Graphic Dependence Research Articles

Finding The Inverse of A Polynomial Modulo in The Ring Z[X] Based on The Method of Undetermined Coefficients

This paper presents the theoretical foundations of finding the inverse of a polynomial modulo in the ring Z[x] based on the method of undetermined coefficients. The use of the latter makes it possible to significantly reduce the time complexity of calculations avoiding the operation of finding the greatest common divisor. An example of calculating the inverse of a polynomial modulo in the ring Z[x] based on the proposed approach is given. Analytical expressions of the time complexities of the developed and classical methods depending on the degrees of polynomials are built. The graphic dependence of the complexity of performing the operation of finding the inverse of a polynomial in the ring Z[x] is presented, which shows the advantages of the method based on undetermined coefficients. It is found that the efficiency of the developed method increases logarithmically with an increase in the degrees of polynomials.

TECHNOLOGY OF STRENGTHENING AND RESTORATION OF SHAFT SURFACES WITH HIGH FREQUENCY CURRENT

The issue of increasing the strength of details by applying high-frequency electric current has become one of the most important and urgent issues of today. Ensuring the corrosion resistance of parts is initially implemented by applying materials obtained in relatively economically efficient ways, which reflected in a constructive solution to the issue. It is possible to increase surfaces of small-sized details of any geometric shape with a high-frequency current 1.5-2.5 times. By increasing the surfaces using the HFC method, it is possible to fully ensure their reliability and longevity. The dependences of the amount of heat and current intensity were determined by using the HFC parameters. Based on the obtained results, it was possible to increase the strength of the shafts by 1.5-2.5 times. Keywords: High-frequency current, shafts, technological mode, main parameters, graphic dependence, increase of strength, reliability, longevity.

In Ukrainian

The review material reveals the question of the influence of impurities on the physical properties of alloys, as well as the influence of gases on processes in alloys. It has been established that the presence of hydrogen affects diffusion in alloys, and gases have a significant effect on the thermoelectromotive force of metals. The paper describes the addition of a third element to binary systems, which can expand or narrow the domain of existence of an ordered phase. The above examples of adding an impurity of vanadium or molybdenum to an alloy of iron and chromium increase the ordering temperature. It has been established that gases can have a significant effect on the thermoelectromotive force of metals and increase the hardness and reduce the ductility of metals, as well as cause their brittleness and delamination. It has been established that hydrogen (H2) in alloys (for example, Fe-Ni and Au-Cu) affects diffusion and atomic ordering processes. Also, a small concentration of hydrogen, as an impurity, can change the electrical resistance of alloys (for example, in a Pd-Au alloy). It has been established that the addition of a third element to binary systems can change the state diagram, which must be taken into account when solving problems for the production of heat treatment modes for alloys, determining the conditions for phase equilibrium, etc. The paper considers the dependence of hydrogen solubility on temperature in metals (Cu, Fe and Al) and establishes the dependence of hydrogen solubility in a metal on the concentration of impurity metals. The temperature dependence of hydrogen solubility in Fe-V alloys is also shown. The shift of the density of state is studied for different distributions of impurity atoms in the alloy in the order-disorder system, and the dependence of the density of states of disordered and ordered solid solutions is studied. The dependence of the relative solubility of atoms introduced into the pores of alloys with an fcc structure (of the Cu3Au type) is indicated, taking into account the solubility, on the parameter χ, which is proportional to the degree of long-range order in the octahedral and tetrahedral pores of the alloys. The dependence of the relative solubility of intercalated atoms in octahedral pores of alloys with a bcc structure (such as CuZn and Fe3Al) is considered. A plot of the dependence of the concentration of dissolved impurity atoms on the degree of order is shown for substitutional alloys with a bcc lattice, where the M2 coefficient is introduced, which does not depend on the degree of order. The effect of pressure as a measure of long-range order is also studied, where its step decreases or increases, or decreases and then increases and vice versa (order-disorder phase transition). An equally important result is the graphic dependence of solubility (c) on pressure (P) in disordered and ordered alloys.

