Title of the article METHODS OF CARTEPILLAR DRIVE VIBRATION MEASUREMENT: MODERN APPROACHES AND TECHNOLOGIES
Authors

TARATORKIN Alexey I., Design Engineer, JSC “Special Design Bureau of Mechanical Engineering”, Kurgan, Russian Federation, This email address is being protected from spambots. You need JavaScript enabled to view it.">This email address is being protected from spambots. You need JavaScript enabled to view it.

ABDULOV Sergey V., Ph. D. in Eng., Assoc. Prof., Executive Director – Chief Designer, JSC “Special Design Bureau of Mechanical Engineering”, Kurgan, Russian Federation, This email address is being protected from spambots. You need JavaScript enabled to view it.">This email address is being protected from spambots. You need JavaScript enabled to view it.

TARATORKIN Igor A., D. Sc. in Eng., Prof., Head of the Department of Mechanics of Transportation Vehicles – Chief Researcher, Institute of Engineering Science, Ural Branch of Russian Academy of Sciences, Yekaterinburg, Russian Federation, This email address is being protected from spambots. You need JavaScript enabled to view it.">This email address is being protected from spambots. You need JavaScript enabled to view it.

TARATORKIN Alexander I., D. Sc. in Eng., Senior Research Fellow, Institute of Engineering Science, Ural Branch of Russian Academy of Sciences, Yekaterinburg, Russian Federation, This email address is being protected from spambots. You need JavaScript enabled to view it.">This email address is being protected from spambots. You need JavaScript enabled to view it.

