@article{Deineka_Naumenko_Myronenko_2021, title={The effect of the filling degree of the tumbling mill chamber on the bifurcation value of the froude number}, url={http://journal.eu-jr.eu/ttfpits/article/view/2170}, DOI={10.21303/2585-6847.2021.002170}, abstractNote={<p>The influence of the filling degree of the drum chamber on the bifurcation value of the Froude number in the case of self-excitation of self-oscillations of a two-fraction granular charge with a minimum swing is considered. Such a pulsating mode of the charge movement is used in the self-oscillating grinding process in a tumbling mill. The coarse fraction that simulated the milling bodies consisted of spherical particles of an incoherent granular material with a relative size in the chamber ψ<em><sub>b</sub></em>=0.00733. The fine fraction, simulating the material to be ground, was cement with a relative particle size ψ<em><sub>m</sub></em>≈0.092∙10<sup>-3</sup>. The value of the adopted analogue of the kinematic viscosity of the two-fraction granular loading approached the value of 10<sup>-3</sup>&nbsp;m<sup>2</sup>/s. The main variable factor in experimental studies was the filling degree of the drum chamber with loading at rest κ<em><sub>b</sub></em>=0.25, 0.35, and 0.45. An additional factor was the degree of filling the gaps between the spherical particles of the coarse fraction with particles of the fine fraction κ<em><sub>b</sub></em>=0, 0.25, 0.5, and 1. The method of visual analysis through the transparent end wall of the chamber of transient processes of the loading behavior with a smooth change and fixation of the velocity was applied. The bifurcation minimum value of the rotation speed was recorded, at which the steady-state circulation mode of the load movement turns into a transient pulsation one with a minimum swing. A decrease in the bifurcation values of the Froude number <em>Fr<sub>b</sub></em> on the cylindrical surface of the chamber with an increase in κ<em><sub>b</sub></em> has been established. An increase in the intensity of the decrease in <em>Fr<sub>b</sub></em> with an increase in κ<em><sub>m</sub></em> was revealed. The recorded effect is due to an increase in the connected properties of a two-fraction loading during self-excitation of self-excited oscillations with an increase in κ<em><sub>b</sub></em> and κ<em><sub>m</sub></em>. The numerical values of the boundaries of the range of bifurcation values of the Froude number for a tumbling mill <em>Fr<sub>b</sub></em>=0.0484–1.17 have been determined. The obtained <em>Fr<sub>b</sub></em> range corresponds to the Reynolds value in the range Re=40–197. The maximum<em> Fr<sub>b</sub></em> value is obtained with coarse grinding. An increase in the likelihood of self-excitation of self-oscillations of the intra-chamber loading with a decrease in the fineness of grinding was revealed</p&gt;}, journal={Technology transfer: fundamental principles and innovative technical solutions}, author={Deineka, Kateryna and Naumenko, Yurii and Myronenko, Tamara}, year={2021}, month={Dec.}, pages={21-24} }