Formation of Professional Competences of Future Bachelors of Vocational Education in the Process of Dual Training

The creation of logistics infrastructure is closely related to the problem of competence-oriented training of future logisticians. This process is implemented in accordance with the theory of contextual teaching. The methodological basis for preparing bachelors for competitive professional activity is the integration of education with science, professional activity and business. The purpose of the article is the investigation the professional competences of future bachelors in vocational education in the process of their dual training. Research methods: theoretical analysis of scientific sources, normative documents, conceptual principles of logistics; systematization, modelling, observation and testing. Results. The article examines such problem situation: the representatives of higher schools and industrial enterprises agree that the list of professional competences should be formed for the graduates of educational institutions, but there are some professional difficulties in «post-graduate» activities of young professionals. Managing the educational process, the research and teaching staff guide students to achieve the goals formulated in educational programs and obtain appropriate results, which are specific competences. The basic employers’ requirements to the specific knowledge and skills of applicants for the position of logistician are established. The authors have shared the experience of cooperation between the Ternopil Volodymyr Hnatiuk National Pedagogical University and the private enterprise «Scientific and Production Association «Energy Saving Technologies»«. On the example of «Energy Saving Technologies» the technological process of heat generation, which has several variable components (cyclic loading of fuel into the storage hopper, calorific value of fuel, its humidity and particle size distribution), is established; it is determined that for timely fuel supply it is necessary to take into account the internal logistics infrastructure of the enterprise. In the process of training specialists in specialty 015.38 Vocational Education (Transport) according to the educational program «Logistics» students study the discipline «Organization of Transportation», do practical work and develop the three-dimensional graphic dependence, which will contribute to the formation of professional competences. It is also determined that the development of professional competences of future bachelors of vocational education is the unity of their theoretical and practical training. Conclusions. The authors concluded that the theoretical and practical classes with the use of active teaching methods for progressive and optimal students' understanding of the main provisions on the organization of freight transportation, which plays a large role in the development of professional competences of future teachers of vocational training, organizers of transportation services. The use of active learning methods in the educational process arouses the interest of students and allows them to develop analytical, research, communicative, professional skills and abilities.

ПОЛЕВЫЕ ИССЛЕДОВАНИЯ СОШНИКА ЗЕРНОВОЙ СЕЯЛКИ С ШАРНИРНЫМ СОЕДИНЕНИЕМ НАПРАВИТЕЛЯ СЕМЯН И РЫХЛИТЕЛЯ ПОЧВЫ С КОРПУСОМ

The uniformity of seed distribution along the length and depth of the row (sowing spacing) depends on the correct operation of the opener of the grain seeder, but not all modern openers have these indicators, so the scientists of the Penza State Agrarian University developed a grain seeder opener with a hinged connection of the seed guide and soil cultivator with the opener body, using which solves this problem. The distribution of seeds of spring barley variety "Sursky Favorit" by the depth of placement when using the developed coulter, compared with the indicators obtained using a standard double-disk coulter, was studied in the course of laboratory and field tests. According to the obtained graphic dependence, which characterizes the distribution of seeds according to the depth of placement depending on the type of coulters, it was found that the number of seeds in a given layer is 4-6 cm when sowing with a coulter of a grain seeder with a hinged connection of the seed guide and soil ripper with the coulter body and a standard double-disk seeder coulter SZ-5.4 is 91% and 71%, respectively. A decrease in the uneven distribution of seeds along the depth of the furrow will occur when using an experimental coulter, which in turn will affect the increase in yield. Yields will increase by 12% on average compared to the standard coulter.

Study of the kinetics of wear of steels from the point of view of the provisions of the adhesive-hydrodynamic theory of wear

The article is devoted to the study of wear resistance of the surface layer of steels 40X and ШX15, when rubbed in oil I-20. A comparison of the surface layer of samples of raw and nitrided steels, before and after the tests. The study of the fine microstructure of the samples with the help of the LDFP microscope, allowed us to conclude that the samples that were subjected to ionic nitriding, improved roughness. In turn, increased the area of linear contact, reduced contact load. The graphic dependence of roughness indicators is constructed. After testing, we can conclude that nitrided steel has a long service life, namely high hardness, resistance to abrasion, durability and corrosion resistance. The mechanism for obtaining increased resources needs further study