In the section DYNAMICS, DURABILITY OF VEHICLES AND STRUCTURES
Year 2026
Issue 1(74)
Pages 41–48
Type of article RAR
Index UDK 629.1
DOI https://doi.org/10.46864/1995-0470-2026-1-74-41-48
Abstract The article focuses on overcoming the limitations of contact methods for measuring the dynamics of tracked vehicles. As a solution, a method is proposed which is based on non-contact measurement of track link displacements using high-speed videography and computer vision algorithms. The implementation of the Lucas–Kanade optical flow, an efficient algorithm for tracking feature points on the surface of the track links, is discussed in detail. It is shown that this approach allows for highly accurate measurement of displacements, velocities, and deformations along the entire track loop without affecting the object of study, meeting the stringent requirements of experimental research. The method enables high-precision identification of frequencies, amplitudes, damping coefficients, and vibration modes of various track branches and provides a complete picture of the kinematics of the track loop branches without influencing the object under study.
Keywords caterpillar drive, dynamics, oscillations, amplitude, frequency, computer vision, Lucas–Kanade optical flow method
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Bibliography
  1. Platonov V.F., Belousov A.F., Oleynikov N.G., Kartsev G.I. Gusenichnye transportery-tyagachi [Tracked tractor haulers]. Moscow, Mashinostroyenie Publ., 1978. 351 p. (in Russ.). 
  2. Berezin I.Ya., Plagov A.I., Rikhter E.E. Dinamika sistemy “grunt — gusenitsa — opornyy katok” [Dynamics of the “soil — track — roadwheel” system]. Prochnost mashin i apparatov pri peremennykh nagruzheniyakh, 1991. Pp. 123–128 (in Russ.). 
  3. Abyzov A.A., Berezin I.Ya., Richter E.E., Byvaltsev V.I. Dinamika gusenichnoy lenty s elastomernymi ushiritelyami [Movement of crawler band with elastomer wideners]. Tractors and agricultural machinery, 2012, vol. 79, no. 5, pp. 36–38. DOI: https://doi.org/10.17816/0321-4443-69400 (in Russ.). 
  4. Abyzov A.A. Modelirovanie dinamiki gusenichnoy lenty s elastomernymi ushiritelyami [Modeling of dynamics of a crawler band with elastomer wideners]. Tractors and agricultural machinery, 2012, vol. 79, no. 7, pp. 48–51. DOI: https://doi. org/10.17816/0321-4443-69480 (in Russ.). 
  5. Abyzov A.A. Razrabotka edinoy matematicheskoy modeli svyazannoy nelineynoy dinamicheskoy sistemy mobilnoy mashiny, vklyuchayushchey elementy dvizhitelya. Razrabotka programmnykh sredstv, identifikatsiya modeli i issledovaniya dinamiki. Otchet o NIR (zaklyuch.) [Development of a unified mathematical model of a coupled nonlinear dynamic system of a mobile machine. Research report (final)]. Chelyabinsk, 2003. 37 p. (in Russ.). 
  6. Abyzov A.A. Razrabotka matematicheskoy modeli dinamiki gibkogo sterzhnya s prisoedinennymi elastomernymi elementami i ego vzaimodeystviya s nelineynoy vyazkouprugoy sredoy. Otchet o NIR (promezhutoch.) [Development of a mathematical model of the dynamics of a flexible rod with attached elastomeric elements and its interaction with a nonlinear viscoelastic medium. Research report (intermediate)]. Chelyabinsk, 2002. 35 p. (in Russ.). 
  7. Huang K., Wang G., Wang P., Zhang J., Miao Y. Three-dimensional nonlinear tooth meshing modeling and analysis for preloaded tracked vehicles. Preprint. DOI: https://doi. org/10.21203/rs.3.rs-5317820/v1. 
  8. Zhdanovich Ch.I., Plishch V.N. Eksperimentalnye issledovaniya kolebaniy verkhney vetvi rezinoarmirovannoy gusenitsy selskokhozyaystvennogo traktora [Experimental studies of oscillations of the upper branch of a rubber-reinforced track of an agricultural tractor]. Agropanorama, 2023, no. 4(158), pp. 4–9. DOI: https://doi.org/10.56619/2078-7138-2023-158-4- 4-9 (in Russ.). 
  9. Chołodowski J., Dudziński P.A., Ketting M. Energy loss due to track vibration in rubber track crawler vehicles. Archives of civil and mechanical engineering, 2021, vol. 21, iss. 2. DOI: https://doi.org/10.1007/s43452-021-00212-8.
