THE TRANSPORTATION OF THE MATERIAL PARTICLE BY THE VERTICAL AUGER

Abstract

The functioning of machines deals with the interaction of the particles of the technological material with the working bodies of devices. Particles of the material are forced to choose a trajectory of sliding along the surface. Moreover, the surface of the working body can be movable, for example, it can make a rotational movement. In this case, the movement of the particle will consist of the relative movement of the particle (sliding of the particle along the surface) and the translational (rotational) movement of the surface itself. The relative motion of a particle is considered relatively to a moving coordinate system. The sum of these movements gives the absolute trajectory along which the particle moves in a fixed coordinate system. Successive differentiation of the length of the trajectory over time will give the absolute speed and acceleration of the particle. In mechanics, during solving problems of the dynamics of a material point, equations of equilibrium of the applied forces are compiled in projections on the axis of the spatial coordinate system. This coordinate system can be fixed or movable. In our case, such a system is a moving coordinate system – the accompanying Frenet trihedron of the guide curve. The movement of the trihedron along the guide curve is a translational movement, the movement of a point in the trihedron system is relative. The article considers the lifting of a particle by a transporting body in the form of a vertical auger, which is limited by a coaxial cylindrical casing. When the auger rotates, the particle moves to the periphery and begins to interact with the cylindrical casing. The particle simultaneously slides along both surfaces and rises up in absolute motion. Its relative movement is sliding along the helical line – the periphery of the auger. The differential equations of the motion of a particle in projections on a moving coordinate system, which rotates together with the auger, have been compiled. The equation is solved by numerical methods and graphs of kinematic characteristics, including relative and absolute trajectories, are constructed. The limiting value of the angle of rising of the helical line – the periphery of the screw, at which the rising of the particle stops at a given angular speed of rotation of the auger – has been determined.