Machinery & Energetics

The article deals with theoretical issues of designing gravitational descents. Movement of goods or material on them is carried out under the influence of self-weight. Such transport is widely used in coal mines, mines, concentrating factories. Transport of the material can be carried out on special surfaces: decks, cascade and screw descents, pipes, gutters, etc. The nature of the particle motion depends on the design features of such descents. It is easier to calculate the descent in the form of an inclined plane. The particle moves along it in a straight line, which is the line of greatest slope. If the working surface of the descent is a curvilinear surface, then the trajectory will be a curve. In this case, there is an additional force of inertia - centrifugal, the value of which depends on the curvature of the trajectory. This force can divert the trajectory of the line of greatest inclination and also increase the particle pressure on the surface, which leads to an increase in the friction force. When drawing up the differential equations of motion, all the forces applied must be taken into account The design of a screw descent in which the working surface is a nondevelopable (skew) helicoid is considered in the work. In order not to set up differential equations of motion of a particle, we propose to describe its motion after stabilization, that is, after it begins to move along a screw line with a constant speed. In this case, the differential equation of motion of a particle is replaced by the equations of equilibrium of the forces applied to it in the projections on the coordinate axis. The equations of equilibrium of forces is set up in the projections of both the fixed coordinate system and unitary vectors of the moving Darboux triad. In both cases, the same analytical dependencies were obtained. They allow you to design the descent at a predetermined calculated velocity of motion of the particle with a known coefficient of friction. The same calculated velocity of motion of a particle at a given coefficient of friction can be provided by a surface of the skew helicoid with different structural parameters.

gravity descent, force of gravity, equilibrium of forces, skew helicoid, steady-state regime