Mathematical modeling of the rotating drum granular fill flow oscillatory stability

Drum-type machines have become widely used in many industries for processing various granular materials. An innovative direction for significantly increasing the energy efficiency of such equipment is the use of self-oscillating working processes. Self-excitation of auto-oscillations allows you to bring into pulsating flow and activate the passive part of the intra-chamber filling and significantly enhance the interaction of granular particles with each other and with the surrounding environment. The purpose of the study is to build a mathematical model of the conditions and factors of oscillatory instability of the flow of polydisperse granular filling in the chamber of a rotating drum. The research methodology includes analytical modeling of wave processes and experimental modeling of manifestations of instability of the filling flow. The inertial mode of flow of the active part of the filling in a shear flow state is analyzed, the behavior of which is described using averaged values. Based on the results obtained, an increase in instability with an increase in the dilatancy of the medium during deformation is established and the destabilizing effect of the damping action of the fine fraction on the interaction of particles of the coarse fraction is revealed. The main scientific novelty of this study is the identification of the regularities of the unsteady motion of the oscillatory system of a filled drum. The study confirms the possibility of generating, under certain conditions, self-excitation of auto-oscillations of the intra-chamber filling, which is a decisive factor in the predicted intensification of the technological process. The results obtained are valuable for researchers and engineers involved in the study and design of innovative energy-efficient working processes of drum machines.