Ukrainian Journal of Mechanical Engineering and Materials Science

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A brief overview of stationary two-dimensional thermoelastic state models in homogeneous and piecewise-homogeneous bodies with cracks
(Видавництво Львівської політехніки, 2023-02-28) Zelenyak, Volodymyr; Kolyasa, Liubov; Klapchuk, Myroslava; Lviv Polytechnic National University
Purpose. A two-dimensional mathematical model of the problem of thermo-elasticity for piecewise-homogeneous component plate containing a crack has been built. The stress intensity coefficients in the vertices of the crack increase affecting strength of the body significantly. This leads to the growth of a crack and, as a result, to further local destruction of a material. Therefore, such a model reflects, to some extent, the destruction mechanism of the elements of engineering structures with cracks. Methodology. Based on the method of the function of a complex variable we have studied the two-dimensional thermoelastic state for the body with crack as stress concentrators. As result, the problem of thermoelasticity was reduced to a system of two singular integral equations (SIE) of the first and second kind, a numerical solution of which was found by the method of mechanical quadratures. Findings. The two-dimensional mathematical model of the thermoelastic state has been built in order to determine the stress intensity factors at the top of the crack and inclusion. The systems of singular integral equations of the first and second kinds of the specified problem on closed (contour of inclusion) and open (crack) contours are constructed. The influence of thermophysical and mechanical properties of inclusion on the SIF sat the crack types was investigated. The dependences of the stress intensity factor which characterizes the distribution of the intensity of stresses at the vertices of a crack have been built, as well as its elastic and thermoelastic characteristics of inclusion. This would make it possible to analyze the intensity of stresses in the neighborhoods of crack vertices depending on the geometrical and mechanical factors. As a result, this allows to determine the critical values of temperature in the three-component plate containing a crack in order to prevent the growth of the crack, as well as to prevent the local destruction of the body. It was found that the appropriate selection of mechanical and thermophysical characteristics of the components of a three-component plate containing a crack can be useful to achieve an improvement in body strength in terms of the mechanics of destruction by reducing stress intensity factors at the crack’s vertices. Originality. The solutions of the new two-dimensional problem of thermoelasticity for a specified region due to the action of constant temperature as well as due to local heating by a heat flux were obtained. The studied model is the generalization of the previous models to determine the two-dimensional thermoelastic state in a piecewise homogeneous plate weakened by internal cracks. Practical value. The practical application of this model is a more complete description of the stress-strain state in piecewise homogeneous structural elements with cracks operating under temperature loads. The results of numerical calculations obtained from the solution of systems of equations and presented in the form of graphs can be used in the design of rational modes of operation of structural elements. This takes into account the possibility of preventing the growth of cracks by the appropriate selection of composite components with appropriate mechanical characteristics.
Algorithm of machine creation using the mechanism of articulated disjunction
(Видавництво Львівської політехніки, 2022-02-22) Zinko, Roman; Hlobchak, Mykhailo; Beshley, Andiy; Pitrenko, Oleksiy; Lviv Polytechnic National University; National Aerospace University “Kharkiv Aviation Institute”
Problem statement. Any methodology is based on knowledge about the problem. The fullness and orderliness of the base determine further volumes and possible options for implementing the methodology. Purpose. To analyze the existing ways of machine creations and propose the new effective algorithm of machine creation using the mechanism of articulated disjunction. Considering the research structure and improvement of the informational and program technologies, changes to the traditional methodology of machine creation are made. The existing paradigm: parametric and functional performance of the machine, the design of which is improved based on existing machines, is a modification of predecessors' parametric and functional performance. Proposed paradigm: parametric and functional performance of the new machine, improved based on the subject area of technical solutions, methods of design and operational conditions more precisely coincide with the technological process to realize what they are called. Proposed hypothesis: there are such methodologies of design that provide an opportunity to provide rational productivity within existing operational conditions. Methodology. Morphological space is used to form qualitative features of the created machine. The peculiarity of the proposed methodology is that the set of features of the created machine also contains subsets of processes and phenomena in which the machine is involved. This allows assessing the compliance of the process in which the machine is involved and the machine operation processes. Findings (results). The algorithm of machine creation using the mechanism of articulated disjunction is proposed. It allows the creation of the new construction at a given sequence of stages to improve at every step in a given direction based on the determined criteria. Originality (novelty). Method of articulated disjunction, which is based on the principle of formation of the set of necessary properties of the structural elements of the machine based on a given primary criterion of machine efficiency. The essence of the method of articulated disjunction is that the sample of elements that have common features and properties is reformulated based on a given criterion. The proposed method provides an opportunity to determine the advantages of one structure described by various factors, in comparison with others, based on the criterion set. Practical value. The algorithm of synthesis and improvement of existing machines allows for determining their main quality features in the initial stages of the design of machines.
