Перегляд за Автор "Hryshchenko I."

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  • 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
  • Документ
    Construction of Mathematical Model of Particle Movement by an Inclined Screw Rotating in a Fixed Casing
    (Eastern-European Journal of Enterprise Technologies, 2023) Volina T.; Pylypaka S.; Kalenyk Mykhailo Viktorovych; Dieniezhnikov Serhii Serhiiovych; Nesvidomin V.; Hryshchenko I.; Lytvynenko Ya.; Borodai A.; Borodai D.; Borodai Ya.; Воліна Т.; Пилипака С.; Каленик Михайло Вікторович; Дєнєжніков Сергій Сергійович; Несвідомін В.; Грищенко І.; Литвиненко Я.; Бородай А.; Бородай Д.; Бородай Я.
    Screw conveyors are used to move bulk materials vertically upwards, horizontally, and at an angle to the horizon. The processes that take place when particles are moved by a screw conveyor in vertical and horizontal directions have been studied. There is a significant difference between them: for transportation in the vertical direction, the necessary conditions must be ensured (sufficient angular speed of rotation of the screw), and for horizontal transportation, the movement of the particle occurs at any angular speed of rotation of the screw. Therefore, when changing the inclination of the axis of the screw, there comes a moment when transportation becomes possible, while it was impossible in the vertical direction. This paper considers the movement of a particle under the condition that it simultaneously contacts two surfaces: the moving surface of the screw and the stationary surface of the cylindrical casing in which the screw rotates. Their common line along which the particle slides is a helical line – the periphery of the screw. The particle slides along the helical line of the rotating screw, i.e., it is in relative motion with respect to it. At the same time, it slides along the surface of the casing, relative to which it is in absolute motion. The trajectory of the particle’s absolute motion is its sliding track on the casing surface. When constructing differential equations of the relative motion of particles, the forces applied to the particle were taken into account. The initial position was taken to be the vertical direction of the screw to transport the particle upwards. If an auger in a cylindrical casing is tilted from the vertical direction to a certain angle, then all applied forces (except the force of weight) will also tilt to this angle. On the basis of this, generalized differential equations of the relative motion of a particle during its transportation by an inclined screw were built. They made it possible to derive a generalized mathematical model of the movement of a particle by an inclined screw that rotates inside a fixed casing.
  • Документ
    Determining the Shape of a Flexible Thread in the Field of Horizontal and Vertical Forces
    (Eastern-European Journal of Enterprise Technologies, 2024) Volina T.; Pylypaka S.; Nesvidomin V.; Kalenyk Mykhailo Viktorovych; Spirintsev D.; Dieniezhnikov Serhii Serhiiovych; Hryshchenko I.; Rebrii A.; Herashchenko T.; Soloshchenko Viktoriia Mykolaivna; Воліна Т.; Пилипака С.; Несвідомін В.; Каленик Михайло Вікторович; Спірінцев Д.; Дєнєжніков Сергій Сергійович; Грищенко І.; Ребрій А.; Геращенко Т.; Солощенко Вікторія Миколаївна
    In theoretical mechanics, the equilibrium of a flexible, inextensible thread is considered, to which the tension force of its ends and the distributed force of weight along the length of its arc are applied. An unsolved problem is finding the shape of the thread under the action of other distributed forces. This study has considered the equilibrium of a completely flexible thread, to which, in addition to this force, a transverse distributed force is applied. A sail serves as an example. Wind of equal intensity in the plane of the orthogonal section of the sail can be considered a distributed force. The sail can be cut into narrow strips with the same shape of the curves of the cross-section, which are equal to the cross-section of the sail as a whole. The theory of flexible thread is applied in the current study. The task is reduced to finding the curve of the cross-section of the sail. The object of research is the formation of a cylindrical surface from a flexible thread under the action of distributed forces applied to it. An important characteristic of the shape of a flexible thread is its curvature. Its dependence on the length of the arc was found and it was established that the found curve is a chain line (catenary). This is the feature of the current research and its distinguishing characteristics. The significance of the results stems from the derived analytical dependences, according to which the change in the ratio between the distributed forces acting on the flexible thread deforms it, but it retains the shape of the catenary. At the same time, the angle of deviation of its axis of symmetry from the vertical changes. In the absence of a horizontal distributed force and the presence of only a distributed force of weight, the axis of symmetry of the chain line is directed vertically – at an angle of 90° to the horizontal. If they are equal, this angle is 45°. Scope of application includes structures with stretched supporting wires, conveyor belts, flexible suspended ceilings, the shape of which can be calculated by using our results.