Ergonomic aspects of modeling the process of material separation on stationary screw surfaces - Pylypaka, S. F.; Nesvidomin, A. V. (Energy and Automation, 2023)
The movement of material particles along gravitational surfaces is used in special devices for their separation by physical and mechanical properties. For this, stationary helical surfaces of constant pitch are used. In the mining industry, screw separators with different axial cross-sections (chute) are used for the enrichment of ores. Grain separation is carried out on linear helical surfaces, which are compartments of an oblique helicoid. Despite the fact that such separators are passive working bodies and do not require energy to drive them, they also have disadvantages. This is relatively low performance and low resolution. Now the calculation of the relationship between the kinematic parameters of the movement, the coefficient of friction and the design parameters of the separator, as well as the case when its surface is an expanding helicoid, has been carried out. The purpose of the research is the analysis of a helical surface with various design parameters for the purpose of improving its resolution using mathematical and geometric modeling of the process without the production of surface models. Solving the problem of building the trajectory of the movement of a material particle along the surface under the action of its own weight is preceded by the problem of finding the trajectory on an inclined plane. It is described by a system of equations, which is non-linear and numerical methods must be used for its integration. Modern software products make it possible not only to find the trajectory of a particle’s movement, but also to show it on the surface and even make an animation, which essentially replaces high-speed photography. This approach makes it possible to study the kinematic parameters of movement on various helical surfaces without full-scale samples of these surfaces, which significantly reduces the cost of searching for the necessary surfaces. The motion of a particle along a helical conoid and a spreading helicoid is considered. It has been established that the nature of the particle movement will also be different for different surfaces. When moving along the surface of a helical conoid, a particle first accelerates in the presence of friction, and then stops at a considerable distance from its axis. To prevent this, it is necessary to take a limited compartment of the conoid both in height and along its periphery. When a particle moves along the surface of an expanding helicoid, its speed becomes constant over time, and the trajectory after that will be a helical line. In further research, it is necessary to use the developed approaches to identify the possibilities of material separation not only after the stabilization of the movement, but also during the transition process, since its visualization has become possible. This will make it possible to select a surface compartment of the optimal size, which will ensure the required separation performance due to the dispersion of particles with different friction coefficients on its surface. Key words: mathematical modeling, trajectory of particle movement, speed of movement, helical conoid, unfolding helicoid