4_2023_sen_2

Title of the article DEVELOPMENT OF A DYNAMIC MODEL FOR CALCULATING THE KINEMATIC ERROR AND EVALUATING ITS EFFECT ON THE EFFICIENCY OF PLANETARY MECHANISMS WITH ROLLING BODIES
Authors

KAPITONOV Alexander V., Ph. D. in Eng., Assoc. Prof., Associate Professor of the Department “Mechanical Engineering Technology”, Belarusian-Russian University, Mogilev, 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 2023
Issue 4(65)
Pages 16–24
Type of article RAR
Index UDK 621.83.06
DOI https://doi.org/10.46864/1995-0470-2023-4-65-16-24
Abstract When studying the characteristics of the mechanisms of small-sized drives, an important task is to develop ways to increase the efficiency of the mechanism. The article discusses theoretical issues related to the influence assessment of kinematic error on the efficiency of gears with rolling bodies. As a result of the research, a generalized dynamic model of planetary ball and roller mechanisms is obtained, taking into account kinematic errors, linking manufacturing errors or elastic deformations and kinematic transmission error. Mathematical dependences of the dynamic model of mechanisms with rolling bodies are derived. The model was tested on the example of calculating the kinematic error of a single-stage planetary ball transmission. Polynomial equations with constant coefficients are obtained for determining kinematic errors from the influence of manufacturing errors of transmission links. It is established that for different kinematic schemes, gear ratios and angular velocities of planetary mechanisms with rolling bodies, the transmission efficiency can vary significantly depending on its kinematic error. For gear ratios from 1.5 to 5, drive shaft rotation speeds from 1,500 to 3,000 rpm, depending on the highest values of the kinematic error from 0.00175 to 0.0349 radians, the transmission efficiency within the driven shaft rotation can decrease from 0.93 to 11 %. At the same time, transmissions constructed according to the sixth kinematic scheme have the highest efficiency values. The average efficiency value per revolution of the driven shaft from the influence of kinematic errors can decrease up to 5 %. Graphs of the dependences of transmission efficiency on their kinematic errors are given.
Keywords dynamic model, mechanisms with rolling bodies, efficiency, kinematic error
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Bibliography
  1. Pashkevich M.F., Pashkevich V.M., Pashkevich A.M., Chertkov S.V. Planetarnye kulachkovo-plunzhernye peredachi. Proektirovanie, kontrol i diagnostika [Planetary cam-plunger gears. Design, control and diagnostics]. Mogilev, Belorussko-Rossiyskiy universitet Publ., 2003. 221 p. (in Russ.).
  2. Lustenkov M.E. Peredachi s promezhutochnymi telami kacheniya: opredelenie i minimizatsiya poter moshchnosti [Transmissions with intermediate rolling elements: determination and minimization of power losses]. Mogilev, Belorussko-Rossiyskiy universitet Publ., 2010. 274 p. (in Russ.).
  3. Taits B.A. Tochnost i kontrol zubchatykh koles [Precision and control of gears]. Moscow, Mashinostroenie Publ., 1972. 368 p. (in Russ.).
  4. Pashkevich V.M., et al. Povyshenie tochnosti mekhanicheskikh peredach na osnove kompyuternogo modelirovaniya i ispolzovaniya tekhnologii iskusstvennogo intellekta [Improving the accuracy of mechanical transmissions based on computer modeling and the use of artificial intelligence technologies]. Mogilev, Belorussko-Rossiyskiy universitet Publ., 2011. 139 p. (in Russ.).
  5. Pleguezuelos M., Pedrero J.I., Sánchez M.B. Analytical expressions of the efficiency of standard and high contact ratio involute spur gears. Mathematical problems in engineering, 2013, vol. 2013. DOI: https://doi.org/10.1155/2013/142849.
  6. Dobreva A., Dobrev V., Mollova G. Research of gear drives. IOP conference series: Materials science and engineering. The XXXI-st SIAR International congress of automotive and transport engineering “Automotive and integrated transport systems” (AITS 2021). Chisinau, 2021, vol. 1220. DOI: https://doi.org/10.1088/1757- 899X/1220/1/012025.
