Abstract
Differential equations of particle movement on the rough surface of the spiral gutter under the effect of the force of its own weight are obtained in the article. The curve of the cross section of the gutter with a vertical plane passing through the axis of the surface is given by parametrical equations in general form. Special cases for individual cross-sectional lines (a straight line and a circle) are considered. If the section is an arc of a circle, a spiral gutter is formed. In the particular case when the cross section is a straight line inclined to the axis upwards, then the helical surface is an oblique helicoid. The equations are solved by numerical methods and trajectories of a particle movement along a helical surface are constructed. After the motion stabilizes, the particle has a constant speed and its trajectory is a helical curve. For this particular case, analytical dependencies that allow calculating the speed of a particle and its distance from the axis of the surface were found. The case, when an angle of elevation of the lowest helical curve of the gutter is equal to the angle of friction of the particle on the surface, is also considered. In the case of a spiral gutter, the elevation angle of its lower helical line should be greater than the friction angle in order to avoid congestions during transportation of particles of the technological material.
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References
Chernenko, V.D.: Calculation of the resources of the continuous conveyance. Politehnica, 386 (2011)
Bulgakov, V., Pilipaka, S., Adamchuk, V., Olt, J.: Theory of motion of a material point along a plane curve with a constant pressure and velocity. Agron Res. Est. Agric. Univ. 12(3), 937–948 (2014)
Loveikin, V.S., Romesevych, YuO: Dynamic optimization of a mine winder acceleration mode. Naukovyi Visnyk Natsionalnoho Hirnychoho Universytetu 4, 81–87 (2017)
Batluk, V., Basov, M., Klymets, V.: Mathematical model for motion of weighted parts in curled flow. Econtechmod. Int. Q. J. 2(3), 17–24 (2013)
Liaposchenko, O., Pavlenko, I., Nastenko, O.: The model of crossed movement and gas-liquid flow interaction with captured liquid film in the inertial-filtering separation channels. Sep. Purif. Technol. 173, 240–243 (2017)
Isaev, YuM, Semashkin, N.M., Nazarova, N.N.: Justification of the moving process of the seeds by the spiral-spiral working part. Bull. Ulyanovsk State Agric. Academy 1, 97–99 (2011)
Matveev, A.I., Lebedev, I.F., Nikiforova, L.V., Yakovlev, B.V.: Modeling of the particles movement in a screw pneumatic separator. Min. Inf. Anal. Bull. 10, 172–178 (2014)
Pavlenko, I., Liaposhchenko, A., Ochowiak, M., Demyanenko, M.: Solving the stationary hydroaeroelasticity problem for dynamic deflection elements of separation devices. In: Vibrations in Physical Systems, 2018026 (2018)
Liaposhchenko, O.O., Sklabinskyi, V.I., Zavialov, V.L., Pavlenko, I.V., Nastenko, O.V., Demianenko, M.M.: Appliance of inertial gas-dynamic separation of gas dispersion flaws in the curvilinear convergent-divergent channels for compressor equipment reliability improvement. In: IOP Conference Series: Materials Science and Engineering, vol. 233, Issue (1), pp. 012025 (2017)
Shevchenko, S., Mukhovaty, A., Krol, O.: Gear clutch with modified tooth profiles. Procedia Eng. 206, 979–984 (2017)
Karpus, V., Ivanov, V., Dehtiarov, I., Zajac, J., Kurochkina, V.: Technological assurance of complex parts manufacturing. In: Ivanov V. et al. (eds.) Advances in Design, Simulation and Manufacturing, DSMIE-2018, Lecture Notes in Mechanical Engineering, pp. 51–61 (2019)
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Pylypaka, S., Nesvidomin, V., Zaharova, T., Pavlenko, O., Klendiy, M. (2020). The Investigation of Particle Movement on a Helical Surface. In: Ivanov, V., et al. Advances in Design, Simulation and Manufacturing II. DSMIE 2019. Lecture Notes in Mechanical Engineering. Springer, Cham. https://doi.org/10.1007/978-3-030-22365-6_67
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DOI: https://doi.org/10.1007/978-3-030-22365-6_67
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