Vibrations in engineering and technology

Mykhalevych Volodymyr – Doctor of Technical Sciences, Professor of the Department of Higher Mathematics, Vinnytsia National Technical University (95 Khmelnytske Shose, Vinnytsia, 21021, Ukraine, email: mykhalevych@vntu.edu.ua, https://orcid.org/0000-0003-1557-7331).

Kolisnyk Mykola – Doctor of Philosophy in Materials Science, Senior Lecturer of the Department of Electric Power Engineering, Electrical Engineering and Electromechanics, Vinnytsia National Agrarian University (3 Soniachna str., Vinnytsia, 21008, Ukraine, email: kolisnik30@gmail.com, https://orcid.org/0000-0001-5502-6556).

Dymnich Igor – Security Advisor, DIDWW (Israel, email: security@didww.com, https://orcid.org/0000-0001-5401-9143)

The paper considers the problem of selecting a rational mode of strain rate change during high-temperature isothermal flat-die upsetting of cylindrical billets. The object of the study is the hot upsetting process; the subject is the law of strain rate change at the critical point of the billet and the corresponding law of motion of the deforming tool. The relevance of the work stems from the fact that upsetting is one of the most energy-intensive forging operations, while the tool speed is in practice assigned as a constant value based on equipment capabilities rather than on conditions for the fullest use of the plastic capacity of the material.

Known results on the optimization of the rate mode of multistage hot deformation have been obtained for processes with a homogeneous stress-strain state, for which the stress triaxiality ratio remains unchanged. During flat-die upsetting this ratio at the critical point on the equator of the lateral surface changes during the process due to barrelling, which formally makes the direct transfer of known results impossible.

To overcome this obstacle, a hypothesis is formulated on the weak dependence of the limiting strain on the stress triaxiality ratio during high-temperature deformation for a certain class of materials. It is shown that a weakened form of the hypothesis is sufficient for a correct transfer of the results, requiring independence from the triaxiality ratio only for the strain rate sensitivity exponent. It is established that the resource dependence parameter enters exclusively into the scale factor of the solution and does not affect the shape of the optimal trajectory, while the relative error of the limiting strain is smaller than the relative error of this parameter.

The problem of matching the optimal law of strain rate change with the tool kinematics is solved. A closed-form analytical expression for the tool speed is obtained, which does not require numerical inversion of the dependence of strain intensity on the upsetting ratio. For exponential and polynomial trajectories the law of tool motion is presented in explicit form. An estimate of the strain rate deviation within a stage is proposed, which gives the number of stages a specific technological meaning.

A numerical calculation for 14Kh17N2 steel at 1150 °C established that the plastic resource of the material is not exhausted during flat-die upsetting, i.e. the process is limited geometrically rather than by deformation. For such materials the problem of minimizing the process time is meaningful. A relation is obtained linking the reduction of deformation time with the increase of the limiting strain; it is shown that an increase of the limiting strain by 5.9 % corresponds to a reduction of the upsetting time by 47 %. The conditions for applicability of the obtained results to processes of local deformation by roller burnishing are determined.

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10. Kraievskyi, V. O., Mykhalevych, V. M. (2015). Optymizatsiia shvydkisnoho rezhymu bahatostupenevoho hariachoho deformuvannia pry odnakovii tryvalosti stupeniv. Visnyk Donetskoho natsionalnoho universytetu. Ser. A: Pryrodnychi nauky, 1–2, 46–52. [in Ukraine].

11. Kraievskyi, V. O., Mykhalevych, V. M., Dobranyuk, Yu. V., Sawicki, D., Mussabekov, K. (2018). Selection of optimal path of strain rate change in the process of multistage hot deformation under the condition of the equal duration of stages. Proceedings of SPIE, 10808, 108084T. https://doi.org/10.1117/12.2501490. [in USA].

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15. Myhalevich, V., Kolisnyk, M., Shtuts, A., Hryhorenko, N. (2025). Study of technological processes of stamping of flange-type parts based on the application of combined expression methods. Herald of Khmelnytskyi National University. Technical Sciences, 351(3.1), 590–599. https://doi.org/10.31891/2307-5732-2025-351-77. [in Ukraine].

16. Myhalevych, V. M., Shtuts, A. A., Kolisnyk, M. A., Zozulyak, I. A., Jelenich, A. P. (2025). Research into the processes of rolling stamping of ring and flange billets with a complex profile. Metallofizika i Noveishie Tekhnologii, 47(6), 647–666. https://doi.org/10.15407/mfint.47.06.0647. [in Ukraine].

17. Mykhalevych, V. M., Kolisnyk, M. A., Shtuts, A. A. (2025). Doslidzhennia napruzheno-deformovanoho stanu materialu zahotovok pid chas plastychnoho shtampuvannia prokatuvanniam. Metallofizika i Noveishie Tekhnologii, 47(1), 57–81. https://doi.org/10.15407/mfint.47.01.0057. [in Ukraine].

18. Matviichuk, V. A., Mykhalevych, V. M., Shtuts, A. A. (2023). Analiz napruzheno-deformovanoho stanu materialu zahotovok pry vysadzhuvanni resursooshchadnym metodom shtampuvannia obkochuvanniam. Tekhnika, enerhetyka, transport APK, 1(120), 76–85. https://doi.org/10.37128/2520-6168-2023-1-9. [in Ukraine].

19. Matviychuk, V., Mikhalevich, V., Shtuts, A. (2023). Analysis of stress-strain state (SSS) of billet material in the course of setting by resource-saving method of roll stamping. Vibratsii v tekhnitsi ta tekhnolohiiakh, 1(108), 63–72. https://doi.org/10.37128/2306-8744-2023-1-7. [in Ukraine].