From 1993 to 1997, the Institute of Technical Mechanics of the National Academy of Sciences of Ukraine and the State Space Agency of Ukraine published an interdepartmental collection of papers entitled Tekhnicheskaya Mekhanika, which in September 1997 received the status of a scientific journal entitled Tekhnicheskaya Mekhanika (in Russian) and Tekhnichna Mekhanika (in Ukrainian). In 2017, the institute was issued a new state registration certificate for the journal, in accordance with which the journal has the official English title of Technical Mechanics, may publish papers in English, and is entitled to international distribution. The journal publishes review and research articles on the following topics: 1.Applied Mechanics 2. Applied Mathematics 3. Aviation and Space Engineering 4. Automation and Computer-Integrated Technologies 5. Physics and Astronomy
COMMON WHEEL PROFILE FOR PASSENGER AND FREIGHT CARS TO BE OPERATED BOTH ON THE UKRAINIAN AND ON THE WEST-EUROPEAN RAILWAYS
DOI: https://doi.org/10.15407/itm2025.04.120 One of the most important problems in the current development of the Ukrainian railway transport is to speed up the integration of Ukraine into the European railway service. For cars to operate on the Ukrainian and West-European railways, it is necessary to use gauge-changeable wheelsets, which can automatically change from one gauge to another, and provide wheel-rail contact pair compatibility on the railways of both standards: with R65 rails of cant 1/20 in Ukraine and UIC rails of cant 1/40 in West Europe. To solve this problem, the Institute of Technical Mechanics of the National Academy of Sciences of Ukraine and the State Space Agency of Ukraine developed wheel profiles for passenger and freight cars: ITM-73EP and ITM-73EC, respectively. The goal of this work was to study the possibility of using one of these profiles as a common wheel profile for passenger and freight cars with prospective trucks to be operated both on the Ukrainian and on the European railways. The study was concerned with passenger cars with 68-7041 trucks and freight cars with 18-7020 (an axle load of 23.5 tf) and 18-9817 (an axle load of 25 tf) trucks. The use of wheels with both profiles was compared in terms of car dynamic stability at service speeds on tangents of the Ukrainian and European railways and wheel-track interaction indices in curves (with account for different degrees of rail side wear). The results of the calculations made it possible to identify the profile expedient to be used as a common one for passenger and freight cars. According to predictive estimates, the use of wheels with this profile will speed up passing between tracks with different gauges and provide a high ride quality and improved indices of wheel-track interaction on both railways. REFERENCES 1. Gauge-changeable wheelsets. URL: https://www.railway.supply/uk/rozsuvni-zaliznichni-kolisni-pari/ (Last accessed on October 10, 2025). (in Ukrainian). 2. Ukrainian National Railway Administration together with Spain will make cars automatically adjustable to the track gauge. URL: https://censor.net/n3498056. (In Ukrainian). 3. Domin P. Yu., Domin Yu. V., Cherniak H. Yu., Mostovych A. V. Scientific and Technical Foundations of the Development of "East-West"-Type Railway Vehicles. Kyiv: Volodymyr Dahl East Ukrainian National University, 2024. 380 pp. (in Ukrainian). 4. Pikh B. P., Korzhenevych I. P., Kurgan M. B. Use of railway vehicles with gauge-changeable wheelsets in the Kyiv-Lviv-Mostyska II route. Bulletin of the Dnipropetrovsk National University of Railway Transport. 2004. Iss. 3. Pp. 82-89. (in Ukrainian). https://doi.org/10.15802/stp2004/20907 5. Kurgan N., Voznaia E. Interoperability increase in the Austria - Slovakia - Ukraine - Russia international railway service. Ukrainski Zaliznytsi. 2014. No. 12 (18). Pp. 24-33. (in Russian). 6. Kalivoda, J., Neduzha, L. Running dynamics of rail vehicles. Energies. 2022. V. 15. 5843. https://doi.org/10.3390/en15165843 7. Mokrii T. F., Malysheva I. Yu., Lapina L. G., Bezrukavyi N. V. Passenger car wheel profile for the operation on the Ukrainian and European railways. Teh. Meh. 2022. No. 4. Pp. 111-120. (In Ukrainian). https://doi.org/10.15407/itm2022.04.111 8. Mokrii T. F., Malysheva I. Yu., Pasichyk S. S. Wheel profile of a freight car with prospective trucks for the combined operation on the Ukrainian and European railways. Teh. Meh. 2023. No. 4. Pp. 90-103. (In Ukrainian). https://doi.org/10.15407/itm2023.04.090 9. Ushkalov V. F., Mokriy T. F., Malysheva I. Yu. Mathematical model of interactions between railway and track considering distributions of contact forces throughout contact spots. Teh. Meh. 2015. No. 2. Pp. 79-89. (in Russian). 10. Model 68-7041 two-axle air-suspension truck. URL: https://www.kvsz.com/index.php/ua/produktsiya/pasazhirske-vagonobuduvannya/khodovi-chastini/item/1932-dvovisnyi-vizok-modeli-68-7041-z-pnevmopidvishuvanniam/ (Last accessed on October 20, 2025). (In Ukrainian). 11. Model 18-7020 type 2 two-axle truck. URL: https://www.kvsz.com/index.php/ua/produktsiya/vantazhne-vagonobuduvannya/vizki-vantazhnogo-vagonobuduvannya/item/1974-vizok-dvovisnyi-model-18-7020-typ-2 (Last accessed on October 11, 2025). (In Ukrainian). 12. 18-9817 TECHPROJECT GROUP two-axle truck, URL: https://tpgroup27.wixsite.com>tp-group (Last accessed on September 1, 2024). (In Ukrainian). 13. Olofsson U., Telliskivi T. Wear, plastic deformation and friction of two rail steels - a full-scale test and a laboratory study. Wear. 2003. No. 254 (1-2). Рp. 80-93. https://doi.org/10.1016/S0043-1648(02)00291-0 14. Podyelnikov I. V. Determination of typical shapes of worn rail heads in curves. Teh. Meh. 2009. No. 3. Pp. 39-43. (in Russian). 15. Ukrainian State Standard GOST 10791:2016 (GOST 10791-2011, IDT). Solid-Rolled Wheels. Specifications. Effective as of September 1, 2016. Kyiv: UkrNDNTs, 2016. 53 pp. (in Ukrainian). 16. Esveld C. Modern Railway Track. Second Edition. MRT-Productions, 2001. 654 pp.
