Received 01.09.2023; Revised 20.09.2023; Accepted 26.09.2023

Published 29.09.2023; First Online 19.10.2023

https://doi.org/10.34229/2707-451X.23.3.1

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MSC 90B85

Optimized Packing of 3D Objects Bounded by Spherical and Conical Surfaces

Andrii Chuhai ^{1, 2} ,   Tetyana Romanova ^{1, 3 *} ,   Georgiy Yaskov ¹ ,   Mykola Gil ¹ ,   Sergiy Shekhotsov ¹

¹ Anatolii Pidhornyi Institute of Mechanical Engineering Problems of the National Academy of Sciences of Ukraine, Kharkiv

² Simon Kuznets Kharkiv National University of Economics, Kharkiv

³ Kharkiv National University of Radiolectronics, Kharkiv

^* Correspondence: This email address is being protected from spambots. You need JavaScript enabled to view it.

 

Introduction. Optimizing the packing of arbitrary geometric objects in additive manufacturing opens up new possibilities for increasing the efficiency of additive manufacturing of parts of a complex configuration due to the saving of energy, material and time resources. Additive manufacturing, a cornerstone in fields such as space engineering, medicine, mechanical engineering, and energy, has its efficiency hinging on the optimization of the 3D printing process. Given its widespread application, refining this process is of utmost importance.

The purpose of the paper. The paper aims to develop an approach for packing assembled parts of complex geometry in the working area of a 3D printer, while adhering to the standards of 3D printing.

Results. For the analytical description of the complex shaped industrial products, a, so called, “composed spherical cone” is used. This generates a family of such objects as spheres, cylinders, spherical cylinders, cones, truncated cones and spherical discs. Using the normalized quasi-phi-function of composed spherical cones, a mathematical model of the problem is presented in the form of a nonlinear programming problem. A solution strategy is developed, encompassing three primary stages: generation of feasible starting points, search of local minima and search of a better local minimum. Numerical examples of packing various industrial products in a 3D printer chamber is provided. 3D-parts are approximated by composed spherical cones with different metric parameters.

Conclusions. The conducted numerical simulation confirms the effectiveness of the proposed optimization approach. This study emphasizes the importance of further research and innovation in the field of 3D printing and its optimization, and also demonstrates the potential of using mathematical models to solve practical problems in a production environment.

 

Keywords: packing, assembled spherical cone, mathematical modeling, optimization, additive manufacturing.

 

Cite as: Chuhai A., Romanova T., Yaskov G., Gil M., Shekhotsov S. Optimized Packing of 3D Objects Bounded by Spherical and Conical Surfaces. Cybernetics and Computer Technologies. 2023. 3. P. 5–15. (in Ukrainian) https://doi.org/10.34229/2707-451X.23.3.1

 

References

           1.     Srivastava M., Rathee S. Additive manufacturing: recent trends, applications and future outlooks. Prog Addit, Manuf 2022. 7. P. 261–287. https://doi.org/10.1007/ s40964-021-00229-8

           2.     Ehlers T., Meyer I., Oel M., Bode B., Gembarski P.C., Lachmayer R. Effect-Engineering by Additive Manufacturing. In: Lachmayer, R., Bode, B., Kaierle, S. (eds) Innovative Product Development by Additive Manufacturing 2021. Springer, Cham. 2023. https://doi.org/10.1007/978-3-031-05918-6_1

           3.     Kaikai X., Yadong G., Qiang Z. Comparison of traditional processing and additive manufacturing technologies in various performance aspects: a review. Archiv.Civ.Mech.Eng. 2023. 23. P. 188. https://doi.org/10.1007/s43452-023-00699-3

           4.     Kadir A.Z.A., Yusof Y., Wahab M.S. Additive manufacturing cost estimation models – a classification review. Int J Adv Manuf Technol. 2020. 107. P. 4033–4053. https://doi.org/10.1007/s00170-020-05262-5.

           5.     Yadav D., Chhabra D., Kumar Garg R., Ahlawat A., Phogat A. Optimization of FDM 3D printing process parameters for multi-material using artificial neural network. Materials Today: Proceedings. 2020. 21 (3). P. 1583–1591. https://doi.org/10.1016/j.matpr.2019.11.225.

           6.     Wibawa T., Mastrisiswadi H., Ismianti I. 3D Print Parameter Optimization: A Literature Review. LPPM UPN "Veteran" Yogyakarta Conference Series Proceeding on Engineering and Science Series 2020. 1 (1). P. 146–151. https://doi.org/10.31098/ess.vlil.105

           7.     Araújo L.J.P., Özcan E., Atkin J.A.D, Baumersumers M. Analysis of irregular three-dimentional packing problems in additive manufacturing: a new taxonomy and dataset. International of Production Research. 2019. 57 (18), P. 5920–5934. https://doi.org/10.1080/00207543.2018.1534016

           8.     Leao A., Toledo F., Oliveira J., Carravilla M., et al. Irregular packing problems: a review of mathematical models. Eur. J. Oper. Res. 2020. 282 (3). P. 803–822. https://doi.org/10.1016/j.ejor.2019.04.045

           9.     Zhao J. Meso-model Optimization of Composite Propellant Based on Hybrid Genetic Algorithm and Mass Spring System. Journal of Physics: Conference Series 202. 2025 (1). P. 012036. https://doi.org/10.1088/1742-6596/2025/1/012036

       10.     Yuan Y., Tole K., Ni, F., He K., Xiong Z., Liu J. Adaptive simulated annealing with greedy search for the circle bin packing problem. Computers & Operations Research. 2022. 144. P. 105826. https://doi.org/10.1016/j.cor.2022.105826

       11.     Li S., Wei Y., Zhu H., Yu Z. New Fast Ant Colony Optimization Algorithm: The Saltatory Evolution Ant Colony Optimization Algorithm. Mathematics. 2022. 10 (6). P. 925. https://doi.org/10.3390/math10060925

       12.     Blum C., Blesa M.J. Probabilistic Beam Search for the Longest Common Subsequence Problem. In: Stützle, T., Birattari, M., H. Hoos, H. (eds) Engineering Stochastic Local Search Algorithms. Designing, Implementing and Analyzing Effective Heuristics. SLS 2007. Lecture Notes in Computer Science. 2007. Vol. 4638. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-74446-7_11

       13.     Stoyan Y., Romanova T., Pankratov A., Chugay A. Optimized object packings using quasi-phi-functions. Optimized packings with applications. 2015. P. 265–293. http://doi.org/10.1007/978-3-319-18899-7_13/

       14.     Kubach T., Bortfeldt A., Tilli T., Gehring H. Greedy algorithms for packing unequal spheres into a cuboidal strip or a cuboid. Asia-Pacific Journal of Operational Research. 2011. 28(06), P. 739–753. https://doi.org/10.1142/S0217595911003326

       15.     Romanova T., Stetsyuk P., Chugay A.M. et al. Parallel Computing Technologies for Solving Optimization Problems of Geometric Design. Cybern Syst Anal. 2019. 55. P. 894–904. https://doi.org/10.1007/s10559-019-00199-4

       16.     Wachter A., Biegler L.T. On the implementation of an interior-point filter line-search algorithm for large-scale nonlinear programming. Math. Program. 2006. 106 (1). P. 25–57. https://doi.org/10.1007/s10107-004-0559-y

 

 

ISSN 2707-451X (Online)

ISSN 2707-4501 (Print)

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