Abstract
Purpose: The purpose of scientific research is to develop a mathematical model for optimizing the stamp topology used in metal forming processes. In the work, it was necessary to determine the volume of the inner region of the stamp as the target optimization function, optimization variables, which are the skeleton, replacing the stamp topology.
Design/methodology/approach: As a method of material redistribution, it is proposed to replace the stamp volume with a system of rods of various widths determined by the required volume change. The dependences of changes in the geometry of the core frame of the stamp on the coefficient of volume reduction are obtained. The mathematical formulation of the optimization problem is presented, the condition for the invariance of the stamp base is given, the loading areas, the stored boundary areas are defined.
Findings: Using the obtained relations, the dependences of the coefficient of reduction of the topology volume, the number of rods approximating the inner region of the stamp, and also the geometric characteristics of the rods, namely, the height and cross section, are presented.
Originality/value: Using the presented patterns will significantly optimize the material costs for the manufacture of forming stamps from polymer materials using additive technologies, as well as develop an algorithm and software code for creating software models of stamps of a minimized volume. The results of the study will allow us to reconsider the approach to choosing the shape of the stamp, reduce the cost of its manufacture.
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Acknowledgments
The reported study was funded by the Russian Fund for Fundamental Research, project “Razrabotka modeli optimizacii form shtampovochnyh osnastok metodom effektivnogo pereraspredeleniya materiala”, project No. 19-38-60020\19.
The study was carried out using the equipment of the Center for Collective Use “New Materials and Technologies” on the basis of KnASU.
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Andrianov, I.K. (2021). The Mathematical Model of the Stamp Material Redistribution Using Uniform Bar Structures. In: Shakirova, O.G., Bashkov, O.V., Khusainov, A.A. (eds) Current Problems and Ways of Industry Development: Equipment and Technologies. Lecture Notes in Networks and Systems, vol 200. Springer, Cham. https://doi.org/10.1007/978-3-030-69421-0_6
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DOI: https://doi.org/10.1007/978-3-030-69421-0_6
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