DEVELOPING THE RESEARCH LINES OF VIKTOR V. PYLYPENKO, AN ACADEMICIAN OF THE NATIONAL ACADEMY OF SCIENCES OF UKRAINE
DOI: https://doi.org/10.15407/itm2025.04.003 This paper presents the results of studies along the principal research lines of Viktor V. Pylypenko, an Academician of the National Academy of Sciences of Ukraine, obtained by his pupils over the recent years. The following lines are considered: the development of a theory of cavitation oscillations in liquid-propellant rocket engine (LPRE) pumps, the study of low-frequency dynamics in liquid-propellant rocket propulsion systems (LPRPSs), the analysis and assurance of liquid-propellant launch vehicle pogo stability, the mathematical simulation of dynamic processes in solid-propellant rocket engines, the development of pneumatic vibration protection modules, and the improvement of drilling technology by using cavitation hydrovibrator. A hydrodynamic model of cavitating LPRE pumps was developed further: it was verified using theoretical and experimental transfer matrices of cavitating pumps, and two new coefficients were introduced: the time of disturbance transfer delay due to the presence of cavities and the cavitation resistance distribution coefficient; from the results of dynamic tests of 26 pumps, the cavity elasticity was determined for pumps with extended ranges of their geometric parameters and operating conditions; a pump choking mechanism was developed, and it was shown that the pump choking characteristic is a specific nonlinearity involving a critical cavity flow; a mechanism of hard excitation of cavitation self-oscillations was proposed, and they were mathematically simulated. A theory of LPRPS low-frequency dynamics was developed further: procedures were developed for determining the effect of a nonsimultaneous engine startup and external and internal factors on LPRE startup thrust spread; a mathematical simulation was conducted to study sustainer engine startup and shutdown transients in the common feed system of the sustainer engine and the liquid-propellant thrust system of the Cyclone-4M launch vehicle’s upper stage. A study was conducted on pogo vibrations in the prototype Cyclone and Dnipro launch vehicles unstable for pogo vibrations during the first-stage engine operation. REFERENCES 1. Pylypenko O. V., Dovgotko N. I. Outstanding scientist in mechanics Viktor Vassilievich Pylypenko. Teh. Meh. 2015. No. 4. Pp. 3-22. (In Russian). 2. Dolgopolov S. I. Verification of a hydrodynamic model of a liquid-propellant rocket engine's cavitating pumps using experimental and theoretical pump transfer matrices. Teh. Meh. 2020. No. 3. Pp. 18-28. (In Ukrainian). https://doi.org/10.15407/itm2020.03.018 3. Brennen C. E., Meissner C., Lo E. Y., Hoffman G. S. Scale effects in the dynamic transfer functions for cavitating inducers. Journal of Fluids Engineering. 1982. V. 104. No. 4. Pp. 428-433. https://doi.org/10.1115/1.3241875 4. Pylypenko V. V., Kvasha Yu. A. Stability of cavity flow past a plate cascade. Teh. Meh. 2001. No. 2. Pp. 144-149. (In Russian). 5. Dolgopolov S. I. Determining the coefficients of a hydrodynamic model of cavitating pumps of liquid-propellant rocket engines from their theoretical transfer matrices. Teh. Meh. 2024. No. 1. Pp. 16 - 25. (In Ukrainian). https://doi.org/10.15407/itm2024.01.016 6. Dolgopolov S. I. Generalization of experimental elasticity of cavitation bubbles in LRE pumps that differ significantly in size and performance. Science and Innovation. 2023. V. 19. No. 19(5). Pp. 71 - 88. 7. Dolgopolov S. I. Experiment-and-calculation determination of the coefficients appearing in a mathematical model of cavitating pumps of liquid-propellant rocket engines. Teh. Meh. 2024. No. 3. Pp. 67 - 85. (in Ukrainian). https://doi.org/10.15407/itm2024.03.067 8. Dolgopolov S. I. Mathematical simulation of choking under self-oscillations in hydraulic systems with cavitating pumps of liquid-propellant rocket engines. Teh. Meh. 2020. No. 4. Pp. 35 - 42. (in Ukrainian). https://doi.org/10.15407/itm2020.04.035 9. Dolgopolov S. I. Mathematical simulation of hard excitation of cavitation self-oscillations in a liquid-propellant rocket engine feed system. Teh. Meh. 2021. No. 1. Pp. 29 - 36. (in Ukrainian). https://doi.org/10.15407/itm2021.01.029 10. Pylypenko O. V., Dolhopolov S. I., Nikolayev O. D., Khoriak N. V. Mathematical simulation of the start of a multiengine liquid-propellant rocket propulsion system. Teh. Meh. 2020. No. 1. Pp. 5 - 18. (In Russian). https://doi.org/10.15407/itm2020.01.005 11. Dolgopolov S., Nikolayev O., Khoriak N. Dynamic interaction between clustered liquid propellant rocket engines under their asynchronous start-ups. Propulsion and Power Research. 2021. V. 10. No. 4. Pp. 347 - 359. https://doi.org/10.1016/j.jppr.2021.12.001 12. Pylypenko O. V., Prokopchuk O. O., Dolgopolov S. I., Nikolayev O. D., Khoriak N. V., Pysarenko V. Yu., Bashliy I. D., Polskykh S. V. Mathematical modeling of start-up transients at clustered propulsion system with POGO-suppressors for Cyclon-4M launch vehicle. Space Science and Technology. 2021. V. 27. No. 6 (133). Pp. 3 - 15. https://doi.org/10.15407/knit2021.06.003 13. Pylypenko O. V., Dolgopolov S. I., Khoriak N. V., Nikolayev O. D. Procedure for determining the effect of internal and external factors on the startup thrust spread of a liquid-propellant rocket engine. Teh. Meh. 2021. No. 4. Pp. 7 - 17. (In Ukrainian). https://doi.org/10.15407/itm2021.04.007 14. Dolgopolov S. I. Determination of the effect of internal and external factors on the thrust spread of a cluster propulsion system. Teh. Meh. 2022. No. 2. Pp. 47 - 58. (In Ukrainian). https://doi.org/10.15407/itm2022.02.047 15. Pylypenko O. V., Dolgopolov S. I., Nikolayev O. D., KhoriaN. V., Kvasha Yu. A., Bashliy I. D. Determination of the thrust spread in the Cyclone-4M first stage multi-engine propulsion system during its start. Science and Innovation. 2022. V. 18. No. 6. Pp. 97 - 112. 16. Pylypenko O. V., Nikolayev O. D., Bashliy I. D., Dolgopolov S. I. Mathematical modeling of dynamic processes in feeding system of space stage main engine of launch vehicle at active and passive flight. Space Science and Technology. 2020. V. 26. No. 1. Pp. 3 - 17. (In Russian). https://doi.org/10.15407/knit2020.01.003 17. Pylypenko O. V., Smolenskyy D. E., Nikolayev O. D., Bashliy I. D. The approach to numerical simulation of the spatial movement of fluid with forming free gas inclusions in propellant tank at space flight conditions. Space Science and Technology. 