Upper-Bound Estimate of Reduced Pressure and Optimisation of Scheme Parameters for Direct Extrusion of Parts with a Conical Cavity

Authors

DOI:

https://doi.org/10.20535/2521-1943.2025.9.4(107).344506

Keywords:

direct extrusion, conical cavity, upper-bound method, rigid triangular elements, reduced pressure, kinematic module, optimisation

Abstract

The object of the study is the process of direct cold extrusion of parts with a conical cavity. The problem addressed is the absence of general analytical estimates of the reduced pressure that simultaneously take into account the geometry of the bottom and wall of conical cavity, contact friction and the parameters of the deformation-zone partition, while remaining suitable for engineering calculations.
The aim of the work is to develop a parametric scheme for partitioning the deformation zone and to determine the partition parameters for which the reduced pressure is minimal.
The deformation zone is divided into a compression and flow-turning region in the bottom and a compression region in the wall of conical cavity; the reduced pressure is represented as the sum of the contributions of these regions. For the bottom, closed-form expressions for the optimal geometric parameters are obtained; for the wall, the minimisation problem is reduced to a one-dimensional search with respect to the partition parameter at a fixed number of similar triangular elements.
It is shown that increasing the relative radius of the cavity from 0.25 to 0.7 and the cone angle of the wall from 5° to 30°, as well as decreasing the relative bottom thickness from 1.5 to 0.75, leads to an increase in reduced pressure by approximately 1.5–2 times. A threshold dependence on the number of similar elements in the wall of conical cavity is revealed: for small relative radii the minimum is achieved with one element, whereas for larger radii the optimal number ranges from two to five.
The partition parameters are not prescribed in advance but are determined from the minimum-pressure condition, which allows the partitions of the bottom and wall to be treated as two kinematic modules. The proposed model accounts for geometry, friction and the number of similar rigid elements and can be used for preliminary design of extrusion processes for parts with a conical cavity and combined extrusion schemes.

