# 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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- 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.
- ItemModeling of elastic state for two joined dissimilar semi-infinite plates with crack under the action of pressure on the shores of the crack(Lviv Politechnic Publishing House, 2019) Zelenyak Volodymyr; Kolyasa LiubovPurpose. A two-dimensional mathematical model for the problem of elasticity theory on joined dissimilar elastic half-planes containing rectilinear crack under the action of mechanical efforts on the shores of a crack is examined. As a consequence, the intensity of stresses in the vicinity of tops of the crack increases, which significantly affects strength of the body. This may lead to the growth of a crack and to the local destruction of a structure. Such a model represents to some extent a mechanism of destruction of the elements of engineering structures with cracks, we determined stress intensity factors (SIF) at the tops of the crack, which are subsequently used to determine critical values of the normal pressure on the shores of the crack. Therefore the aim of present work is to determine the two-dimensional elastic state in joined dissimilar half-endless plates containing a rectilinear randomly-oriented crack under conditions of power load on the shores of the crack. This will make it possible to determine critical values of mechanical load on the shores of a crack in order to prevent crack growth, which will not allow the local destruction of the body. Methodology. The methods of studying two-dimensional elastic state body with crack as stress concentrators based on the function of complex variable method by which the problem of stationary elasticity are reduced to a SIF of the first kind, a numerical solution which was obtained by the method of mechanical quadratures. Findings. In this paper, two-dimensional mathematical model in the form of singular integral equations on the contours of cracks in order to determine perturbed power stresses due to the presence of cracks are obtained; numerical solutions to singular integral equations of the problem of elasticity theory for a specified region under the action of normally distributed pressure on the shores of the crack are found; stress intensity factors at the tops of a crack and to detect the effects of mechanical character are identify and explored. Graphical dependences of SIF, which characterize distribution of the intensity of stresses at the tops of a crack, on the angle of crack inclination and elastic characteristics of half-planes is obtained. This makes it possible to analyze the intensity of stresses in the vicinity of a crack's tops depending on the geometrical and mechanical factors, as well as to determine the limit of permissible values of normal pressure on the shores of the crack at which the growth of the crack starts, as well as the local destruction of the body. It is shown that the proper selection of elastic characteristics of the components of joined dissimilar half-planes can help achieve an improvement in the strength of the body in terms of the mechanics of destruction by reducing SIF at the crack's tops. Originality. Scientific novelty lies in the fact that the solutions of the new two-dimensional problems of elasticity for a specified region ( joined dissimilar half-endless plates containing a rectilinear randomly-oriented crack ) under the action of normally distributed pressure on the shores of the crack are obtained. Practical value. Practical value of the present work lies in the possibility of a more complete accounting of actal stressed-strained state in the piecewise-homogeneous elements of a structure with cracks that work under conditions of different mechanical loads. The results of specific studies that are given in the form of graphs could be used when designing rational operational modes of structural elements. In this case, the possibility is obtained for preventing the growth of a crack through the appropriate selection of composite's components with the corresponding mechanical characteristics.
- 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.
- 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.
- 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.
- 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.
- ItemThe influence of metal oxide powders on the physical and mechanical properties of epoxy composites for the protection of constructions made of aluminum alloys(Lviv Politechnic Publishing House, 2019) Savchuk Petro; Matrunchyk Dmytro; Kashytskyi Vitalii; Sadova Oksana; Moroz IrynaProtection of designs of vehicles made of aluminum alloys is an urgent application problem because these alloys are being extensively destroyed under the influence of aggressive environments, climatic factors, cyclic changes of temperature, the influence of the flow of abrasive particles. The protective coating increases significantly duration of operation of the construction and reduce the number of overhaul operations associated with restoring the surface of the product. However, there is a problem associated with the complexity of the coating technology on the constructions made of aluminum alloys, because these surfaces are inert due to the presence of oxide films. To ensure reliable protection of the surface of the construction, it is necessary to provide high adhesion strength of coating with substrate, cohesive strength and corrosion resistance of the coatings. An effective solution to this problem is the use of polymer coatings based on epoxy resins, characterized by high adaptability, specific strength, high operated properties. The use of epoxy oligomers as a polymeric matrix allows you to meet the requirements, however, it requires the development of composition of epoxy composite material and coatings technology. The purpose of the work is determination of the influence of highly dispersed powders of metal oxides on the structuring process and mechanical characteristics of epoxy omposites, and optimization of the composition for the formation of protective coatings of construction made of aluminum alloys. The classical methods of research of physical and mechanical characteristics of epoxy composites are used in the work: the gel fraction content, adhesion strength, compressive strength, impact energy. The optimum content of titanium oxide powder is found to be 8 wt % because these epoxy composites have the highest impact energy compared to composites having a different stoichiometric ratio of components. Considerable increase in impact energy of epoxy composites take place as a result of treatment of the composition at the mixing stage of the components with ultrasound, which ensures high uniformity of the composition and the lyophilicity of the powder particles. The developed coatings have increased adhesion strength, impact energy and compressive strength, which ensures their use as coatings of designs of vehicles made of aluminum alloys for protection against climatic conditions, abrasive wear and corrosion. A promising area of research is the introduction of modifying additives into the epoxy composites developed to increase their resistance to cyclic change of temperature and the application of treatment of the compositions in physical fields to ensure the high uniformity of the composition and increase the lyophilicity of the powder particles.
- ItemTheory and practice of obtaining composite materials based on polymer blends(Lviv Politechnic Publishing House, 2019) Shixaliyev Karam; Abbasov Ibrahim; Sadig KhaverThe regularities of the thermodynamic compatibility of various industrially produced polyolefins and heterochain polymers and the possibility of obtaining composite materials based on their mixtures with significantly increased performance properties based on existing production facilities and process equipment have been identified. The methods have been developed for the chemical and physical modification of individual polymers, their mixtures to improve the performance properties of composite materials; including the method of modification of polyethylene, which made it possible to significantly increase its thermal stability in air and in vacuum, anti-corrosion properties. The effectiveness of the use in composite materials of the petroleum resin PPC intended to produce the products operated under conditions of increased mechanical wear, temperatures, pressures and deformations. Developed composite materials based on mixtures of PVC, TPU, CCPE+PVC, CCPE+PU, LDPE+BR, technology of their manufacturing and processing, application of new efficient products with extreme operating conditions: injection molded tires for agricultural machines, casing stabbing baskets, nuclear magnetic logging probes, scrapers and bucket elevators, sealing rings for pneumatic radiators, indented surface of the grain cleaning machines.