Revealing the mechanism of stability loss of a two-fraction granular flow in a rotating drum

Abstract

The qualitative nature and quantitative parameters of motion instability of a two-fraction granular filler of a rotating drum were determined. The factors of motion instability and key parameters of the oscillating system were identified and their influence on the self-excitation of pulsed self-oscillations was estimated. Two continuous and one periodic steady-state modes of filler motion were found. Periodic self-oscillations due to the development of instability during the transition from continuous circulation mode to the wall layer mode were revealed. As factors of motion instability, filler dilatancy and damping effect of fine fraction particles on the pulsed interaction of coarse fraction particles were taken. It turned out that the main key parameter of the oscillating system is the drum speed, which determines a change in dilatancy. The increase in instability is realized as a reduction of the bifurcation values of speed and dilatancy. Other key parameters are the content of the fine fraction in the filler κff and the filling degree of the chamber κlf, the growth of which increases the self-oscillating instability. The features of the oscillatory system are the relaxation type, discontinuous nature of self-oscillations and hard self-excitation mode under bistability. The discontinuous character and oscillatory hysteresis increase with decreasing κff and κlf. The limit values of the dynamic motion parameters corresponding to the conditions of self-excitation of self-oscillations in the absence and presence of fine fraction were determined: 0.96–1.11 and 0.218–0.382 for the bifurcation value of relative speed, 0.745–0.855 and 0.24–0.322 for the bifurcation value of dilatancy. The effects found make it possible to substantiate the parameters of the self-oscillating process of processing polygranular materials in drum-type machines.