2022. V. 28. No. 5. Pp. 3 - 14. https://doi.org/10.15407/knit2022.05.003 18. Pylypenko O. V., Nikolayev O. D., Bashliy I. D., Zavoloka O. M. Approach to numerical simulation of the spatial motions of a gas/liquid medium in a space stage propellant tank in microgravity with account for the hot zone. Teh. Meh. 2022. No. 4. Pp. 3 - 15. (In Ukrainian). https://doi.org/10.15407/itm2022.04.003 19. Nikolayev O. D., Bashliy I. D., Sviridenko N. F., Khoriak N. V. Determination of the parameters of motion of the gas-liquid interface in the fuel tanks of launch vehicle space stages in passive portions of the flight. Teh. Meh. 2017. No. 4. Pp. 26 - 40. (In Russian). https://doi.org/10.15407/itm2017.04.026 20. Pylypenko O. V., Dolgopolov S. I., Nikolayev O. D., Khoriak N. V. Mathematical modeling of the transient processes in propulsion system of the upper stage of the Cyclone-4M launch vehicle. Science and Innovation. 2024. V. 20. No. 1. Pp. 49 - 67. 21. Pylypenko O. V., Nikolayev O. D., Bashliy I. D., Khoriak N. V. Approach to the POGO stability analysis of a liquid-propellant "core and strap-on boosters" launch vehicle. Teh. Meh. 2022. No. 3. Pp. 3 - 15. (In Ukrainian). https://doi.org/10.15407/itm2022.03.003 22. Pylypenko O. V., Degtyarev M. A., Nikolayev O. D., Klimenko D. V., Dolgopolov S. I., Khoriak N. V., Bashliy I. D., Silkin L. A. Providing of POGO stability of the Cyclone-4M launch vehicle. Space Science and Technology. 2020. V. 26. No. 4 (125). Pp. 3 - 20. https://doi.org/10.15407/knit2020.04.003 23. Nikolayev O. D., Bashliy I. D., Khoryak N. V. Сomputation of the POGO self-oscillation parameters in dynamic "propulsion - rocket structure" system by using of 3D structural model. Teh. Meh. 2018. No. 2. Рp. 17 - 29. https://doi.org/10.15407/itm2018.02.017 24. Nikolaev A. D., Khoryak N. V., Serenko V. A., Klimenko D. V., Khodorenko V. F., Bashliy I. D. Considering dissipative forces for mathematical modeling longitudinal vibrations of liquid launch vehicle body. Teh. Meh. 2016. No. 2. Pp. 16 - 31. (In Russian). 25. Dolgopolov S., Nikolayev O. Features of mathematical modeling of nonlinear Pogo oscillations of launch vehicles. CEAS Space Journal. 2024. V. 16. Iss. 2. Pp. 32 - 48. https://doi.org/10.1007/s12567-024-00541-3 26. Pylypenko O. V., Dolgopolov S. I., Khoriak N. V., Nikolayev O. D. Evaluation of the scatter of liquid launch vehicle POGO oscillation amplitudes due to the influence of the scatter of internal factors. Space Science and Technology. 2024. V. 30. No. 3 (148). Pp. 3-15. https://doi.org/10.15407/knit2024.03.003 27. Nikolayev O. D., Bashliy I. D., Khoriak N. V., Bondarenko S. H. Effect of the surface roughness of a power plant chamber on low-frequency self-oscillations of a cold working gas. Teh. Meh. 2023. No. 3. Pp. 3 - 17. (In Ukrainian). https://doi.org/10.15407/itm2023.03.003 28. Bashlii I., Nikolayev O., Marchan R. Low-frequency oscillations of combustion products in the chamber of a low-thrust liquid rocket engine manufactured using additive technologies. Aerospace Technic and Technology. 2024. No. 4sup1. Pp. 60-68. (In Ukrainian). 29. Dolgopolov S. I., Nikolayev O. D. Development of an approach to mathematical simulation of dynamic processes in a solid-propellant rocket engine. Teh. Meh. 2024. No. 4. Pp. 10-16. (In Ukrainian). https://doi.org/10.15407/itm2024.04.010 30. Nikolaev O. D., Bashliy I. D., Klymenko D. V., Khoriak N. V. Interaction of the acoustic oscillations of the combustion products in the chamber of a propulsion system with structural vibrations. Teh. Meh. 2025. No. 1. Pp. 3- 17. (In Ukrainian). https://doi.org/10.15407/itm2025.01.028 31. Nikolaev O. D., Bashliy I. D., Sukachevskyi V. O. Features of the development of acoustic oscillations in the combustion product flow in power plant chambers when using propellant components derived from lunar regolith. Teh. Meh. 2025. No. 2. Pp. 3-16. (In Ukrainian). https://doi.org/10.15407/itm2025.02.003 32. Pylypenko M. V. System for space hardware vibration protection in transportation. Teh. Meh. 2020. No. 1. Pp. 120-130. (In Ukrainian). https://doi.org/10.15407/itm2020.01.120 33. Nikolayev D. O., Khoroshylov S. V. Prediction of dynamic loads on spacecraft in the active light of the launch vehicle using the results of liquid-propellant rocket engine fire tests. Teh. Meh. 2024. No. 1. Pp. 3-15. (In Ukrainian). https://doi.org/10.15407/itm2024.01.003 34. Nikolayev O., Zhulay Yu., Kvasha Yu., Dzoz N. Determination of the vibration accelerations of drill bits with the rotative-vibration well drilling method using the cavitation hydrovibrator. Int. J. Mining and Mineral Engineering. 2020. V. 11. No. 2. Pp. 102-120. https://doi.org/10.1504/IJMME.2020.108643 35. Zhulay Yu. O., Nikolaev O. D. Results of testing and modelling the "drilling rig with hydraulic vibrator - rock" system. Naukovyi Visnyk Natsionalnoho Hirnychoho Universytetu. 2020. No. 1. Pp. 11-17. https://doi.org/10.33271/nvngu/2020-1/011 36. Zhulay Yu. O., Nikolayev O. D. Evaluation of hydraulic power of drilling string with a cavitation hydrovibrator. Naukovyi Visnyk Natsionalnoho Hirnychoho Universytetu. 2021. No. 3. Pp. 31-37. https://doi.org/10.33271/nvngu/2021-3/031
MODELING OF THE CHECK VALVE OPERATION IN THE RECONFIGURABLE HYDRAULIC FEED SYSTEM OF A LIQUID ROCKET ENGINE
DOI: https://doi.org/10.15407/itm2025.04.019 Among the various automation units used in pneumatic–hydraulic systems of rocket hardware, check valves are widely employed. They are most commonly used in the filling lines of different tanks and in the pressurization lines of launch vehicle propellant tanks, where they prevent reverse flow and the ingress of vapors into the pressurization system. In liquid rocket engines (LREs), check valves are installed in drainage lines and in inert gas purging circuits. Particular attention is given to the use of check valves in reconfigurable hydraulic systems, in which the flow direction changes during the LRE operation. The goal of this study is to develop a mathematical model of dynamic processes in a check valve, verify it using CFD simulations of the pressure distribution over the valve poppet surface, and apply it to the analysis of transient processes in a reconfigurable hydraulic system. To determine the flow force acting on the valve poppet, this paper proposes an approach in the lumped-parameter approximation based on the flow rate balance of the working fluid in the valve flow passage. The model considers the radial inflow at the valve inlet, which depends on the poppet travel, and the peripheral flow through the narrow clearance between the valve body and the poppet. To implement this approach, it is sufficient to know the valve geometry and the discharge coefficients, which are assumed to be constant. For a reconfigurable propellant feed system containing check valves, a mathematical model of low-frequency dynamic processes was developed, and transient processes during the LRE startup were simulated. During the startup, the propellant feed of the LRE gas generator is automatically switched by the check valves from the start tank supply to the pump supply. Transient processes were simulated for the flow force acting on the check valve poppet determined using CFD simulation and the lumped-parameter approximation. A satisfactory agreement between the results of these two approaches was demonstrated. The possibility of using the proposed lumped-parameter approximation to determine the flow force acting on the check valve poppet was justified, thus enabling the development of mathematical models of dynamic processes in reconfigurable hydraulic systems without resorting to computationally expensive CFD simulations. REFERENCES 1. Sutton G. P., Biblarz O. Rocket Propulsion Elements. 