DYNAMICS OF THE NUMBER OF DUST-CARTS GROWTH IN UKRAINE

In the period of 2014 – 2020 the growth of the dust-carts fleet in Ukraine was 14 %. Determination of the regression dependence, describing the dynamics of the number of dust-carts growth in Ukraine is an important scientific-technical problem. Objective of the study is determination of the regression dependence, describing the dynamics of the dust-carts growth in Ukraine and can be used for the prediction of the amount of the dust-carts. In the process of the study the method of regression analysis of the results of single-factor experiments and other paired dependences with the selection of the rational type of function from the sixteen most widely used variants by the criterion of the maximum value of the correlation coefficient has been used. Regression was performed on the base of the linearizing transformations, which enable to reduce the non-linear dependence to linear one. Determination of the coefficients of the regression equations was carried out, applying the method of the least squares by means of the developed computer program "RegAnaliz", protected by the Certificate of the State registration of the rights to the copyright object. Adequate regression arch-tangential dependence, describing the dynamics of dust-carts quantity growth in Ukraine has been obtained, it can be used for the prediction of the number of dust-carts. Graphic dependence, describing the dynamics of the dust-carts number increase in Ukraine, allows to illustrate this dynamics and show the sufficient convergence of the theoretical results with actual data has been constructed. Using the obtained dependence, it is predicted that the number of the dust-carts in Ukraine, taking into account the existing rate of growth will reach 3873 units in 2030.

FORMATION DYNAMICS OF THE VOLUMES OF THE SUBSTANDARD MACHINES AND EQUIPMENT OF GENERAL ENGINEERING DESIGNATION IN UKRAINE

Industrial scrap, substandard machines and equipment of general engineering designation as types of solid industrial waste can be widely used in the construction sphere for obtaining valuable materials: for the manufacturing of the construction materials with protective properties against electromagnetic radiation and static electricity, for the production of the anodic earthings, etc. That is why, determination of the regressional dependence, describing the dynamics of the volumes of the substandard machines and equipment of general engineering designation formation in Ukraine is an important scientific-engineering problem. Aim of the research is determination of the regressional dependence, describing the dynamics of the volumes of the substandard machines and equipment of general engineering designation formation in Ukraine and can be used for the forecast of these volumes. In the process of studies method of the regressional analysis of the results of single factor experiments and other paired dependences with the selection of the rational type of function from sixteen most widely used variants by the criterion of maximum value of the correlation coefficient was used. Regression was carried out on the base of linearised transformation, enabling to reduce non-linear dependence to linear one . Determination of the coefficients of regression equations was performed, applying the least-square method by means of the developed computer program "RegAnaliz”, the program is protected by the Certificate of the State Registration of the rights to the copyright object. Adequate regression power dependence, describing the dynamics of the volumes of substandard machines and equipment of general engineering designation formation in Ukraine is obtained, it can be used for the forecast of such volumes. Graphic dependence, describing the dynamics of the formation of the volumes of the substandard machines and equipment is constructed, it enables to illustrate this dynamics and show the sufficient coincidence of the theoretical results with actual ones. It is established that in Ukraine in the period of 2017 – 2019 volumes of the substandard machines and equipment of general engineering designation formation decreased according to linear dependence.

Расчет кривой Столетова конструкционных сталей по параметрам предельной петли магнитного гистерезиса

A formula has been developed for calculating the steel Stoletov curve (a graphic dependence of magnetic susceptibility χ on the magnetic field strength H in a ferromagnet) based on the results of measuring the coercive force Hc, technical saturation magnetization Ms and residual magnetization Mr. The derived formula is substantiated by a statistical analysis of a comparison between the calculation and experimental results obtained for grade SHX15 steel in its delivery and hardened states. The correlation coefficient between the calculated and measured values of χ in the entire variation range of H was 0.99, and the mean square deviation was 8.7%. By using the developed formula, it is possible to construct the dependence χ(H) and analyze it in different magnetic field strength variation ranges for any steel the measured values of Hc, Ms and Mr for which are given in the reference literature. The application of the formula is illustrated by analyzing the effect the tempering temperature of grade 30 steel after its quenching has on the steel Stoletov curves. The grade 30 steel tempering temperature has been established at which the required magnetic susceptibility value can be obtained in a given magnetic field strength variation range in a ferromagnet with its required hardness.

