Issue 2(42), 2016


Operating process of shelving friction separator with curvilinear ramp of variable curvature pdf

P. M. Anokhin, A. I. Afanas’ev, Yu. M. Kazakov, V. Ya. Potapov

Separation by the elasticity and friction is widely used in mining and construction industries. The simplest device for separating by friction is a shelf separator, which consists of the inclined shelf designed to disperse a particle to a speed that will be dependent from friction coefficient. Inclined shelf ends in the bottom with the curved ramp. Curved ramp can be made in an arc with a constant and a variable radius, and it can be considered as the second stage of the preparation of particles with different coefficients of friction for the separation. Authors established experimentally that the friction in this area varies depending on the location of the particle, i.e. radius. At different points of the concave trajectory, the normal pressure of a particle on a curved surface is different. Thus, setting the law of radius variation lets us to control descent speed of the particle from the curved ramp and, thus, the separation efficiency. Using Newton’s second law in the research allowed obtaining in polar coordinates differential equation of motion of the rock particles in the curved trampline made in the form of a logarithmic spiral. The equation includes spiral parameters: polar radius, the angle between the path tangent and polar radius vector, and the friction coefficient. As a result of the integration of these equations authors obtained velocity of the particle during its descent from the curved ramp, as well as the direction of speed, which allows to determine the initial conditions of motion in free flight of the particle. According to the well-known separation speed of the particle from the curved ramp one can identify its horizontal and vertical components. Then, using the law of conservation of energy and the differential equations of motion of a particle in free flight, authors determined the distance of the particle falling on the horizontal plane, measured from the edge of ramp. The study shows the results of calculations on the model and the results of experiments on a physical model that demonstrates the adequacy of the mathematical model. A curved ramp with a variable radius of curvature provides a larger range of particle distribution that indicates as an increase in the efficiency of the separation process.

Keywords: shelving friction separator; friction coefficient; equation of motion of a particle; particle velocity; curvilinear ramp; logarithmic spiral.



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