9th ed. Hoboken: John Wiley & Sons, 2017. 800 pp. 2. Huze D. K., Huang D. H. Design of Liquid Propellant Rocket Engines. NASA SP 125. Washington: NASA, 1971. 472 pp. 3. Cherniavskyi O. S., Chevchenko S. A., Dolgopolov S. I. Mathematical modeling of the dynamic processes during check valve operation in the branched reconfigurable system of a liquid rocket engine. Aerospace Technic and Technology. 2025. No. 4. Special Iss. 2. Pp. 93-101. 4. Pylypenko O., Dolgopolov S., Nikolayev O., Khoriak N., Kvasha Yu., Bashliy I. Determination of the thrust spread in the Cyclone-4M first stage multi-engine propulsion system during its start. Science and Innovation. 2022. V. 18. No. 6. Pp. 97-112. 5. Koptilyy D., Marchan R., Dolgopolov S., Nikolayev O. Mathematical modeling of transient processes during start-up of main liquid propellant engine under hot test conditions. Proceedings of the 8th European Conference on Aeronautics and Space Sciences (EUCASS), Madrid, Spain, 1-4 July 2019. 15 pp. 6. Kobielski M. J., Skarka W., Skarka M. Comparison of pressure loss evaluation fidelity in turbulent energy dissipation models of poppet check valves using computational fluid dynamics (CFD) software. Technical Sciences, 2024. V. 27. Pp. 19-31. https://doi.org/10.31648/ts.9732 7. Filo G., Lisowski E., Rajda J. Design and flow analysis of an adjustable check valve by means of CFD method. Energies. 2021. V. 14. No. 8. 2237. https://doi.org/10.3390/en14082237 8. Klas R., Habán V., Rudolf P. Analysis of in line check valve with respect to the pipeline dynamics. EPJ Web of Conferences. 2017. V. 143. 02051. https://doi.org/10.1051/epjconf/201714302051 9. Lang S. A review of check valves in unsteady flow. Proceedings of the 2024 ASME Pressure Vessels & Piping Conference, V003T04A001. 10. Domagała M., Fabis Domagała J. A. Review of the CFD method in the modeling of flow forces. Energies. 2023. V. 16. No. 16. 6059. https://doi.org/10.3390/en16166059 11. Pusztai T., Siménfalvi Z. CFD analysis on a direct spring loaded safety valve to determine flow forces. Pollack Periodica. 2021. V. 16. No. 1. Pp. 109-113. https://doi.org/10.1556/606.2020.00122 12. Zong C., Zheng F., Chen D., Dempster W., Song X. CFD analysis of the flow force exerted on the disc of a direct operated pressure safety valve in energy system. Journal of Pressure Vessel Technology, 2020. V. 142. No. 1. 011702. https://doi.org/10.1115/1.4045131 13. Finesso R., Rundo M. Numerical and experimental investigation on a conical poppet relief valve with flow force compensation. International Journal of Fluid Power. 2017. V. 18. No. Pp. 111-122. https://doi.org/10.1080/14399776.2017.1296740 14. Wu D., Li S., Wu P. CFD simulation of flow pressure characteristics of a pressure control valve for automotive fuel supply system. Energy Conversion and Management. 2015. V. 101. Pp. 410-419. https://doi.org/10.1016/j.enconman.2015.06.025 15. Lisowski E., Rajda J. Analysis of the design of a poppet valve by transitory simulation. Energies. 2019. V. 12. No. 5. 889. https://doi.org/10.3390/en12050889 16. Marchan R. A. Small-scale supersonic combustion chamber with a gas-dynamic ignition system. Combustion Science and Technology. 2011. V. 183. No. 11. Pp. 1236-1265. https://doi.org/10.1080/00102202.2011.589874 17. Marchan R., Oleshchenko A., Vekilov S., Arsenuk M., Bobrov O. 3D printed acoustic igniter of oxygen-kerosene mixtures for aerospace applications. Proceedings of the 8th European Conference on Aeronautics and Space Sciences (EUCASS), Madrid, Spain, 1-4 July 2019. 14 pp. 18. Raman, G., Srinivasan, K. The powered resonance tube: From Hartmann's discovery to current active flow control applications. Progress in Aerospace Sciences, 2009. V. 45. No. 4 5. Pp. 97-123. https://doi.org/10.1016/j.paerosci.2009.05.001 19. Guillon M. Hydraulic Servo Systems: Analysis and Design. Butterworth, 1969. 462 pp. 20.Habing R. A., Peters M. C. A. M. An experimental method for validating compressor valve vibration theory. Journal of Fluids and Structures. 2006. V. 22. No. 5. Pp. 683-697. https://doi.org/10.1016/j.jfluidstructs.2006.03.003
SINGLE-LAYER MARCHING ALGORITHM TO CALCULATE SUPERSONIC FLOW ABOUT ROCKETS WITH THE COMPUTATIONAL REGION DIVIDED INTO SEVERAL SUBREGIONS
DOI: https://doi.org/10.15407/itm2025.04.031 This paper presents a single-layer marching algorithm to calculate supersonic flow about rockets that may be equipped with wings, stabilizers, rudders, and superstructures. In this algorithm, the rocket along its axis is divided into sections of two types: sections along the rocket structure without additional elements (type 1 sections), which are calculated using a standard one-zone algorithm, and sections along the rocket structure with additional elements, which are calculated using a multizone algorithm. To calculate supersonic flow about additional elements of arbitrary shape (wings, stabilizers, rudders, and superstructures) installed on the rocket body, use is made of a Cartesian system of coordinates with the computational region divided into several computational subregions (CSRs), whose outer boundaries are the rocket structure surface, the surfaces of the additional elements, and the bow shock front. In each specific case, the method of division of the computational region into several CSRs is determined by the shape of the additional elements installed on the rocket structure along the type 2 section under consideration. Five methods are proposed to divide the computational region into CSRs using Cartesian, cylindrical, or polar coordinates for constructing computational meshes in different CSRs, which is a reasonably universal approach to calculating supersonic flow about rockets with variously shaped additional elements. Based on the above algorithm, the development of software is underway, whose use will greatly reduce the time taken for numerical calculations of supersonic flow about rockets with variously shaped wings, stabilizers, rudders, and superstructures to a design accuracy. The advantage of the software under development is the promptness of parametric calculations, which allows one to greatly reduce the time taken for rocket pre-characterization at the tryout stage of the design parameters of rocket components. REFERENCES 1. Special Course on Missile Aerodynamic. 1994. AGARD-R-804. 350 pp. 2. Liptak P., Jozefek M. Moments having effect on a flying missile. Science&Military. 2010. No. 1. Pp. 51 - 57. 