References

  1. S.H. Zhang et al., “Some new features in the development of metal forming technology”, J. Mater. Process. Technol., Vol. 1, pp. 39–47, 2004, doi: https://doi.org/10.1016/j.jmatprotec.2004.04.098
  2. I. S. Aliiev, N. S. Hrudkina, Kh. V. Malii, and L. V. Tagan, “Modeliuvannia ta rozrobka protsesiv tochnoho ob’emnoho shtam-puvannia vydavliuvanniam [“Modeling and development of precision bulk stamping extrusion processes”], Kramatorsk: DDMA, 2021, 208 p. ISBN 978-617-7889-08-2.
  3. I. S. Aliiev, M. Yu. Kordenko, and A. D. Samohliadov, “Kombinirovannoe vydavlivanie polykh konicheskikh detalei”, [“Com-bined extrusion of hollow conical parts”], Obrabotka materialov davleniem, No. 47, pp. 90–95, 2018.
  4. I. S. Aliiev, L. V. Tagan, A. D. Samohliadov, and K. D. Makhmudov, “Combined backward–forward extrusion of hollow coni-cal parts,” Obrabotka materialov davleniem, No. 49, pp. 98–105, 2019. doi: https://doi.org/10.37142/2076-2151/2019-2(49)98.
  5. I. S. Aliiev, V. M. Levchenko, O. Ye. Markov, P. B. Abkhari, and Kh. V. Malii, “Simulation of extrusion process of hollow conical parts,” Matematychne modeliuvannia, Vol. 48, pp. 147–156, 2023. doi: https://doi.org/10.31319/2519-8106.1(48)2023.280802.
  6. I. S. Aliev, “Metodika analiza protsessov tochnoi obyemnoi shtampovki s pomoshch’iu modul’nykh polei skorostei” [“Method-ology for analyzing precision bulk forming processes using modular velocity fields”], Kyiv: UMK VO, 1990, pp. 7–17.
  7. I. S. Aliiev, “Enerhetychni metody doslidzhen protsesiv obrobky metaliv tyskom” [“Energy methods for studying metal forming processes”], Kramatorsk–Ternopil: DDMA, 2023, 179 p. ISBN 978-617-7889-54-9.
  8. V. M. Levchenko, L. I. Aliieva, A. V. Titov, P. B. Abkhari, and O. Yu. Chepelenko, “Simulation of the force regime for lateral extrusion in a die with rounded areas,” Materials working by pressure, No. 53, pp. 10–23, 2024. doi: https://doi.org/10.37142/2076-2151/2024-1(53)10.
  9. I. S. Aliiev, V. M. Levchenko, O. V. Chuchyn, D. O. Kartamyshev, and K. I. Kotsiubivska, “Upper-bound estimation of force parameters of transverse-angular extrusion,” Materials working by pressure, No. 52, pp. 20–31, 2023. doi: https://doi.org/10.37142/2076-2151/2023-1(52)20.
  10. V. M. Levchenko, I. S. Aliiev, O. Yu. Chepelenko, D. O. Kartamyshev, and O. G. Malii, “Simulation of the process of trans-verse-forward extrusion with expansion,” Materials working by pressure, No. 53, pp. 24–33, 2024. doi: https://doi.org/10.37142/2076-2151/2024-1(53)24.
  11. V. L. Kaliuzhnyi and V. M. Levchenko, “Use of power-balance and engineering methods for steady-stage analysis of cold backward extrusion with expansion,” Materials working by pressure, No. 48, pp. 45–52, 2019.
  12. M. V. Kosenko, I. V. Nagorskaya, and O. V. Gulkova, “Analysis of the initial stage of extrusion of hollow conical parts,” Obrabotka materialov davleniem, No. 21, pp. 61–65, 2009.
  13. I. S. Aliiev and P. V. Hnezdylov, “Kombinirovannoe vydavlivanie polykh konicheskikh detalei iz zagotovok razlichnoi formy” [“Combined extrusion of hollow conical parts from billets of various shapes”], Obrabotka materialov davleniem, No. 41, pp. 162–165, 2015.
  14. S. F. Sabol, V. V. Pimanov and Ye. V. Korobka, “Combined cold extrusion of a conical hollow billet for a special-purpose product,” Visnyk NTU “KhPI”, No. 1133, pp. 103–107, 2015.
  15. I. S. Aliiev and A. D. Samohliadov, “Manufacturing of hollow conical parts using combined backward–forward extrusion schemes,” in Proc. Int. Sci.–Pract. Conf. “Prohresyvna tekhnika, tekhnolohiia ta inzhenerna osvita”, Kyiv, No XX, pp. 93–95, 2019. Accessed Sept. 10, 2019, Available: https://proc.mmi.kpi.ua/article/view/174481.
  16. A. Ye. Hranovskyi, “Upper-bound estimation of the conical cavity wall contribution to the reduced pressure in forward extru-sion,” Global Development of Science, Technology and Culture: Proceedings of the International scientific and practical confer-ence, Nov. 28–30, 2025, Oxford, United Kingdom, 2025, pp. 76–83, ISBN 978-617-8680-22-0, doi: https://doi.org/10.64828/conf-75-2025 .
  17. A. Ye. Hranovskyi, “Modeling of the conical cup extrusion process using the upper-bound method,” Perspektyvy rozvytku mashynobuduvannia ta transport, 2025: Abstracts of papers presented at IV International scientific and technical conference, June 3–5, 2025, Vinnytsia, VNTU, 2025, pp. 300–301, ISBN 978-617-8163-51-8.
  18. V. A. Evstratov, “Theory of Metal Forming Processes,” Kharkiv: Vyshcha Shkola, 1981.
  19. R. A. Horn and C. R. Johnson, “Matrix Analysis”, 2nd ed., Cambridge Univ. Press, 2013.

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Published

2025-12-29

How to Cite

[1]
A. Hranovskyi, “Upper-Bound Estimate of Reduced Pressure and Optimisation of Scheme Parameters for Direct Extrusion of Parts with a Conical Cavity”, Mech. Adv. Technol., vol. 9, no. 4(107), pp. 442–455, Dec. 2025.

Issue

Vol. 9 No. 4(107) (2025)

Section

Mechanics

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