  10. Guo W., Li J., Hu Y. Vision-based displacement measurement method of large-scale bridges using tilt shift camera and fast spatio-temporal context learning. Mechanical systems and signal processing, vol. 224. DOI: https://doi.org/10.1016/j. ymssp.2024.112165. 
  11. Diwan T., Anirudh G., Tembhurne J.V. Object detection using YOLO: challenges, architectural successors, datasets and applications. Multimedia tools and applications, 2023, vol. 82, iss. 6, pp. 9243–9275. DOI: https://doi.org/10.1007/s11042- 022-13644-y. 
  12. Liu W., et al. SSD: single shot multibox detector. Proc. 14th European conference “Computer Vision – ECCV 2016”. Amsterdam, 2016, vol. 1, pp. 21–37. DOI: https://doi. org/10.1007/978-3-319-46448-0_2. 
  13. Bharati P, Pramanik A. Deep learning techniques—R-CNN to Mask R-CNN: a survey. Proc. 1st international conference “Computational intelligence in pattern recognition”. Shibpur, 2020, pp. 657–668. DOI: http://dx.doi.org/10.1007/978-981- 13-9042-5_56. 
  14. Bajpai R, Joshi D. MoveNet: a deep neural network for joint profile prediction across variable walking speeds and slopes. IEEE transactions on instrumentation and measurement, 2021, vol. 70, pp. 1–11. DOI: http://dx.doi.org/10.1109/ TIM.2021.3073720. 
  15. Ghanbari S., Ashtyani Z.P., Masouleh M.T. User identification based on hand geometrical biometrics using Media-Pipe. Proc. 30th international conference on electrical engineering (ICEE). Tehran, 2022, pp. 373−378. DOI: http://dx.doi.org/10.1109/ ICEE55646.2022.9827056. 
  16. Mai W., et al. A fall detection alert system based on lightweight openpose and spatial-temporal graph convolution network. Journal of physics: conference series, 2021, vol. 2035. DOI: http://dx.doi.org/10.1088/1742-6596/2035/1/012036. 
  17. Obukhov A.D., Dedov D.L., Surkova E.O., Korobova I.L. 3D human motion capture method based on computer vision. Advanced engineering research (Rostov-on-Don), 2023, vol. 23, no. 3, pp. 317–328. DOI: https://doi.org/10.23947/2687-1653-2023-23-3-317-328. 
  18. Chung J.-L., Ong L.-Y., Leow M.-C. Comparative analysis of skeleton-based human pose estimation. Future internet, 2022, vol. 14, iss. 12. DOI: https://doi.org/10.3390/fi14120380. 
  19. Chen J., et al. Multi-view triangulation: systematic comparison and an improved method. IEEE access, 2020, vol. 8, pp. 21017−21027. DOI: https://doi.org/10.1109/AC CESS.2020.2969082. 
  20. Lucas B.D., Kanade T. An iterative image registration technique with an application to stereo vision. Proc. 7th international joint conference on artificial intelligence. San Francisco, 1981, vol. 2, pp. 674–679. 
  21. Kotelnikov V.A. O propusknoy sposobnosti “efira” i provoloki v elektrosvyazi [On the transmission capacity of ’ether’ and wire in electric communications]. Uspekhi fizicheskikh nauk, 2006, vol. 176, no. 7, pp. 762–770. DOI: https://doi.org/10.3367/UF Nr.0176.200607h.0762 (in Russ.). 
  22. Shannon C.E. Communication in the presence of noise. Proceedings of the IRE, 1949, vol. 37, iss. 1, pp. 10–21. 
  23. Radiotekhnika. Entsiklopediya [Radio engineering. Encyclopedia]. Moscow, Dodeka-XXI Publ., 2002. 944 p. (in Russ.). 
  24. Vasin V.A., et al. Radiosistemy peredachi informatsii [Radio systems for information transmission]. Moscow, Goryachaya liniya–Telekom Publ., 2005. P. 29. (in Russ.). 
  25. ISO 8608:2016. Mechanical vibration — Road surface profiles — Reporting of measured data. 2016. 36 p. Available at: https://www.iso.org/standard/71202.html. 
  26. Taratorkin A.I., et al. Raschetno-eksperimentalnoe issledovanie dinamiki obvoda gusenichnogo dvizhitelya transportnoy mashiny vysokoy prokhodimosti [Calculation and experimental study of the dynamics of the track mover bypass of a cross-country transport vehicle]. Mechanics machines, mechanisms and materials, 2024, no. 4(69), pp. 50–60. DOI: https:// doi.org/10.46864/1995-0470-2024-4-69-50-60 (in Russ.).