Analysis and improvement of design diagrams and mathematical models of vibratory lapping machines
(Lviv Politechnic Publishing House, 2019) Zakharov Viktor; Kuzio Ihor; Korendiy Vitaliy; Dmyterko Petro
Problem 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.
Analysis and improvement of two-mass vibrating tubular conveyers with two-cycle electromagnetic drive
(Publishing House of Lviv Polytechnic National University, 2016) Shenbor, Vladyslav; Koruniak, Petro; Korendiy, Vitaliy; Brusentsov, Volodymyr; Brusentsova, Marta
The analysis of structure diagrams of the two-mass tubular conveyer with two-cycle electromagnetic drive is carried out in the article. Two methods of designing of the elastic system are considered; calculation formulas for elastic system computation are deduced according to different requirements for the operating parameters of conveyers; the comparative analysis of two types of elastic systems is conducted. The recommendations for designing the lengthy tubular vibrating conveyers are presented. According to the considered structural diagrams of the elastic system the models of the lengthy vibrating conveyers with the transporting distances l =1,5...4 m are developed. On the basis of these models the lengthy vibrotransporting systems with the transporting distance l = 5...30 m were developed, manufactured and applied in industry. The considered systems ensures the transportation of loose materials (porcelain composition, sand etc.) with maximal speeds up to 800 mm/sec and productivities (for tubes with internal diameter D =100 mm) up to 30 tons per hour for. It is reasonable to use both considered schemes of elastic systems for development of vibrating tubular conveyers with electromagnetic drive. The conveyers may be designed in two modifications: overhead and supporting. The obtained dependencies allow optimization of the structure and considering the important technical parameters of conveyers (maximal permissible oscillations amplitude, springs stresses, productivity etc.) in the design phase.
Analysis of environmental hazard parameters of the workplaces in steel plants in Nigeria
(Lviv Politechnic Publishing House, 2021) Saheed, Babatunde Lateef; Adeshina, Bamidele Kayode; Bello, Bashir Olawale; Obajemihi, Obafemi Ibitayo; Department of Mechanical Engineering, University of Ilorin; Department of Mechanical Engineering, Dangote Cement Plc; Department of Food Engineering, University of Ilorin; School of Food Science and Engineering, South China University of Technology
The steel plant’s workplace environmental hazard parameters in Ilorin, Nigeria was evaluated using response surface methodology (RSM). Three environmental parameters (illumination, temperature and noise level) were measured. The data obtained were compared with the Occupational Safety and Health (OSHA) standard for the workplace environment. Based on the preliminary analysis of the workplace environment, five variables (No. of lightings, no. of windows, no. of machines, no. of workers and age of machines) were considered as input parameters. RSM was used to perform the modelling and optimization to identify functional relationships between the input and output parameters. Three (3) model equations one for each of the output parameters were developed and checked for adequacy and validity. All developed model equations were found to present functional relationships between input and output parameters. Hence, all developed model equations can be used as reliable tools for estimating, predicting, and conducting analysis for workplace environmental hazard. Best optimized results were selected based on desirability (0–1). Illumination, temperature and noise level got desirability rate of 0.921, 1.000 and 0.983 respectively. The outcome of this study suggested that the environmental parameters studied within the workplace do not conform with the OSHA standard and as a result may constitute long-term health risks to the workers.
