Mathematical Model Of Process Research Articles

Improvement of mathematical model for catalytic reforming process with a stationary catalyst layer

Improvement of mathematical model for catalytic reforming process with a stationary catalyst layer

Mathematical Modeling of the Heat Transfer Process in Spherical Objects with Flat, Cylindrical and Spherical Defects

This paper proposes a method for determining the optimal parameters for the thermal testing of plant tissues of fruits and vegetables containing surface and subsurface defects in the form of areas of plant tissues with different thermophysical characteristics. Based on well-known mathematical models for objects of predominantly flat, cylindrical and spherical shapes containing flat, spherical and cylindrical regions of defects, numerical solutions of three-dimensional, non-stationary temperature fields were found, making it possible to measure the power and time of the thermal exposure of the sample surface to the radiation from infrared lamps using the finite element method. This made it possible to ensure the reliable detection of a temperature contrast of up to 4 °C between the defect and defect-free regions of the test object using modern thermal imaging cameras. In this case, subsurface defects can be detected at a depth of up to 3 mm from the surface. To determine the parameters of mathematical models of temperature fields, such as thermal conductivity and a coefficient of the thermal diffusivity of plant tissues, a new method of a pulsed heat flux from a flat heater is proposed; this differs in the method of processing experimental data and makes it possible to determine the required characteristics with high accuracy during the active stage of the experiment in a period not exceeding 1–3 min.

Аналіз впливу на прохідність автобронетанкової техніки конструктивних факторів та методика її збільшення шляхом автоматичного регулювання тиску повітря в шинах коліс

The purpose of the study is to analyze and determine the influence of various factors on the patency of armored vehicles (AMT) operated by the National Guard of Ukraine. Determination of the change in patency during the movement of AMT in different road and climatic conditions. Analysis of static and dynamic loads, which are characteristic of AMT movement over rough terrain, and their impact on the efficiency of the vehicle. The theoretical component of the study was carried out using mathematical modeling of the work process of regulating the air pressure in tires of AMT wheels, using the example of changes in the characteristics of adhesion coefficients with the supporting surface and rolling resistance depending on the change in pressure and load on the tires of the wheels when the AMT is moving off-road. As a result of mathematical modeling, the dependences of air pressure in tires of AMT wheels were obtained, depending on the coefficient of rolling resistance and the load on each of the wheels. Which, in turn, makes it possible to move to a sufficiently complete mathematical modeling of the movement of AMT on off-road, taking into account the reference cross-country ability. In the process of theoretical research, the structural parameters of the impact on the patency of AMT were analyzed quite completely, and a generalized comparative indicator of the patency parameters of vehicles was proposed. When analyzing it, it was found that the AMT tire and, specifically, the change in air pressure in it, have a significant impact on the bearing capacity. The authors propose to use the following evaluation criteria as criteria for assessing the efficiency of the passability when driving on deformable surfaces: a generalized comparative indicator of the parameters of the passability of vehicles. As a result of consideration of which, a significant influence on the patency parameters of the tires and directly the air pressure in them was established. Regulation and change of the air pressure in the tires of the wheels depending on the change in the coefficient of rolling resistance as well as the change in the load on each wheel, which are the ratio of the work that is spent on the traction force when overcoming different degrees of heaviness of the resistance of the supporting surfaces with the effect of deformation. And the load that falls on each of the AMT wheels allowed us to draw conclusions about the improvement of the regular tire pressure regulation system (RPRS) of the wheels.

THE AIRCRAFT ENGINE PROPELLER MAIN CHARACTERISTICS DETERMINATION IMPROVED METHOD

An improved method of the fixed and variable pitch propeller aerodynamic characteristics determining that based on the vortex theory is presented. It is shown that the design of propellers has it`s peculiarities, it does not take into account a number of factors that affect the propeller operation to one or another degree. This actualized the special purpose unmanned aerial vehicles engines propellers aerodynamic characteristics calculating methodology improvement. Since the use of the propeller profiles performances in the design requires the air compressibility correction introduction already after the selection of the propeller, that complicates the design, therefore the mathematical model of the variable-pitch propeller working process has been improved based on the profile model with the correct consideration of the Mach and Reynolds numbers influence on the aerodynamic characteristics of the air screw. This advantage of the developed airfoil model allows the design and verification of a subsonic propeller for ground and flight operations. Methods of design and verification calculations of propeller blades are presented. Verification of the improved methodology was carried out by comparing calculated data with known experimental data. The reliability of the improved aircraft engine propeller main performances determination methodology is substantiated by the correct application of the numerical and experimental methods of aerodynamics, the consistency of theoretical provisions with experimental data. The satisfactory coincidence of the calculated data obtained by the improved method of the engine propeller main performances determination allowed us to draw a conclusion concerning its efficiency. The improved technique for the main performances of an aircraft engine propeller determination does not require knowledge on the propeller profiles aerodynamic characteristics from which the blade is drawn, since these characteristics are calculated based on known geometric data, taking into account the Mach and Reynolds numbers. This allows you to design and build a subsonic propeller of both fixed pitch and variable pitch.

