The Organization of Transportation of a Particle by an Inclined Cylinder Rotating Around its Axis

Abstract

The movement of a material particle on the inner surface of an inclined cylinder, which rotates around its axis with a constant angular velocity, is investigated in the article. When a particle hits the surface of a horizontal cylinder, it begins to oscillate in the cross-sectional plane of the cylinder with a certain amplitude in the angular dimension. Its value depends on the incidence point, the coefficient of friction and the initial absolute velocity. Differential equations of movement in projections on the axis of a fixed coordinate system are compiled. They are solved by numerical methods. Under the appropriate initial conditions, which are determined analytically, the particle in absolute movement can be stationary, being at a point on the cylinder at a certain distance from the lower point in the angular dimension in the direction of the rotation of the cylinder. Some cases of movement when the angle of inclination of the axis of the cylinder to the horizontal plane is greater, equal or less than the angle of friction of the particle on the surface of the cylinder are described. An analytical solution for the last case that describes the movement of the particle after stabilization is found. Visualization of the obtained results is made.