Перегляд за Автор "Tarelnyk N."

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  • Документ
    Constructing a Model of the Axis Form in a S-Shaped Riser of a Cultivator Paw
    (Eastern-European Journal of Enterprise Technologies, 2024) Pylypaka S.; Hropost V.; Volina T.; Kalenyk Mykhailo Viktorovych; Ruzhilo Z.; Dieniezhnikov Serhii Serhiiovych; Tarelnyk N.; Tatsenko O.; Semirnenko S.; Motsak Svitlana Ivanivna; Пилипака С.; Хропост В.; Воліна Т.; Каленик Михайло Вікторович; Ружило З.; Дєнєжніков Сергій Сергійович; Тарельник Н.; Таценко О.; Семірненко С.; Моцак Світлана Іванівна
    When cultivating the soil, a force of resistance to the movement of cultivator paw acts on it. It has a variable value and causes a moment of force applied to the riser of the paw. Under the action of the moment, the elastic axis of the riser changes its shape. This affects the position of the paw in the soil. The form of an S-shaped riser whose elastic axis consists of two circle arcs has been considered in this study. During cultivator operation, one part of the riser bends, increasing the curvature of the elastic axis, and the other, on the contrary, unbends, that is, its curvature decreases. The modeling of the shape of the elastic axis of the paw riser is based on the theory of resistance of materials, according to which the curvature of the elastic axis of the cantilevered band is directly proportional to the applied moment and inversely proportional to its stiffness. If the shape of the cross-section of the riser along its entire length is unchanged and the properties of the metal are also the same, then the stiffness is constant. In the case of small deflections of the band, the linear theory of bending is used, but the deflections in the riser are significant, so the nonlinear theory has been used for this case. At the same time, it is taken into account that the elastic axis of the riser already has an initial curvature, the sign of which changes after passing through the point of connection of the component arcs. To model the shape of the elastic axis of the S-shaped paw riser, the deformation of the arcs of the circles that form this paw was calculated separately. Numerical integration methods were used to find the shape of the deformed elastic axes of both parts of the riser. They were connected into a whole and a deformed elastic axis of the S-shaped riser was obtained. Two variants of the riser with different lengths of their elastic axis, but the same height and the same angle of entry into the soil, were considered. The combination of the component arcs of the riser shows that, under the action of the same force, the deviation from the specified movement depth for one riser is 2 cm, and for the other – 4 cm
  • Документ
    Constructing Geometrical Models of Spherical Analogs of the Involute of a Circle and Cycloid
    (Eastern-European Journal of Enterprise Technologies, 2023) Nesvidomin A.; Pylypaka S.; Volina T.; Kalenyk Mykhailo Viktorovych; Shuliak I.; Semirnenko Y.; Tarelnyk N.; Hryshchenko I.; Kholodniak Y.; Sierykh L.; Несвідомін А.; Пилипака С.; Воліна Т.; Каленик Михайло Вікторович; Шуляк І.; Семірненко Ю.; Тарельник Н.; Грищенко І.; Холодняк Ю.; Сєрих Л.
    The common properties of images on a plane and a sphere are considered in the scientific works by scientists-designers of spherical mechanisms. This is due to the fact that the plane and the sphere share common geometric parameters. They include constancy at all points of the Gaussian curve, which has a zero value for a plane and a positive value for a sphere. Figures belonging to them can slide freely on both surfaces. With unlimited growth of the radius of the sphere, its limited section approaches the plane, and the spherical shape transforms into a plane. Thus, a loxodrome that crosses all meridians at a constant angle is transformed into a logarithmic spiral that intersects at a constant angle the radius vectors that come from the pole. The tooth profile of cylindrical gears is outlined by the involute of a circle. A spherical involute is used for the corresponding bevel gears. Other spherical curves are also known, which are analogs of flat ones. The formation of a cycloid and an involute of a circle are associated with the mutual rolling of a line segment with each of these figures. If the segment is fixed and the circle rolls along it, then the point of the circle describes the cycloid. In the case of a stationary circle along which a segment is rolled, the point of the segment will execute the involute. To move to the spherical analogs of these curves, it is necessary to replace the circle with a cone, and the straight line with a plane. The spherical prototype of the cycloid will be the trajectory of the point of the base of the cone, which rolls along the plane, that is, along the sweep of the cone. The sweep of a cone is a sector, the radius of the limiting circle of which is equal to the generating cone. If this sweep, like a section of a plane, is rolled around a fixed cone, when its top coincides with the center of the sector, then the point of the limiting radius of the sector will execute a spherical involute. This paper analytically implements these two motions and reports the parametric equations of the spherical analogs of the circle involute and the cycloid