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Kashirin Dmitry Evgenievich
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associated professor
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• Ryazan State Agrotechnological University named after P.A. Kostychev
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Articles count: 2
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THE USE OF FOKKERPLANCK EQUATION FOR ANALYTICAL REASONING OF MIXING PROCESS IN THE SCREW MIXER
DescriptionIn the current economic situation, the developing of cattle breeding is taking on special significance. It is well known that the effective way to develop cattle breeding is to increase the total number of efficient livestock. The numerous researches show that the high concentrated fodder premix diet gives the highest effect in increasing animal indicators [1, 2, 3]. Traditionally, the premix is a powder mass, which should be added into the mixture of grain components. Exact following the recipe of prepared fodder allows the maximum usage of forage potential of the concentrate components [4, 5, 6, 7]. In view of the foregoing, food enrichers have special actuality in making high concentrated fodder [8, 9, 10]. The usage of differential Fokker – Planck equation systems allows determining the laws of the mixing process of various granulated products. As a result, it becomes possible to optimize the technological process of the mixerenrichers of concentrated feed so that the resulting mixture of feed would have high quality and technological characteristics. At the same time the duration of sewerenricher’s work and, as a consequence, the energy intensity of the technological process would accept the minimum possible values [1116]. The given theoretical approach is based on the consideration of the motion of an individual particle contained in a loose grain mass (phase). Concerning this, it is necessary to accept a number of assumptions about making effort to the feed particles, and the velocity vectors of its initial motion should be taken into account. Taking into account the complexity of the mathematically derived differential equation, its literal analytical solution seems very difficult. Therefore, the first step of the solution is aimed at the obtaining the nonstationary diffusion equation of Fokker  Planck and the boundary conditions for isolating the only one solution. The second step of the solution is implemented by the tabulation at the gridbased points, that is, considering the differential equation not at a random point of the area, but only at the grid nodes. Moreover, it is necessary to apply the approximation of the derivatives at each node. The solution of the equation system allows determining the module of the minimum, average, and maximum values of the phase particle motion in different parts of the mixing chamber, respectively. In connection with this, the aim of the study is to substantiate the processes of motion of various types of granulated products

Description
The mathematical model presented in this article allows you to choose rational values and ranges of design and technological parameters of body separation, as well as their further optimization