ItemClassical approach to determining the natural frequency of continual subsystem of three-mass inter-resonant vibratory machine(Lviv Politechnic Publishing House, 2019) Lanets Oleksii; Kachur Oleksandr; Korendiy VitaliyProblem statement. The three-mass vibratory system can be defined by five basic parameters: inertial parameters of the masses and stiffness parameters of two spring sets. Unlike the classical discrete system, the discrete-and-continual one consists of two rigid bodies connected by one spring set that form the discrete subsystem, and of the reactive mass considered as deformable (elastic) body characterized by certain stiffness and inertial parameters, which are related with one another. Purpose. The main objective of the paper consists in determining the first natural frequency of the continual subsystem of the three-mass discrete-and-continual vibratory machine. Methodology. While carrying out the investigations, it is used the classical theory of oscillations of straight elastic rods. Findings (results). The engineering technique of determining the first natural frequency of the continual subsystem of the three-mass vibratory machine is developed and approved by means of analytical calculations and numerical simulation. Originality (novelty). The optimal diagram of supporting the continual subsystem (elastic rod) is substantiated. The possibilities of exciting the vibrations of the three-mass discrete-and-continual mechanical system using the eccentric drive are considered. Practical value. The obtained research results and the developed calculation techniques can be used be engineers and designers dealing with various technological and manufacturing equipment that use vibratory drive. Scopes of further investiga tions. While carrying out further investigations, it is necessary to develop the model of combined discreteand-continual system of three-mass vibratory machine, and to carry out the numerical simulation of the system’s motion under different operational conditions. ItemModeling of “combined cutter - cone” connection in tricone drill bits(Lviv Politechnic Publishing House, 2019) Slipchuk Andrii; Kuk Andrii; Kusyi YaroslavA theoretical analysis of the stiffness of the “cutter-cone” connection was performed. In the article the character and magnitude of the tension at the contact of "cutter-cone" are investigated. An analysis of the surface of the openings for carbide inserts revealed traces of plastic deformation and fretting wear. Since the contact bond of the cutter with the body of cone is the only factor that provides the strength of the connection, let consider the effect of mechanical properties of the cones body and a cutter on the magnitude of the forces of contact and tension in the connection. The surface of the shaft of this design consists of equal parts of solid alloy and steel. If you make a ring at a smaller diameter of the shank of a carbide cutter, this will increase the reliability of the connection of the insertion with the body of the rock cutting tool, optimize toughness of cutter fastening, and ensure high stability of the hard-alloyed inset cutter before fracture. As a result of the conducted researches, a qualitative correlation between the hardness of the carbide insertion fastening in the holes of cone and the nature of the destruction of the carbide cutters has been established. Due to the conducted research, the character of the distribution of contact tensions in the conjugated areas “combined cutter - a hole of cone” was established. The theme of the development of new rational constructions of rock-destructive equipment of cones, rock-destructive inserts, schemes of its effective arrangement on the brushes of cone is still actual. A separate issue of further research is the study of functional and energy interaction of elements of propulsion and rock-destructive equipment. ItemDevelopment of the finishing and strengthening technological operations using SADT-technologies(Lviv Politechnic Publishing House, 2019) Kusyi Yaroslav; Lychak Oleh; Topilnytskyy Volodymyr; Bošanský MiroslavThe rational design of technological processes of parts manufacturing in single and small-scale production is inefficient without wide introduction of modern tools of part manufactu ring automation with modern computer-based equipment and software. It is desirable to carry out of automated synthesis of single route technological processes with minimal influence of the operator on the technological environment. The technology of computer-aided design of technological processes is used to develop effective algorithms of functioning of adapted systems for control of technological processes and their mplementation when taking into account interrelations with the technological environment. Automated development of technological environments of a given level of design concerning a dedicated technical system is possible on the basis of their rational functional models, created by means of CALS-technologies. The rational use of the SADT methodology with application of the principle of decomposition and development of the SADT-diagrams allows to solve the given technical problems. Therefore, the purpose of this paper is to develop and study the vibrational centrifugal surface strengthening at the finishing and hardening technological operation to provide the required quality parameters and operational characteristics of the parts. The object of this research is a finishing and hardening technological operation. The subject of this research is method and parameters of vibrational-centrifugal surface strengthening to provide the required quality parameters and operational characteristics of the parts. The development of SADT diagrams allows to divide the technological process to technological operations, cutter–setting positions, technological steps, main machining steps etc. In this paper the principles of control of technological operation for vibration-centrifugal strengthening of surfaces of parts are suggested. The experimental device for machining of inner surfaces of