Mathematical description of the process of bulk material movement in horizontal continuous drums

The article considers the process of moving a single particle in a bulk medium, which partially fills a horizontally placed rotating drum of continuous action. As the degree of the bulk material filling in the drum (filling segment) at the inlet to the drum is greater than that at the outlet of the drum, an inclined plane of bulk material is formed, through which the particle moves along the longitudinal axis of the drum. The mathematical description of the process of the bulk material particles moving in a horizontal rotating drum is given. It is established that the process of motion of a particle is pulsating. The process is described by the equation of a particle rise along a circle (along the cylinder) together with the filling segment and by the equation of a particle motion along a rupture plane. It is found that during one period of rupture the particle moves along the drum axis along the surface of the rupture plane by the value of the next section, in which the degree of filling will decrease and the origin of coordinates of particle motion will change. Parameters of the rupture plane depend on material properties (dynamic rupture angle), on degree of the drum filling with the material at the inlet and outlet, on the length of the drum. The spatial line of a particle rupture located on the surface of the rupture plane is described mathematically. In the article the formulas describe the trajectories of the bulk material particles movement in the drum and the drawings visually demonstrate these trajectories. Mathematical description of the process and calculations justify the optimal filling of the drum with bulk material. The authors propose the design of the drums to ensure optimal conditions for bulk material treatment. The research was performed within the framework of the scientific school «Innovative developments in the field of logging industry and forestry».