https://journal.mmi.kpi.ua/issue/feed Mechanics and Advanced Technologies 2024-12-26T10:20:08+02:00 Iryna Babiienko MaAT@kpi.ua Open Journal Systems <p><strong>ISSN 2522-4255 </strong>(Online) <br /><strong>ISSN 2521-1943 </strong>(Print)</p> <p>Dear Authors!<br />We cordially invite you to submit your original articles journal<strong> "Mechanics and Advanced Technologies"</strong>. The purpose of the international science-and-technology journal is to familiarize scientists worldwide with the latest advances in the field of mechanical engineering as well as with the scientific research in the field of advanced computational methods and design methodology in mechanical engineering. <br />We welcome scientists, scientific and technical experts in the field of mechanical engineering to collaborate with us on expanding the horizons of science.</p> <p>The international science-and-technology journal <strong>"Mechanics and Advanced Technologies"</strong> is the successor to the reader in mechanical engineering <strong>"Journal of Mechanical Engineering NTUU "Kyiv Polytechnic Institute" </strong>(ISSN 2305-9001, e-ISSN 2409-5966) which was released before 2017.</p> <p>Registration Certificate - "КВ №22698-12598ПР" on May 04, 2017.</p> <p>According to the Ministry of Education and Science of Ukraine orders №1643 on December 28, 2019 Mechanics and Advanced Technologies was included to the List of academic editions of Ukraine on technical sciences, category "B": (Specialties: 131, 133, 134).</p> <p><strong>Founder and Publisher:</strong> <a href="https://kpi.ua/en/publication-vm" target="_blank" rel="noopener">National Technical University of Ukraine "Igor Sikorsky Kyiv Polytechnic Institute"</a>.</p> <p><strong>Frequency:</strong> from 2024, 4 issues a year (March, June, September, December). </p> <p><strong>We accept papers in following languages:</strong> English, Ukrainian.</p> <p><strong>Cite the title as:</strong> Mech. 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target="_blank" rel="noopener">EuroPub</a></p> https://journal.mmi.kpi.ua/article/view/313399 Analysis of tearing test results for joining tips of metal-composite joints 2024-10-15T11:35:22+03:00 Igor Taranenko igor.taranenko@khai.edu <p><strong><em>Background</em></strong><strong><em>:</em></strong> <em>Designing highly loaded joints of metal-composite ends of aerospace engineering units meets the problem of assessing their bearing capacity, checking the adequacy of created mathematical calculation models to real testing results, and studying the dependence of the production technology of such joints on their final load-bearing capacity.</em></p> <p><strong><em>Objective</em></strong><strong><em>:</em></strong> <em>The study of the dependence of the load-bearing capacity of "metal-composite" joints on the technology of their creation and the evaluation of the quality control process of combined joints with cylindrical transversal microelements and the adhesive bond between connecting parts was chosen as the goal of the research.</em></p> <p><strong><em>Methods</em></strong><strong><em>:</em></strong> <em>The joint of a flat metal tip with a carbon fiber part using transverse cylindrical pins and adhesive is considered as an object of research. Transversal pins of different diameters are inserted into the composite package. Various technological processes of preparing the surface of the metal part and pins for subsequent adhesive joining are considered in order to maximize the adhesion between the polymer binder and the metal elements of the joint. Also, for a more rational distribution of stiffness and corresponding stresses in the parts, the metal tip has a variable stepped thickness along the length of the joint.</em></p> <p><strong><em>Results.</em></strong> <em>As the results of the study, the theoretical failure load of the joints was evaluated and compared with the results of experimental tests. Also the technological process of preparing the surface of the metal part and the pins for further joining with the composite part is recommended, which ensures maximum adhesion between the joining parts.</em></p> <p><em>A conclusion was made regarding the diameter of the pins and the shape of the profiled metal part, which ensure the maximum load-bearing capacity of the connection.</em></p> <p><em>The types of joint failure were analyzed and conclusions were drawn regarding changes in the technology of surface preparation, the layout of the pins and the choice of their diameter.</em></p> <p><strong><em>Conclusions:</em></strong><em> As conclusions, recommendations were formulated regarding a certain technology for surface treatment of a metal part, which guarantees maximum adhesion between the metal part, pins and composite, and actual processes of quality control of "metal-composite" joints with transversal microelements were selected.