THE RESULTS OF THE INVESTIGATION OF THE PARTICLE MOVEMENT ON THE CYLINDER OUTER SURFACE DURING ITS PROGRESSIVE OSCILLATIONS IN HORIZONTAL PLANES

Abstract

The results of the investigation of the material particle movement on the cylinder outer surface during its progressive oscillations is considered in the article. All points of the cylinder describe circles in horizontal planes. During the oscillating motion of a horizontal cylinder, the material particle also performs an oscillating motion and moves along its outer surface in the transverse direction relatively the rectilinear generators of the cylinder. The relative motion of the material particle is very sensitive to the frequency of oscillations: when the frequency of oscillations is growing, the length of the path increases significantly. The particles with different coefficients of friction have different trajectories and the distance between them increases as they slide on the surface. The trajectories of the relative motion of the particle on the surface of the cylinder are constructed. The graphs of other kinematic characteristics as a function of time are given. Partial cases when the axis of the cylinder is located horizontally or at an angle of friction to the horizontal plane are considered. When the cylinder is inclined, even at a little angle, the trajectory of the material particles changes significantly, deviating from the transverse direction toward the inclination of the cylinder. The case of motion of a material particle on a stationary cylinder inclined at an angle to the horizontal plane is considered. When the angle of inclination is equal to the angle of friction, the motion of the particle depends on the initial conditions. If the initial velocity is given along the highest rectilinear generatrix of the cylinder, it will continue to move along it with this speed. If the initial speed is given in the other direction, the trajectory will be curved and the movement accelerates. The results of the research of the laws of motion of material particles on the outer surface of the cylinder can be used to separate the technological material by its frictional properties.

Keywords: relative motion, inclined cylinder, outer surface, particle, differential equations, kinematic parameters.