The analytical method of calculation of a withstand motion of fine-grained mixture is worked out in the vertical cylindrical sieve of vibrocentrifuge. Integration of differential equalization of motion is show out the reserved formulas for the calculation of kinematics descriptions of grain flow. The two-parameter continual model of the state of separation mixture is used in researches, as a heterogeneous continuous environment with variable specific mass (by porosity) on the thickness of movable layer of friable material. Change of specific mass on a radial coordinate in the cylindrical layer of mixture approximated by the function of degree, the coefficients of that are certain by the Aitken's method. Due to such approximation, the analytical decision of differential equalization of the grain flow, shown out with the use of two-parameter rheological dependence, in that the constituent of linear viscid resistance is complemented by the constituent of remaining internal dry friction, proportional overpressure in mixture, is built. An analytical decision is expressed as squaring that is not expressed through elementary functions in closed form, the close method of calculation of integral offers that is why, with the use of partial sum of row of degree. The results got close formulas result in that well comport with the results of numerical computer integration of squaring. Such method the continual models of grain flow on vibrosieves, it is assumed in that friable material is fully confined internal dry friction, are generalized known for, as a result of vibrodilution. The examples of calculations are considered, where influence of different factors is investigational, in particular values of rheological coefficients and change of porosity, on kinematics descriptions. It is set that calculation kinematics descriptions of grain flow substantially depend not only on the thickness of movable layer and rheological constants, and also from the concentration of grains near free surface of the mixture. Thus, worked out here a method of research of vertical grain flow in the cylindrical sieve of vibrocentrifuge can be an alternative to other methods in that for the calculation of motion of grain mixture of variable porosity conducted numerical computer integration of nonlinear differential equalizations.
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