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Typically, in the technological processes of agricultural production, machines and equipment are used, where self-loading containers, bunkers, operating on the principle of natural gravitational leakage of friable, grain materials are used for transportation or overload of bulk materials. But the use of such components is justified only for use in the process of harvesting maize ears in the swaths and provided that the start is fed to the collecting hopper of the combine harvester, and after filling it is overloaded in the technological transport by the principle of “dump truck”. When trying to go beyond these limitations to increase transportation or overload of bulk materials, there are objective difficulties that arise from the freezing and sticking of the bulk material in the absence of the gravitational leakage phenomenon. As part of the study described in this article, an analytical description of overcoming these difficulties is proposed. It is based on the fact that the analytical equations of motion of a grain mixture, such as quasi-liquids, allow taking into account the bunker’s turn around the fastening axis during unloading of the grain mixture. This analytical approach allows us to further substantiate the kinematic parameters of self-propelled bunkers of harvesting machines. The mode of the technological process of unloading the dump of the hopper with grain material with a minimum unloading time is analyzed. This means that the obtained scientific result in the form of the equation of motion of a grain mixture, as quasi-liquids, on a sloping plane is interesting from the theoretical point of view. From the practical point of view, the analytical equations of motion of the grain mixture, such as quasi-liquids, allow us to determine the conditions of use of combine harvesters in the technology of plant production. Thus, the applied aspect of using the obtained scientific result is the possibility of improving the typical technological process of harvesting agricultural crops. This is a prerequisite for the transfer of technological solutions to agro-industrial production.

Mathematical modeling of grain mictures in optimatization tasks of the dump bunker’s kinematic parameters