Title of the article ENGINEERING APPROACH TO DESIGNING AND CALCULATION OF THE MAIN ELEMENTS OF DRIVE AXLES OF HEAVY-DUTY QUARRY DUMP TRUCKS
Authors

SHYSHKO Sergei A., Deputy Chief Designer – Head of Mechanical Transmissions Department of the Chief Design Engineer Division of the Scientific and Technical Center n.a. A.N. Egorov, OJSC “BELAZ” — Management Company of Holding “BELAZ-HOLDING”, Zhodino, Republic of Belarus, This email address is being protected from spambots. You need JavaScript enabled to view it.">This email address is being protected from spambots. You need JavaScript enabled to view it.

ISHIN Nikolay N., D. Sc. in Eng., Assoc. Prof.,Chief of the R&D Center “Mining Machinery”, Joint Institute of Mechanical Engineering of the NAS of Belarus, Minsk, Republic of Belarus, This email address is being protected from spambots. You need JavaScript enabled to view it.">This email address is being protected from spambots. You need JavaScript enabled to view it.

GOMAN Arkadiy M., Ph. D. in Eng., Assoc. Prof., Head of the Department of Dynamic Analysis and Vibration-based Diagnostics of Machines of the R&D Center “Mining Machinery”, Joint Institute of Mechanical Engineering of the NAS of Belarus, Minsk, Republic of Belarus, This email address is being protected from spambots. You need JavaScript enabled to view it.">This email address is being protected from spambots. You need JavaScript enabled to view it.

NATURJEVA Marina K., Researcher of the Department of Dynamic Analysis and Vibration-based Diagnostics of Machines of the R&D Center “Mining Machinery”, Joint Institute of Mechanical Engineering of the NAS of Belarus, Minsk, Republic of Belarus, This email address is being protected from spambots. You need JavaScript enabled to view it.">This email address is being protected from spambots. You need JavaScript enabled to view it. 

