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The article presents the results of resonant oscillations theoretical research of the telescopic screw granular material system caused by external periodic forces. In the theoretical part a mathematical model of bending vibrations of an elastic body is described, which rotates along a fixed axis with a constant angular velocity, provided that it moves with a constant relative linear velocity along the elastic body. In the experimental part, according to the obtained equations, it has been established for the various kinematic characteristics of the system, a telescopic screw-granular media of amplitude passing through resonance at the frequency of external periodic perturbation.The results of experimental research and recommendations for the selection of constructive kinematic for telescopic screw conveyor have been presented. РЕЗЮМЕ У статті наведено теоретичні дослідження резонансних коливань системи телескопічний гвинт – сипкий матеріал зумовлених зовнішніми періодичними силами. В теоретичній частині описано математичну модель згинальних коливань пружного тіла, яке обертається вздовж нерухомої осі із сталою кутовою швидкістю за умови, що вздовж нього рухається зі сталою відносною лінійною швидкістю. В експериментальній частині відповідно до отриманих рівнянь, представлено для різних кінематичних характеристик системи телескопічний гвинт – сипке середовище амплітуду проходження через резонанс на частоті зовнішнього періодичного збурення. Представлені результати експериментальних досліджень та наведені рекомендації для вибору конструктивно-кінематичних телескопічних гвинтових транспортерів. INTRODUCTION One of the premises for the high efficiency of machine-building enterprises is to improve the existing and to introduce new competitive products, which can fully meet the needs of consumers. Screw transport mechanisms are one of the most commonly used mechanical means in agricultural production and other sectors of the economy as individual elements, as well as in other machines. According to various data, their specific gravity in loading and unloading operations of different types is 40-45%. They are especially widely used as elements of agricultural machines when overloading agricultural loads in the field conditions. Often, the universal units for loading seeders, hoppers, reloaders and combine harvesters are complicated (the term is used for composition and decomposition) in order to obtain a significant material overload path. To achieve the required overload distance, they are decomposed composed with the use of hydraulic or pneumatic equipment. This makes their constructions too complicated and expensive. The examples are the universal hoppers-reloaders of the companies “EGRITECH”, “Liliani MBA”, combine harvesters CASE 8120 AXIAL FLOW, New Holland CR10.90 and others. Therefore, using the telescope principle will have widespread use in the design of agricultural machinery equipped with screw conveyors. Despite a large number of scientific works devoted to the development and research of the features of screw conveyors operation, there is a wide range of unexplored issues related to their constructive and 1 Hud V.Z., Assoc. Prof. PhD. Eng.; Rogatynskyi R.M., Prof. PhD. Eng.; Hevko I.B., Prof.PhD.Eng.; Lyashuk O.L., Prof.PhD.Eng.; Pіk A.I., Assoc. Prof. PhD. Eng.; Huryk O.Y., Assoc. Prof. PhD. Eng. Vol. 60, No. 1 / 2020 INMATEH – 30 functional characteristics. Therefore, the development of telescopic screw conveyors makes it possible to improve the efficiency of the overload of loose materials. However, due to the significant angular velocities of the screw rotation in telescopic screw conveyors, the asymmetry of the telescopic screw and external perturbations, fluctuations often occur, which result in significant dynamic loads in the screw (Hevko I.B., 2013; Lyashuk O.L., et al., 2016), especially in resonant cases. The works of Lyashuk O.L. et al. (2018) show the movement of the grain mixture along the working body of the loader. Differential equations are obtained that describe the bending fluctuations of the horizontal screw of the mixer loader. The results of theoretical and experimental studies of simultaneous transportation and mixing of feed mixtures components on the curved lines of tubular conveyors are presented. A mathematical model is constructed that characterizes the dependence of the change of elementary work, which is performed when the elemental mass of loose material moves along the curvilinear region (Hevko R.B., et al., 2018). The method of carrying out researches on determining the power indicators of different movement types of loose materials is presented. Therefore, the study of dynamic loads in the screw of a telescopic conveyor during the movement of loose material enables to choose the rational modes of operation of the conveyor, which minimize these negative phenomena and increase the life of exploitation of telescopic screw conveyor. MATERIALS AND METHODS To study the principle of telescopes in screw conveyors based on a patent search and analysis of scientific literature and synthesis (Rogatynsky R.M., et al., 2014), a pilot installation has been developed, designed, manufactured and shown in Figures 1 3.

RESEARCH ON RESONANT OSCILLATIONS OF THE TELESCOPIC SCREW – GRANULAR MEDIA SYSTEM CAUSED BY EXTERNAL PERIODIC FORCES