3. Missile Aerodynamics. In two books. M. Hemsch and J. Nielsen (Eds.). Moscow: Mir, 1989. Book 1 - 433 pp. Book 2. - 513 pp. (in Russian). 4. Vasek D., Polacek J., Konecny P. Improved estimation of air-to-air missile aerodynamic characteristics with using CFD method. Advances in Military Technology. 2020. V. 15. No. 2. Pp. 301 - 315. https://doi.org/10.3849/aimt.01373 5. Guzelbey I. A Review of aerodynamic shape optimization for a missile. The Eurasia Proceedings of Science, Technology, Engineering & Mathematics (EPSTEM). 2018. V. 4. Pp. 94 - 102. 6. Şumnu A., Güzelbey I. H., Öğücü O. Aerodynamic shape optimization of a missile using a multiobjective genetic algorithm. International Journal of Aerospace Engineering. 2020. V. 2020. 17 pp. https://doi.org/10.1155/2020/1528435 7. Ocokoljić G. J., Rašuo B. P., Bengin A. Č. Aerodynamic shape optimization of guided missile based on wind tunnel testing and computational fluid dynamics simulation. Thermal Science. 2017. V. 21. No. 3. Pp. 1543 - 1554. https://doi.org/10.2298/TSCI150515184O 8. Shelton A., Martiny C. Characterizing Aerodynamic Damping of a Supersonic Missile with CFD. American Institute of Aeronautics and Astronautics. 2017. N 96TW-2017-0404. 25 pp. 9. Sahu J. Unsteady computational fluid dynamics modeling of free-flight projectile aerodynamics. Computational Ballistics III. WIT Transactions on Modeling and Simulation. 2007. V. 45. 10 pp. https://doi.org/10.2495/CBAL070011 10. Zhang L. A. et al. CFD-based numerical virtual flight simulator and its application in control law design of a maneuverable missile model. Chinese Journal of Aeronautics. 2019. V. 32. No. 12. Pp. 2577 - 2591. https://doi.org/10.1016/j.cja.2019.07.001 11. Timoshenko V. I., Galinskiy V. P. Numerical simulation of a supersonic flow around finned boost vehicles. Space Sci. & Technol. 2017. V. 23. No. 5. Pp. 33 - 43. (in Russian). https://doi.org/10.15407/knit2017.05.033 12. Zarubin A. G. On the accuracy of Galerkin's method in different systems of coordinates. Uchenye Zapiski TsaGi. 1977. V. 8. No. 4. Pp. 110 - 115. (In Russian). 13. Numerical Solution of Multidimensional Gas-Dynamic Problems. S. K. Godunov (Ed.). Moscow: Nauka, 1976. 400 pp. (In Russian).
PARAMETERS OF THE ST-40M HALL-EFFECT THRUSTER IN ITS OPERATION ON XENON AND KRYPTON
DOI: https://doi.org/10.15407/itm2025.04.043 This article presents the results of an experimental study of the parameters of the ST-40M Hall-effect thruster developed by SETS (Space Electric Propulsion Systems) in its operation on xenon and krypton. Electric propulsion systems based on Hall-effect thrusters have found wide application due to their high performance and relative simplicity of design and operation compared to other types of propulsion systems. Traditionally, xenon is used as propellant in Hall-effect thrusters. It is an inert gas with a low ionization energy and a high atomic mass, which makes it possible to achieve a high performance of the electric propulsion system while maintaining operational simplicity. However, the high cost of xenon significantly affects the overall expenses during the testing and operation of the thruster and the propulsion system. Therefore, research is underway on the use of alternative propellants that could reduce operating costs while maintaining the thruster performance at an acceptable level. The most promising alternative to xenon is considered to be krypton. It has a lower cost and ensures operational simplicity, but its higher ionization energy negatively affects the thruster efficiency. The goal of this work was to compare the main parameters of the thruster operating on xenon and krypton under identical conditions. Experimental tests were carried out in a vacuum chamber at discharge voltages ranging from 250 to 500 V and propellant mass flow rates from 1 to 1.78 mg/s for xenon and from 1 to 1.6 mg/s for krypton. A comparative analysis of the thruster parameters in its operation on xenon and krypton at a mass flow rate of 1 mg/s showed that the use of krypton leads to a deterioration in thruster performance. The anode thrust and specific impulse decreased by 25 %–37 %, while the anode efficiency dropped by 15 %–24 %. REFERENCES 1. Frongello B., Hoskins W., Cassagy R., Kalkowska L., Maliga R. Spacecraft electric propulsion at an inflection point. Proceedings of the ASCEND Conference, AIAA paper 2021-4151, 2021. https://doi.org/10.2514/6.2021-4151 2. Tirila V. G., Demairé A., Ryan C. N. Review of alternative propellants in Hall thrusters. Acta Astronautica. 2023. V. 212, Pp. 284-306. https://doi.org/10.1016/j.actaastro.2023.07.047 3. Asmolovskyi, S., Yurkov, B. Analysis of the effect of changing the working substance from xenon to alternative inert gases on the parameters of the Hall-type electric propulsion system. System Design and Analysis of Aerospace Technique Characteristics. 2023. V. 33. No. 2. Pp. 3-22. (In Ukrainian). https://doi.org/10.15421/472308 4. Thomas F., Munro-O'Brien, Ryan C. N. Effect of channel width on the performance of a modular Hall effect thruster operating on Xenon, Krypton, and Argon. 39th International Electric Propulsion Conference 2025, IEPC-2025-193. 5. Thoreau P., Little J. M., Johansen A., Holmes M. R. Modeling and optimization of propellant mixtures for Hall thrusters. 39th International Electric Propulsion Conference 2025, IEPC-2025-071. 6. Moghaddasi M. B., Byrne M., Glascock M., Foster A. Qualification of ExoTerra's Halo8 Hall-effect thruster on krypton propellant. 39th International Electric Propulsion Conference 2025, IEPC-2025-441. 7. Kitaeva A., Di Sarli A., Giusti N., Pisano V., Pieri L., Cecconi M., Binetti C., Torre L., Gregucci S., Cardelli M., Ciampini D. SITAEL HT5k and HT20k propulsion systems readiness. 38th International Electric Propulsion Conference 2024, IEPC-2024-726. 8. Petrenko, O., Troyan, A., Pererva, V. Parameters of the ST-40M Hall thruster with increased power discharge supply. Journal of Rocket-Space Technology. 2023. V. 31. No. 4. Pp. 50-58. https://doi.org/10.15421/452307 9. Tolok S., Shcherbak D., Petrenko O., Troian A., Yurkov B. LAB6 hollow cathode with wide range current operation. У 73rd International Astronautical Congress, 2022. 10. Voronovskyi D., Kulahin S., Yurkov B., Asmolovskyi S. Performance comparison of a traditional and a magnetically shielded Hall thruster. Teh. Meh. 2025. No. 2. Pp. 50-62. (in Ukrainian). https://doi.org/10.15407/itm2025.02.050 11. Glascock M. S., Kiefer E., VanWoerkom M. Performance and capability overview of the Halo electric propulsion system. 37th International Electric Propulsion Conference 2022, IEPC-2022-301. 12. Jakubczak M., Riazantsev A., Jardin A., Kurzyna J. Experimental optimization of small krypton Hall thruster for operation at high voltage. 37th International Electric Propulsion Conference 2022, IEPC-2022-360. 13. Xia G., Li H., Ding Y., Wei L., Chen S., Yu D. Performance optimization of a krypton Hall thruster with a rotating propellant supply. Acta Astronautica, 2020 V. 171. Pp. 290-299. https://doi.org/10.1016/j.actaastro.2020.03.021
