DEPENDENCE OF RESISTANCE OF MOVEMENT OF THE FLEXIBLE STRIP ON THE SURFACE FROM THE CURVATURE OF ITS AXIS

Abstract

During considering the movement of the body on the surface, it is usually replaced by a material particle. It greatly simplifies the analytical description of the movement, which makes it possible with some probability to predict the impact of certain factors on the process. The particles can create a continuous environment, one of which may be a flexible strip. It is deformed during moving on the surface, acquiring its shape. This movement can occur during plowing the soil, permeated with roots. In this case, the slice can be taken as a strip of the rectilinear cross-section, the length of which does not change during deformation, i.e. it is incompressible. The article considers the movement of such a strip on a cylindrical surface with a horizontal arrangement of rectilinear generatrices. The strip can enter the surface perpendicularly to the generatrices and moves farther in this direction. In this case, the trajectory will be a flat curve – in fact, a cross-section of the cylinder. The article considers the variant when the strip enters the surface of the cylinder at a certain angle to the generatrices. In this case, the trajectory of the strip movement will be a spatial curve. Some effort is required to overcome the slip resistance of the strip. It is the sum of certain components: the effort to lift the strip, to overcome the friction, to its deformation in the case of an elastic strip.

The article considers the forces, the magnitude of which is influenced by the curvature of the trajectory of the strip, for which its axis is taken. The force is determined by the summation of the elementary forces acting on the elements of the strip along its axis. It is considered that at the deformation of a strip the profile of its cross-section does not change and remains rectangular. On the basis of this rectangle, an elementary parallelepiped of a strip is formed, one of the dimensions of which is the differential of the arc of its axis. Thus, the definition of the force is reduced to the integration of the forces applied to the elementary parallelepiped along the length of the arc of the axis of the strip. One of such forces is the centrifugal force, which depends on the curvature of the trajectory along which the strip moves on the surface. The component of this force causes the pressure of the strip element on the surface, which causes the appearance of friction. If the strip is elastic, then there are deformation forces, which also depend on the curvature of the axis of the strip.

Keywords: flexible strip, cylindrical surface, axis curvature, centrifugal force, friction force.