DOI 10.36461/NP.2024.70.2.004
UDC 637.131.2

THEORETICAL STUDIES OF THE MOVEMENT OF A RELEASED IMPURITY PARTICLE IN THE INTERDISK SPACE OF A MILK SEPARATOR
A.V. Yashin, Candidate of Engineering Sciences, Associate Professor;
A.A. Gusev, postgraduate student; N.S. Chirkova, Master's degree
Penza State Agrarian University,
Penza, Russia, e-mail: This email address is being protected from spambots. You need JavaScript enabled to view it.

Theoretically, the movement of the released impurity particle in the interdisk space of a milk separator in the section from its initial position to the final one on the bar is investigated. In this case, the Lagrange method and the corresponding equation of the second kind are used, since in the initial position of the isolated particle, the expected direction of its movement and (or) trajectory are not known. By solving the Lagrangian equation of the second kind, the equation of the trajectory of motion of the extracted impurity particle on the section from its initial position to the final one on the bar is obtained. The impurity particle in the interdisk space of the milk separator moves along a logarithmic spiral (exponentially), like an equiangular spiral or a spiral of growth, in which distance between the coils increases exponentially. At the same time, the type of logarithmic spiral depends on the initial position of the particle, physico-mechanical properties of the impurity particle (radius and density), physico-mechanical properties of milk (density and dynamic viscosity), design parameter – the angle of inclination of the separation plate to the horizontal and kinematic parameter – the angular velocity of the drum. From the obtained equation of the trajectory of motion of the extracted impurity particle on the section from its initial position to the final position on the bar by mathematical transformations can be obtained such characteristics as: velocity, acceleration, time of stay of the impurity particle in the interdisk space of the milk separator drum and the angle by which it will move, pitch angle or inclination of the tangent to the normal, restored to the radius-vector, length of the arc of the logarithmic spiral or the path traveled by the impurity particle on the section from its initial position to the final one on the bar.
Keywords: impurity particle, interdisk space, milk separator, generalized coordinate, radius vector.

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