</em></p> 2024-12-26T00:00:00+02:00 Copyright (c) 2024 Ігор Тараненко https://journal.mmi.kpi.ua/article/view/311624 Determination of influence factores and stress concentration factor for express strength calculations of single-cut bolted connections of layered composite plates. Message 1 2024-09-17T10:00:17+03:00 Konstantin Rudakov knrudakov@ukr.net Yurii Dyfuchyn dif62@ukr.net <p><em>When designing bolted joints (BJ), it is necessary, in particular, to carry out their verification calculations for strength. At the same time, it is desirable to use express analysis: calculations by simple formulas of sufficient accuracy.</em> <em>For BJ of plates made of layered polymer composite materials (PCM), the problem has not been solved yet</em><strong><em>.</em></strong></p> <p><strong><em>Objective.</em></strong><em> To revise, to rethink and structure the formulas for the express calculation of the maximum stress when the hole is in contact with a rigid cylinder (bolt). Carry out a review on contrasting examples of materials and schemes of PCM plate reinforcement, taking into account possible lateral bolt/hole clearances in a practically relevant range, based on previously obtained and new results.</em></p> <p><em>Numerical calculations were carried out using the finite element method (contact problem) for the B</em><em>J</em><em> plate made of laminated PCM. 3D orthotropy of each monolayer was assumed. Several simple express analysis formulas were checked, and their structuring was carried out. The results are summarized in a table, illustrations are given.</em></p> <p><em>Five factores influencing the value of the maximum tensile stress near the hole in the laminated PCM plate are separated. Numerical estimates were obtained that characterize the degree of influence on the stress concentration on the surface of the hole: material characteristics, reinforcement scheme, and bolt/hole gap sizes in the laminated PCM plate, as well as the accuracy of the considered formulas.</em></p> <p><em>A change in the material and scheme of reinforcement of the layered PCM leads to a significant change in the values ​​of the maximum stresses and stress concentration factor (SCF) in the bolt-loaded hole in the cross-section of the plate weakened by the hole. The considered express analysis formulas have insufficient accuracy for contrasting cases of materials and plate reinforcement schemes. Additional research is needed, especially for the reinforcement scheme [φ/-φ]<sub>2s</sub></em> <em> at 0&lt;φ&lt;90</em><em>.</em></p> 2024-12-26T00:00:00+02:00 Copyright (c) 2024 Костянтин Рудаков, Юрій Дифучин https://journal.mmi.kpi.ua/article/view/313260 Increasing the geometric accuracy of flange walls when flanging holes by using profiled sheet metal workpieces 2024-10-14T13:57:57+03:00 Volodymyr Dragobetskyi Av-k@ukr.net Oleksandr Kaliuzhnyi Av-k@ukr.net Volodymyr Kaliuzhnyi kwl_2011@ukr.net <p><strong><em>Problem.</em></strong><em> Flanging of holes to produce flanges in sheet metal blanks and profiles is widely used in the manufacture of parts in many industries, including aircraft and instrumentation. Significant disadvantages of flanging holes are the low geometric accuracy of the flanges obtained due to the presence of significant wall thinning along the length of the flanges and the deviation of the flange wall from the cylindrical surface of the hole of the flanging die. The wall deviation occurs due to elastic deformation after the punch is removed from the deformed workpiece. To eliminate such deficiencies, flange calibration operations are used by performing additional thinning of the cylindrical part of the flange wall. Additional thinning is also used to increase the height of the flanges to be flanged. The use of thinning leads to certain limitations when connecting the flanged parts to other products using threads. Therefore, research aimed at improving the geometric accuracy of flanges in the direction of reducing wall thinning along the length and reducing wall curvature during flanging is relevant. One way to solve this problem is to use a pre-profiled workpiese.<br /></em><strong><em>Objective. </em></strong><em>To increase the geometric accuracy of the walls of the resulting flanges after flanging the holes by using a pre-profiled sheet blank</em><em>.<br /></em><strong><em>Method of realization. </em></strong><em>The use of a pre-profiled sheet workpiese with the largest profile thickness near the hole with a gradual decrease in thickness to the original thickness at the beginning of the rounding radius of the flanging die will significantly reduce the thinning and curvature of the flange wall after flanging the hole.