In the section DYNAMICS, DURABILITY OF VEHICLES AND STRUCTURES
Year 2026
Issue 1(74)
Pages 31–40
Type of article RAR
Index UDK 621.833.65: 539.43
DOI https://doi.org/10.46864/1995-0470-2026-1-74-31-40
Abstract The paper considers scientific and engineering aspects of design, optimization, calculation, construction and ensuring manufacturability of production of drive axles of heavy-duty quarry dump trucks. A new method of engineering analysis has been developed for express assessment and limitation of the selection area of the main parameters of gear transmissions of drive axles of BELAZ quarry dump trucks: gear module; number of gear teeth; load on input (output) shafts; maximum rotation frequency of input (output) links; maximum dynamic factor. Distribution of the drive axle gear ratio uвм is made according to the principle of maximizing the torque in the final stage, i.e. in the planetary wheel transmission, which reduces the loads on the differential and axle shafts and their dimensions. When distributing gear ratios, it is necessary to take into account the limitations of ensuring the technological possibility of cutting teeth of bevel gears with a circular tooth of the main transmission on the equipment available at the enterprise. For the first time, the Bbha scheme of a single-row planetary wheel reduction gear with a double-crown satellite has been used on BELAZ extra-large-capacity quarry dump trucks. The adopted design provides an increase in the gear ratio by 1.7...1.8 times compared to a single-row classic Abha planetary reduction gear.
Keywords heavy-duty dump truck, hydromechanical transmission, drive axle, final drive, helical-conical gears, differential, planetary wheel transmission
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Bibliography
  1. Mariev P.L., Voitov V.T., Shyshko S.A. Otsenka effektivnosti gidromekhanicheskoy i elektromekhanicheskoy transmissii dvukhosnykh karernykh samosvalov po velichine KPD [Design procedure and results of analysis of efficiency coefficient of hydromechanical and electromechanical transmission of mining dump trucks are given]. Ore and metals, 2015, no. 3, pp. 83–87. DOI: https://doi.org/10.17580/gzh.2015.03.13 (in Russ.). 
  2. Shyshko S.A., Ishin N.N., Goman A.M. Osobennosti rascheta i proektirovaniya uzlov gidromekhanicheskikh transmissiy bolshegruznykh samosvalov BELAZ [Features of calculation and design of hydromechanical transmission units of BELAZ heavy-duty dump trucks]. Aktualnye voprosy mashinovedeniya, 2023, iss. 12, pp. 198–202 (in Russ.). 
  3. Shyshko S.A., Moiseenko V.I. Obosnovanie vybora peredatochnykh otnosheniy GMT karyernykh samosvalov osobo bolshoy gruzopodyemnosti [Rationale for selection of gear ratio of hydromechanical transmission of dump trucks of extra heavy payload capacity]. Mechanics of machines, mechanisms and materials, 2016, no. 4(37), pp. 52–59 (in Russ.). 
  4. Algin V.B., Bokovets Е.N., Kuznetsov Е.V. Vysokomoshchnye gidromekhanicheskie peredachi: patento-informatsionnoe i raschetnoe issledovanie. Chast I. Metodika [High-power hydromechanical transmissions: patent-informational and computational investigation. part 1. methodology]. Mechanics of machines, mechanisms and materials, 2015, no. 2(31), pp. 5–15 (in Russ.). 
  5. Algin V.B., Bokovets Е.N., Kuznetsov Е.V. Razvitie vysokomoshchnykh otechestvennykh i zarubezhnykh GMT: patentnyy landshaft, raschetnyy analiz, tendentsii. Chast 1. Analiz problemy [Development of local and foreign high-powerhydromechanical transmissions: patent landscape, analysis, trends. Part 1. Case analysis]. Mechanics of machines, mechanisms and materials, 2017, no. 1(38), pp. 5–20 (in Russ.). 
  6. Shyshko S.A., Ishin N.N., Goman A.M., Naturjeva M.K. Metodika proektirovaniya spiralno-konicheskikh shesteren glavnoy peredachi karernykh samosvalov bolshoy gruzopodemnosti [Design methodology for spiral-bevel gears of the main transmission of heavy-duty mining dump trucks]. Mechanics of machines, mechanisms and materials, 2025, no. 1(70), pp. 17–29. DOI: https://doi.org/10.46864/1995-0470-2025-1-70-17-29 (in Russ.). 
  7. Karernyy samosval 797F [Quarry dump truck 797F]. Available at: https://s7d2.scene7.com/is/content/Caterpillar/C10512495 (accessed May 23, 2025) (in Russ.). 
  8. Lisichik A.S., Shyshko S.A., Ishin N.N., Sidorenko A.G., Maksimchenko N.N. Prognozirovanie resursa glavnoy peredachi samosvala BELAZ na stadii proektirovaniya [Prediction of the main gear lifetime of belaz dump truck at the design stage]. Mechanics of machines, mechanisms and materials, 2023, no. 2(63), pp. 31–41. DOI: https://doi.org/10.46864/1995- 0470-2023-2-63-31-41 (in Russ.). 
  9. Tsiafis I., Mamouri P., Kyriakidis K. Design of a spiral bevel gear acc. to ISO 23509:2006 standards. MATEC web of conferences, 2020, vol. 318. DOI: https://doi.org/10.1051/matec conf/202031801020. 
  10. Zhang R., Zhang B., Fu S. The designing and modeling of equal base circle herringbone curved bevel gears. Scientific reports, 2023, vol. 13. DOI: https://doi. org/10.1038/s41598-023- 28934-0. 
  11. Raji N.A., Adedeji K.A., Oyetunji E.O., Agbelusi A.D. Design analysis of bevel gear for gearmotor selection in revolving platform. Modern mechanical engineering, 2021, vol. 11, no. 1, pp. 1–11. DOI: https://doi.org/10.4236/mme.2021.111001. 
  12. Geng L., Deng X., Zhang H., Nie S., Jiang C. Theory and experimental research on spiral bevel gear by double-side milling method. Mechanics & industry, 2021, vol. 22. DOI: https://doi. org/10.1051/meca/2021032. 
  13. Geng L., Nie S., Jiang C. A method to manufacture spiral bevel gears by equivalent completing. Mechanics & industry, 2024, vol. 25. DOI: https://doi.org/10.1051/meca/2024013. 
  14. BELAZ. CAGE Software. 2001. 1 CD-ROM. 
  15. Afanasev B.A., et al. Proektirovanie polnoprivodnykh kolesnykh mashin. T. 2 [Design of four-wheel drive wheeled vehicles. Vol. 2]. Moscow, Moskovskiy gosudarstvennyy tekhnicheskiy universitet im. N.E. Baumana Publ., 2000. 640 p. (in Russ.).

