MATHEMATICAL MODEL OF THE MOVEMENT OF TABLE BEET ROOT CROP ALONG THE SPIRALS OF A VIBRATING CLEANER

A pressing issue in the technological process of table beet production is the cleaning of root crops from adhered soil, loose impurities, and plant residues after harvesting. The efficiency of this process significantly determines the quality of the final product, its suitability for long-term storage, and subsequent processing. Modern root crop cleaning technologies widely use mechanical methods, among which vibrational and spiral cleaning systems hold a special place. However, many existing designs have several shortcomings, such as insufficient impurity removal efficiency or an increased risk of root crop damage. This study presents a new design of a vibrational spiral cleaner developed to enhance the efficiency of table beet root cleaning. A mathematical model of the root crop's movement along the working channel of the cleaner was constructed to analyze and optimize the operation of this design. It is during this movement that adhered soil, loose impurities, and plant residues are removed. Based on the developed equivalent scheme, a system of differential equations describing the dynamics of the root crop's movement along the surface of the working channel was formulated. Numerical solutions of this system on a personal computer made it possible to study the influence of structural parameters (spiral geometry, pitch, and material) and kinematic parameters (vibration frequency and amplitude) on the speed of root crop movement and the cleaning quality. The analysis of the obtained results showed that optimizing the cleaner's parameters ensures uniform cleaning, reduces the likelihood of root crop damage, and increases the overall process efficiency. The results of this research have practical significance for the further improvement of cleaner designs and their implementation in industrial technologies. The application of the proposed technical solutions will contribute to improving the cleaning quality of table beet root crops, enhancing production efficiency, and reducing equipment maintenance costs.