parts is described. The initial and detailed model of the operation of the vibrational-centrifugal strengthening is offered. Statistical and structural analysis of technological process made it possible to establish the influence of the parameters of the vibrational-centrifugal strengthening on the geometric and physical mechanical parameters of the surface quality and associated operational characteristics. Further research in that field will be related on the development of practical recommendations for using of the vibrational centrifugal surface treatment for improving of the geometric and physical and mechanical parameters of parts surfaces. ItemAnalysis and improvement of design diagrams and mathematical models of vibratory lapping machines(Lviv Politechnic Publishing House, 2019) Zakharov Viktor; Kuzio Ihor; Korendiy Vitaliy; Dmyterko PetroProblem statement. The development of energy-efficient and high-performance vibratory lapping machines demands the improvement of their design diagrams and calculation techniques. Purpose. The main objectives of this research consist in detailed analysis of existent design diagrams and mathematical models of vibratory lapping machines; designing the three-mass hanger-type structures of such machines providing circular oscillations of laps; derivation of differential equations describing the motion of their oscillatory systems. Methodology. The technique of the research is based on fundamental concepts of engineering mechanics, strength of materials and theory of mechanical vibrations. Findings (results). The improved design diagrams of vibratory lapping machines with circular oscillations of laps are proposed and the corresponding differential equations describing the motion of the working elements are derived. Originality (novelty). The mathematical model of circular oscillations of the three-mass mechanical oscillatory system of vibratory lapping machine is developed. The possibilities of performing the double-side lapping of cylindrical and prismatic parts are considered. Practical value. The results of the performed investiga tions can be used during creating new designs and improving existent structures of vibratory finishing machines for lapping flat surfaces of cylindrical and prismatic parts. Scopes of further investigations. In further investigations, it is necessary to perform the numerical modelling of the system’s motion using the derived differential equations, and to compare the obtained theoretical results with the results of experimental investigations. ItemDifferences of the effect of thermal treatment in an oxygen-containing gas medium on properties of the surface layer Ti, Zr, Hf(Lviv Politechnic Publishing House, 2019) Trush Vasyl; Fedirko Viktor; Luk’yanenko Aleksander; Stoev Petro; Tikhonovsky Mykhail; Kovtun KostiantynThe paper presents the characteristics of the surface layer of d-elements of the IV group (titanium, zirconium and hafnium) after thermal diffusion saturation from a controlled oxygen-containing gas medium. Saturation was carried out at T = 750 °C for t = 5 hours at different pressures (P = 1.33∙10–1 Pa, P = 1.33∙10–2 Pa, P = 1.33∙10–3 Pa). Experimentally revealed differences in the characteristics of the surface layer of titanium, zirconium and hafnium. It was shown that a hardened diffuse layer is formed with a higher hardness relative to the metal core in the reverse order of their affinity for oxygen. On titanium, zirconium and hafnium, only a diffuse layer is formed without a phase film. The appearance of the surface of the samples before and after processing is given. According to the results of the study, chemical-thermal treatment in an oxygen-containing gas medium leads to changes in the surface layer of sheet material from titanium, zirconium and hafnium. The state of the surface layers directly affects the characteristics of finished products, in particular, fatigue life. Therefore, this treatment is a good tool for controlling the state of the surface layers of the aforementioned metals, and then their properties. ItemMicrostructure and microhardness of nickel-base heat-resistant alloys obtained by directional and equilibrium crystallization(Lviv Politechnic Publishing House, 2019) Trostianchyn Andriy; Shvachko Serhii; Kulyk Volodymyr; Pleshakov Eduard; Molkov Yuriy; Lenkovskiy TarasIn order to determine the safe operational life of the components of gas turbine engines (GTE), introductory tests of nickel-base heat-resistant alloys (NHRA) have been performed. X-ray fluorescence and X-ray diffraction analyzes, optical microscopy and Vickers hardness measurements provided data on the phase-structural state and mechanical properties of the pristine ZhS6K-VI and ZhS32-VI alloys obtained by equilibrium and high-speed directional crystallization, respectively. Almost complete compliance of the investigated materials with the certified alloys in chemical and phase composition has been found. A significant difference in the parameters of the fragments of the microstructure of the investigated alloys, which is naturally consistent with the conditions of equilibrium and high-speed directional crystallizations, was revealed. A slightly lower anisotropy of microhardness (2.8 %), measured in transverse and longitudinal sections, was found in the ZhS6K-VI alloy as compared to the anisotropy (5.1 %) in the ZhS32-VI alloy. The obtained results will be used to test a nondestructive method for determining the safe operational life of gas turbine engine components. ItemDevelopment and investigation of device for processing polymer materials by 3d-printing method(Lviv Politechnic Publishing House, 2019)The analysis of the current state of 3d industry and prospects for its future. In the work, calculations were made and graphs of dependence were obtained, which influence the work of the auger and the installation itself. A new method of printing parts with polymer granules is described and the principle of operation of the equipment used is described. The picture of the working installation with the main components and the