Reducing Cost of Product by Optimizing Design Dimensional Chains

The purpose of calculating dimensional chains is to ensure the accuracy of the closing link necessary for the functioning of the object. Traditionally used methods of assigning tolerances to the component links of the dimension chain are aimed at ensuring their accuracy equivalence without linking the design process with production. In practice, the accuracy of the structural elements of the parts determines the cost of processing the corresponding surfaces, therefore, different options for distributing the accuracy of the master link among the component links lead to different costs for manufacturing

the entire set of parts included in the dimensional chain. The paper solves the problem of optimizing design dimensional chains according to the criterion of minimum cost. An integrated approach to solving this problem includes a method for determining the tolerance-cost dependencies, the formation of the necessary information base and directly an algorithm for optimizing the tolerances of the component links of the dimensional chain. The definition of the “tolerance cost” dependencies is based on the method of aggregated calculation of technological cost using the coefficients of the relative cost of the technological operation and the time of its execution. The obtained dependencies are approximated by power functions. The optimization problem is solved on the basis of the necessary and sufficient condition for the existence of an extremum using the method of indefinite Lagrange multipliers. Dependencies for determining optimized tolerances of links of dimensional chains are obtained for the maximum-minimum and probabilistic methods. The formation of an information base for determining the “tolerance cost” dependencies is based on the classification and typification of structural elements of parts according to features that determine the type of processing and technological equipment. Optimization of design dimensional chains based on the proposed approach can be used in mass production conditions as one of the ways to reduce the cost of a product and ensure its competitiveness.

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