Analysis of modern investigations of vibratory processes of wheeled vehicles
(Publishing House of Lviv Polytechnic National University, 2016) Zalutskyi, Yurii; Zhytenko, Oleksandr; Kuzio, Ihor
The history and modern tendencies of development of cushioning systems are analyzed in this paper. The development of mathematical modelling as a process is denoted, the methods and means are described and the necessary information of model choosing is presented. It is focused on the development of simulation modelling. The approaches of researchers, recommendations, indexes and specific features of evaluation of motion evenness are described. The works of many scientists are dedicated to analysis of car vibrations, evaluation of motion evenness and vibration-proof features. Many of them are devoted to investigation of vibrations, to optimization of basic design parameters of the cushioning system of cars and to development of new cushioning systems which allow reducing of vibratory overloading of trucks of general purpose. Taking into account the problems of motion evenness from the point of view of vibration of cushioning parts, the works of scientists are based on the linear theory of cushioning and the simplest one-mass car models are considered. It is also established that the drawback of usage of such theory consists in the fact that it is impossible to overview separately the vibrations of cushioning parts, which weight transfers to elastic elements of the suspension, and non-cushioning parts. The overview of scientific works dedicated to investigation of dynamics of wheeled vehicles allows to show the limited possibilities of traditional passive suspension system according to continuously increasing requirements to modern structures and to substantiate the necessity of usage of controlled cushioning systems. Among the existing variants of controlled cushioning systems, the half-controlled systems, which are the most optimal from the point of view of motion evenness increasing, energy consumption, complexity of structural implementation and usage safety, are of the greatest interest nowadays. On the basis of analyzed materials, it may be concluded that there exists a great amount of scientific investigations in the field of motor vehicles vibrations many of which are devoted to improvement of vibration-proof features of cars. Also a number of works are dedicated to investigation of vibratory overloading of industrial, construction and agricultural motor vehicles which are engaged in transportation of cargo of general purpose. However, too small attention is payed to development of techniques of determination of design parameters of cushioning systems of trucks which are engaged in transportation of cargo of special purpose, for example, cars transportation, where essentially greater attention should be payed to vibratory loadings which act upon such cargo during uneven motion.
Analysis of structure and kinematics of four-bar crank-rocker walkingmechanism
(Publishing House of Lviv Polytechnic National University, 2015) Korendiy, Vitaliy
Problems and prospects of using the walking mode for producing motion of robotic systems are considered. Advantages and spheres of the use of mobile robotic systems equipped with walking movers are substantiated. Preferences of cyclic (lever) walking mechanisms are analyzed. The kinematic parameters of four-bar crank-rocker walking mechanism, constructed on the basis of Chebyshov-Umnov mechanism, are accepted as the subject of research. The process of motion of the supporting foot of the walking mechanism is accepted as the object of research. The main aim of the investigation consists in carrying out structure and kinematics analysis of the mentioned mechanism with further derivation of analytical dependencies for calculating kinematic parameters of the supporting foot motion. The special features of the structure of four-bar walking mechanism and theoretical foot loci (paths) are considered. The form of the most reasonable path for further research is established. As a result of carried out structure analysis, it is ascertained that the mechanism consists of two structural groups: that of the first class and that of the second class second order first type. As a result of kinematics analysis, the analytical expressions for calculation of coordinates of the supporting foot hinge of the walking mechanism depending on geometric parameters of the mechanism and the angle of the crank rotation are deduced. The prospects of further investigation under the themes of the paper are analyzed. In particular, the goal function, which may be used for further optimization of structural parameters of the mechanism, is considered and the use of applied software for solving optimization problem is suggested. The optimization problem consists in evaluating such geometric parameters of the walking mechanism which allow the motion of the supporting foot in accordance with the prescribed (specified) path.
