# Ukrainian Journal of Mechanical Engineering And Materials Science. – 2019. – Vol. 5, No. 2

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Науковий журнал

Засновник і видавець Національний університет «Львівська політехніка». Виходить двічі на рік з 2015 року.

**Ukrainian Journal of Mechanical Engineering and Materials Science = Український журнал із машинобудування і матеріалознавства : науковий журнал / Lviv Politechnic National University ; editor-in-chief Oleksiy Lanets . – Lviv : Lviv Politechnic Publishing House, 2019. – Volume 5, number 2. – 84 p. **

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- ItemStructural and kinematic analysis of pantograph-type manipulator with three degrees of freedom(Lviv Politechnic Publishing House, 2019) Korendiy Vitaliy; Zinko Roman; Cherevko YuriiProblem statement. The processes of development and improvement of autonomous mobile robots are significantly constrained because of the lack of an open-access comprehensive scientific and theoretical framework for calculating and designing of autonomous mobile robotic systems Purpose. The main objective of the paper consists in carrying out kinematic analysis and motion simulation of pantograph-type manipulator with three degrees of freedom. Methodology. The method of closed vector loops is used for deriving the equations of motion of the robot’s manipulator. In order to perform simulation (virtual experiment), the 3D-model of the robot was designed in SolidWorks software. Findings (results). The motion equations of the pantograph-type manipulator are derived, and the graphical dependencies describing the trajectories (paths) of the gripping device are constructed. In order to substantiate the correctness of the derived equations, and of the presented laws of the gripper motion, the corresponding 3D-model of the robot was designed and investigated in SolidWorks software. Scopes of further investigations. In the present paper, there are analysed kinematic parameters of the manipulator motion. While carrying out further investigations, it is necessary to perform its dynamic analysis taking into account all the forces acting upon the elements of the robot, as well as the influence of drives. This will allow to catty out the optimization synthesis of the robots structure, namely the geometrical parameters of the mechanism, operational parameters of drives, etc.
- ItemCalculation of strength of heated curvilinear bar structural elements of tubular cross-sections(Lviv Politechnic Publishing House, 2019) Voytovych Mykola; Velychko Lev; Lampika Roman; Lishchynska KhrystynaPractical importance. The analytical and numerical results obtained can be used in the study of the stress state and, respectively, to evaluate the strength and stiffness of curvilinear tubular structural elements, in particular, the pipeline bends and pipes of economizers. The purpose. Investigation of the temperature field and the thermoelastic state of the curvilinear rod with a tubular cross-section caused by it; analysis of the influence of geometrical and thermophysical parameters on the characteristics of its temperature field, as well as on the forces and moments in it. The research method. The object of research is the curvilinear rod with a tubular crosssection, which is in the conditions of convective heat exchange with the external and internal environments. The thermal conductivity equation for a large curvature rod was used to describe its temperature field. For determining the characteristics of the stress-strain state due to the described temperature field, the equations of thermal elasticity of curvilinear rods in displacements were used; the case was analyzed when radial and tangential displacements are absent in the extreme cross sections of the curvilinear part of the rod, and there are no turns of these cross-sections. Results. The studies have shown that the specific coefficients of heat transfer of the outer and inner surfaces of the rod affect its stress state in a different way; as the heat transfer coefficient from the outer surface increases, the absolute values of the longitudinal and transverse forces, as well as of the bending moment, decrease, and with the increase of the heat transfer coefficient from the inner surface, they increase. In contrast to the stress problem, in the case of heating, the value of the bending moment in a certain cross-section of a curvilinear rod depends on the geometrical parameters of the cross-section. The scientific novelty. Analytical-numerical method shows for the first time that there is such a cross-section in which the heat-induced bending moment changes its sign; the position of this cross-section depends on the curvature of the axis, the thickness of the wall, the bend angle of the curvilinear part of the rod and practically does not depend on the specific coefficients of heat transfer from its inner and outer surfaces. There are values of the bend angle at which the bending moment and transverse force in the curvilinear part of the rod reach their maximums.
- ItemSolution of the equation of force of impact of solids expressed by the ateb-sine(Lviv Politechnic Publishing House, 2019) Olshanskiy Vasyl; Burlaka Volodymyr; Slipchenko MaksymAbstract. A nonlinear differential equation of the force of direct central quasistatic impact of elastic bodies bounded in the area of their contact by rotation surfaces is compiled. To determine the coefficients of the equation and the order of its degree nonlinear force, we used the well-known solution of the axisymmetric contact problem of elasticity theory, constructed in due time by I. Ya. Shtaerman, for the case of dense static contact of bodies, when the order of their boundary surfaces is not lower than the second. In the case of the second order, it goes into the well-known static solution of G. Hertz, whose assumption in the theory of shock is also taken here in the formulation of the dynamics problem. A closed analytic solution of the composite differential equation with respect to the force of impact as a function of time is constructed. It is expressed through Ateb-sine. This function also describes the process of motion of the centers of mass of bodies in the stages of their compression and expansion. Compact formulas are derived for calculating the maximum values of the impact force, the approach of the centers of mass of the bodies and the duration of the impact. Thanks to the use of the Ateb-sine and its approximation by elementary functions, it was possible to obtain a fairly simple scan of the fleeting process of mechanical shock in time. It is shown that well-known dependencies that describe the impact of elastic balls follow from the derived formulas. Examples of calculations are given in which the influence of various factors on the main characteristics of the impact is investigated. It is noted that the theory set forth concerns only the impact of bodies with low velocities, when plastic deformation does not occur during their dynamic compression. To extend the theory beyond the limits of elasticity, it is necessary to determine a constant for the stage of compression in the impact force equation not by calculation, but by experimental method. Then, during compression and decompression of bodies, the impact force will be described by different analytical expressions, and the speed recovery coefficient will become less than one, which is consistent with practice.
