Analytical model of skip motion taking into account influence of head and balancing ropes

Authors

  • Mikhail A. Zhuravkov Belarusian State University, 4 Niezaliežnasci Avenue, Minsk 220030, Belarus https://orcid.org/0000-0002-7420-5821
  • Vladimir P. Savchuk Belarusian State University, 4 Niezaliežnasci Avenue, Minsk 220030, Belarus
  • Michael A. Nikolaitchik Belarusian State University, 4 Niezaliežnasci Avenue, Minsk 220030, Belarus

Keywords:

skip, guides, mine skip dynamics, vertical vibrations, forces principal vector, forces principal moment, horizontal accelerations

Abstract

The article describes an analytical model of mine skip dynamics taking into account the presence of the head and balancing ropes and the existing curvilinearity of the guides. Expressions for the forces acting on the skip from the side of the guides have been constructed. It is shown, that the frequencies of natural vibrations of skip depend on the vertical acceleration and the distance traveled during its lifting. A graph (diagram) of skips vertical speed which observance does not lead to the appearance of skips vertical vibrations due to elasticity of the ropes is developed. An algorithm for finding the forces principal vector and the forces principal moment acting on the skip based on the reading of three accelerometers recording horizontal accelerations of skip during its movement is presented.

Author Biographies

  • Mikhail A. Zhuravkov, Belarusian State University, 4 Niezaliežnasci Avenue, Minsk 220030, Belarus

    doctor of science (physics and mathematics), full professor; head of the department of theoretical and applied mechanics, faculty of mechanics and mathematics

  • Vladimir P. Savchuk, Belarusian State University, 4 Niezaliežnasci Avenue, Minsk 220030, Belarus

    PhD (physics and mathematics); associate professor at the department of theoretical and applied mechanics, faculty of mechanics and mathematics

  • Michael A. Nikolaitchik, Belarusian State University, 4 Niezaliežnasci Avenue, Minsk 220030, Belarus

    head of the laboratory of applied mechanics, faculty of mechanics and mathematics

References

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  4. Savchuk VP, Medvedev DG, Vyarvil’skaya ON. Teoreticheskaya mekhanika. Minsk: Belarusian State University; 2016. 231 p. Russian.
  5. Moiseev NN. Asimptoticheskie metody nelineinoi mekhaniki. Moscow: Science; 1969. 380 p. Russian.
  6. Sneddon IN. Fourier transforms. Moscow: McGraw-Hill; 1951. 542 p. Russian edition: Sneddon IN. Preobrazovaniya Fur’e. Matveev AN, translator. Moscow: Izdatel’stvo inostrannoi literatury; 1955. 667 p.

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Published

2021-08-05

Issue

No. 2 (2021): Journal of the Belarusian State University. Mathematics and Informatics

Section

Theoretical and Applied Mechanics

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How to Cite

[1]
Zhuravkov, M.A. et al. 2021. Analytical model of skip motion taking into account influence of head and balancing ropes. Journal of the Belarusian State University. Mathematics and Informatics. 2 (Aug. 2021), 105–113. DOI:https://doi.org/10.33581/2520-6508-2021-2-105-113.