Communications - Scientific Letters of the University of Zilina 2021, 23(2):C54-C64 | DOI: 10.26552/com.C.2021.2.C54-C64

Mathematical Modelling of Oscillatory Processes in Transmission of Movement of an Electric Drive with Non-Linear Long Elastic Elements

Andriy Chaban ORCID...1, Tomasz Perzyński ORCID...1,*
1 Faculty of Transport, Electrical Engineering and Computer Science, Kazimierz Pulaski University of Technology and Humanities in Radom, Radom, Poland

Mathematical model of transmission of movement of an electric drive system that includes long elastic elements, including the non-linear relation between tensors of strength and deformation is presented in this article. Mentioned type of transmission is applied in the tasks related to special-purpose transport. A method that is based on integral modification of variational Hamilton-Ostrogradsky principle was applied for the presented model. Results of the computer simulation of oscillatory processes in transmission of movement of an electromechanical system are presented in the article.

Keywords: modelling of transport systems; Hamilton-Ostrogradsky principle; mathematical modelling; systems of distributed parameters; computer simulation

Received: March 9, 2020; Accepted: August 10, 2020; Prepublished online: February 25, 2021; Published: April 1, 2021  Show citation

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Chaban, A., & Perzyński, T. (2021). Mathematical Modelling of Oscillatory Processes in Transmission of Movement of an Electric Drive with Non-Linear Long Elastic Elements. Communications - Scientific Letters of the University of Zilina23(2), C54-64. doi: 10.26552/com.C.2021.2.C54-C64
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References

