Ergonomic aspects of material separation process modeling on stationary screw surfaces

The motion of material particles on gravitational surfaces, ie the motion of particles on surfaces under the action of its own weight, is used in special devices for their separation by physical and mechanical properties. For this purpose stationary screw surfaces of a steady step are applied.A number of papers have now considered the relationship between the kinematic parameters of motion, the coefficient of friction and the design parameters of the separator, when its surface is a deployable helicoid.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 finding 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. If a material particle with a certain initial velocity vо and a certain angle of inclination to the horizon falls on an inclined plane, it will move along a certain curve (in the absence of friction and air resistance, the trajectory will be a parabola).A system of equations is obtained, which describes the motion of a material point on the gravitational surface in the general case. If it is created for a specific surface, nonlinear and numerical methods must be used to integrate it. Modern software products allow not only to find the trajectory of the particle, but also to show it on the surface and even make an animation that essentially replaces high-speed shooting. 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 right surfaces.The motion of particles along a helical conoid and a deployable helicoid is considered. Simulation of the motion of a material particle on helical surfaces and its study by modern means of numerical integration and visualization have shown that for different surfaces the nature of the motion of the particle will also be different. When moving on the surface of the helical conoid, the particle in the presence of friction first accelerates, and then stops at a considerable distance from its axis. To prevent this, you 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 deployed helicoid, its velocity becomes constant over time, and the trajectory after that will be a helical line.Key words: particle motion, helical surfaces, helical conoid, deployable helicoid, simulation