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## Analytical Method for Determining Porosity in the Layer of Vibro Separated Grain Mixture

### Abstract

The formulas have been entered and approved for the calculation of porosity distribution on the thickness of layer of fine-grained mixture during its separation by the inclined flat or vertical cylinder vibro sieves. It has been attained as a result of approximation of tabular information of the obtained numerical computer integration of the specially worked out nonlinear differential equations of the second order in a dimensionless form. For approximation, the function of degree coefficients and index is used for the degrees which are certain by the Aitken's method. Coefficients of the entered analytical dependence are the vibro sieves related to the parameters obtained by mechanical descriptions of the separated material. Coefficients of the entered analytical dependence are related to the parameters of vibro sieves and mechanical descriptions of the separated material. In the case of cylinder vertical vibro sieve the action of centrifugal force is also taken into account. The method of mixture porosity calculation does not need a computer numerical integration of nonlinear differential equations conducted by other authors for solving this problem. Comparison of numerical results of the proposed analytical method of calculation with the ones described in literature, have confirmed its high accuracy results, for the differences do not exceed one percent. The expounded method is universal enough and simple in use, besides it opens the possibilities of subsequent analytical integration of differential equalizations of motion at the calculation of kinematics descriptions of grain flow. The developed method gives the opportunity to also solve the inverse task when, according to experimental measurements of porosity values of grain mixtures on the thickness of movable separated layer, it is needed to find the value of phenomenological permanent that is included in the expressions of coefficients of initial differential equalization. In this way, the adequacy of the mathematical model is improved. The use of approximation of degree considerably simplifies the method of authentication of differential equalization coefficients. In the article, the examples of grain mixture porosity calculation as well as the examples of phenomenological permanent authentication have been resulted after experimental calculations for both the variants of vibro sieves.
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