Analysis of the privacy-performance tradeoff of reference testing in Forensic Investigative Genetic Genealogy.

During an investigation using Forensic Investigative Genetic Genealogy, which is a novel approach for solving violent crimes and identifying human remains, reference testing-when law enforcement requests a DNA sample from a person in a partially constructed family tree-is sometimes used when an investigation has stalled. Because the people considered for a reference test have not opted in to allow law enforcement to use their DNA profile in this way, reference testing is viewed by many as an invasion of privacy and by some as unethical. We generalize an existing mathematical optimization model of the genealogy process by incorporating the option of reference testing. Using simulated versions of 17 DNA Doe Project cases, we find that reference testing can solve cases more quickly (although many reference tests are required to substantially hasten the investigative process), but only rarely (<1%) solves cases that cannot otherwise be solved. Through a mixture of mathematical and computational analysis, we find that the most desirable people to test are at the bottom of a path descending from an ancestral couple that is most likely to be related to the target. We also characterize the rare cases where reference testing is necessary for solving the case: when there is only one descending path from an ancestral couple, which precludes the possibility of identifying an intersection (e.g., marriage) between two descendants of two different ancestral couples.

A Physical Insight into Computational Fluid Dynamics and Heat Transfer

Mathematical equations that describe all physical processes are valid only under certain assumptions. One of them is the minimum scales used for the given description. In fact, this prohibits the use of derivatives in the mathematical models of the physical processes. This article represents a derivative-free approach for the mathematical modelling. The proposed approach for CFD and numerical heat transfer is based on the conservation and phenomenological laws, and physical constraints on the minimum problem-dependent spatial and temporal scales (for example, on the average free path of molecules and the average time of their collisions for gases). This leads to the derivative-free governing equations (the discontinuum approximation) that are very convenient for numerical simulation. The theoretical analysis of governing equations describing the fundamental conservation laws in the continuum and discontinuum approximations is given. The article demonstrates the derivative-free approach based on the correctly defined macroparameters (pressure, temperature, density, etc.) for the mathematical description of physical and chemical processes. This eliminates the finite-difference, finite-volume, finite-element or other approximations of the governing equations from the computational algorithms.

A Physical Insight into Computational Fluid Dynamics and Heat Transfer

Mathematical equations that describe all physical processes are valid only under certain assumptions. One of them is the minimum scales used for the given description. In fact, this prohibits the use of derivatives in the mathematical models of the physical processes. This article represents a derivative-free approach for the mathematical modelling. The proposed approach for CFD and numerical heat transfer is based on the conservation and phenomenological laws, and physical constraints on the minimum problem-dependent spatial and temporal scales (for example, on the average free path of molecules and the average time of their collisions for gases). This leads to the derivative-free governing equations (the discontinuum approximation) that are very convenient for numerical simulation. The theoretical analysis of governing equations describing the fundamental conservation laws in the continuum and discontinuum approximations is given. The article demonstrates the derivative-free approach based on the correctly defined macroparameters (pressure, temperature, density, etc.) for the mathematical description of physical and chemical processes. This eliminates the finite-difference, finite-volume, finite-element or other approximations of the governing equations from the computational algorithms.