Title of the article DIGITAL TECHNOLOGIES APPLICATION IN DIESEL ENGINE DESIGN: FROM CONCEPT TO SERIAL PRODUCTION
Authors

POPOV Igor A., Corresponding Member of TAS, D. Sc. in Eng., Professor of the Department for Heat and Power Engineering, Head of the Laboratory of Modeling Physical and Technical Processes, Kazan National Research Technical University named after A.N. Tupolev-KAI, Kazan, Republic of Tatarstan, Russian Federation, This email address is being protected from spambots. You need JavaScript enabled to view it.">This email address is being protected from spambots. You need JavaScript enabled to view it.

GUREEV Victor M., D. Sc. in Eng., Leading Researcher of the Laboratory of Modeling Physical and Technical Processes, Kazan National Research Technical University named after A.N. Tupolev-KAI, Kazan, Republic of Tatarstan, Russian Federation, This email address is being protected from spambots. You need JavaScript enabled to view it.">This email address is being protected from spambots. You need JavaScript enabled to view it.

ZHUKOVA Yuliya V., Ph. D. in Phys. and Math., Assoc. Prof., Leading Researcher of Turbulence Laboratory, A.V. Luikov Heat and Mass Transfer Institute of the NAS of Belarus, Minsk, Republic of Belarus, This email address is being protected from spambots. You need JavaScript enabled to view it.">This email address is being protected from spambots. You need JavaScript enabled to view it. 

CHORNY Andrei D., Ph. D. in Phys. and Math., Assoc. Prof., Head of Turbulence Laboratory, A.V. Luikov Heat and Mass Transfer Institute of the NAS of Belarus, Minsk, Republic of Belarus, This email address is being protected from spambots. You need JavaScript enabled to view it.">This email address is being protected from spambots. You need JavaScript enabled to view it.

BARANOVA Tatsiana A., Senior Researcher of Turbulence Laboratory, A.V. Luikov Heat and Mass Transfer Institute of the NAS of Belarus, Minsk, Republic of Belarus, This email address is being protected from spambots. You need JavaScript enabled to view it.">This email address is being protected from spambots. You need JavaScript enabled to view it.

KUKHARCHUK Igor G., Researcher of Turbulence Laboratory, A.V. Luikov Heat and Mass Transfer Institute of the NAS of Belarus, Minsk, Republic of Belarus, This email address is being protected from spambots. You need JavaScript enabled to view it.">This email address is being protected from spambots. You need JavaScript enabled to view it. 

