@misc{Olshanskii_Vasily_Analytical,
author={Olshanskii, Vasily and Olshanskii, Alexander and Kharchenko, Sergey and Kharchenko, Farida},
publisher={The Lublin Branch of the Polish Academy of Sciences},
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.},
title={Analytical Method for Determining Porosity in the Layer of Vibro Separated Grain Mixture},
type={ArtykuĹ‚y / Articles},
keywords={vibro sieve separation, grain mixture layer, porosity calculation, analytical method, approximation of degree, authentication of phenomenological permanent},
}