Математичне моделювання процесу розділення матеріалу на стаціонарних гвинтових поверхнях

Abstract

The motion of material particles on gravitational surfaces is used in special devices for their separation by physical and mechanical properties. For this purpose stationary screw surfaces of a constant step are applied. The purpose of the study is to investigate helical surfaces with different design parameters in order to improve their separation ability through mathematical and geometric modeling of the process without making surface models. The problem of constructing the trajectory of a material particle on the surface under the action of its own weight is preceded by the problem of finding the trajectory on an inclined plane. Modern software products make it possible not only to find the trajectory of the particle, but also to show it on the surface and even make an animation, which essentially replaces high-speed camera recording. This approach makes it possible to study the kinematic parameters of motion on different helical surfaces without full-scale samples of these surfaces, which significantly reduces the cost of finding the desired surfaces. The trajectories of the particle on the surface of the helical conoid and the deployable helicoid are obtained. It is established that when moving on the surface of a helical conoid, the particle in the presence of friction first accelerates, and then stops at a considerable distance from its axis. To prevent this, its need to take a limited compartment of the conoid both in height and on its periphery. When a particle moves on the surface of a helicoid, its velocity becomes constant over time, and the trajectory after that will be a helical line. The developed approaches make it possible to study the process of material separation not only after stabilization of motion, but also during the transition process, as it became possible to visualize it. This will allow you to choose the surface compartment of the optimal size, which will provide the desired productivity of separation due to the dispersion of particles with different coefficients of friction on its surface. Key words: material particle, trajectory, material separation, helical conoid, helicoid