  7. Jiang N., Wang S., Yang A., Zhou W., Zhang J. Transmission efficiency of cycloid–pinion system considering the assembly dimensional chain. Applied sciences, 2022, vol. 12, iss. 23. DOI: https://doi.org/10.3390/app122311917.
  8. Cheremnov A.V., I-Kan A., Ivkina O.P. Sintez prostranstvennoy peredachi s promezhutochnymi telami kacheniya s uluchshennymi kachestvennymi kharakteristikami [Synthesis of spatial transmission with intermediate rolling elements with improved quality characteristics]. Bulletin of the Tomsk Polytechnic University, 2012, vol. 321, no. 2, pp. 26–30 (in Russ.).
  9. Pabiszczak S., Ptaszyński W. Effect of manufacturing errors on the operation of the eccentric rolling transmission. Advances in science and technology research journal, 2020, vol. 14, iss. 3, pp. 213–222. DOI: https://doi.org/10.12913/22998624/122604.
  10. Lustenkova E.S. Experimental estimation of efficiency and kinematic accuracy of a spherical roller transmission. IOP conference series: Materials science and engineering. International conference on mechanical engineering and modern technologies (MEMT 2020). Tomsk, 2020, vol. 1118. DOI: https://doi.org/10.1088/1757-899X/1118/1/012007.
  11. Gromyko P.N., Khatetovsky S.N., Yurkova V.L. Ispolzovanie udlinennoy epitsikloidy dlya formoobrazovaniya zubchatykh poverkhnostey peredach ekstsentrikovogo tipa [Use of an elongated epicycloide for forming gear surfaces of excentric gears]. Vestnik Belorussko-Rossiyskogo universiteta, 2019, no. 1(62), pp. 14–21 (in Russ.).
  12. Frolov K.V., et al. Teoriya mekhanizmov i mekhanika mashin [Theory of mechanisms and mechanics of machines]. Moscow, Vysshaya shkola Publ., 1998. 500 p. (in Russ.).
  13. Kapitonov A.V., Saskovets K.V., Kasyanov А.I., Leshko D.V., Filchenko P.A. Avtomatizirovannoe proektirovanie konstruktsiy malogabaritnykh radialno-plunzhernykh reduktorov s ispolzovaniem sovremennykh SAPR [Computer-aided design of small-size radial plunger reducers using advanced CAD]. Vestnik Belorussko-Rossiyskogo universiteta, 2015, no. 3(48), pp. 25–32 (in Russ.).
  14. Kapitonov А.V., Saskovets K.V., Kasyanov А.I. Planetarnaya radialno-plunzhernaya peredacha s uluchshennymi ekspluatatsionnymi kharakteristikami [Radial plunger planetary gearing with improved operating characteristics]. Vestnik Belorussko-Rossiyskogo universiteta, 2017, no. 3(56), pp. 27–34 (in Russ.).
  15. Pashkevich M.F., Gerashchenko V.V. Planetarnte sharikovye i rolikovye reduktory i ikh ispytaniya [Planetary ball and roller gearboxes and their tests]. Minsk, BelNIINTI Publ., 1992. 248 p. (in Russ.).
  16. Kapitonov A.V., Pashkevich V.M. Kinematicheskie i massogabaritnye kharakteristiki resursoeffektivnykh mekhanicheskikh peredach. Kompyuternoe modelirovanie, eksperimentalnaya otsenka [Kinematic and mass-dimensional characteristics of lifetime-efficient mechanical transmissions. Computer modeling, experimental evaluation]. Mogilev, Belorussko-Rossiyskiy universitet Publ., 2017. 248 p. (in Russ.).
  17. Kapitonov A.V., Chernyakov S.G. Issledovanie kinematicheskoy tochnosti planetarnykh rolikovykh peredach metodami garmonicheskogo analiza i kontrolya v sbore [Investigation of the kinematic accuracy of planetary roller gears by methods of harmonic analysis and assembly control]. Vestnik Belorussko-Rossiyskogo universiteta, 2011, no. 4(33), pp. 40–50 (in Russ.).
  18. Kapitonov A.V. Matematicheskoe modelirovanie kinematicheskikh pogreshnostey planetarnykh rolikovykh peredach [Mathematical modeling kinematical inaccuracy planetary roller transfers]. Vestnik Belorussko-Rossiyskogo universiteta, 2003, no. 2(5), pp. 44–48 (in Russ.).