ON-OFF SPACECRAFT RELATIVE CONTROL IN SLIDING MODE VIA REINFORCEMENT LEARNING
DOI: https://doi.org/10.15407/itm2025.04.077 The paper addresses the problem of on-off spacecraft relative control in sliding mode for autonomous on-orbit servicing operations under actuator amplitude limits, action discreteness, and parametric uncertainties. The goal is to develop and assess an approach that combines sliding-mode control with modern reinforcement-learning methods tailored for resource-constrained onboard implementation. Relative motion dynamics is formulated in an orbital coordinate frame with normalized states and discretized in time. Binary actions with pulse-width modulation, subject to constraints on the thrust level, pulse duration, and duty cycle, represent the impulsive nature of actuation. We propose a combined synthesis in which the sliding-surface parameters and switching rules are tuned via proximal policy optimization within an actor-critic architecture. The actor and critic are implemented as neural networks that approximate the policy and the value function, respectively. The actor neural network takes the state vector as input information and outputs the mean and standard deviation of the parameters of the sliding mode control law. The value function penalizes both the state error and control effort, thus enabling a trade-off among the response speed, accuracy, and propellant consumption. Two uncoupled agents are designed to control spacecraft relative orbital motion in in-plane and out-of-plane directions independently. The proximal policy optimization hyperparameters are selected to ensure a trade-off among the learning time, stability, and control performance. The reinforcement-learning agents are trained and analyzed considering four cases that differ in the thrust levels and weighting matrices. The quality functional combines state deviation and thrust use penalties, thus enabling a trade-off among the response speed, accuracy, and propellant consumption. The results confirm the potential of this approach for autonomous spacecraft control under constraints and uncertainty. Compared with reported baselines, the trained agent shows superior robustness to plant-parameter uncertainty, which we attribute to the inherent robust properties of sliding-mode control. These findings have the potential to improve the efficiency and autonomy of on-orbit servicing operations. REFERENCES 1. Chandra A., Kalita H., Furfaro R., Thangavelautham J. End to End Satellite Servicing and Space Debris Management. arXiv:1901.11121, 2019. 2. Li W., Cheng D., Liu X., et al. On-orbit service (OOS) of spacecraft: A review of engineering developments. Progress in Aerospace Sciences. 2019. V. 108. Pp. 32-120. https://doi.org/10.1016/j.paerosci.2019.01.004 3. Khosravi A., Sarhadi P. Tuning of pulse-width pulse-frequency modulator using PSO: An engineering approach to spacecraft attitude controller design. Automatika. 2016. V. 57. Pp. 212-220. https://doi.org/10.7305/automatika.2016.07.618 4. Anthony T., Wie B., Carroll S. Pulse-modulated control synthesis for a flexible spacecraft. Journal of Guidance. 1989. V. 13. No. 6. Pp. 1014-1022. https://doi.org/10.2514/3.20574 5. Alpatov A., Khoroshylov S., Lapkhanov E. Synthesizing an algorithm to control the angular motion of spacecraft equipped with an aeromagnetic deorbiting system. Eastern-European Journal of Enterprise Technologies. 2020. V. 1. No. 5. Pp. 37-46. https://doi.org/10.15587/1729-4061.2020.192813 6. Goodfellow I., Bengio Y., Courville A. Deep Learning. MIT Press, 2016. 7. Krizhevsky A., Sutskever I., Hinton G. E. ImageNet classification with deep convolutional neural networks. Communications of the ACM. 2017. V. 60. No. 6. Pp. 84-90. https://doi.org/10.1145/3065386 8. Pierson H., Gashler M. Deep learning in robotics: a review of recent research. Advanced Robotics. 2017. V. 31. No. 16. Pp. 821-835. https://doi.org/10.1080/01691864.2017.1365009 9. Sallab A. E., Abdou M., Perot E., Yogamani S. Deep reinforcement learning framework for autonomous driving. Electronic Imaging. 2017. V. 19. Pp. 70-76. https://doi.org/10.2352/ISSN.2470-1173.2017.19.AVM-023 10. Silver D., Schrittwieser J., Simonyan K. Mastering the game of Go without human knowledge. Nature. 2017. V. 550. Pp. 354-359. https://doi.org/10.1038/nature24270 11. Izzo D., Märtens M., Pan B. A survey on artificial intelligence trends in spacecraft guidance dynamics and control. Astrodynamics. 2019. No. 3. Pp. 287-299. https://doi.org/10.1007/s42064-018-0053-6 12. Khoroshylov S. V., Redka M. O. Deep learning for space guidance, navigation, and control. Space Science and Technology. 2021. V. 27. No. 6. Pp. 38-52. https://doi.org/10.15407/knit2021.06.038 13. Oestreich C. E., Linares R., Gondhalekar R. Autonomous six-degree-of-freedom spacecraft docking maneuvers via reinforcement learning. Journal of Aerospace Information Systems. 2021. V. 18. No. 7. https://doi.org/10.2514/1.I010914 14. Gaudet B., Linares R., Furfaro R. Six degree-of-freedom hovering using LIDAR altimetry via reinforcement meta-learning. Acta Astronautica. 2020. V. 172. Pp. 90-99. https://doi.org/10.1016/j.actaastro.2020.03.026 15. Gaudet B., Linares R., Furfaro R. Seeker based adaptive guidance via reinforcement meta-learning applied to asteroid close proximity operations. Acta Astronautica. 2020. V. 171. Pp. 1-13. https://doi.org/10.1016/j.actaastro.2020.02.036 16. Redka M. O., Khoroshylov S. V. Determination of the force impact of an ion thruster plume on an orbital object via deep learning. Space Science and Technology. 2022. V. 28. No. 5. Pp. 15-26. https://doi.org/10.15407/knit2022.05.015 17. Khoroshylov S. V., Wang C. Spacecraft relative on-off control via reinforcement learning. Space Science and Technology. 2024. V. 30. No. 2. Pp. 3-14. https://doi.org/10.15407/knit2024.02.003 18. Khoroshylov S. V. Relative motion control system of SC for contactless space debris removal. Sci. Innov. 2018. V. 14. No. 4. Pp. 5-16. https://doi.org/10.15407/scine14.04.005 19. Steinberger M., Horn M., Fridman L. (Eds). Variable-Structure Systems and Sliding-Mode Control. Springer-Verlag, 2020. (Studies in Systems, Decision and Control; Vol. 271). https://doi.org/10.1007/978-3-030-36621-6 20. Bryson A. E., Ho Y. C. Applied Optimal Control: Optimization, Estimation, and Control. Hemisphere Publishing, 1975. Pp. 224-235. 21. Sutton R. S., Barto A. G. Reinforcement Learning: An Introduction. 2nd ed. MIT Press, 2018. Pp. 47-65. 22. Schulman J., Wolski F., Dhariwal P., Radford A., Klimov O. Proximal Policy Optimization Algorithms. arXiv:1707.06347, 2017. 13 pp. 23. Mnih V., Badia A., Mirza M., Graves A., Lillicrap T., Harley T., Silver D. Asynchronous Methods for Deep Reinforcement Learning. arXiv:1602.01783, 2016.