Analysis of the drive of electric vehicles with its different configurations
(Видавництво Львівської політехніки, 2023-02-28) Myskiv, Teodozii; Lviv Polytechnic National University
In the process of car development, its drive is continuously improved. The properties of different types of driving with an internal combustion engine (ICE) are well-studied [1]. ICE's bleak future has forced major automotive manufacturers to turn to electric mobility. The motor, integrated with final drive and differential, is compact and takes up little axle space, making it easier to assemble the drive into one axle or all-wheel drive. Electric vehicles have many advantages over vehicles with ICE: no emissions, high efficiency, quiet and smooth operation, braking energy recovery, simplified maintenance, etc. The functional and fundamental principles of electric vehicles and vehicles with ICE are similar, but there are some features. The characteristic of the electric motor (hereinafter referred to as the motor) is ideal for the drive – it has a large zone of constant maximum power, and the maximumtorque appears immediately during starting. The motor, integrated with final drive and differential, is compact and takes up little axle space, making it easier to assemble the drive into one axle or all-wheel drive. Possible drive designs without a differential with two motors and two final drives on the axle, or with low-speed motors without final drives. The heavy battery is placed in the floor, so the stability of the electric car is high. The maximum possible recovery of braking energy is added to all the positive properties of allwheel drive in the case of an electric car. To reduce the power consumption in the drive, two motors provide a drive mode with only one motor. Among electric vehicles with one-axle drive, front-wheel drive prevails due to using multienergetic front-wheel drive platforms, stable stability and handling performance and good traction properties in winter conditions. The advantage of rear-wheel drive is the ability to realize greater traction forces during acceleration or movement on the rise due to the dynamic redistribution of the load on the rear axle. However, during braking, due to the dynamic redistribution of the load on the front axle, the possibility of recuperation of braking energy decreases. For amore detailed analysis of the drive, typical electric vehicles are selected, the characteristics of their drive motors are given, traction characteristics are calculated and constructed in the traction force coordinates – speed of movement, the realized adhesion coefficients are determined, and appropriate conclusions have been drawn.
Analysis of the influence of the displacement of the gear rack profile of the pair evolution gearing on the quality indicators of the transmission
(Видавництво Львівської політехніки, 2023-02-28) Protasov, Roman; Magdolen, Ľuboš; Danko, Jan; Lanets, Olena; Vorontsov, Borys; Slovak University of Technology in Bratislava; Lviv Polytechnic National University; National Technical University of Ukraine “Igor Sikorsky Kyiv Polytechnic Institute”
The article is devoted to the study of the influence of the modification of the paired evolute gearing with convex-concave contact on the quality indicators of transmission, namely, the contact pressure and the speed of slippage in the engagement. Previous studies of evolute gears showed the presence of characteristic zones on the side surface of the tooth, which have worse values of quality indicators than in similar involute gear. One of the ways to remove these zones or to reduce their impact on the load capacity of the transmission is to modify the tooth profile, which will be implemented by shifting the profile of the processing gear rack. A displacement factor is added to the equation of the rail profile curve, which has the same value for the gear and wheel teeth, but the opposite sign. On the basis of the developed equation, the side profiles of the teeth of the gear and the wheel were constructed. Several values of the rack displacement coefficient with a positive and negative sign for the gear teeth are considered. The results of the research allow us to evaluate the influence of the amount and direction of the rail displacement on the curvature of the tooth profiles, the contact pressure in engagement along the height of the tooth, and the relative and absolute speed of sliding. Themodifications of the profile of the processing toothed rack proposed in thisworkwill expand the existence of paired evolute gears with a different set of quality indicators. This will make it possible to design gears with rational values of contact pressures and slip speeds when they are used in heavily loaded transmissions created for specific operating conditions. Gears with relatively high slip speeds can be used in road and construction equipment transmissions, which are characterized by lowshaft rotation frequency, in which the speed of slip between the teeth does not have a significant effect on the life or efficiency of the transmission. Otherwise, gears with relatively low slip speeds are very relevant when they are implemented in the transmission of modern and promising vehicles with a hybrid or fully electric power unit, especially in the case of passenger cars with high-speed electric motors.
Analysis of thermal comfort models of users of public urban and intercity transport
(Видавництво Львівської політехніки, 2022-02-22) Yakovenko, Yevheniia; Voichyshyn, Yurii; Horbay, Orest; Lviv Polytechnic National University
Regardless of the vehicle's application, the thermal comfort of the vehicle's occupants and driver is given increased attention. Maintaining a sense of thermal comfort, whether for safety, health or occupant thermal well-being reasons, is one of the most important goals of heating, ventilation and air conditioning (HVAC) systems. There are a significant number of physical variables that affect thermal comfort. Therefore, evaluating thermal comfort has always been a complex issue and has attracted the attention of researchers. The feeling of thermal comfort is provided by factors that depend on the heat exchange between the human body and the external environment. It is well known that one of the requirements to be fulfilled is to find a person in thermal neutrality in the environment according to the comfort equation. The article describes and evaluates the following indicators: DTS (dynamic thermal sensitivity), TS (thermal sensitivity), PMV (predicted mean voice) and PPD (predicted percentage of dissatisfaction). The most common models for evaluating thermal comfort, namely the Predicted Mean Vote (PMV), Taniguchi’s model, Zhang’s model and Nilsson’s model in a variety of car cabin conditions, have been reviewed. The limitations of these models in terms of the objectivity of the results obtained are analysed.