Heat Exchange and Hydrodynamic Characteristics of Unified Package of Cold Layer of RAH

Heating the air in the boiler air heater with the heat of fuel combustion products performs the functions of increasing the fuel combustion temperature, increasing the temperature level of gases in convective heating surfaces, improving ignition and fuel combustion conditions, increasing boiler efficiency by utilizing waste gas heat, improving fuel quality due to its preliminary supply, etc. However, the peculiarities of the process of heating the air in the air heaters do not allow to achieve a decrease in the temperature of the exhaust gases. This is due to the unfavorable ratio of heat capacities of flue gases and air, as well as corrosion and contamination of the heating surfaces of air heaters. The research of heat transfer processes and hydraulic resistance of unified package of cold layer of RAH is depicted at this work. The graphic dependence of the change in the coefficient of hydraulic resistance and Nu number for unified packages with single line of sheets and simplified profile with corrosion resistance enamel from the Reynolds number for different values of the length of the replaced areas was constructed. The unified packing of the simplified profile has increased by 1.17 times equivalent diameter and is characterized by good operational parameters and takes into account the risk of contamination of heating surfaces due to the enamel coating.

EXPERIMENTAL EVALUATION OF ENERGY PARAMETERS OF BULK VIBROSEPARATION OF BULK PRODUCTS

The article presents the results of experiments to evaluate vibration parameters when using spatial oscillation excitation drive. Among the main directions of the intensification of the vibration technological action during separation of bulk agricultural products, not only the adjustment of amplitude-frequency characteristics can be noted, but also the improvement of the geometric and structural parameters of the drive mechanisms. Currently, in the processes of separation or classification of bulk masses by the method of siting separation, fixed sieves are displaced by sieves receiving an additional power pulse in order to intensify this processing process. The developed scheme of the drained vibration process involves the oblique location of the working body, which allows to implement the creation of spatial oscillations of the sieve surface. The developed experimental model of the spatial oscillation screen and the studies carried out to obtain graphic dependence of the energy consumption on the process of treating crushed grain material from changes in mass, geometric and structural parameters of the oscillating system. When choosing a rational mode of vibration cutting of bulk products as the evaluation criteria used the eccentricity of the drive shaft, the angle of the tilt surface, the value of the energy consumption and the pattern of its change in the conditions of variation of the power pulse when the eccentricity of the drive shaft, the trajectory of the movement of the sieve elements and the, bulk mass by changing the angle the inclination of the working container, the measurability of the oscillatory movement from the flat to the spatial parameters of the developed vibro-industry, corresponding to the configuration of the structural parameters. Experimental studies have shown the effectiveness of the use of spatial oscillations of the sieve surface during separation of bulk masses, made it possible to substantiate the structural parameters of the vibratory screen.

Kinematic and dynamic analysis and distribution of stress for seven-item mechanism by means of the SolidWorks program

This paper presents a kinematic and dynamic analysis and distribution of the stress for seven-item planar mechanism by means of the SolidWorks software. The authors of the introduced paper deal with the kinematic analysis of planar mechanisms as well as with the implementation of the vector method into the SolidWorks software program in order to determine the kinematic variables (quantities) of the individual bodies in the whole complex system. The dynamic analysis is performed on the basis of the kinematic analysis. Dynamic analysis allows us to design a system of bodies correctly and it is with the respect to the dynamic loading. For the interpretation of the introduced analysis, the seven-item planar mechanism was selected. Graphic dependence of kinematic and dynamic magnitudes of some points is given in dependence on the angle of rotation of the driving item and in dependence on time. In relation to the kinematic and dynamic analysis and subsequent simulation of the planar as well as spatial mechanisms, it is perfect solution to use SolidWorks software program. The considerable advantage of this mentioned program is based on its simplicity from the aspect of modeling and moreover, it is important to point out that utilisation of the mentioned program leads to results which are precise and accurate in the case of the numerical solution of the equations in the whole magnitude referring to motion of mechanism while the given results are obtained in the graphic form.

