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Optimized Filling of a Given Cuboid with Spherical Powders for Additive Manufacturing

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Abstract

In additive manufacturing (also known as 3D printing), a layer-by-layer buildup process is used for manufacturing parts. Modern laser 3D printers can work with various materials including metal powders. In particular, mixing various-sized spherical powders of titanium alloys is considered most promising for the aerospace industry. To achieve desired mechanical properties of the final product, it is necessary to maintain a certain proportional ratio between different powder fractions. In this paper, a modeling approach for filling up a rectangular 3D volume by unequal spheres in a layer-by-layer manner is proposed. A relative number of spheres of a given radius (relative frequency) are known and have to be fulfilled in the final packing. A fast heuristic has been developed to solve this special packing problem. Numerical results are compared with experimental findings for titanium alloy spherical powders. The relative frequencies obtained by using the imposed algorithm are very close to those obtained by the experiment. This provides an opportunity for using a cheap numerical modeling instead of expensive experimental study.

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Authors and Affiliations

  1. Lviv Polytechnic National University, Lviv, 79013, Ukraine

    Zoya Duriagina & Igor Lemishka

  2. Katolicki Uniwersytet Lubelski Jana Pawła II, Al. Racławickie 14, 20950, Lublin, Poland

    Zoya Duriagina

  3. Graduate Program in Systems Engineering, Nuevo Leon State University (UANL), Monterrey, CP 66455, San Nicolas de los Garza, Nuevo Leon, Mexico

    Igor Litvinchev

  4. Engineering Department, Panamerican University, CP 03920, Mexico City, Mexico

    Jose Antonio Marmolejo

  5. Department of Mathematical Modeling and Optimal Design, Institute for Mechanical Engineering Problems, the National Academy of Sciences of Ukraine, Kharkiv, 61046, Ukraine

    Alexander Pankratov, Tatiana Romanova & Georgy Yaskov

  6. Department of Systems Engineering of Kharkiv National University of Radio Electronics, Kharkiv, 61166, Ukraine

    Alexander Pankratov & Tatiana Romanova

Authors
  1. Zoya Duriagina
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  2. Igor Lemishka
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  3. Igor Litvinchev
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  4. Jose Antonio Marmolejo
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  5. Alexander Pankratov
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  6. Tatiana Romanova
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  7. Georgy Yaskov
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Corresponding author

Correspondence to Tatiana Romanova.

Additional information

This research was partially supported by CONACYT (No. 167019). A. Pankratov and T. Romanova were partially supported by the Program for the State Priority Scientific Research and Technological (Experimental) Development of the Department of Physical and Technical Problems of Energy of the National Academy of Sciences of Ukraine (No. 6541230).

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Duriagina, Z., Lemishka, I., Litvinchev, I. et al. Optimized Filling of a Given Cuboid with Spherical Powders for Additive Manufacturing. J. Oper. Res. Soc. China 9, 853–868 (2021). https://doi.org/10.1007/s40305-020-00314-9

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  • DOI: https://doi.org/10.1007/s40305-020-00314-9

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