  1. WANG, J., LIU, Y., SUN, C. Adaptive neural boundary control design for nonlinear flexible distributed parameter systems. IEEE Transactions on Control Systems Technology [online]. 2018, p. 1-15. ISSN 1063-6536, eISSN 1558-0865. Available from: https://doi.org/10.1109/TCST.2018.2849072 Go to original source...
  2. WANG, Z., WU, H., HAN, K. Sampled-data control for linear time-delay distributed parameter systems. ISA Transactions [online]. 2018, 92, p. 75-83. ISSN 0019-0578. Available from: https://doi.org/10.1016/j.isatra.2019.02.002 Go to original source...
  3. POPENDA, A. Mathematical modelling of transmission shafts based on electrical and mechanical similarities. Przeglad Elektrotechniczny. 2019, 12, p. 196-199. ISSN 0033-2097, eISSN 2449-9544. Go to original source...
  4. ORLOWSKA-KOWALSKA, T., SZABAT, K. Control of the driver system with stiff and elastic couplings using adaptive neuro-fuzzy approach. IEEE Transactions on Industrial Electronics [online]. 2007, 54(1), p. 228-240. ISSN 0278-0046. Available from: https://doi.org/10.1109/TIE.2006.888787 Go to original source...
  5. CHABAN, A. Principle Hamilton-Ostrogradski in electromechanical systems. Lviv, 2015. ISBN 978-966-2598-46-9.
  6. KUCERA, L., GAJDAC, I., MRUZEK, M. Simulation of parameters influencing the electric vehicle range. Communications - Scientific Letters of the University of Zilina [online]. 2016, 18(1A), p. 59-63. ISSN 1335-4205, eISSN 2585-7878. Available from: http://komunikacie.uniza.sk/index.php/communications/article/view/360 Go to original source...
  7. KORENCIAK, D., GUTTEN, M., ADAMEC, J., GLOWACZ, A., CICHY, A. Analysis of engine knock sensor. Communications - Scientific Letters of the University of Zilina [online]. 2018, 20(1), p. 37-41. ISSN 1335-4205, eISSN 2585-7878. Available from: http://komunikacie.uniza.sk/index.php/communications/article/view/43 Go to original source...
  8. LEWINSKI, A., TORUN, A., PERZYNSKI, T. Risk analysis as a basic method of safety transmission system certification. In: Modern Transport Telematics TST 2011: proceedings [online]. Vol 239. Communications in Computer and Information Science. Berlin, Heidelberg: Springer, 2011. ISBN 978-3-642-24659-3, eISBN 978-3-642-24660-9, p. 47-53. Available from: https://doi.org/10.1007/978-3-642-24660-9_6 Go to original source...
  9. LEWINSKI, A., PERZYNSKI, T. Telematics as a new method of transport system safety verification. In: Research Methods and Solutions to Current Transport Problems ISCT21 2019: proceedings [online]. Vol 1032. Advances in Intelligent Systems and Computing. Cham: Springer, 2020. ISBN 978-3-030-27686-7, eISBN 978-3-030-27687-4. Available from: https://doi.org/10.1007/978-3-030-27687-4_27 Go to original source...
  10. BOJIC, N., NIKOLIC, R., BANIC, M., HADZIMA, B. Evaluation of mechanical properties of the two PVC conveyor belts. Communications - Scientific Letters of the University of Zilina [online]. 2018, 20(4), p. 47-51. ISSN 1335-4205, eISSN 2585-7878. Available from: https://doi.org/10.26552/com.C.2018.4.47-51 Go to original source...
  11. LUKASIK Z., CZABAN A., SZAFRANIEC, A. Mathematical model of asynchronous pump drive with distributed mechanical parameters. Przeglad Elektrotechniczny. 2018, 6, p.155-159. ISSN 0033-2097, eISSN 2449-9544. Go to original source...
  12. LIS, M., SZAFRANIEC, A. Analysis of transient processes in a drive system with vertical pumps of susceptible motion transmission (in Polish). Przeglad Elektrotechniczny. 2019, 8, p. 21-24. ISSN 0033-2097, eISSN 2449-9544.
  13. CZABAN A., LIS, M. The use of the Hamilton formalism for modelling of power systems with a synchronous motors and susceptible transmission of mechanical power (in Polish). Przeglad Elektrotechniczny. 2018, 1, p. 21-24. ISSN 0033-2097, eISSN 2449-9544.
  14. CZABAN, A., LIS, M. Application of an artificial neural network for determination of rotor current in a driver system: a PMSM motor - a DC generator (in Polish). Przeglad Elektrotechniczny. 2014, 6, p. 272 - 274. ISSN 0033-2097, eISSN 2449-9544.
  15. RABOTNOW, J. Mechanics of deformed bodies (in Russian). Vol. 3. URSS, 2019, ISBN 978-5-9710-5637-9.
  16. WASHIZU, K. Variational methods in elasticity and plasticity. Kittery, ME, U.S.A.: Pergamon Press, 1982. ISBN 978-0080267234.
  17. PUKACH, P. Y. Qualitative methods for the investigation of a mathematical model of nonlinear vibrations of a conveyer belt. Journal of Mathematical Sciences [online]. 2014, 198(1), p. 31-38. ISSN 1072-3374, eISSN 1573-8795. Available from: https://doi.org/10.1007/s10958-014-1770-x Go to original source...
  18. WHITE, D. C., WOODSON, H. H. Electromagnetic energy conversion. New-York: John Wiley & Sons Inc, 1958. ISBN 978-1124129310.
  19. ORTEGA, R., LORIA PEREZ, A., NICKLASSON, P. J., SIRA-RAMIREZ, H. Passivity-based control of Euler-Lagrange systems: mechanical, electrical and electromechanical applications. London: Springer Verlag, 1998. ISBN 978-1-4471-3603-3. Go to original source...
  20. SPORYKHIN, A. N. Hamilton-Ostrogradski principle in the theory of nonlinear elasticity with the combined approach. International Applied Mechanics [online]. 1995, 31, p. 294-297. ISSN 1063-7095, eISSN 1573-8582. Available from: https://doi.org/10.1007/BF00846778 Go to original source...
  21. ELSGOLTS, L. Differential equations and the calculus of variations. Moscow: Mir publishers,1977.
  22. YABUKI, A., OHISHI, K., MIYAZAKI, T., YOKOKURA, Y. Force control including contact process using acceleration-sensor-based instantaneous state observer for high-stiffness gear drive. In: IEEE 25th International Symposium on Industrial Electronics: proceedings [online]. 2016. eISSN 2163-5145, p. 651-656. Available from: https://doi.org/10.1109/ISIE.2016.7744966 Go to original source...
  23. SZAFRANIEC, A., Mathematical model of asynchronous pump drive and power transformer drive system with complex motion transmission. In: 13th International Scientific Conference Control of Power Systems: proceedings. 2018. p. 104-109.
  24. XU, S., SUN, G., CHENG, Z. Fractional order modeling and residual vibration suppression for flexible two-mass system. In: 29th Chinese Control and Decision Conference CCDC 2017: proceedings [online]. 2017. eISSN 1948-9447, p. 3658-3664. Available from: https://doi.org/10.1109/CCDC.2017.7979140 Go to original source...

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