In the section GENERAL ISSUES OF MECHANICS
Year 2026
Issue 1(74)
Pages 15–22
Type of article RAR
Index UDK 004.942
DOI https://doi.org/10.46864/1995-0470-2026-1-74-15-22
Abstract The paper presents the key aspects of using digital technologies in mechanical engineering covering the stages of design and technological preparation of production. The methodology for creating 3D CAD models, forming design and technological documentation, creating virtual assemblies and digital twins using 1D and 3D modeling are described. Examples of numerical tests and practical implementation of developments are given on the example of diesel engine components and assemblies for transport systems.
Keywords digital technologies, decomposition, digital twins, heat and mass transfer, numerical simulation, verified and validated physical and mathematical model, aerodynamics, strength
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Bibliography
  1. Grieves M.W. Digital twins: past, present, and future. The digital twin, 2023, pp. 97–121. DOI: https://doi.org/10.1007/978-3- 031-21343-4_4. 
  2. Grieves M., Vickers J. Digital twin: mitigating unpredictable, undesirable emergent behavior in complex systems. Transdisciplinary perspectives and complex systems: New findings and approaches, 2017, pp. 85–113. DOI: https://doi. org/10.1007/9783-319-38756-7_4. 
  3. Borovkov A.I., Gamzikova A.A., Kukushkin K.V., Ryabov Yu.A. Tsifrovye dvoyniki v vysokotekhnologichnoy promyshlennosti. Kratkiy doklad [Digital twins in the high-tech industry. Brief report]. Saint Petersburg, POLITEKh-PRESS Publ., 2019. 62 p. DOI: https://doi.org/10.18720/SPBPU/2/i20-130 (in Russ.). 
  4. Poddubko S.N., Shmelyev A.V. Tsifrovoe proizvodstvo: osnovy i tendentsii formirovaniya. Informatsionno-analiticheskiy obzor [Digital production: fundamentals and trends development. Informational-analytical review]. Mechanics of machines, mechanisms and materials, 2016, no. 4(37), pp. 66–74 (in Russ.). 
  5. Dozortsev V.M. Tsifrovye dvoyniki v promyshlennosti: zhizn posle khaypa [Digital twins in industry: life after hype]. Avtomatizatsiya v promyshlennosti, 2023, no. 12, pp. 7–13. DOI: https://doi.org/10.25728/avtprom.2023.12.01 (in Russ.). 
  6. Prokhorov A., Lysachev M. Tsifrovoy dvoynik: analiz, trendy, mirovoy opyt [Digital twin. Analysis, trends, world experience]. Moscow, AlyansPrint Publ., 2020. 401 p. (in Russ.). 
  7. State Standard R 57700.37-2021. Kompyuternye modeli i modelirovanie. Tsifrovye dvoyniki izdeliy. Obshchie polozheniya [Computer models and simulation. Digital twins of products. General provisions]. Moscow, Rossiyskiy institut standartizatsii Publ., 2021. 15 p. (in Russ.). 
  8. State Standard R 57700.21-2020. Kompyuternoe modelirovanie v protsessakh razrabotki, proizvodstva i obespecheniya ekspluatatsii izdeliy. Terminy i opredeleniya [Computer modelling in the processes of development, manufacturing and maintenance of products. Terms and definitions]. Moscow, Rossiyskiy institut standartizatsii Publ., 2020. 8 p. (in Russ.). 
  9. Gureyev V.M., Gortyshov Yu.F., Popov I.A., Makarov Е.G., Kulikov A.S. Tsifrovye dvoyniki – osnova prinyatiya optimalnykh tekhnicheskikh resheniy i povysheniya finansovoy effektivnosti razrabotok [Digital twins as the basis for optimal technical solutions and increased financial efficiency of developments]. Mezhdunarodnyy forum KAZAN DIGITAL WEEK – 2023 [International forum KAZAN DIGITAL WEEK – 2023], Kazan, 2023, part 1, pp. 313–323 (in Russ.). 
  10. Chorny A.D., Zhukova Yu.V., Baranova T.A., Kukharchuk I.G., Popov I.A. Opyt sozdaniya tsifrovykh dvoynikov dlya modelirovaniya ekspluatatsionnykh rezhimov transportnykh sistem [Experience in creating digital twins for modeling operational modes of transport systems]. Mezhdunarodnyy forum KAZAN DIGITAL WEEK – 2023 [International forum KAZAN DIGITAL WEEK – 2023], Kazan, 2023, part 1, pp. 442–450 (in Russ.). 
  11. Popov I.A., Gureev V.M., Makarov E.G., Kulikov A.S., Andriyanov S.M. Tsifrovye dvoyniki – ideologiya, opyt i perspektivy [Digital twins – ideology, experience and prospects]. Vestnik NTsBZhD, 2024, no. 3(61), pp. 80–87 (in Russ.). 
  12. Obozov А.А., Novikov R.A., Grishanov P.A. Gidrodinamicheskiy analiz protsessov toplivnykh system tipa “COMMON RAIL” v srede imitatsionnogo modelirovaniya AVL BOOST HYDSIM [Hydrodynamic analysis of processes of COMMON RAIL fuel systems in AVL BOOST HYDSIM simulation environment]. Transport engineering, 2022, no. 9(9), pp. 4–10. DOI: https://doi.org/10.30987/2782-5957-2022-9-4-10 (in Russ.). 
  13. Bellér G., Árpád I., Kiss J.T., Kocsis D. AVL Boost: a powerful tool for research and education. Journal of physics: conference series, 2021, vol. 1935. DOI: https://doi.org/10.1088/1742- 6596/1935/1/012015. 
  14. Salakhov R.R., Ermakov A.М., Khismatullin R.M., Smolyakov Yu.А., Razvalyaev S.V. Issledovanie parametrov sistemy smazki dvigatelya gruzovogo avtomobilya pri razlichnykh rabochikh temperaturakh motornogo masla [Investigation of the parameters of the lubrication system of a truck engine at various operating oil temperatures]. Truck, 2022, no. 4, pp. 3–9 (in Russ.). 
  15. Popov, I.A., Gureev M.V., Gureev V.M., Zhukova Yu.V., Chorny A.D. Chislennoe modelirovanie sistemy smazki aviatsionnykh porshnevykh dvigateley [Numerical simulation of the lubrication system of aircraft piston engines]. Izvestiya vysshykh uchebnykh zavedenii. Aviatsionnaya tekhnika, 2024, no. 1, pp. 94–100 (in Russ.). 
  16. Chorny A.D., et al. Opredelenie poter davleniya v glavnoy maslyanoy magistrali i forsunkakh sistemy smazki dizelnykh dvigateley bolshegruznykh avtomobiley: chislennoe modelirovanie [Determining the pressure losses in the main oil line and injectors of the lubrication system of diesel engines of heavy vehicles: numerical simulation]. Mechanics of machines, mechanisms and materials, 2024, no. 3(68), pp. 28–35. DOI: https://doi.org/10.46864/1995-0470-2024-3-68-28-35 (in Russ.). 
  17. Popov I.A., et al. Chislennoe modelirovanie gerotornogo nasosa sistemy smazki dizelnykh dvigateley [Numerical modeling of hydrodynamic processes in the gerotor pump of the lubrication system of diesel engines]. Mechanics of machines, mechanisms and materials, 2024, no. 4(69), pp. 28–38. DOI: https://doi.org/10.46864/1995-0470-2024-4-69-28-38 (in Russ.). 
  18. Popov I.A., et al. Gidrodinamika i teploobmen v kanalakh slozhnoy formy dvigatelnykh ustanovok transportnykh sistem [Hydrodynamics and heat transfer in intricately shaped channels of power units of transportation systems]. Inzhenerno-fizicheskii zhurnal, 2024, vol. 97, iss. 7, pp. 1838–1852 (in Russ.). 
  19. Popov I.A., et al. Gidrodinamicheskie i teplovye protsessy v okhladitele masla sistemy smazki dizelnykh dvigateley: chislennoe modelirovanie [Hydrodynamic and thermal processes in the oil cooler of the lubrication system of diesel engines: numerical simulation]. Mechanics of machines, mechanisms and materials, 2025, no. 3(72), pp. 5–17. DOI: https://doi. org/10.46864/1995-0470-2025-3-72-5-17 (in Russ.).

