Application of experimental planning methods for the analytical description of marine electromechanical systems

The study examines the possibility of applying electrical circuit analysis methods to the mathematical description of marine mechanical systems. It is shown that marine mechanical systems constitute key components of marine power plants and electric drive systems and are characterized by significant structural diversity and complexity due to the presence of elastic bonds and vibration damping. It is demonstrated that the computational schemes of mechanical systems can be represented in the form of chain operator circuits that are structurally analogous to electrical circuits and consist of mechanical impedances and admittances. Equations describing the dynamics of mechanical systems in terms of these impedances and admittances are derived. In such circuit representations, angular velocities of rotating masses play the role of currents, while torques acting in elastic bonds correspond to voltages. It is established that representing mechanical systems as chain mechanical circuits enables the use of calculation methods well known from electrical circuit theory for their mathematical description. Loop and nodal equations of mechanical systems are obtained and analyzed using the example of a three-mass mechanical system. The possibility of applying the equivalent generator method to derive analytical relationships for an arbitrary rotating mass and an elastic bond is considered. Examples of the application of this method to two-mass and three-mass mechanical systems are presented. It is noted that the twomass mechanical system is a widely used model in the analysis of mechanical system dynamics, and various forms of its mathematical representation that are of practical importance are obtained. The frequency-domain analysis of a twomass mechanical system based on the derived mathematical description is also discussed.

1. Safronov, A. A., V. D. Rozhdestvenskiy and Yu. D. Dudnik. "Mathematical model of turbine unit considering shaft line torsional vibrations." Leti Transactions on Electrical Engineering & Computer Science 18.5 (2025): 108–115. DOI: 10.32603/2071-8985-2025-18-5-108-115.

2. Neyman, L. A. and V. Yu. Neyman. "Influence offriction forces on dynamics of the two-mass model of an electromagnetic vibrator." Elektrotekhnika 5 (2023): 18–22. DOI: 10.53891/00135860_2023_5_18.

3. Tsarenko, S. N., A. N. Rak and B. N. Bezlobenko. "Propeller shaft line dynamics at acceleration mode." Vestnik gosudarstvennogo universiteta morskogo i rechnogo flota im. admirala S.O. Makarova 13.4 (2021): 548–558. DOI: 10.21821/2309-5180-2021-13-4-548-558.

4. Sultanov, T. T., Z. R. Burnaev and G. M. Tlepieva. " analysis of the dynamic stress-strain state of ship mechanisms with elastic anisotropic links." Vestnik gosudarstvennogo universiteta morskogo i rechnogo flota im. admirala S.O. Makarova 12.2 (2020): 369–380. DOI: 10.21821/2309-5180-2020-12-2-369-380.

5. Karnovsky, I. A. and E. Lebed. Theory of Vibration ProtectionSpringer, 2016: 708.

6. Eliseev, S. V. and A. I. Artyunin. Prikladnaya teoriya kolebaniy v zadachakh dinamiki lineynykh mekhanicheskikh sistem Novosibirsk: Novosibirskoe otdelenie izdatel'stva "Nauka", 2016: 459.

7. Pyatibratov, G. Ya. "Parametricheskie sposoby dempfirovaniya elektroprivodom uprugikh kolebaniy mekhanizmov." Russian Electromechanics 4 (2013): 21–26.

8. Koperchak, O. P. "Methods for optimizing the operation of propulsion system elements on sea-going transport ships." Operation of marine transport 1(106) (2023): 165–170. DOI: 10.34046/aumsuomt106/28.

9. Moseyko, E. S. and E. O. Ol'khovik. "Tasks of risks assessment and failures prevention of the ship’s mechanical systems." Vestnik gosudarstvennogo universiteta morskogo i rechnogo flota im. admirala S.O. Makarova 14.6 (2022): 931–944. DOI: 10.21821/2309-5180-2022-14-6-931-944.

10. Korolev, V. V. "Diagnosis and control of mechanical stresses and vibrations in the ship's electrotechnical complexes and systems." Operation of marine transport 3(61) (2010): 52–57.

11. Chura, M. N. and A. V. Fayvisovich. "To assess the operational life of ship's propeller shafts." Operation of Marine Transport 3(96) (2020): 123–127. DOI: 10.34046/aumsuomt96/17.

12. Eliseev, S. V. and A. P. Khomenko. Dinamicheskoe gashenie kolebaniy: kontseptsiya obratnoy svyazi i strukturnye metody matematicheskogo modelirovaniya Novosibirsk: Novosibirskoe otdelenie izdatel'stva "Nauka", 2014: 357.

13. Ermakov, A. V. "Description of the simplified method of modeling systems with elastic links in Matlab with Simulink SimMechanics extension package." Science and Business: Ways of Development 8(38) (2014): 107–111.

14. Kargapol'tsev, S. K. and R. S. Bol'shakov. "Identification of dynamic interactions in a mechanical oscillatory system with additional connections." Systems. Methods. Technologies. 4(64) (2024): 7–14. DOI: 10.18324/20775415-2024-4-7-14.

15. Belokobyl'skiy, S. V., S. V. Eliseev and V. B. Kashuba. "Impedance approaches as an estimation form for dynamical properties of mechanical oscillation systems in structural mathematical modelling." Systems. Methods. Technologies. 4(28) (2015): 7–15.

16. Kashuba, V. B., N. Zh. Kinash, A. V. Eliseev and A. V. Nikolaev. "Structural mathematical modelling in problems of an estimation of dynamic properties of mechanical oscillatory systems." Systems. Methods. Technologies. 3(31) (2016): 16–28. DOI: 10.18324/2077-5415-2016-3-16-28.

17. Zhikhar', A. I. and V. N. Lubenko. "Vibrating mathematical model of ship pipelines." Vestnik of Astrakhan State Technical University 2(37) (2007): 103–106.

18. Andrianov, E. N., A. V. Saushev and D. I. Troyan. "Modelirovanie mekhanicheskikh sistem morskoy peregruzochnoy tekhniki metodom elektricheskoy analogii." Morskoy vestnik 1(53) (2015): 49–52.

19. Belokobyl'skiy, S. V., A. V. Eliseev, I. S. Sitov and A. I. Artyunin. "On the issue of mathematical model of chain mechanical system." Systems. Methods. Technologies. 1(33) (2017): 7–18. DOI: 10.18324/2077-5415-2017-1-7-18.

20. Saushev, A. V. "Matematicheskoe opisanie mnogomassovykh mekhanicheskikh sistem elektroprivoda." Elektrichestvo 3 (2013): 27–33.

21. S Saushev, A. V. and V. A. Shoshmin. "Modelirovanie mnogomassovykh mekhanicheskikh sistem elektroprivodov metodom elektricheskoy analogii." Zhurnal universiteta vodnykh kommunikatsiy 4 (2010): 57–64.