</em></p> <p><strong><em>Results. </em></strong><em>Using the finite element method (FEM), the processes of profiling the workpiece by extrusion to obtain a bridge and punching the bridge, as well as the subsequent flanging of holes with flat, conical and spherical punches were modeled. The dependence of the flanging forces and the forces for removing the punches from the deformed workpieces on the displacement of the punches was determined. For a spherical punch with a minimum flanging force, the dimensions of the flange were determined and compared with those of a traditional workpiece. The stress state of the metal at the maximum flanging force of a profiled workpiese with a spherical punch and the final deformed state after the punch is removed were determined. The design of the punch with a set of parts for profiling and flanging was developed and manufactured. Experimental studies were conducted, the results of which showed good agreement with the modeling data on the forces of extrusion and flanging and the dimensions of the resulting flanges.<br /></em><strong><em>Conclusions. </em></strong><em>By using a profiled workpiese made of aluminum alloy D16, the geometric accuracy of the flanges obtained after flanging the hole was increased. The wall thickness of the resulting flange in length is almost the same as the thickness of the original workpiese and the deviation of the wall from the cylindrical surface of the hole of the flanging die is significantly reduced<strong>.</strong></em></p> 2024-12-26T00:00:00+02:00 Copyright (c) 2024 Володимир Драгобецький, Олександр Калюжний, Володимир Калюжний https://journal.mmi.kpi.ua/article/view/316187 Study of the possibility of using cavitation microcurrents in an ultrasonic scalpel for the glaucoma treatment 2024-11-25T21:20:19+02:00 Serhii Sharhorodskyi shargorodskyy@gmail.com Oleksandr Luhovskyi atoll-sonic@ukr.net <p><em>The development of new medical instruments for surgical treatment of glaucoma patients is an urgent scientific and applied task of modern mechanical engineering, since the number of visually impaired people in Ukraine due to glaucoma is growing every year. Today, the phenomenon of ultrasonic cavitation is widely used in technology, which occurs when high-intensity ultrasonic vibrations are introduced into a liquid and provides high-quality removal of contaminants from surfaces, disinfection, fine atomization, the formation of intense microcurrents, etc. Our work investigates changes in biomechanical reactions as a result of minimally invasive glaucoma surgery - expansion of physiological pathways for the outflow of intraocular fluid (trabecular apparatus, Schlemm's canal, etc.) using procedures using ultrasonic cavitation. By modernizing the phacoemulsifier, an ultrasonic glaucoma scalpel was created, which will allow cleaning the pores of the trabecular meshwork, restoring and maintaining its elasticity, reducing resistance to the outflow of ocular fluid, and reducing intraocular pressure. The use of such a tool will help ophthalmologists perform minimally invasive interventions aimed at normalizing the level of intraocular pressure in a less invasive and safer way, which will contribute to the prevention of progression and successful treatment of glaucoma. The development of the latest medical tools will make it possible to develop individual treatment strategies based on the specific needs and severity of the disease of each patient and create a perfect system of treatment for glaucoma patients.</em></p> 2024-12-26T00:00:00+02:00 Copyright (c) 2024 Сергій Шаргородський, Олександр Луговський https://journal.mmi.kpi.ua/article/view/315657 Finite-element two-stage modelling of stress-strain state parameters of a planar truss with parallel chords 2024-11-20T00:08:27+02:00 Maksym Omelian mak_omelyan@ukr.net <p><em>This paper investigates a planar truss with parallel belts made of VCt3ps steel. The stress-strain state (SSS) of such a truss is studied using a two-stage numerical modelling method based on the application of LIRA-SAPR 2016 R5 and ANSYS Workbench 14.5 software packages.</em><br /><em>The main problem is to improve the accuracy of determining the parameters of the stress-strain state of flat trusses, which will reduce their material consumption and design complexity. This will facilitate the optimization of manufacturing processes in construction and engineering.</em><br /><em>The paper proposes a two-stage modelling methodology that involves the use of two software packages. At the first stage, a finite-element model is created in LIRA-SAPR, where the preliminary parameters of the SSS are determined. At the second stage, this model was detailed in ANSYS Workbench. Critical zones in the truss nodes where stresses are maximum were identified, which is key for further design.</em><br /><em>The modelling efficiency is due to the integration of data from both software packages. This makes it possible to compensate for the limitations of each of them separately, in particular in modelling nodes with stress concentrations. The methodology provides visibility of the stress-strain state parameters, which contributes to the effective analysis of the data obtained.</em><br /><em>The work demonstrates the effectiveness of a two-stage approach to modelling the stress-strain state, which has made it possible to achieve efficiency in determining the parameters of the stress-strain state of a truss. The combination of LIRA-CAD and ANSYS allows to effectively take into account both the overall strength characteristics of the structure and local deformations and stress concentration zones.