Analysis of vehicles drive with different characteristics of power supply
(Видавництво Львівської політехніки, 2022-02-22) Myskiv, Teodozii; Sorokivskyi, Oleg; Lviv Polytechnic National University
The characteristics of internal combustion engines (hereinafter referred to as ICE) have the following disadvantages: there is a gap between zero and minimum angular velocity, so it is impossible to move out of a state of rest; the dependence of torque on angular velocity is not ideal. They are corrected by the following converters: the first by a clutch or torque converter, and the second by a gearbox or variator. In addition, the ICE characteristics can be partially close themselves to ideal. Electric motors (here in after referred to as motors) of electric vehicles have an ideal characteristic that starts from scratch and has a large zone with a sustainable maximum power. The addition of the drive with the ICE motor in hybrid electric cars solves these problems. The different characteristics of ICE, motors and converters increase the number of possible configurations that affect the characteristics of the supply of power to the wheels. According to the traction characteristics of the car, the indicators of the traction and speed properties of the car are determined: the ability to overcome climbs, maximum acceleration, maximum speed on a horizontal road, acceleration time to a given speed, etc. The last two indicators depend primarily on the maximum power of ice or motor and are important for supercars, while for conventional cars or electric vehicles with close values of maximum speed and acceleration time to a given speed, they mean nothing. The authors propose to evaluate the efficiency of the drive during acceleration with maximum acceleration of the power utilization factor kN 0–100 – the particles from the division of the average value of the realized power on the wheels in the interval of speeds (0; 100) km/h by the maximum power value on the wheels. The characteristics of ICE and motors are given, traction characteristics in power coordinates are calculated – the speed of movement of cars with typical drive configurations, their power utilization coefficients are determined and appropriate conclusions are made. In the future, it is planned to investigate the use of power in more complex drive systems of hybrid cars with the recovery of braking energy.
Applicability assessment of the vickers indentation for determining the fracture toughness of yttria-stabilized zirconia
(Видавництво Львівської політехніки, 2023-02-28) Vavrukh, Valentyna; Klimczyk, Piotr; Priakhin, Volodymyr; Petryk, Vitalii; Momot, Kinga; Lviv Polytechnic National University; Krakow Institute of Technology
Crack growth resistance of ZrO2-(3-8) mol% Y2O3 ceramics was investigated. Young's modulus by the ultrasonic flaw detection method were determined. Vickers hardness and parameters of cracks after Vickers indentation were obtained. Based on the Young's modulus values, Vickers hardness, and parameters of cracks, the fracture toughness of the investigated ceramics was calculated using 9 different equations of the Vickers indentation method. A comparative analysis of the calculated fracture toughness values with those obtained by the single-edge notch beam method was carried out. It was found that choosing the optimal equation for calculating fracture toughness by the Vickers indentation method is quite difficult and requires comparison with the results of standardized tests. It was shown that to determine crack resistance characteristics of the yttria-stabilized zirconia ceramics, the use of only the Vickers indentation method without comparison with other methods of fracture mechanics is incorrect.
Application of taguchi method for optimization of continuous drive frictionwelding process parameters
(Publishing House of Lviv Polytechnic National University, 2016) Bhagi, Loveleen Kumar; Singh, Shankar; Singh, Indraj
The objective of present study was to determine optimal conditions to achieve satisfactory friction welds between two dissimilar metals namely copper and carbon steel bars of same diameter. Three process parameters namely speed of rotation, axial pressure, and forge pressure were considered for the present study. Two multiple performance characteristics, considered were breaking load strength and upset. The optimization of the process parameters was done using ANOVA. The obtained results indicated that the most significant process parameters are axial pressure and rotational speed that affect the optimization of multiple performance characteristics.
