PARTICLE MOTION OVER THE EDGE OF AN INCLINED PLANE THAT PERFORMS AXIAL MOVEMENT IN A VERTICAL LIMITING CYLINDER

Abstract

Differential equations of a relative material particle motion over the edge of an inclined flat ellipse that rotates around the axis of a vertical limiting cylinder have been deduced. The position of a plane relative to the axis of the rotation is set by the angle ranging from zero to ninety degrees in its value. If the angle is equal to zero, the plane is perpendicular to the axis of rotation and if the angle is equal to ninety degrees, it passes through the axis of rotation. The equations have been solved using numerical methods. Analytical solution has been found for certain angles. The aim of the research is to investigate the transportability of a technological material in a vertical direction by a cascade operating element that rotates in a cylindrical cover. The working part of the operating element is an inclined rigid plane, which is limited by an ellipse — the line of its contact with a cover. The objective of the research is to analytically describe the movement of a single particle of the technological material on two surfaces, namely, an inclined plane and a vertical cover. The research methodology is based on the methods of differential geometry and the theory of surfaces, theoretical mechanics and numerical methods of solving differential equations. The paper presents a first developed analytical description of the relative particle motion in an ellipse — a contact line of an inclined plane and a limiting vertical cylinder, in which the inclined plane rotates. The kinematic characteristics of such motion have been determined.