</em><br /><em>The results of the study can be applied in the construction of industrial and public buildings, bridges, as well as in other industries, including mechanical engineering, where parallel girders are used. The methodology ensures the optimisation of material costs and labour costs during design, which is critical for large-scale engineering projects.</em></p> 2024-12-26T00:00:00+02:00 Copyright (c) 2024 Максим Омелян https://journal.mmi.kpi.ua/article/view/314279 Zirconium-based tribotechnical self-lubricating detonation coatings 2024-10-30T12:05:19+02:00 Vitaly Shchepetov akita1305@ukr.net Nataliia Fialko akita1305@ukr.net Serhii Bys akita1305@ukr.net Constantine Zvorykin akita1305@ukr.net <div>The operation of modern high-tech equipment requires a clear definition of safe conditions for its operation. </div> 2024-12-26T00:00:00+02:00 Copyright (c) 2024 Віталій Щепетов, Наталія Фіалко, Сергій Бись, Костянтин Зворикін https://journal.mmi.kpi.ua/article/view/313292 Position control systems with friction compensation for servo pneumatic actuators 2024-10-14T15:55:11+03:00 Artur Nikitin nikitin.artour@gmail.com Oleh Levchenko Olehlevch@gmail.com <p><em>Article is devoted to the development of control systems for a pneumatic system taking into account the current position of the working body of the actuator and the amount of friction in the friction pairs of the actuator. This work also examines control systems for pneumatic drives based on the position of the working body, taking into account the nonlinearity of the motion caused by friction forces in the pneumatic actuator. The study demonstrates existing control systems and implemented static and dynamic models of friction compensation and the impact of such models on the accuracy and controllability of systems with various types of regulators and implementation schemes, including proportional valves with analog control and high-speed direct-acting valves. An analysis of positioning systems with the possibility of adjusting the input pressure and the impact of such system solutions on the rigidity of the system and its speed is carried out. The work formulates the goal for further scientific research and identifies a list of tasks necessary to implement the goal set in the work. A design solution for a test stand with the possibility of implementing adaptive regulation of the force of the actuator depending on changes in the operational parameters of the technological operation is also presented.</em></p> 2024-12-26T00:00:00+02:00 Copyright (c) 2024 Артур Нікітін, Олег Левченко https://journal.mmi.kpi.ua/article/view/313412 Numeric analysis of elastic plane body static problem by the method of matched sections 2024-10-15T12:33:55+03:00 Kirill Danylenko k.a.danylenko@gmail.com Igor Orynyak igor_orinyak@yahoo.com <p><em>The paper continues the series</em> <em>of authors' works on the elaboration of a principally new variant of the finite element method, FEM, for the treatment of various problems of mathematical physics, namely the method of matched section, MMS. The elastic plane body under static loading is considered here. As in FEM, the whole body is meshed into the small elements of, preferably, rectangular form. The main peculiarity of the method consists in the introduction of a set of main parameters dependent only on one coordinate variable, i.e. either </em><em> or </em><em>. So, any differential equilibrium equation with two partial derivatives concerning </em><em> or </em><em> is broken out into two relatively simple equations concerning only one independent variable. This leads to the introduction of one additional constant showing the interchange between these two equations. The introduced constants can be derived from the equation of continuity of kinematic parameters in the center of each element. The main, for example, </em><em>-dependent parameters are: </em><em> and </em><em> displacements in vertical (</em><em>-) and horizontal (</em><em>-) directions, respectively; normal </em><em> and tangential (shear) </em><em> forces in </em><em> direction, and </em><em> direction, respectively; and bending moment </em><em> and angle of rotation </em><em>. Similar parameters are established for </em><em>-direction. Based on the methodology of the transfer matrix method the analytical matrix-form dependence between these parameters in any point </em><em> or </em><em> and those at the lower and/or left border of the element are established. For the treatment of oblique and curvilinear boundaries, the right triangular element as a special degenerate case of the rectangular element is derived. The resulting system of linear equations is formulated for unknownThe paper continues the series of authors' works on the elaboration of a principally new variant of the finite element method, FEM, for