Mathematical modeling of separation velocity of hydrogel granules from the edge of the metering device in the seeding unit of an air-seeder

Abstract

The movement of granular materials with variable physical and mechanical properties (in particular, hydrogel which characteristics are highly dependent on moisture content) along a complex trajectory on a coil and at the moment of separation presents a significant challenge for theoretical description and calculation. Determining the velocity of a granule at the moment of its separation from the edge of the metering device is a key parameter for calculating its further trajectory in the fertilizer tube and predicting the point of impact in the furrow opener. The research goal is to develop a mathematical model and determine the absolute velocity of a hydrogel granule at the moment of its separation from the edge of the metering device of the seeding unit of an air-seeder as well as to investigate the dependence of this velocity on the angular velocity of the metering device (ω) and the absolute moisture content of the hydrogel. Mathematical simulation of the dynamics of a hydrogel granule motion at the section of the separation from the edge of the metering device of the seeding unit of an air-seeder is presented. The developed physical-mathematical model accounts for the motion of a granule under the action of gravity, centrifugal force, friction force, air flow resistance force, and the Coriolis inertial force. Based on the solution of the system of differential equations, analytical expressions were obtained to determine the time of a granule movement along the metering device edge and its relative velocity. The dependence of the absolute separation velocity on the key parameters was determined: the angular velocity of the metering device (ω), length of its edge (l), friction coefficient (f), absolute moisture content of the hydrogel, and the air flow velocity. The calculation results performed in the Mathcad environment are visualized as graphical dependencies. The obtained dependencies allow for predicting the granule feed velocity into the fertilizer tube and optimizing the operating parameters of the seeder metering unit for hydrogel granules to improve seeding uniformity.