ABSTRACTS OF ARTICLES OF THE JOURNAL "INFORMATION TECHNOLOGIES".
No. 7. Vol. 24. 2018

DOI: 10.17587/it.24.454-463

A. N. Bozhko, Assistant Professor, e-mail: abozhko@inbox.ru, Bauman Moscow State Technical University, Moscow

Formalization of Dimensional Constraints on Design Decisions of the Assembly Stage

The paper considers the influence of the system of design dimensional chains on permissible sequences of assembling and splitting the product into assembly units. When assembling products, the rules of connectivity and closure of design dimensional chains must be fulfilled. It is shown that admissible assembly sequences are linear extensions of a hierarchical order that is induced by a dimensional scheme on a set of parts of the product. Numerical estimates of the strength of constraints are given, which dimensional schemes impose design solutions of the assembly stage. It turned out that the chain method of dimensioning is the most rigid one, coordinating — the most "tolerant" one. A mathematical description of the principle of the closure of a dimensional chain is developed. It is shown that the localization of a dimensional problem requires the coincidence of two equivalence relations on the set of parts of the product. On the basis of the results obtained, two principles for reconciling the dimensional and mechanical structures of the product are formulated. The obtained results can be used to generate rational dimensional schemes in integrated CAD/CAM-systems.
Keywords: dimensional chain, assembly sequence, splitting into assembly units, hierarchical order, linear order, dimensional graph, tolerance relation, equivalence relation

P. 454–463

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