# Mathematical modeling of oscillations in novel-type vibration mills

The vibration mill enables vibration of the grinding chamber at any smoothly variable amplitudes and frequencies, which allows the size of the feed an order of magnitude larger than it is common in the industry. The mechanics-based mathematical modeling is built for the oscillatory processes in the vibration mill bin. It is assumed that milling inside the mill is ensured by vertical harmonic oscillations of the bin. The oscillation model is based on the formulation and solution of a boundary problem for the differential equation of the motional energy of the milled material in the bin. A set of the formulas for calculating the height, velocity and time of the coarse material intrusion in the layer of the milled suspension is obtained. Using this set of formulas, the transcendental algebraic equation is constructed to calculate the vertical oscillation frequency of the bin with a view to synchronizing vibrations of particles and grinding chamber. The synchronization enables straight-line collision of the particle and grinding chamber bottom. As a result, the grinding chamber bottom gives extra impulse (momentum) to the particle. This intensifies destruction and milling.

Keywords: vibration mill, vibration synchronization, differential energy equation, frequency equation, transcendental algebraic equation, milling coarse particle (component).
For citation:

Sergeev V. V., Muzaev I. D., Dmitrak Ju. V., Gerasimenko T. E. Mathematical modeling of oscillations in novel-type vibration mills. MIAB. Mining Inf. Anal. Bull. 2021;(8):114128. [In Russ]. DOI: 10.25018/0236_1493_2021_8_0_114.

Acknowledgements:
Issue number: 8
Year: 2021
Page number: 114-128
ISBN: 0236-1493
UDK: 664.734
DOI: 10.25018/0236_1493_2021_8_0_114
Article receipt date: 25.02.2021
Date of review receipt: 29.03.2021
Date of the editorial board′s decision on the article′s publishing: 10.07.2021

V.V. Sergeev1, Dr. Sci. (Eng.), Professor,
I.D. Muzaev, Dr. Sci. (Eng.), Professor, Chief Researcher, Geophysical Institute, Vladikavkaz Scientific Center of the Russian Academy of Sciences, 362020, Vladikavkaz, Russia; Professor, Vladikavkaz Branch of the Financial University under the Government of the Russian Federation, Vladikavkaz, Russia,
Ju.V. Dmitrak1, Dr. Sci. (Eng.), Professor, Rector,
T.E. Gerasimenko1, Cand. Sci. (Eng.), Assistant Professor, e-mail: gerasimenko_74@mail.ru,
1 North Caucasus Mining-and-Metallurgy Institute (State Technological University), 362021, Vladikavkaz, Republic of North Ossetia-Alania, Russia.

For contacts:

T.E. Gerasimenko, e-mail: gerasimenko_74@mail.ru.

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