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Mathematical Model of Lifting Particles of Technological Material by Vertical Auger

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Advances in Design, Simulation and Manufacturing V (DSMIE 2022)

Part of the book series: Lecture Notes in Mechanical Engineering ((LNME))

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Abstract

This research aims to investigate the transportation of a material particle by a vertically placed auger limited by a cylindrical casing. The surfaces are coaxial. When the auger rotates, the particle moves to the periphery and interacts with the cylindrical casing. The particle simultaneously slides on both surfaces and rises in absolute movement. Its relative motion is sliding along the periphery of the auger. Differential equations of particle movement in projections on a moving coordinate system that rotates with an auger were compiled. Numerical methods have solved the equations, and graphs of kinematic characteristics were built. The limit value of the rising angle for the helical line was found as the periphery of the auger. At such a position, the rise of the particle stops at a given angular velocity of the auger. It was found that the velocity of particle rising is influenced by constructive and technological parameters. In particular, for a given radius of the cylindrical casing, friction coefficients, and the edge angle of the auger, there is a minimum value of the angular velocity of its rotation. Then the particle “sticks” and rotates together with the auger, describing in absolute motion a circle on the inner surface of the cylindrical casing.

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Change history

  • 11 February 2023

    The book has been inadvertently published with misattributed affiliations in chapter 11. The affiliations of Serhii Dieniezhnikov and Iryna Rybenko were revised and updated with the correct information.

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Authors and Affiliations

  1. National University of Life and Environmental Sciences of Ukraine, 15, Heroyiv Oborony Street, Kyiv, 03041, Ukraine

    Serhii Pylypaka, Tatiana Volina & Iryna Hryshchenko

  2. Sumy State Pedagogical University named after A.S. Makarenko, 87, Romenskaya Street, Sumy, 40002, Ukraine

    Tatiana Volina & Serhii Dieniezhnikov

  3. Sumy National Agrarian University, 160, Kondratieva Street, Sumy, 40021, Ukraine

    Iryna Rybenko

Authors
  1. Serhii Pylypaka
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  2. Tatiana Volina
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  3. Iryna Hryshchenko
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  4. Serhii Dieniezhnikov
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  5. Iryna Rybenko
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Corresponding author

Correspondence to Tatiana Volina .

Editor information

Editors and Affiliations

  1. Sumy State University, Sumy, Ukraine

    Vitalii Ivanov

  2. Sumy State University, Sumy, Ukraine

    Ivan Pavlenko

  3. Sumy State University, Sumy, Ukraine

    Oleksandr Liaposhchenko

  4. University of Minho, Guimaräes, Portugal

    José Machado

  5. University of West Bohemia, Pilsen, Czech Republic

    Milan Edl

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Pylypaka, S., Volina, T., Hryshchenko, I., Dieniezhnikov, S., Rybenko, I. (2022). Mathematical Model of Lifting Particles of Technological Material by Vertical Auger. In: Ivanov, V., Pavlenko, I., Liaposhchenko, O., Machado, J., Edl, M. (eds) Advances in Design, Simulation and Manufacturing V. DSMIE 2022. Lecture Notes in Mechanical Engineering. Springer, Cham. https://doi.org/10.1007/978-3-031-06044-1_11

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  • DOI: https://doi.org/10.1007/978-3-031-06044-1_11

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-031-06043-4

  • Online ISBN: 978-3-031-06044-1

  • eBook Packages: EngineeringEngineering (R0)

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