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A mathematical model of particles movement of separated material in a friction separator is proposed. It includes equations of their movement at each stage of separation (along a rough inclined plane, on a curvilinear part of a springboard, impact of a particle on the surface of a drum, free motion before leaving the separation zone), and differential equations of particle movement in circulating air flow created by a rotating drum; Each of these phases of motion is described by a system of equations obtained on the basis of basic laws of mechanics. An analysis of a particle motion along aslope plane was carried out on the basis of the law on energy changes. Depending on the ratios of the recovery factor and instantaneous friction, being random variables and also the coordinates of a point impact the particle is possible to move along different trajectories with different initial conditions. The mathematical model of the process of separation of loose multicomponent materials on a friction drum-shelf separator makes it possible to investigate comprehensively the process of separation of particles on friction and elastic properties and to optimize the operating modes of the apparatus at relatively low costs without using macaques and prototypes and investigate them experimentally. On the basis of analysis of the proposed theories of particles motion, the main ways are formulated of further improvement of methodology for designing and creating friction devices.

The authors develop a numerical scheme allowing to find a joint solution to the equations of diffusion of heat and moisture, A.V. Lykov and Maxwell's equations in electromagnetic drying of a sample with a flat geometry. Calculation scheme is based on two algorithms: a) for a given distribution of the dielectric constant the problem is to estimate the field density of electromagnetic losses, reflection coefficients and transmission; b) when there are electromagnetic losses of specified field density, the problem of calculation of fields of temperature and moisture content should be solved. The role of a bridge between these two algorithms performs the formula of Debye (it determines the dielectric permittivity of each of the two components of the mixture, the solid base and water, frequency and temperature) and mixing formula of Maxwell (on the basis of the Debye formulas for the solid base and water, it determines the dielectric permittivity of the mixture of these components as a function of frequency, temperature and moisture content). The calculation according to this scheme allows to take into account the reverse impact of distributions of temperature and moisture content at some point in time, on the distribution of absorbed electromagnetic energy in the same moment. Numerical experiment (drying the moist zeolite electromagnetic radiation in the microwave range), the results of which are in good agreement with available published experimental data.

The article provides an overview of the methods for pre-sorting sulfide ores, as well as the design of separators for implementing these methods. The practical prospects of the use of radioresonance and X-ray fluorescence separation for the preliminary preparation of sulfide ores are shown. The use of not one, but two or more different physical properties of the separated ore components during radiometric beneficiation opens up additional possibilities in increasing the selectivity of this process and expanding the scope of its application. It is proposed to reduce the energy intensity of crushing processes, due to the impact on the rock electrical breakdown of ore in order to reduce its strength. In this case, the processes of crushing and grinding are replaced by processes of selective destruction along the boundaries of inclusions of the useful component. The substantiation of the technology for the separation of poor copper-zinc ores is presented. The relationship of sulfide content and electrical breakdown voltage is shown.The results of experiments in determination the specific energy consumption for the electrical processing of lean ore, depending on the sulfide content, are presented. The principle is substantiated, and a simulation model of the separation process is developed. The block diagram of the separation process algorithm is given.A description of the methodology for working with software is done. The energy costs of a new technology for the separation of poor sulfide ores are determined.

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