Mathematical model of oriented planting of bulbs with bulb stem pointing downwards

Abstract

Theoretical studies are carried out on the substantiation of design and technological parameters of vibration and pneumatic planting unit of a bulb-planting machine, and of a disc coverer with soil deflectors. The subject of research is the process of oriented planting and embedding of seed onion bulbs into soil. The article considers the process of bulbs orienting during planting and their orientation maintaining during interaction with the soil, taking into account the regularities of bulbs motion by means of vibrating chute and pneumatic drum, as well as the work of coverers during covering of bulbs with soil. The research is done on the basis of laws of classical mechanics and Lagrange's equations of the second kind. Theoretical studies of the working process of vibration and pneumatic planting unit of a bulb-planting machine are carried out. As a result, analytical dependences are obtained for determination of its design and operational parameters: the groove radius, the distance between chute and groove bottom, the diameter of suction opening, the rotation speed of pneumatic drum, the height of planting unit installation above the soil level. The studies allowed to determine: the condition of oriented embedding of bulbs into furrow with bulb stem pointing downwards; the analytical dependences for determining the trajectory of soil particles motion on the working surface of deflector of a disc coverer; the equation of soil particles motion after detachment from deflector’s surface, during covering with soil of bulbs oriented in furrow with bulb stem pointing downwards; the equations of relative, transfer and absolute velocities of soil particles. The expressions are obtained that allow to determine the technological parameters of disc coverer with soil deflectors: the forward velocity of disc coverer, the angle of attack, the center distance between discs.