Transportation of a material particle by the operating mechanism of an agricultural machine in the form of a vertical screw confined by a coaxial stationary cylinder

Abstract

The use of vertical augers in screw conveyors significantly expands the operational capabilities of such mechanisation equipment for performing loading and unloading technological operations. However, the existing designs of vertical screws do not fully meet the operational requirements. Their main disadvantages are increased energy consumption, especially with their significant overall dimensions, which depend on the influence of friction of the process material on the conveyor surfaces. Therefore, the study considers the movement of a material particle by the operating mechanism of an agricultural machine in the form of a vertical screw confined by a coaxial stationary cylinder and establishes the dependence of the speed of transportation of a material particle on the influence of the particle friction coefficient on the surface of the screw and on the surface of the limiting cylinder. The purpose of the study is to determine the parameters of the movement of agricultural material particles when they interact with the helical surface of the operating mechanism of a vertical conveyor in the form of a screw that rotates around the axis and the surface of a coaxial fixed cylindrical casing. Mathematical modelling of the processes of movement of soil particles along the helical surface of the operating mechanism is described on the basis of general laws and principles of analytical and differential mathematics, theoretical and analytical mechanics. As a result of the study, the differential equations of movement of a particle of agricultural material on the helical surface of the screw, which rotates around its axis in a fixed cylinder, were compiled. The equation is solved using numerical methods and the trajectories of the relative motion of the particle along the helical line – the edge of the screw, which is common to the surface of the screw and the limiting cylinder are constructed. The friction forces of the material particle on the surfaces of the screw and casing are also considered. The limit value of the helical line lifting angle is found when the particle lifting becomes impossible at a given angular velocity of screw rotation. The influence of the friction angles and radius of the limiting cylinder on the particle lifting speed is estimated. Graphs of kinematic characteristics as a function of time are given. The materials of the study can be used by researchers for further investigation and by practitioners in the selection of conveyors for transporting agricultural materials