Mathematical model of the movement of a potato body along the surface of a spiral separator

The potato is grown in over one hundred countries spread over all latitudes, with the most diverse climatic conditions, from the areas near the Arctic Circle to the southern end of the South American continent. The potato is an irreplaceable component of the food tradition of many countries and is the most cultivated species after cereals (wheat, rice and corn). The authors set up and developed a new clod and rubbish spiral separator for potatoes, which is protected by the patent of Ukraine. The operation modalities of this machine are briefly described in the paper. The aim of this study is the development of a mathematical model concerning the movement of a potato body along the surface the spiral separator. In particular, equations are found for determining the coordinates of the position of a potato tuber on the surface of a spiral separator depending on the parameters of the spiral (spiral line) and the size of the tuber. Furthermore, the velocity of tuber movement in the stream formed by the surfaces of two neighboring spirals in the direction of the horizontal, vertical and longitudinal axis are determined. The results of this study will be used in the future to analytically considering the dynamics of movement of a potato tuber on the surface of a spiral separator, taking into account the conditions that exclude its damage.