Application of wear-resistant coating by electrospark alloying method using an eutectic electrode material
(Lviv Politechnic Publishing House, 2018-01-29) Bilous, Oleksiy; Mahura, Bohdan; Lviv Polytechnic National University
Analysis of the literature database connected with the usage of an electro-spark alloying (ESA) for tool hardening has been carried out in the article. Necessity of developing a new tungstenless electrode materials with eutectic structure for improvement of an electro-spark alloying technologies has been proved. Therefore, the structure of a new eutectic Fe-Mn-C-B-Si-Cr-Li alloy system has been developed and manufacturing techniques of an alloying by a sintering method has been offered. The article presents the scientific data obtained on the modern equipment. Electronic spectroscopy – spectral analysis of an eutectic electrode alloy has been carried out by an electronic spectrometer of JAMP-10S model (JEOL). X-ray phase analysis of the alloy has been carried out on the “Dron-UM1”.
Applied model of assessment of intensity of the stressed deformed state of pipelines by evaluation ofmagnetic anisotropy of coercive forces. Part 1
(Lviv Politechnic Publishing House, 2017-01-01) Biloborodchenko, Volodymyr; Lviv Polytechnic National University, Lviv, Ukraine
The problem of applied diagnostics, statistically rigorous by the proposed model analogue, running stressed-deformed state of the main (trunk) shell is studied by the method of magnetic coercimetria. The relationship between the parameters of the loop of magnetic hysteresis is stochastically related with structural and mechanical state of the material of the pipeline wall and with the rest of equal conditions allows to effectively detect the zone of concentration of local stresses on the stage of their forming and development (propagation) on the basis of quantitative comparative analysis of their value with calculated equivalent mechanical stresses in principal (main) planes for particular pipe material considering that the operational stresses shouldn’t be larger than 30–50 %of the yield limit. The hypothesis H0 about the possibility of description of the measurement data of the stressed mechanical state by the magnetic-static method of coercimetria is made taking into account the peculiarities of disturbances caused by the operation of electric chains of the measuring apparatus during its metrological calibration. This hypothesis confirms that the arcsine function is a law of distribution probability density of the measured values of the coefficient of magnetic anisotropy as a response of the mechanical state of the pipe shell, that the parameter Q equals 0.95 on the confidence level and substantiates the evaluation of frequency of the influencing equivalent stresses in the whole range of loads applied to the shell by the inside normalized variable pressure. On the basis of corresponding scaling and renormalization of investigative values of the coefficient of magnetic anisotropy, the technique of determination of the level of mechanical stresses in the object of diagnostics is developed and the statistically rigorous compatibility in the certain range of influence of internal pressure in the pipeline is demonstrated using the results of preliminary metrological calibration of coercimeters obtained for different pipe steels.
Approximate calculation of natural frequencies of oscillations of the plate with variable cross-section of the discrete-continuous inter-resonance vibrating table
(Видавництво Львівської політехніки, 2022-02-22) Lanets, Oleksii; Maistruk, Pavlo; Maistruk, Volodymyr; Derevenko, Iryna; Lviv Polytechnic National University
Problem statement. To ensure highly efficient inter-resonance modes of operation of vibrating equipment, the oscillating masses of the system must have certain inertia-rigid parameters, as well as a certain frequency of natural oscillations. The disadvantage of highly efficient inter-resonance oscillatory systems is that the third reactive mass must be small, and therefore the use of complex and large structures is impossible. Therefore, it is best to use the reactive mass as a continuous section. The continuous section, which is a flexible body, optimally combines inertial and rigid parameters. Scientific works have already considered the design of the vibrating table, in which the continuous section is an ordinary rectangular plate hinged in the intermediate mass. This decision looks quite promising. However, likely, the rectangular shape of the plate is not the best option to ensure maximum energy efficiency. Purpose. Extend the method of calculating the natural frequency of oscillations of the plates by the approximate Rayleigh-Ritz method using the general hyperboloid equation to plates with variable cross-section for the proposed types of plates and check the results with the calculation in Ansys software. Methodology. The calculations of the plates were performed using the basic principles of the theory of oscillations, in particular the Rayleigh-Ritz method in the software product MathCAD. Findings (results) and originality (novelty). Two types of elastic plates with variable cross-sections are considered. In the first case, the shape of the plate was given by quadratic functions, in the second case, it was described by trigonometric functions of cosine. In both cases, the same conditions of attachment in the intermediate mass were observed. The calculation of the first natural frequency of oscillations of the considered plates was performed using the approximate Rayleigh-Ritz method with the assumption that the deflection of the plates occurs on the surface of the hyperboloid. The reliability of the obtained results was verified by numerical calculation in the software product Ansys. Practical value. It is assumed that the proposed types of plates can increase the dynamic potential of the vibrating machine. Scopes of further investigations. For further study of the considered types of plates as a continuous section of the inter-resonance vibrating machine, it is necessary to calculate their deflections at forced oscillations.