method of its attachment on a 3D printer is presented. The heating modes of the extruder itself are simulated and a thermal diagram of the device is shown, which accurately displays the temperature distribution across the sections. ItemMathematical modeling of stationary thermoelastic state in a half plane containing a periodic system of cracks due to periodic local heating by a heat flux(Lviv Politechnic Publishing House, 2019) Zelenyak Volodymyr; Kolyasa Liubov; Klapchuk MyroslavaPurpose. To determine the two-dimensional thermoelastic state in a semi-infinite solid (half-plane), weakened by a system of periodic internal cracks under conditions of local heating on the edge of the half plane. Heat flux due to frictional heating on the local area of the body, causes changes in temperature and stresses in the body, which significantly affects its strength, as it can lead to crack growth and local destruction. Therefore, the study of the problem of frictional heat is of a practical interest. This paper proposes to investigate the stress-deformed state in the vicinity of the crack tip, depending on the period of cracks placement.Methodology. The methods for studying two-dimensional thermoelastic state of a body with crack as stress concentrators are based on the method of complex variable function. Reducing the problem of stationary heat conduction and thermoelasticity to singular integral equations (SIE) of the first kind, the numerical solution by the method of mechanical quadrature was obtained. Findings. In this paper, we present graphical dependencies of stress intensity factors (SIF) at the crack tip on the angle of orientation and on the relative position of cracks. The obtained results will be used later to determine the critical value of the intensity of the local heat flux from equations of limit equilibrium at which crack growth and the local destruction of the body occur. Originality. The originality of our solution lies in the fact that the new two-dimensional problems of heat conduction and thermoelasticity for a half plane containing a periodic cracks due to local heating by a heat flux are obtained. Practical value. The practical value is the ability to extend our knowledge of the real situation in the thermoelastic elements of engineering structures with cracks that operate under conditions of heat stress (frictional heat) in various industries, particularly in mechanical engineering. The results of specific values of SIF at the crack tip in graphs may be useful in the development of sustainable modes of structural elements in terms of preventing the growth of cracks. ItemWave concept of motion in mathematical models of the dynamics of two-dimensional media studying(Lviv Politechnic Publishing House, 2019) Andrukhiv Andrij; Sokil Bohdan; Sokil MariiaThe methodology of the studying of dynamic processes in two-dimensional systems by mathematical models containing nonlinear equation of Klein-Gordon was developed. The methodology contains such underlying: the concept of the motion wave theory; the single - frequency fluctuations principle in nonlinear systems; the asymptotic methods of nonlinear mechanics. The aggregate content allowed describing the dynamic process for the undisturbed (linear) analogue of the mathematical model of movement. The value determining the impact of nonlinear forces on the basic parameters of the waves for the disturbed analogue is defined. ItemStatement and solution of non-stationary problem of liquid filtering in a deformed porous medium(Lviv Politechnic Publishing House, 2019) Molchanov VitaliiThe paper discusses the laws behind the filtering procedures of process liquids through porous materials. At metalwork finishing operations, the use of cutting fluids is of particular importance. During operation, liquids are continuously and intensively contaminated with solid metal parts. To restore the original properties, process fluids are cleaned of mechanical admixtures. The most widely used methods for purifying process liquids are those by filtration. The use of filtration for the purification of process fluids is most effective, since filtering through a layer of porous materials results in complete extraction and removal of solids from liquids. However, the structural features of the pores in the porous environment trigger a number of specific phenomena that arise when liquids move in the porous channels of a porous medium. The research purpose is to discuss and establish the laws behind the filtering procedures of process fluids through porous materials. When filtering process liquids through a layer of porous materials, the porous medium of the filter membrane expands with a change in porosity. The change in porosity occurs due to a decrease in the pore volume of the porous environment, since the solid parts together with the liquid penetrate into the porous channels of the porous environment and hover in them. The conducted studies permitted the authors to identify and study the laws of the filtering process and establish the law of change in porosity of the porous environment. Based on the established law, a differential equation is derived. It allowed, for given initial and border-line conditions, stating the problem of filtering the liquid through a layer of solid particles of a variable porous medium of the filtering membrane. The solution of the non-stationary problem with initial and border-line conditions by the finite difference method allowed determining the hydrodynamic parameters of fluid filtration through a layer of particles of the porous environment of the filter membrane and to obtain a solution of the non-stationary boundary problem of fluid filtration in a deformed porous medium. The use of research results promotes complete clarification of the process fluid and thorough removal of the solid parts of valuable secondary raw materials of metal processing, in particular for powder metallurgy, facilitates the launching of waste-free production, and increases the level of environmental cleanliness in the operating area of cutting fluids.