Vibrations in engineering and technology

Gurskyi Volodymyr, Doctor of Technical Sciences, Professor in the Department of Robotics and Integrated Mechanical Engineering Technologies at Lviv Polytechnic National University, Lviv, Ukraine, email: Volodymyr.M.Hurskyi@lpnu.ua , https://orcid.org/0000-0002-7141-0280

Zaniuk Vitaliy, postgraduate student at the National University “Lviv Polytechnic”.

The aim of this study is to develop and investigate a vibratory machine with a toroidal bowl intended for post-processing polymer components of bionic prosthetic devices manufactured using additive manufacturing technologies. A design of a laboratory vibratory installation is proposed, in which the toroidal geometry of the working bowl is used to ensure the formation of a closed spiral trajectory of motion of the abrasive media and processed parts. 

To analyze the operation of the device, a mathematical model of spatial oscillations of the vibrating system was developed, in which the working bowl is considered as a rigid body with six degrees of freedom, taking into account the action of the unbalanced excitation drive, elastic suspension, and damping. Numerical solution of the system of differential equations of motion was performed in the Maple environment, which made it possible to obtain time dependencies of the center-of-mass displacements and to study the spatial nature of the oscillations. 

To verify the adequacy of the mathematical model, spatial trajectories of a characteristic point located on the mean radius of the torus were constructed for different separation angles of the unbalances. The obtained results demonstrated the possibility of controlling the spatial character of the oscillatory motion and forming operating modes required for the circulating movement of the working media in the toroidal bowl. 

For the first time, the use of a toroidal bowl in a vibratory finishing machine for post-processing bionic prosthetic components with the realization of a closed spiral trajectory as the working path has been substantiated. An approach for verifying the dynamic model of the vibratory machine by analyzing the trajectories of a characteristic point obtained from the numerical solution of the equations of motion in the Maple environment has been proposed.

1. Van Hooreweder, B., Moens, D., Boonen, R., Kruth, J.-P., & Sas, P. (2013). On the difference in material structure and fatigue properties of nylon specimens produced by injection molding and selective laser sintering. Polymer Testing, 32(5), 972–981. https://doi.org/10.1016/j.polymertesting.2013.04.014

2. Priyadarshini, B. M., Kok, W. K., Dikshit, V., Feng, S., Li, K. H. H., & Zhang, Y. (2022). 3D printing biocompatible materials with Multi Jet Fusion for bioreactor applications. International Journal of Bioprinting, 9(1), 623. https://doi.org/10.18063/ijb.v9i1.623

3. Górski, F., Wichniarek, R., Kuczko, W., Żukowska, M., & Suszek, E. (2020). Rapid manufacturing of individualized prosthetic sockets. Advances in Science and Technology Research Journal, 14(1), 42–49. https://doi.org/10.12913/22998624/113425

4. Turek, P., Budzik, G., Oleksy, M., & Bulanda, K. (2020). Polymer materials used in medicine processed by additive techniques. Polimery, 65(7–8), 510–515. https://doi.org/10.14314/polimery.2020.7.2

5. Salmi, M. (2021). Additive manufacturing processes in medical applications. Materials, 14(1), 191. https://doi.org/10.3390/ma14010191

6. Khorasani, M., et al. (2024). Multi Jet Fusion (MJF) of polymeric components: A review of process, properties and opportunities. Additive Manufacturing, 91, 104331. https://doi.org/10.1016/j.addma.2024.104331

7. Ryu, W., Choi, Y., Choi, Y. J., & Lee, S. (2020). Development of a lightweight prosthetic hand for patients with amputated fingers. Applied Sciences, 10(10), 3536. https://doi.org/10.3390/app10103536

8. Zakręcki, A., Cieślik, J., Bazan, A., & Turek, P. (2024). Innovative approaches to 3D printing of PA12 forearm orthoses: A comprehensive analysis of mechanical properties and production efficiency. Materials, 17(3), 663. https://doi.org/10.3390/ma17030663

9. Terekhina, S., Tarasova, T., Egorov, S., Guillaumat, L., & Hattali, M. L. (2020). On the difference in material structure and fatigue properties of polyamide specimens produced by fused filament fabrication and selective laser sintering. The International Journal of Advanced Manufacturing Technology, 111(1–2), 93–107. https://doi.org/10.1007/s00170-020-06026-x

10. Kantaros, A., Ganetsos, T., Petrescu, F., Ungureanu, L., & Munteanu, I. (2024). Post-production finishing processes utilized in 3D printing technologies. Processes, 12(3), 595. https://doi.org/10.3390/pr12030595

