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A mathematical model of root crops after-cleaning and their movement pattern in a technological run for loading into means of transportation has been presented. The impact of both controlled and uncontrolled factors on the efficient continuous transportation of root crops has been determined on the basis of the above-mentioned model. The use of the suggested mathematical model will enable to narrow the search of the most efficient design, kinematic and dynamic parameters in conducting some experimental research on efficient operation of after-cleaning systems of harvesters with their possible adjustment according to the natural and climatic conditions of harvesting. Keywords: mathematical model of root crops after-cleaning, root crops movement pattern, transportingseparating system, design, kinematic and dynamic parameters of tools.Серия Математика . № 4(96)/2019

The paper covers theoretical substantiation of the rational parameters of a horizontal conveyer-cleaner of sugar beets providing their minimum loss during process performance. The procedure of conducting experimental investigations on the developed design of a horizontal conveyer-cleaner of root crops in configuration with a root crop harvester is presented. The results of the experimental research on determining root crop loss, damage and impurity depending on the design and kinematic parameters of a cleaner are provided. In order to choose the rational parameters, specific recommendations are provided.

The scheme of arrangement of grooves of partially regular microrelief of type II shifted by 0.5 angular pitch is considered. Such grooves are formed by vibration on end faces of rotary bodies. An analytical dependence was obtained to determine the relative area of a partially regular microrelief depending on the geometric parameters of V-shaped grooves. The parameters of the grooves of a partially regular microrelief formed at different distances from the center of rotation are determined, at which the value of the relative area of the partially regular microrelief formed on the treated surface will be stable.

The results of an elastic sectional screw operating tool development and its production technique are presented in the article under consideration. The operating tool has been made to fix the elastic sections, providing the transportation of bulk materials of agricultural production, in order to ensure their minimal damage and the process minimal power capacity. The article presents constructed regression dependencies and response surfaces for the effects of the design, kinematic and technological parameters of a sectional screw operating tool on power consumption and the damage rate of grain material in the process of its transportation. As the result of the conducted experimental research, authors came to a conclusion that the arrangement of an elastic auger without a gap between its peripheral part and the inner surface of the guiding tube significantly reduces vibrations in the process of conveying bulk material.

The article presents the results of analysis of modern literature sources in search of mathematical models describing the dynamics of the process of forming regular microrelief on the inner cylindrical surfaces of parts operating in difficult conditions, in order to increase their life cycle. The absence of mathematical models describing this process and the peculiarities of its implementation with the point action of the deforming element on the surface of the body part are established. The movements of the tool during the process of forming a regular microrelief on the inner cylindrical surface of the body of the part are considered and the driving forces that follow this process are analyzed. Based on the results of the analysis, a mathematical model of the dynamic process of forming regular microrelief on the inner cylindrical surface of the body of the part was developed. The peculiarity of this process is that microrelief is formed by concentrated force, the point of application of which is constantly changing in the radial and axial directions relative to the part. Therefore, the mathematical model that describes this process will have a discrete right-hand side. It is proposed to model such an action using Dirac delta functions with linear and temporal variables, using the method of regularization of these features, in particular, existing methods of integrating the corresponding nonlinear mathematical models of torsional vibrations of a part. Analytical relations describing these vibrations in the process of forming a regular microrelief are obtained. Using Maple software 3D changes in torsion angle depending on different values of the source data are constructed. The conducted research will allow to consider torsional oscillations that is crucial for long cylindrical details, such as sleeves of hydraulic cylinders, parts of drilling mechanisms and others.