The effect of the filling degree of the tumbling mill chamber on the bifurcation value of the froude number

Abstract

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_b=0.00733. The fine fraction, simulating the material to be ground, was cement with a relative particle size ψ_m≈0.092∙10^-3. The value of the adopted analogue of the kinematic viscosity of the two-fraction granular loading approached the value of 10^-3 m²/s. The main variable factor in experimental studies was the filling degree of the drum chamber with loading at rest κ_b=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_b=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 Fr_b on the cylindrical surface of the chamber with an increase in κ_b has been established. An increase in the intensity of the decrease in Fr_b with an increase in κ_m 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_b and κ_m. The numerical values of the boundaries of the range of bifurcation values of the Froude number for a tumbling mill Fr_b=0.0484–1.17 have been determined. The obtained Fr_b range corresponds to the Reynolds value in the range Re=40–197. The maximum Fr_b 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