Mathematical model of movement and cleaning beetroots from soil lumps with spiral separator

An urgent problem in the technological process of table beet production is cleaning of the root crops from adhering soil, soil impurities and plant residues after digging them out of the soil. Therefore, it is necessary to develop new, more advanced designs of beet heap separators that could provide not only high quality cleaning but also eliminate damage and loss of the root crops when performing this technological process. A new design of a spiral separator has been developed, which, based on the results of preliminary experimental studies, satisfies the above requirements. Therefore, it is necessary to conduct fundamental theoretical investigations to substantiate the rational parameters of the specified separator. The purpose of this research is to determine the design and kinematic parameters of an improved design of the spiral separator for the table beet roots, ensuring high-quality cleaning of the root crops from the soil impurities and plant residues, based on the development of a mathematical model of the movement of the root crops along the working surface of the separator. An equivalent diagram of the interaction of the beet root as a material particle, located in the working channel, formed by three cantilever-mounted spirals, has been constructed. The separator spirals are driven into rotational motion and, at the same time, can oscillate in a vertical plane under the impact of the variable mass of the beet heap, supplied to the working surface. Based on an equivalent circuit, a system of differential equations for the movement of the beet root along the surface of the working channel has been compiled. The solution of the resulting system of differential equations makes it possible to study the influence of the design and kinematic parameters of the separator on the speed of movement of the root crop in the working channel before it leaves the spirals. By determining the design and kinematic parameters in this way it will ensure improved quality of cleaning the beet roots from the soil impurities and plant residues.