- ItemSimulation of micro-cutting in the process of finishing anti-friction non-abrasive treatment(Lviv Politechnic Publishing House, 2019) Shepelenko Ihor; Tsekhanov Yuriy; Nemyrovskyi Yakiv; Posvyatenko Eduard; Eremin PavloThe influence of the shapes and sizes of microroughnesses on the creation of favorable conditions for micro-cutting of antifriction material by modeling the contact interaction of microroughnesses with the treated surface during the finishing antifriction non-abrasive treatment (FANT) is studied in the work. It is shown that the formation of the anti-friction coating FANT depends on the conditions of contact interaction of the tool with the treated surface, and the shape and size of the microroughness determine the quality of the resulting coating. In the study of FANT at the stage of micro-cutting, a similarity and dimension theory method was used, according to which cutters made of gray cast iron SCh20 were made, the geometry of the cutting part of which simulated a separate microroughness of the surface of the workpiece with different front cutting angles. As a contacting surface and coating material used brass L63. The micro cutting process is considered as a low-temperature process of deep plastic deformations with a predominance of a simple shear of the processed material in the chip formation zone according to the free orthogonal cutting scheme. A scheme for the interaction of microroughness with the treated surface is constructed with the friction-mechanical method FANT. It has been established that the cutting blade of a cast-iron micro-cutter wears out intensively in the process of interacting with a brass surface, and the process of changing the geometry of the tip of the cutter occurs in accordance with the principle of adaptability of the entire system of the cutter - the part according to which the minimum of micro-cutting energy is realized. It is proved that with a decrease in the cutting front angle, the blunting radius of the cutting edge increases, and the actual cutting depth and the volume of microchips decrease. Reducing the cutting front angle contributes to the strain hardening of the rubbed material, which reduces the chip formation process of the antifriction material. In order to intensify micro-cutting and obtain a high-quality FANT coating, single microroughnesses of the treated surface should have a cutting front angle γ ≥ 0°. The obtained experimental data and simulation results made it possible to present contact interaction diagrams of the tool with the surface being machined for various angles during FANT at the stage of microcuts, and also to establish the basic laws of their parameters. An analysis of the characteristic microcutting patterns in FANT by the friction-mechanical method made it possible to recommend the parameters of the initial surface microrelief, thereby creating favorable conditions for micro-cutting of the antifriction material and to improve the quality of the formation of the antifriction coating.
- ItemOptimization of geometric parameters of a semi-spheroidal solid oxide fuel cell anode using the 3d stress and strain distribution graphs(Lviv Politechnic Publishing House, 2019) Kuzio Ihor; Vasyliv Bogdan; Korendiy Vitaliy; Borovets VolodymyrThe purpose. Determination of radii ranges for cylindrical and convex (semispheroidal) parts of the solid oxide fuel cell (SOFC) semi-spheroidal shape anode based on stress and strain parameters calculated; comparison of 3D graphs of stress/strain distribution in anodes of proposed and spheroidal shapes; substantiation of the semi-spheroidal anode potential to withstand deformation and stress gradient under operational conditions. The research method. The object of research is a solid oxide fuel cell anode of a semi spheroidal shape loaded with a fixing pressure along the closed-loop fixing and with an external gas pressure applied to the anode working surface. Stress and strain distributions in the anode were calculated by finite element analysis using software for calculating three-dimensional tasks Mechanical Desktop 6 Power Pack. Three-dimensional (3D) dependences of stress/strain distribution in anodes of proposed and spheroidal shapes at a variety of R / Rc ratios were plotted. Based on these curves, 3D surfaces of stress distribution along the axis and closed-loop fixing of semi-spheroidal shape anodes were constructed. Results. Three-dimensional curves of the graphic intersections of the surfaces of stress distribution along the axis and closed-loop fixing of semi-spheroidal shape anodes, with their projections on three coordinate planes, were plotted. The curves display the values of balanced stresses depending on geometric parameters. Domains of these curves were also defined. The scientific novelty. The proposed method of building 3D surfaces of stress/strain distribution in anodes depending on their geometric parameters shows for the first time that there exists an area of geometric parameters that allows the appropriate stress level to be reached ensuing safe long-term operation of the semi-spheroidal shape anode. The domain of this area was graphically defined. Based on the plotted isolines showing levels of strain in anodes with the 0.5 mm, 1 mm, and 1.5 mm thick cylindrical parts and a variety of spheroid to cylinder radii ratios, an advantage of a semi-spheroidal shape anode over spheroidal one was substantiated. The practical value. The obtained calculation results and their 3D graphical interpretation can be used in the study of the stress state and, respectively, to evaluate the strength and stiffness of the anode supported SOFCs of various shapes.