NUMERICAL ANALYSIS OF THE EFFECT OF THE DESIGN AND MANUFACTURING PARAMETERS OF STARTER LEAD-ACID BATTERIES ON THEIR DISCHARGE CHARACTERISTIC
DOI: https://doi.org/10.15407/itm2025.04.093 Because the battery uses chemically active substances, monitoring its operation and condition is important. Therefore, of importance is also the study of electrochemical processes that take place during its operation. This paper presents the results of a mathematical simulation of the mass exchange in an electrochemical cell of a starter battery during its discharge. The simulation is based on known equations. The elucidation of the effect of different factors on the battery’s discharge characteristics is of importance in terms of areas of its possible application. The mathematical model accounts for the design features of the electrodes, which consist of a porous active mass and a conductive grid. The solution shows the effect of the design and manufacturing parameters on the discharge curves. As can be seen from the solution, the effect of the electric current magnitude is most pronounced. Of interest are also calculated results that show how the discharge curves vary, for example, with decreasing grid conductivity. The effect of the electrode design parameters on the discharge properties is considered. Their features are elucidated, and a numerical estimate of their effect on the battery discharge indices is given. It is shown that a decrease in the porosity of the porous space due to gas bubbles that form when charging the battery and remain in pores may also markedly affect the discharge process. It is shown that the discharge curves also depend on the diameter of the cells that form the active porous mass of the electrodes. The scientific novelty lies in complementing the mathematical model with relationships that include the design parameters of the battery electrodes. The practical value of the obtained results lies in the possibility of accounting for the effect of the electrode material porosity and particle diameter on the battery performance at the battery design stage. REFERENCES 1. Dzenzersky V. A., Plaksin S. V., Zhitnik N. E., Shirman O. I. Chemical Current Source Condition Monitoring Kyiv, Naukova Dumka, 2014. 132 pp. (In Russian). 2. Khrustalev D. A. Batteries. Moscow: Izumrud, 2003. 224 pp. (In Russian). 3. Dasoyan M.A., Aguf I.A. Current Theory of Lead Acid Batteries. Stonechouse Glos. Technicopy Limited, 1979. 371 pp. 4. Bagotsky D. A., Skundin A. M. Chemical Current Sources. Moscow: Energoizdat, 1981. 360 pp. (In Russian). 5. Koshel M. D. Theoretical Foundations of Electrochemical Power Engineering. Dnipro: Ukrainian State University of Chemical Technology, 2002. 430 pp. (In Ukrainian). 6. Vahid Esfahanian, Torabi Farschad, Mosahebi Ali. An improved model of lead-acid batteries for simulation of VRLA batteries. Journal of Power Sources Symposium. 2007. 9 pp. URL: https://wp.kntu.ac.ir/ftorabi/Resources/Publications/An%20Improved%20Mathematical%20Model%20of%20Lead%E2%80%93Acid%20Batteries%20for%20Simulation%20of%20VRLA%20Batteries.pdf (Last accessed on November 25, 2025). 7. Vahid Esfahanian, Pooyan Kheirhan, Hassan Bahramian, Amir Babac Ansori, Goodarz Ahmadi. The effects of electrode parameters on lead-acid battery performance. Advanced Materials Research. 2013. V. 651. Pp. 492 -498. https://doi.org/10.4028/www.scientific.net/AMR.651.492 8. Gu H., Nguyen T. V., White R. E. A mathematical model of a lead-acid cell: discharge, rest and charge. J. Electrochem. Soc. Electrochemical Science and Technology. 1987. V. 134. No. 12. Pp. 2953 - 2960. https://doi.org/10.1149/1.2100322 9. Shah A. A., Li X., Wills R. G. A., Walsh F. C. A mathematical model for the soluble lead-acid flow battery. J. of the Electrochemical Society. 2010. V. 157. No. 5. Pp. A589 - A599. https://doi.org/10.1149/1.3328520 10. Yeliseyev V. I., Sovit Yu. P., Katrenko M. O. Mass transfer in the porous electrodes of a lead-acid battery during its discharge. Teh. Meh. 2024. No. 2. Pp. 124 - 136. (In Ukrainian). https://doi.org/10.15407/itm2024.02.124 11. How one can calculate the service time of an uninterrupted power supply. Guaranteed power supply systems. URL: https://dbz.systems/2023/07/06/rozrahunok-chasu-roboti-dbzh/ (Last accessed on November 6, 2025). (In Ukrainian). 12. Acid batteries. MEDIA-CENTER. URL: https://real-el.ua/ua/media/useful/e1798/ 06.11.25. (Last accessed on November 6, 2025). (In Ukrainian).
