Substantiation of the process of gravitational grain separation by modeling method

The article suggests one need to increase the capacity of the separator and intensify the process, carry out gravitational separation using a slit hole located perpendicular to the direction of movement of the mixture, with a length limited only by the dimensions of the separating surface, being made in the form of a brachystochronous curve. Such grain separation using brachystochronous surfaces with slotted holes ensures the separation of grains from large to small ones and feeding each fraction separately to a separate part of the sieve for final sieving, which increases productivity and reduces the energy intensity of the process due to gravitational separation and does not require additional energy costs. The purpose of the presented study was to perform mathematical modeling and substantiation of design parameters: a slit hole located perpendicular to the direction of movement of the mixture with a width limited only by the dimensions of the separating surface, made in the form of a brachystochronous curve, with admitting kinematic parameters of particle motion along the separating surface to ensure their effective separation. To isolate a particle with an equivalent radius re = 2,0-3,0 mm into the slot opening of the separating surfaces with a length of the acceleration section S0 = 0,15-0,20 m, its initial velocity should be within v0 = 0,5-0,72 m/s, and the critical velocity within vк = 0,70-0,88 m/s. Besides it is necessary to have a width of the gaps between the opposite edges of the separating surfaces within L = 14-20 mm, and the height difference between the edges of the separating surfaces H = 1-2 mm.