Theoretical determination of absolute speed of mineral fertiliser particles from centrifugal spreading disc

Abstract

One of the main technological approaches for ensuring favourable conditions of growth and development of plants is depositing mineral fertilisers. The quality of it influences the soil fertility and harvest of agricultural crops. We have developed a new construction of the spreader working body, the axis of which is at the angle to the horizon. Theoretical and experimental research is conducted on the kinematic parameters of such working body. The aim of the present research is determination of the constructive and kinematic parameters that ensure maximal distance of spreading mineral fertiliser particles from the spreading disc with the angle to the horizontal plane. In the research the methods of modeling, theoretical mechanics and mathematics, as well as calculations and presentations of graphical dependences are used. The present article describes the obtained analitical expressions for determination of the absolute speed of mineral fertiliser particles from the spreader disc with an inclined working body, considering the initial speed of moving the aggregate for spreading mineral fertilisers on the surface. The mineral fertiliser particle absolute speed from the spreading disc of the working body is presented as a vector through its projection on the axis of specially developed system of Cartesian coordinates at a moment of time. Based on the obtained analytical expressions, graphical dependences are presented characterising the studied process. It is proved that at increasing the coefficient of friction of the mineral fertiliser particles from 0.1 to 0.7, the angle of the mineral fertiliser particles leaving the disc increases from 2 to 33 deg at the initial speed of movement of the aggregate 2 m·s-1 and from 2 to 37 deg at the initial speed 4 m·s-1. Therefore, some of the fertiliser particles will leave the disc at the agle bigger than the inclination of the disc to the horizontal plane within 20…30 deg. Changes of the angle speed of the disc rotation do not essentially influence changes of the angle of the fertiliser particles leaving the disc.