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Sparsest balanced packing of irregular 3D objects in a cylindrical container

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  • Romanova, Tatiana
  • Stoyan, Yurij
  • Pankratov, Alexander
  • Litvinchev, Igor
  • Plankovskyy, Sergiy
  • Tsegelnyk, Yevgen
  • Shypul, Olga

Abstract

Sparsest packing for irregular 3D objects is introduced. This problem is motivated by the thermal deburring – modern clean and energy saving technology of removing burrs from machine parts (objects) by detonating gas mixtures in a deburring chamber. The objects in the chamber are placed in a vertical cylindrical rack (container) divided into sub-containers by horizontal shelves rigidly fixed on a thin rod passing through the centre of the rack. To achieve a stable processing quality and the most uniform distribution of thermal and power effects, the parts have to be placed sufficiently distant one from another, as well as from the lateral cylindrical surface of the container. The objects are assigned to specific shelves and are represented by a union of basic convex 3D shapes (e.g., cylinders, prisms, cuboids, cones). The sparsest packing is aimed to place the 3D objects as distant as possible, freely sliding and rotating on the shelves subject to balancing conditions. Using the phi-function technique a corresponding nonlinear programming model is constructed. A solution algorithm is proposed and computational results are presented.

Suggested Citation

  • Romanova, Tatiana & Stoyan, Yurij & Pankratov, Alexander & Litvinchev, Igor & Plankovskyy, Sergiy & Tsegelnyk, Yevgen & Shypul, Olga, 2021. "Sparsest balanced packing of irregular 3D objects in a cylindrical container," European Journal of Operational Research, Elsevier, vol. 291(1), pages 84-100.
    • Handle: RePEc:eee:ejores:v:291:y:2021:i:1:p:84-100
    DOI: 10.1016/j.ejor.2020.09.021
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    References listed on IDEAS

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