MOVEMENT OF A PARTICLE BY A MOVING VERTICAL AUGER BOUNDED BY A CASING

Abstract

During the various technological operations in various fields of industry and production, the working bodies of machines and tools interact with particles of technological material. At the same time, the geometric shape of the surface of the working bodies determines the character of the movement of particles on it. Particles of the technological material are often considered as material particles, which is acceptable because of their small dimensions. In this case, inertial forces from the rotation of the material are not taken into account, and as a result, the obtained analytical dependencies of its movement are somewhat approximate, however, it can be applied to a certain extent to the material and determine the direction of further research. A fairly common method of transporting technological material is the use of screws – a curved blade in the form of a strip of a helical conoid. Usually, a screw is moving and limited by a stationary coaxial cylindrical casing. In the article, the movement of a particle inside the vertical structure, which is made up of a cylinder and a coaxial strip of a helical conoid, and which rotates around a common vertical axis, is investigated. The differential equations of the relative movement of the particle along the periphery of the screw have been received. A special case, when the surfaces are stationary, was considered. A qualitative analysis of the obtained equations was made and based on this, the patterns of particle movement along the helical line – the curve of the intersection of the screw with the cylinder – were found. Constructive and kinematic parameters, when the particle moves up during sliding along a helical line or falls down, were found. It was established that if the angle of rising of the curve of the intersection of the limiting cylinder with the surface of the screw is less than or equal to the angle of friction of the particle on it, then the movement of the particle in both directions becomes impossible. This applies to both moving and stationary surfaces. The relative and absolute trajectories of particle movement are constructed in the article.