the treatment of various problems of mathematical physics, namely the method of matched section, MMS. The elastic plane body under static loading is considered here. As in FEM, the whole body is meshed into the small elements of, preferably, rectangular form. The main peculiarity of the method consists in the introduction of a set of main parameters dependent only on one coordinate variable, i.e. either or . So, any differential equilibrium equation with two partial derivatives concerning or is broken out into two relatively simple equations concerning only one independent variable. This leads to the introduction of one additional constant showing the interchange between these two equations. The introduced constants can be derived from the equation of continuity of kinematic parameters in the center of each element. The main, for example, -dependent parameters are: and displacements in vertical (-) and horizontal (-) directions, respectively; normal and tangential (shear) forces in direction, and direction, respectively; and bending moment and angle of rotation . Similar parameters are established for -direction. Based on the methodology of the transfer matrix method the analytical matrix-form dependence between these parameters in any point or and those at the lower and/or left border of the element are established. For the treatment of oblique and curvilinear boundaries, the right triangular element as a special degenerate case of the rectangular element is derived. The resulting system of linear equations is formulated for unknown values of all parameters specified at the border of all elements. The efficiency and the superb accuracy of the MMS are demonstrated in the classical examples of bending of a long rectangular body (beam-like geometry) and tension at infinity of a 2D body with a small circular hole values of all parameters specified at the border of all elements. The efficiency and the superb accuracy of the MMS are demonstrated in the classical examples of bending of a long rectangular body (beam-like geometry) and tension at infinity of a 2D body with a small circular hole.</em></p> 2024-12-26T00:00:00+02:00 Copyright (c) 2024 Кірілл Даниленко, Ігор Ориняк https://journal.mmi.kpi.ua/article/view/305837 Identification of dynamics for machining systems 2024-06-08T10:16:38+03:00 Yuri Petrakov ypetrakov.86@gmail.com Oleksandr Okhrimenko tm_mmi@kpi.ua Maksim Sikailo ypetrakov.86@gmail.com <p><em>Cutting processes are carried out in an elastic machining system, which is multi-mass with negative and positive loop control with a delay in construed mathematical models. Its behavior during the cutting process is entirely determined by dynamic properties and an adequate parameters of mathematical model is necessary to control the process. The paper proposes a method for identifying such dynamic parameters of the machining system, which include natural vibration frequencies, vibration damping coefficients, and stiffness of the replacement model of single-mass system in the direction of the machine-CNC coordinate axes. </em></p> <p><em>It is proposed to identify such parameters as a result of experimental modal analysis by impacting the elements of the tool and workpiece with an impact hammer and processing the impulse signal with a fast Fourier transform. It is proposed to adapt the results obtained to the adopted mathematical model of the machining system, presented in the form of two masses, each with two degrees of freedom, according to the equivalence of the spectrum signal power or its spectral density. The cutting force model in the form of a linearized dependence on the area of undeformed chips needs to be clarified by the coefficient using experimental oscillograms obtained during milling of a workpiece mounted on a dynamometer table. Based on the identified parameters of the machining system, a stability diagram was constructed in the “spindle speed – feed” coordinates and experiments were carried out under conditions in the zone of stable and unstable cutting. Evaluation of the roughness of the machined surface confirmed the correspondence to the location of the stability lobes diagram constructed using the identified parameters, which indicates the effectiveness of the proposed identification method.</em></p> 2024-12-26T00:00:00+02:00 Copyright (c) 2024 Юрій Петраков, Олександр Охріменко, Максим Сікайло https://journal.mmi.kpi.ua/article/view/311389 The method of calculation and research of dynamic loads and energy losses during the operation of the lifting mechanism of the overhead crane 2024-09-11T17:46:52+03:00 Oleksiy Nyezhentsev nezhentsev@meta.ua Oleksandr Kravchenko avtoap@ukr.net Hryhorii Boiko bojkogo@snu.edu.ua Ihor Tsymbalenko tsymbalenko.i@gmail.com <p><em>The object of the study is overhead cranes.<br /></em><em>The work solves the problem of reducing dynamic loads and energy consumption of cargo lifting cranes thanks to the improvement of the method of calculating energy losses and dynamic loads during the lifting period. The mathematical model of the crane takes into account all the main parameters of the electromechanical system "drive - metal structure - load".