Kinematic and dynamic analysis and distribution of stress for six-item mechanism by means of the SolidWorks program

This paper presents a kinematic and dynamic analysis and distribution of the stress for six-item planar mechanism by means of the SolidWorks software. The main purpose of the investigation is connected with the kinematic analysis of planar mechanisms as well as with the implementation of the vector method into the SolidWorks software program in order to determine the kinematic variables of the individual bodies in the whole investigated system. The process of the dynamic analysis is based on the kinematic analysis. The dynamic analysis makes possible to design a system of bodies correctly and it is with the respect to the dynamic loading. For the interpretation of the introduced analysis, the six-item planar mechanism was used as example (representative). Graphic dependence of kinematic and dynamic magnitudes of some points is given in dependence on the angle of rotation of the driving item and in dependence on time. In relation to the kinematic and dynamic analysis and subsequent simulation of the planar as well as spatial mechanisms, it is great solution to use SolidWorks software program. The considerable advantage of this mentioned program is based on its simplicity from the aspect of modeling and moreover, it is important to point out that utilisation of the mentioned program leads to results which are precise and accurate in the case of the numerical solution of the equations in the whole magnitude referring to motion of mechanism while the given results are obtained in the graphic form.

DYNAMICS OF SCAP VOLUMEFORMATION INCREASE IN UKRAINE

Solid industrial waste, in particular, metal working waste, can be widely used in the construction sphere for obtaining valuable materials for the production of the construction materials with the protective qualities against electromagnetic radiation and static electricity, for manufacturing of the anode earthing, etc. That is why, determination of the regression dependence, describing the dynamics of the scrap volume growth in Ukraine is an actual scientific-engineering problem. Aim of the research is determination of the regression dependence, which describes the dynamics of the scrap volume growth in Ukraine and can be used for the prediction of these volumes. In the process of the research the method of the regressive analysis of the results of the single factor experiments and other pairwise dependences with the selection of the rational type of the function from the sixteen most widely used variants by the criterion of maximum value of the correlation coefficient was applied. Regression was carried out on the base of the linearized transformations, which allow to reduce the non-linear dependence to linear one. Determination of the coefficients of the regression equations was carried out applying the method of the least squares by means of the developed computer program "RegAnaliz", protected by the Certificate of the State Registration of the rights to the copyright object. Adequate regression power dependence is obtained, it describes the dynamics of the scrap volume formation in Ukraine and can be used for the prediction of these volumes. Graphic dependence, describing the dynamics of the scrap formation volume in Ukraine is constructed, it enables to illustrate this dynamics and show sufficient coincidence of the theoretical results with actual results. It is established that in Ukraine in the period of 2017 – 2020 volumes of scrap formation increased by hyperbolic dependence. Using the obtained dependence it is forecast that the volumes of the scrap formation in Ukraine in 2030 at present rate of growth will increase to 1132 thousand tons.

DYNAMICS OF SOLID MUNICIPAL WASTE COMPOSTING SPEADING IN UKRAINE

Composting is the technology of solid municipal waste processing, it is based on the principle of natural biodecomposition, its end product is compost, used in urban management and agriculture. Determination of the regressive dependence that describes the rate of spreading the process of solid municipal waste composting is Ukraine an important scientific engineering problem. Aim of the study is to determine the regressive dependence, describing the rate of solid municipal waste composting spread in Ukraine and can be used for the forecasting the spreading  the solid municipal waste management methods. During the research process the method of regressive analysis of the results of single factoral experiments and other paired dependences was used with the selection of the rational type of the function from sixteen most widely-spread variants by the criterion of the maximum value of the correlation factor. Regression was performed on the base of the linearized transformations, which enable to reduce the non-linear dependence to linear one. Determination of the regression equations coefficients was carried out, applying the method of the least squares, by means of the developed computer program "RegAnaliz", protected by the certificate of the State Registration of the rights to the copyright object. Adequate regression dependence is obtained, it describes the rate of spreading the process of solid municipal waste composting in Ukraine and can be used for the forecasting the spreading of the solid municipal waste management methods. Graphic dependence, describing the rate of spreading solid municipal waste management methods in Ukraine and allows to illustrate this rate, show sufficient coincidence of the theoretic results with actual data is constructed. Using the obtained dependence, it is forecast that in Ukraine the level of composting solid municipal waste, comparable with the level of the EU countries at present rate of growth can be achieved by 2035.

