Mathematical Model of Lifting Particles of Technological Material by Vertical Auger

Abstract

The purpose of this research is to investigate the transportation of a material particle by a vertically placed auger limited by a cylindrical casing. The surfaces are coaxial. When the auger rotates, the particle moves to the periphery and also begins to interact with the cylindrical casing. The particle simultaneously slides on both surfaces and rises in absolute movement. Its relative motion is sliding along the periphery of the auger. Differential equations of particle movement in projections on a moving coordinate system that rotates together with an auger have been compiled. The equations have been solved by numerical methods and graphs of kinematic characteristics have been constructed. The limit value of the angle of rising of the helical line – the periphery of the auger, at which the rise of the particle stops at a given angular velocity of rotation of the auger, has been found. It was found that the velocity of particle rising is influenced by constructive and technological parameters. In particular, for a given radius of the cylindrical casing, friction coefficients and the angle of the edge of the auger there is a minimum value of the angular velocity of its rotation. Then the particle "sticks" and rotates together with the auger, describing in absolute motion a circle on the inner surface of the cylindrical casing.