Calculation of strength of heated curvilinear bar structural elements of tubular cross-sections
(Lviv Politechnic Publishing House, 2019) Voytovych Mykola; Velychko Lev; Lampika Roman; Lishchynska Khrystyna
Practical 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.
Causes of ductility-dip cracks formation In In52 and In52 MSS alloys during fusion welding
(Publishing House of Lviv Polytechnic National University, 2015) Beliaiev, Grigorii; Volosatov, Ivan; Kakhovskyi, Mykola
The aim of the paper is to investigate one of the causes of ductility-dip cracks (DDC) formation. The main aim of this work is calculation of grain boundaries (GB) cohesive energy in nickel based In52 and In52 MSS alloys. For measuring the GB energy anisotropy methods of thermal etching and light interferometry were used. DDC form on the grain boundaries of nickel based alloys due to adsorption of impurities during multipass welding. The In52 alloy has tendency to form DDC during multipass welding fusion unlike In52 MSS one doped with Mo and Nb. The main cause is the change of thermodynamic state of the GB, as it is indicated by the decrease in the cohesive energy to 1.8-1.26 J/m2. During multipass fusion welding in In52 alloy adsorption of S and O from the grains body to GB takes place. The average concentration of O and S on the surface of DDC for high angle boundaries is within 2.3-4.5 and 0.5-1 at. %, respectively. Presented in this paper results have shown the influence of welding heat for reduce the cohesive strength of GB and, as a result, of the formation of DDC. Quantitative effect of S and O as embrittlement elements on the value of decrease in the cohesive energy was shown.
Choose of optimal regimes of traffic light control in operating zone of pedestrian crossing
(Lviv Politechnic Publishing House, 2018-01-29) Royko, Yuriy; Hrytsun, Oleg; Bura, Romana; Lviv Polytechnic National University
On the given stage of motorization level development and increase of traffic flow intensity, with increasing frequency apply to the implementation of intelligent automated systems of traffic control. The quality of their work depends foremost from study of the primary factors of road users, their behavior, including the factor of a person as movement operator, geometric parameters of communication routes, road conditions as movement environment. Such study is held by methods of field research, documentary research and mathematical modelling. Considering transport system, it is necessary to have in mind that we are concerned with the large array of stochastic indicators which, during its normal operation, comply with the normal law of distribution. If the process of traffic flows movement control, including their attachment to the roadway, parameters of which are clearly regulated by standards, is studied relatively in detail, then regularities in pedestrian flows are underexplored only due to the fact that their behavior quite frequently is regulated. However, enough amounts of mathematical methods of description the different stochastic systems have appeared, based on which it is possible to perform the simulation of road users’ behavior, in particular pedestrians. In this work it is undertaken experimental research on pedestrians’ behavior on signaled pedestrian crossings in Lviv city for different functional zones and in different time of day, and also it is investigated dynamic factors in traffic flow with the aim of determination the rational (by duration) regimes of traffic light control, during which the amount and duration of delays in traffic flows and the possibility of accidents commission is reduced, which are the consequence of road users behavior. The backgrounds of these negative phenomena are: fluctuation of traffic flow intensity, when pedestrian during longtime restrictive signals can start to move on restrictive signal of traffic light, what is unexpected for vehicle driver, especially in nighttime when blinding appears; observation only the demands of normative documents during designing the communication routes what is not always adequate for different functional areas of settlements; absence of distinct regulation of range of traffic light control parameters which would create its optimal regimes considering traffic and pedestrian flows behavior.
Classical 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 Vitaliy
Problem 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.