Title of the article ANALYTICAL APPROACH TO DETERMINING THE ANGULAR COORDINATES OF LINKS OF PLANETARY MECHANISMS
Authors

PROTASENYA Oleg N., Ph. D. in Eng., Assoc. Prof., Associate Professor of the Department “Mechanical Engineering and Machine Parts”, Belarusian National Technical University, Minsk, Republic of Belarus, This email address is being protected from spambots. You need JavaScript enabled to view it.">This email address is being protected from spambots. You need JavaScript enabled to view it.

KALINA Alla A., Ph. D. in Eng., Assoc. Prof., Head of the Department “Mechanical Engineering and Machine Parts”, Belarusian National Technical University, Minsk, Republic of Belarus, This email address is being protected from spambots. You need JavaScript enabled to view it.">This email address is being protected from spambots. You need JavaScript enabled to view it.

In the section GENERAL ISSUES OF MECHANICS
Year 2026
Issue 1(74)
Pages 23–30
Type of article RAR
Index UDK 621.8
DOI https://doi.org/10.46864/1995-0470-2026-1-74-23-30
Abstract The article considers the generally accepted kinematic theory of calculation of planetary mechanisms, based on the principle of equivalence of the real and reversed mechanisms (Willis method). The paper proposes evaluation criteria (relative angular velocity of the satellite; number of satellite teeth engaged with the central wheel per unit of time) that prove, using specific examples of calculating a planetary mechanism and its reversed versions (planetary with zero inversion and differential with arbitrary inversion), the equivalence of the real kinematic scheme and its virtual states. A universal equation is also provided for determining the rotation angles of the satellite during one revolution of the sun gear. An algorithm is given for distributing circumferential forces and their reactions in the engagement of the satellite and central wheels based on the Archimedean lever. The paper considers the issues of complex rotational motion of a planetary mechanism’s satellite, determines the relative and absolute gear ratios between the mechanism’s links, and calculates the satellite’s force balance.
Keywords planetary series, differential mechanism, Willis method for planetary gears, relative angular velocity, law of lever forces
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Bibliography
  1. Kudryavtsev V.N. Detali mashin [Machine parts]. Leningrad, Mashinostroenie Publ., 1980. 464 p. (in Russ.). 
  2. Kudryavtsev V.N., et al. Planetarnye peredachi [Planetary transmissions]. Leningrad, Mashinostroenie Publ., 1977. 536 p. (in Russ.). 
  3. Rudenko N.F. Planetarnye peredachi: teoriya, primenenie, raschet i proektirovanie [Planetary gears: theory, application, calculation and design]. Moscow, Leningrad, Mashgiz Publ., 1947. 756 p. (in Russ.). 
  4. Rudenko V.N. Planetarnye i volnovye peredachi [Planetary and wave gears]. Moscow, Mashinostroenie Publ., 1980. 148 p. (in Russ.). 
  5. Tkachenko V.A. Proektirovanie mnogosatellitnykh planetarnykh peredach [Designing multi-satellite planetary transmissions]. Kharkov, Kharkovskiy universitet Publ., 1961. 182 p. (in Russ.). 
  6. Baranov G.G. Kurs teorii mekhanizmov i mashin [Course of theory of mechanisms and machines]. Moscow, Mashinostroenie Publ., 1975. 494 p. (in Russ.). 
  7. Detali mashin. Ch. 1. Mekhanicheskie peredachi [Machine parts. Part 1. Mechanical gears]. Minsk, Belorusskiy natsionalnyy tekhnicheskiy universitet Publ., 2019. 215 p. (in Russ.). 
  8. Smirnov L.P. Issledovanie vrashchatelnogo dvizheniya pri pomoshchi treugolnikov skorostey [Investigation of rotational motion using velocity triangles]. Vestnik inzhenerov i tekhnikov, 1932, no. 8 (in Russ.). 
  9. Semenov M.V. Teoriya odno- i dvukhstupenchatykh planetarnykh peredach [Theory of single- and two-stage planetary gears]. Moscow, Leningrad, Mashinostroenie Publ., 1966. 164 p. (in Russ.). 
  10. Kudryavtsev V.N. Planetarnye peredachi [Planetary transmissions]. Moscow, Leningrad, Mashinostroenie Publ., 1966. 308 p. (in Russ.). 
  11. Kudryavtsev V.N., et al. Kursovoe proektirovanie detaley mashin [Course design of machine parts]. Leningrad, Mashinostroenie Publ., 1984. 400 p. (in Russ.). 
  12. Krasnenkov V.I., Vashets A.D. Proektirovanie planetarnykh mekhanizmov transportnykh mashin [Design of planetary mechanisms of transport vehicles]. Moscow, Mashinostroenie Publ., 1986. 272 p. (in Russ.). 
  13. Detali mashin. Ch. 2. Soedineniya detaley mashin [Machine parts. Part 2. Machine parts connections]. Minsk, Belorusskiy natsionalnyy tekhnicheskiy universitet Publ., 2022. 179 p. (in Russ.). 
  14. Gromyko P.N., et al. Pretsessionnye redutsiruyushchie mekhanizmy dlya privodnykh ustroystv razlichnogo naznacheniya [Precession reduction mechanisms for various purpose drive devices]. Mogilev, Belorussko-Rossiyskiy universitet Publ., 2013. 272 p. (in Russ.). 
  15. Detali mashin. Ch. 3. Valy i opory detaley mashin [Machine parts. Part 3. Shafts and supports of machine parts]. Minsk, Belorusskiy natsionalnyy tekhnicheskiy universitet Publ., 2024. 147 p. (in Russ.). 
  16. Kirdyashev Yu.N. Mnogopotochnye peredachi differentsialnogo tipa [Multithreaded differential type transfers]. Leningrad, Mashinostroenie Publ., 1981. 223 p. (in Russ.).

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