## Development of mathematical model of plane-parallel movement of trailer harvesting machine

This paper presents the basic principles of building a mathematical model of trailer harvesting, for which an example of a trailed combine harvester is considered. To develop this mathematical model, all the components are given, starting with the assembly of an equivalent scheme of plane-parallel movement of this harvesting unit, which consists of a wheeled aggregate tractor of classic layout and trailed behind the combine. And behind the combine is attached a cart for the harvest. Differential equations of relative motion of the collecting unit are compiled and solved on the basis of the Lagrange equation of the second kind.

## Investigation the process of soil seeding during cleaning of rootbull fruits by spiral type cleaner

Cleaning of root crop bodies from impurities during their digging from the soil is a complex and energy-consuming technological process. Therefore, the development of new types of cleaners of root crop pile from impurities, in particular spiral type cleaners, allowing to intensify this process and improve the quality of cleaning is a step to successfully overcome this problem. The paper presents a study of the technological process of sifting soil particles during the cleaning of the heap of root crops with a spiral-type cleaner. In particular, a calculated mathematical model was constructed, which reflects the movement along the spiral of the body cleaner (soil particles) of variable mass. Using the differential equation of volume change, the differential equation of mass change, i.e. the mass that is sifted through the coils of the spiral cleaner was compiled. Based on the theoretical study, it was found that many factors influence the intensity of soil sifting on the spiral separator – the initial mass of particles, the design dimensions of the cleaner, frictional properties of the surface, angular parameters of body placement on the spiral surface and angular velocity of the spiral roller rotation, and the intensity of these parameters has been studied. Using PC, graphical dependences of the intensity of soil sieving on the angle of rotation of the cleaning spiral when changing the angular velocity of the spiral were constructed.