DEPENDENCE OF THE CELEBRAL APOPLEXY MOBIDITY RATE OF THE PRODUCTIVE AGE POPULATION ON THE PERFORMANCE OF THE WASTE INCINERATION PLANT

Flue gases of the incineration plants is a complex multicomponent mixture of 27 components, which may cause the diseases of respiratory system and blood circulation, in particular, cerebral apoplexy. Determination of the regression dependence of the cerebral apoplexy morbidity rate of the population of the productive age on the performance of incineration plant, which can be used for the prediction of such morbidity rate is an  important  scientific-engineering task. Aim of the research is the construction by means of the regression analysis the regressional dependence of the cerebral apoplexy morbidity rate indices of the working age population on the performance of the incineration plant, these dependences can be used for the prediction of the morbidity indices. In the process of the study the method of regressional analysis of the results of single-factor experiments and other paired dependences with the selection of the most adequate type of function from the  sixteen most widely used variants by the criterion of maximum value of the correlation coefficient was used. Regression was carried out on the base of the linearized transformations, which allow to reduce nonlinear dependence to linear dependence. Determination of the coefficients of the regression equations was performed, applying the method of the least squares by means of the developed computer program "RegAnaliz". Regressional dependence of the disease prevalence among the population of the productive age on the performance of the incineration plant was obtained, the dependence can be used for the prediction of the morbidity indices. Graphic dependence of the cerebral apoplexy morbidity prevalence of the working age population on the performance of the incineration plant was constructed, this dependence allows to illustrate the sufficient coincidence of theoretical results with actual results. It is established that the cerebral apoplexy prevalence of the working age population increases with the performance growth of the incineration plant by exponential law.

Researching the efficiency of buck converter synchronous rectifier

The object of study is synchronous buck-voltage converter with digital control system. One of the most problematic things is energy changing and transmission in converters to reach certain numerical range with minimal losses in the components of the electrical circuit. An enormous calculated parameters of electrical scheme. There was advised and described both structure and electrical scheme of synchronous converter, which, thanks to digital system, provides dates with more accuracy connected with an impact on working scheme. There was shown detailed analysis example with a numerical value for the certain elements of electrical scheme. It’s a fundament in order to choose certain parts of electrical scheme according to the certain categories.During research there was used selection of hardware and software tools: elements for buck-converter – key, diode and capacitor; certain voltage and frequency range for microcontroller; control of the power keys of the circuit with the corresponding operating parameters for driver. There was analyzed and calculated all over the possible losses during the process bucking of the voltage to the certain level, an enormous losses in the components of the converter electrical scheme – induction coil, keys and capacitors. It’s an important part of synchronous buck-converter. There was calculated power losses and efficiency through the received graphics of keys commutation in electrical scheme. There were received graphic dependence of converter efficiency on output power; time characteristics of the control signal pulse-width modulation (PWM) and output voltage; dependence on the commutation losses. This is because advised synchronous converter has a set of features. Particularly analog to digital converter in the capacity of feedback, digital regulation system with a discrete step and rectification by replacing diodes with actively controlled switches. There are keys of low-side and high-side levels according to the passing voltage and current values. Therewith provides possibility for receiving more accuracy value. In comparison with analogic buck-converters, this converter has voltage parameter with fractional error.

Moisture regime of enclosing structures with different thickness of insulation layer

Construction industry has different problems including the moisture regime of enclosing structures. If we want to protect an enclosing structure from the negative impact of moisture, we need to evaluate a moisture balance transfer. We used well-known graphical method to calculate the maximum wetting plane positions in three enclosing structures, which are represented the composite insulating systems with external plaster layers, aerated concrete bases and mineral wool insulations. These researching encloses differ only by thicknesses of insulation layers. It was found that the maximum wetting plane is located between the insulation layer and the external plaster layer. Moreover, when the indoor climate parameters change, the position of the maximum wetting plane does not change. However, it is determined that with a significant increase in the thickness of the insulation, the second maximum wetting plane appears inside the aerated concrete layer. This phenomenon was called as «overheating effect». To assess the position of the second maximum wetting plane we developed the criterion “relative displacement coordinate of maximum wetting plane” and obtained the graphic dependence of the introduced criterion and the thickness of the insulation.