11. Bazan, A., Turek, P., & Zakręcki, A. (2023). Influence of antibacterial coating and mechanical and chemical treatment on the surface properties of PA12 parts manufactured with SLS and MJF techniques in the context of medical applications. Materials, 16(6), 2405. https://doi.org/10.3390/ma16062405

12. Zakręcki, A., & Cieślik, J. (2025). Influence of ageing and post-processing on the mechanical and aesthetic stability of PA12-based 3D-printed components for medical devices. Materials, 18(19), 4478. https://doi.org/10.3390/ma18194478

13. Johansson, I. (2020). Post-processing for roughness reduction of additive manufactured polyamide 12 using a fully automated chemical vapor technique (Master’s thesis, KTH Royal Institute of Technology). https://urn.kb.se/resolve?urn=urn:nbn:se:kth:diva-279316

14. Eckhardt, L., et al. (2023). Laser beam polishing of PA12 parts manufactured by powder bed fusion. Lasers in Manufacturing and Materials Processing, 10(4), 563–585. https://doi.org/10.1007/s40516-023-00213-w

15. Rohrsen, N. C., & Hagedorn, D. (2024). Improving the surface quality of additive manufactured polyamide parts using conventional treatment methods. The International Journal of Advanced Manufacturing Technology, 132(5–6), 2347–2358. https://doi.org/10.1007/s00170-024-13279-3

16. Nebiolo, W. P. (n.d.). Vibratory bowl optimization by proper mechanical set-up and the use of chemical accelerators to virtually eliminate hand polishing of steel parts. In SUR/FIN Proceedings. National Association for Surface Finishing (NASF).

17. Liu, W., Wang, S., Jiang, Q., Morgan, M., & Liu, X. (2022). Study on the motion characteristics of abrasive media in vibratory finishing. Journal of Physics: Conference Series, 2198(1), 012035. https://doi.org/10.1088/1742-6596/2198/1/012035

18. Wan, S., Fong, W. S., & Tay, Z. H. (2010). Process modelling and simulation of vibratory finishing of fixtured components.

19. Kang, Y. S., Hashimoto, F., Johnson, S. P., & Rhodes, J. P. (2017). Discrete element modeling of 3D media motion in vibratory finishing process. CIRP Annals, 66(1), 313–316. https://doi.org/10.1016/j.cirp.2017.04.092

20. Wang, X., Yang, S., Li, W., & Wang, Y. (2018). Vibratory finishing co-simulation based on ADAMS–EDEM with experimental validation. The International Journal of Advanced Manufacturing Technology, 96(1–4), 1175–1185. https://doi.org/10.1007/s00170-018-1639-0

21. Silman, T., & Domblesky, J. (2007). Investigation of workload fluid characteristics in vibratory finishing. In SUR/FIN Proceedings. National Association for Surface Finishing (NASF).

22. Lanets, O. Osnovy rozrakhunku ta konstruiuvannia vibratsiinykh mashyn. Knyha 1. Teoriia ta praktyka stvorennia vibratsiinykh mashyn z harmoniinym rukhom robochoho orhana. Lviv: Vydavnytstvo Lvivskoi politekhniky. 2008. 620. [in Ukrainian].

23. Gurskyi, V., Korendiy, V., Krot, P., Zimroz, R., Kachur, O., & Maherus, N. (2023). On the dynamics of an enhanced coaxial inertial exciter for vibratory machines. Machines, 11(1), 97. https://doi.org/10.3390/machines11010097

24. Yaroshevich, N., Gursky, V., Puts, V., Yaroshevych, O., & Martyniuk, V. (2022). On the dynamics of vibrational capture of rotation of an unbalanced rotor. Vibroengineering Procedia, 42, 1–6. https://doi.org/10.21595/vp.2022.22413

25. Yaroshevich, N., Yaroshevych, O., & Lyshuk, V. (2021). Drive dynamics of vibratory machines with inertia excitation. In J. M. Balthazar (Ed.), Vibration engineering and technology of machinery (Vol. 95, pp. 37–47). Springer. https://doi.org/10.1007/978-3-030-60694-7_2

26. Yaroshenko, L. V., & Slobodianyk, A. D. (2025). Elastic suspensions of vibrating machines with adjustable electromechanical drive. Vibration Engineering and Technology of Machinery, 3(118), 45–54. https://doi.org/10.37128/2306-8744-2025-3-5