Structural models of product in CAD-systems

Bozhko A.N.
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Computer-aided assembly planning of complex products is an important area of modern information technology. The sequence of assembly and decomposition of the product into assembly units largely depend on the mechanical structure of a technical system (machine, mechanical device, etc.). In most modern research, the mechanical structure of products is modeled using a graph of connections and its various modifications. The coordination of parts during assembly can be achieved by implementing several connections at the same time. This generates a $k$-ary basing relation on a set of product parts, which cannot be correctly described by graph means. A hypergraph model of the mechanical structure of a product is proposed. Modern discrete manufacturing uses sequential coherent assembly operations. The mathematical description of such operations is the normal contraction of edges of the hypergraph model. The sequence of contractions that transform the hypergraph into a point is a description of the assembly plan. Hypergraphs for which such a transformation exists are called $s$-hypergraphs. $S$-hypergraphs are correct mathematical models of the mechanical structures of any assembled products. A theorem on necessary conditions for the contractibility of $s$-hypergraphs is given. It is shown that the necessary conditions are not sufficient. An example of a noncontractible hypergraph for which the necessary conditions are satisfied is given. This means that the design of a complex technical system may contain hidden structural errors that make assembly of the product impossible. Therefore, finding sufficient conditions for contractibility is an important task. Two theorems on sufficient conditions for contractibility are proved. They provide a theoretical basis for developing an efficient computational procedure for finding all $s$-subgraphs of an $s$-hypergraph. An $s$-subgraph is a model of any part of a product that can be assembled independently. These are, first of all, assembly units of various levels of hierarchy. The set of all $s$-subgraphs of an $s$-hypergraph, ordered by inclusion, is a lattice. This model can be used to synthesize all possible sequences of assembly and disassembly of a product and its components. The lattice model of the product allows you to analyze geometric obstacles during assembly using algebraic means.

Keywords: computer aided assembly planning (CAAP), hypergraph model of product structure, contraction, mechanical structure, contractibility conditions, lattice model
Citation in English: Bozhko A.N. Structural models of product in CAD-systems // Computer Research and Modeling, 2024, vol. 16, no. 5, pp. 1079-1091
Citation in English: Bozhko A.N. Structural models of product in CAD-systems // Computer Research and Modeling, 2024, vol. 16, no. 5, pp. 1079-1091
DOI: 10.20537/2076-7633-2024-16-5-1079-1091
URL: http://crm-en.ics.org.ru/journal/article/3518/
Creative Commons License This work is licensed under a Creative Commons Attribution-NoDerivs 3.0 Unported License.

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