The theory of cleaning the crowns of standing beet roots with the use of elastic blades

ArticleA standing beet root crown cleaner has been designed. The design comprises the vertical drive shaft that carries two flat elastic cleaning blades installed on axes and connected through the articulated connection. The aim of the study was to develop the new theory of cleaning the crowns of standing roots with the use of an elastic blade installed on the vertical drive shaft in order to determine its optimal design and kinematic parameters. The first step was to design an equivalent schematic model of the interaction between the elastic cleaning blade installed on the vertical drive shaft and the spherical surface of the beet root fixed in the soil. The interaction between the blade and the root's crown took place at the point, where all the forces that can arise during such interaction are applied. A three-dimensional coordinate system was set and the design and kinematic parameters of the considered interaction were designated. Using the original differential equations projected on the set coordinate axes, the system of four nonlinear differential equations of the three-dimensional motion of the elastic cleaning blade on the spherical surface of the root crown was set up, then it was transformed into the system of two differential equations in the normal form. Further, to determine the force that strips off the remaining haulm, which is part of the obtained system of differential equations, the problem of its analytical determination was solved separately. Also, the additional equivalent schematic model of the interaction between the elastic blade as a cantilever beam and the root's crown was designed, the differential equation of the beam's deflection curve (taking into account the beam's simultaneous bending and twisting) was set up and, on the basis of it, the projections of the stripping force on the coordinate axes were found. The values of the force were substituted in the earlier obtained system of differential equations