MOVEMENT OF A PARTICLE ALONG AN INCLINED CYLINDER ROTATING AROUND ITS AXIS

Abstract

It is well known that parts of agricultural machinery often have a cylindrical shape. This shape, for example, can be observed in the casing of lifting and transport machines, where the active working body rotates. Furthermore, drum grain dryers and triers use an inclined cylinder that rotates around its axis. In this case, the particles of the technological material interact with the rotating surface, which leads to their sliding, the nature of which depends on the value of the angle of inclination of the cylinder. In this study, the methods of differential geometry, vector algebra, theoretical mechanics, and numerical integration of differential equations consider the motion of a particle along the inner surface of an inclined cylinder rotating at a constant angular velocity around its axis. The axes of a fixed coordinate system are used to compose differential equations of motion. It was established that the proper initial conditions under which the particle would be stationary at a certain distance from the lower forming cylinder towards its rotation can be determined analytically. In case of movement along an inclined cylinder, the particle moves, among other things, in the axial direction, while reducing the amplitude of vibrations. Furthermore, it was found that the angle of inclination of the cylinder plays a significant role. If the latter is less than the angle of friction, then the vibrations stop, the movement of the particle stabilises, and it performs a rectilinear movement at a constant speed in the axial direction. If the angle of inclination of the cylinder is greater than or equal to the angle of friction, then the particle moves rapidly in the axial direction and its movement does not stabilise. The value of the angular velocity of rotation also plays a significant role. A certain amount of it provokes “sticking” of the particle, which does not depend on the inclination angle of the cylinder. The obtained analytical dependences can be used in the design of cylindrical working bodies of agricultural machines.