<br /></em><em>A methodology has been developed for the study of dynamic loads and energy losses during the operation of the lifting mechanism of overhead cranes. The results of the study of dynamic loads and energy losses by overhead cranes with a load capacity of 5 tons with spans from 19.5 to 31.5 m depending on the height of the load, weight of the load, span of the crane and other factors are presented, which made it possible to increase the accuracy of calculations by 13-25%.<br /></em><em>The analysis of research results showed that energy losses largely depend on the lifting height, the weight of the load, the mechanical characteristics of the electric drive, the moment of inertia of the electric motor rotor and the couplings on the high-speed shaft.<br /></em><em>Research results can be applied in calculations, design and operation of overhead cranes.</em></p> 2024-12-26T00:00:00+02:00 Copyright (c) 2024 Олексій Нєженцев, Олександр Кравченко, Григорій Бойко, Ігор Цимбаленко https://journal.mmi.kpi.ua/article/view/316691 Distribution of magnetic field strength along a wheel tooth depending on the shape of the inductor 2024-12-04T00:58:54+02:00 Olha Dubinina olhadubinina777@gmail.com Vadym Medvedev vadim.medvedev@ua.fm <p><em>The research is aimed at determining the optimal shape of the inductor for processing the teeth of a large-sized gear wheel by magnetic pulse processing. The work studies the distribution of the magnetic field strength along the area of ​​the wheel tooth, depending on the type of inductor. This is necessary in order to predict the distribution of changes in the metal structure caused by MIO and their effect on the wear resistance of the wheel. The main task of the research is to establish the dependence of the magnetic field strength indicators on the shape and length of the inductor. Identifying the need for the presence or absence of a core.</em></p> <p><em>Two types of inductors were considered: the first involute shape is worn on the wheel tooth, the second is located in the cavity between the wheel teeth. The calculation of the magnetic field strength distribution was carried out using the ANSYS Maxwel software package.</em></p> <p><em>As a result of the research, it was found that the most effective for conducting magnetic pulse processing is the inductor of the first type, which is worn on the wheel tooth. The average values ​​of the magnetic field strength are 330-380 kA/m, which is sufficient for structural changes in the surface layer of the metal over the entire area of ​​the working surface of the tooth. The inductor of the second type, the length of which corresponds to the width of the gear crown, is ineffective. Since the magnitude of the magnetic field strength generated by it in the working area of ​​the wheel reaches only 29-67 kA/m and does not lead to structural changes in the surface layer of the metal. Increasing the length, as well as using cores of round and triangular shapes, did not give significant changes in the magnitude of the strength. It was also determined that the use of a shortened inductor of the second type is promising. In further studies of the optimal length of the inductor, it is recommended to study the direction and find out whether it is possible to process the gear wheel by stepwise movement of the inductor along the working surface of the tooth.</em></p> 2024-12-26T00:00:00+02:00 Copyright (c) 2024 Ольга Дубініна, Вадим Медведєв https://journal.mmi.kpi.ua/article/view/314110 The Pushing Mechanism Design of Jumping Robot 2024-10-28T11:04:22+02:00 Roman Zinko Roman.V.Zinko@lpnu.ua Mykhaylo Lobur Mykhaylo.V.Lobur@lpnu.ua Andriy Zdobytskyi Andrii.Y.Zdobytskyi@lpnu.ua Tetyana Stefanovych Tetyana.O.Stefanovych@lpnu.ua <p><em>The paper presents the features of the design and possible application areas of the cam mechanism of a jumping robot. The design and technological parameters of the robot are substantiated according to its mass, the stiffness of the spring, the impact system, as well as the profile surface of the cam using the environment of Autodesk Inventor.<br /></em><em>Directions for the development of jumping robot designs are highlighted, and the feasibility of developing cam mechanisms for robots is substantiated, considering the direction of its jump according to the distribution of forces and applied loads.<br /></em><em>The calculation of the forces, power, and structural parameters of the impact system is presented, and all stages of the jumping process are thoroughly analyzed. These stages include the compression of the spring by a lever-type device, the removal of the compressing device, the release of the spring, and the final ballistic phase (flight phase).</em></p> 2024-12-26T00:00:00+02:00 Copyright (c) 2024 Роман Зінько, Михайло Лобур, Андрій Здобуцький, Тетяна Стефанович