Velocity rate of screw streams in the site of submerged vanes

Introduction. The formation mechanism of longitudinal screw streams (LSS) along the upstream and downstream face of submerged vanes (SV) is considered. Acting along with the artificial transversal circulation (ATC), these streams protect the water intake from the channel sediments. The intensities and directions of LSS and ATC depend on the regime of flow, the planned-geometric characteristics of the vanes. Recommendations concerning the purpose of SV’s rational characteristics in the aspect of steady formation of all three protective streams in the flow for river damless intakes are contradictory and require clarification. The purpose of the study is to analyze the velocity rate of the LSS in SV site at various planned-geometric characteristics of the vane and hydraulic modes of its operation based on a physical model with an erosion-resistant channel (without water separation), as well as to determine an efficient range of setting angles of the SV’s to the tray board in terms of formation of steady and intensive LSS along the upstream and downstream face of the vane.
 Materials and methods. Model physical hydraulic studies and theoretical calculations were used. Five hydraulic modes of SV’s operation were studied, with various planned-geometric characteristics, using the physical model with an erosion-resistant channel (without water separation). The obtained experimental data were summarized and analyzed.
 Results. Results of laboratory hydraulic studies of LSS velocity rate in LSS site were presented. Experimental graphic dependence diagrams were plotted characterizing the intensity and direction of the LSS along upstream and downstream faces of the vane.
 Conclusions. A determining influence of the setting angle of the vane to the tray board (bank line) on the intensity and direction of the LSS in SV’s site was found out. Experimentally, an efficient SV setting angle was determined in terms of the formation of steady and intensive LSS along the upstream and the downstream vane face with practically usable direction.

Thermodynamic Simulation of Silicothermic Reduction of Chromium

Thermodynamic simulation of chromium reduction from the oxide system of the composition (wt %) was conducted as follows: 25.0–37.5 CaO, 25.0–12.5 SiO2, 25.0 Cr2O3, 5.0 FeO, 14.0 MgO, 3.0 MnO, and 3.0 Al2O3. Silicon of FeSi20, FeSi45, and FeSi65 ferrosilicon grades was used as a reducing agent in an amount of 110% for the quantity stoichiometrically required for the reduction of iron, manganese, and chromium. The simulation was performed using the HSC Chemistry 6.12 software package developed from Outokumpu, Finland. Calculations were performed using the “Equilibrium Compositions” module in the initial nitrogen atmosphere at a total pressure of 0.1 MPa within the temperature range 1500–1700°C at a temperature increment of 50°C. The thermodynamic characteristics of the CrO(II) compound were entered into the software package’s database. The thermodynamic constants of CaCr2O4 available in the database were adjusted. The calculated results are represented in the graphic dependence form of changes in the reduction degree of chromium ηCr on the temperature T, the slag basicity (CaO)/(SiO2), and the silicon concentration in ferrosilicon [Si]FeSi. It is shown that the increase in the process temperature from 1500 to 1700°C at (CaO)/(SiO2) = 2 decreases ηCr by 1.87, 6.04, and 7.38% when FeSi20, FeSi45, and FeSi65, respectively, are used as reducing agents. It has been found that the increase in (CaO)/(SiO2) from 1 to 3 at a temperature of 1600°C results in an increase in ηCr by 17.3, 14.2, and 12.5% when FeSi20, FeSi45, and FeSi65, respectively, are used as reducing agents. The increase in the silicon concentration in ferrosilicon from 20 to 65% [Si]FeSi increases ηCr by 9.5, 5.9, and 4.2% at a slag basicity of 1, 2, and 3, respectively, at a temperature of 1600°C. The metal’s chemical composition has been determined. The thermodynamic simulation results can be used to calculate the reduction degree of chromium from the reduction period slags of the argon–oxygen refining during stainless steel production.