly architecture. The advantage of this approach is its robustness for treating even over-constrained mechanisms i.e. mechanisms in which some degrees of freedom are suppressed in a redundant way. However, the sum of constraints, which must be computed when simulating the accumulation of defects in serial joints, is a very time-consuming operation. In this work, we compare three methods for summing sets of constraints using polyhedral objects. The difference between them lie in the way the degrees of freedom (DOFs) (or invariance) of joints and features are treated. The first method proposes to virtually limit the DOFs of the toleranced features and joints to turn the polyhedra into polytopes and avoid manipulating unbounded objects. Even though this approach enables to sum, it also introduces bounding or cap facets which increase the complexity of the operand sets. This complexity increases after each operation until becoming far too significant. The second method aims to face this problem by cleaning, after each sum, the calculated polytope to keep under control the effects of the propagation of the DOFs. The third method is new and based on the identification of the sub-space in which the projection of the operands are bounded sets. Calculating the sum in this sub-space allows reducing significantly the operands complexity and consequently the computational time. After presenting the geometric properties on which the approaches rely, we demonstrate them on an industrial case. Then we compare the computation times and deduce the equality of the results of all the methods.
Sponsorship	Design Engineering Division Computers and Information in Engineering Division
File Format	PDF
ISBN	9780791851722
DOI	10.1115/DETC2018-85366
Volume Number	Volume 1A: 38th Computers and Information in Engineering Conference
Conference Proceedings	ASME 2018 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference
Language	English
Publisher Date	2018-08-26
Publisher Place	Quebec City, Quebec, Canada
Access Restriction	Subscribed
Subject Keyword	Design engineering Degrees of freedom Robustness Manufacturing Computation
Content Type	Text
Resource Type	Article

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