MODEL OF 3-D PRINTING ZONE HEATING CONTROL
DOI: https://doi.org/10.15407/itm2025.04.102 Innovative technologies of layer-by-layer product manufacturing by fast 3-D printing open up new opportunities for producing parts of a given shape. But sometimes, during the printing process with the use of specific materials, it is necessary to additionally heat or cool the part with an air flow over it. To improve the part quality, this process must be controlled, but for production safety, 3-D printing with special materials must be unmanned. Thus, it is necessary to develop an automated system for controlling the 3-printing process. This system should include several subsystems, in particular, a system for controlling the material supply through the extruder, a system for controlling the cooling (or heating) temperature of the printing zone, and a system for controlling the printing speed, which affects the part quality. The parameters of all the systems depend on the material characteristics and the printed part shape. This paper presents a mathematical model of a control object: a subsystem for 3-D printing zine air heating control, which is based on experimental data obtained in real conditions, and structural and parametric identification procedures for this subsystem. As a result of the identification, the model parameters were obtained as a function of the control action. The analysis of these relationships showed that the model of this subsystem as an automatic control object is complex with a variable structure and non-stationary parameters that change randomly over a wide range. It was found that the whole range of the control action can be divided into five sections, within which the structure of the control object model does not change and the model parameters change over relatively small ranges. Taking this into account, recommendations were formed regarding the procedure for further synthesis of the subsystem for automatic control of the air blowing temperature. In developing this printing control subsystem, to ensure the quality of the transient process, the control action values must be checked for different model structures with variable parameters over certain ranges. The control system developed must be interfaced with other printing control systems to get a complete finished automatic control system. REFERENCES 1. Abduganiyeva Yulduzoy Shakhabidinovna. Automation of technological processes. European Journal of Humanities and Educational Advancements. 2022. V. 3. No. 12. Pp. 130-131. 2. Davim J. P., Markopoulos A. P., Markopoulos A. Advanced Machining Processes: Innovative Modeling Techniques. Taylor & Francis Group, 2017. 327 pp. https://doi.org/10.1201/b21863 3. Ivakhnenko A. G. Simulation of Complex Systems: Information Approach. V. V. Pavlov (Ed.). Kyiv: Vyshcha Shkola, 1987. 62 pp. (In Russian). 4. Shevchenko V. V., Kapinos I. V., Hrabovskyi D. O. System of unmanned part machining control. Advanced Technologies and Devices. 2011. No. 1. Pp. 223-231. (In Ukrainian). 5. Bublikov A., Tkachov V. Simulation Study of a Mining Machine's Automatic Control System. Dnipropetrovsk: National Mining University, 2015. 182 pp. (In Ukrainian).
COMPUTER SIMULATION OF THE EFFECT OF ELLIPTICAL INCLUSION ARRANGEMENT ON THE STRAINING OF A CYLINDRICAL SHELL WITH A CIRCULAR HOLE
DOI: https://doi.org/10.15407/itm2025.04.052 Thin-walled plate-shell structural elements find wide application in many sectors of engineering and the national economy, particularly in the aerospace and the oil and gas industry, power engineering, mechanical engineering, construction, etc. The integrity and homogeneity of structures can be compromised by the presence of inhomogeneities. Such structures often have various manufacturing defects or design inhomogeneities: holes, cutouts, recesses, inclusions, microcracks, and other similar formations, which act as local stress concentrators. Under real-world operating conditions, an increased stress concentration in the zones of local stress concentrators significantly affects the strength and durability of structural elements, thus making a search for ways to reduce stress concentration a key issue in solid mechanics. When designing up-to-date equipment, optimizing material consumption and extending the service life of components using novel materials and technologies is a priority, which determines their competitiveness in various industries. This study involves a computer simulation and a finite element analysis of the stress and strain fields of thin-walled cylindrical shells with a small circular through hole and several elliptical inclusions of a different material symmetrically arranged around it. For definiteness, it is assumed that the inclusions are homogeneous and located in the plane of the shell. This paper analyzes the effect of the geometry, the mechanical properties, the number, and the arrangement of the inclusions on the stress and strain fields of the shells in the vicinity of the holes under the action of a uniaxial uniform tensile load applied to the shell ends. The distributions of the stress and strain intensities in the zones of local stress concentration are obtained. The obtained numerical results are compared with the results for shells without inclusions and with known similar results for plates. It is shown that the use of "stiff" elliptical inclusions contributes to stress concentration reduction by ~ (10 – 36) % depending on their number and arrangement. In the case of two diagonal inclusions, the stress concentration zone shifts, which is in agreement with the results for a similar problem for a plate. REFERENCES 1. Avdonin A. S. Applied Methods for the Design of Shells and Thin-Walled Structures. Moscow: Mashinostroyeniye, 1969. 402 pp. (In Russian). 2. Balashova S. D., Tavadze E. L. On the convergence of the projection-iteration method for solving an extremal problem with constraints. Mathematical Models and Computational Methods in Applied Problems. Dnipropetrovsk: Dnipropetrovsk State University, 1996. Рp. 128-134. (In Russian). 3. Hart E. L., Rybalko Ya. V. Interaction of a circular hole and the surrounding elliptic inclusions under elastic deformation of a rectangular plate. Problems in Computational Mechanics and Structural Strength. Dnipro: Lira, 2019. V. 30. Pp. 5-18. (In Ukrainian). 4. Hart E. L., Shebanov O. D. Stress concentration around a circular hole in a cylindrical shell in the presence of surrounding elliptical inclusions. Problems in Computational Mechanics and Strength of Structures. Dnipro: Lira, 2024. V. 38. P. 36-50. (In Ukrainian). 5. Hudramovich V. S., Hart E. L., Strunin K. A. Simulation of straining the plate with elastic extended inclusions based on finite element method. Teh. Meh. 2014. No. 2. Pp. 12-23. (In Russian). 6. Guz A. N., Chernyshenko I. S. et al. Theory of Thin Shells Weakened by Holes. Kyiv: Naukova Diumka, 1980. 636 pp. (In Russian). 7. Kraiko A. N. Numerical Methods for Shell Analysis. Moscow: Mashinostroyeniye, 1986. 368 pp. (In Russian). 8. Pidstrygach Ya. S. Selected Works. 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MATHEMATICAL MODELING OF ELECTRON DENSITY DETERMINATION USING A STATIONARY CYLINDRICAL LANGMUIR PROBE UNDER IONOSPHERIC CONDITIONS
DOI: https://doi.org/10.15407/itm2025.04.067 The goal of this article is to theoretically substantiate the applicability of the classical formula of the single cylindrical probe theory to determining the electron density based on measurements of the currents of a floating probe system in ionospheric conditions. Probe measurements in the ionosphere are modeled using a cylindrical probe and the body of a very small satellite placed transversely in the incident supersonic flow of a collisionless plasma. The ionospheric plasma is considered to be Maxwellian and consists of electrons and singly charged atomic ions of oxygen and hydrogen. A mathematical model of current collection by the floating probe system “probe – plasma – satellite body” was developed based on classical relationships for the electron and ion currents to a thin cylinder placed transversally in the incident flow. To model the collection of the hydrogen ion current by the satellite body, the results of numerical calculations of the ion current to the cylinder using the two-dimensional Vlasov-Poisson model were approximated. The probe bias potential was determined such that, under ionospheric conditions, the electron region of the floating probe system's current-voltage characteristic is closest to that of a single probe. The determination of the electron density using the classical calculation formula of the single-probe theory was simulated for probe current measurements in the low voltage portion of the electron region of the current-voltage characteristic of the floating probe system. The limiting methodological error in determining the electron density under ionospheric conditions within the framework of the probe system model considered was estimated. 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