Shortcut model to evaluate the performance of continuous preferential crystallization for conglomerates forming chiral systems

The separation of two enantiomers of a chiral molecule is one of the most difficult tasks for separation technology. Among the available methods, Preferential Crystallization (PC) offers a relatively simple and efficient possibility to separate pairs of enantiomers of conglomerate forming chiral systems. To estimate the potential and to design PC processes, mathematical process models are required. Recently, a short-cut model (SCM) was developed which was found capable to predict the course of batch-wise operated PC until nucleation of the unseeded counter-enantiomer terminates the exploitable production period. In this paper the SCM is reformulated in a dimensionless way and extended to describe also more productive continuous operation of PC. Characteristic dimensionless numbers are demonstrated to be instructive to evaluate effects of system specific kinetic parameters and to identify suitable operating conditions. The sensitivity of the continuous PC process with respect to the most relevant model parameters is investigated based on simulation results. Finally, the role of the SCM in the workflow of designing continuous PC processes is summarized.

Mathematical modeling and performance evaluations of a wood drying process using photovoltaic thermal and double-pass solar air collectors

This research conducts a novel and complete 4E assessments and introduces an innovative method for examining solar wood drying systems. The software TRNSYS and MATLAB programming are combined to simulate and create a numerical program. This novel combination allows for a thorough examination that goes beyond conventional assessments of wood drying. The aim is to evaluate the effectiveness of a solar wood dryer using two different collectors, a double-pass and a photovoltaic thermal collectors, in terms of four key aspects: energy, exergy, economic, and environmental. Further, the drying process was investigated under various climates in three African cities (Errachidia, Dakar, and Nouakchott). The moisture content of wood was reduced from 74% to 12% in the three cities. Elaborate simulations were performed and the results were confirmed by experimental validation, using methods including Mean Absolute Error, Mean Relative Error, and Root Mean Square Error.The primary findings of this study are the following: In the double-pass dryer, the drying time required in Errachidia, Dakar, and Nouakchott was 139h, 189h, and 170h, respectively. Whereas in the photovoltaic thermal dryer, it needed 192h in Errachidia, 210h in Dakar, and 189h in Nouakchott. Further, using photovoltaic thermal, the dryer exhibited superior exergy efficiency compared to the use of double pass collector. Photovoltaic thermal collector reduces yearly CO2 emissions by an average of 54.87, 66.2, and 44.11 tonnesCO2 in Errachidia, Dakar, and Nouakchott, respectively. In contrast, double pass collector reduces CO2 emissions by an average of 38.49, 57.9, and 38.56 tonnesCO2 in Errachidia, Dakar, and Nouakchott, respectively, throughout the year. Further, the solar dryer, using double pass collector, has a shorter payback time than using photovoltaic thermal collector, indicating a quicker economic return.

Применение принципа Понтрягина для оптимального отключения энергетического ядерного реактора

The theory of optimal control is based on two approaches, the dynamic programming method (Bellman equation) and Pontryagin maximum principle. Pontryagin maximum principle is applied in the physics of nuclear reactors when optimizing various transient processes. The mathematical justification of this theory is based on the elements of convex analysis, which is not used by physicists and engineers, so the physical issues are less studied in scientific literature. The subject of the study is a nuclear power reactor of the WWER type. The problem of minimizing its shutdown time, bypassing the iodine pit is solved and it is possible to start up the reactor at any moment after its shutdown. Analytical and numerical methods are used. The paper considers an example of applying the maximum principle for optimal control of the process of shutting down a nuclear reactor bypassing the iodine pit. A physical mathematical model of the Pontryagin principle is formulated. The process of optimal control of reactor shutdown for large and small reactivity margins is justified and calculated. Pontryagin principle does not contain an algorithm to find an optimization process; the stages of the process must be selected based on physical considerations, but these stages must satisfy the specified principle. Based on the Pontryagin principle, the results of the study make it possible to draw up a step-by-step action plan when shutting down a WWER-type reactor with any value of the reactivity margin and its switching is possible at any time after the transition process, which avoids downtime. The proposed plan can be used both in mathematical modeling of transient processes in a reactor and in reactor control systems to improve its controllability and, consequently, to improve safety.

Anthropogenic impact on agricultural landscapes of the Akmola region of the Republic of Kazakhstan

The relevance of research topic is confirmed by the presence of environmental problems of steppe land use and the need for its rationalization. The article examines the issues of ecological stability of agrolandscapes of the steppe zone in agricultural circulation and determines environmental and economic damage that occurs when their functioning is disrupted. The goal is to assess the degree of anthropogenic influence when using agricultural landscapes based on the example of the Akmola region. The content of research topic determined the choice of the following methods: historical, logical, statistical, system analysis, graphic modeling. Results - taking into account factors that destabilize the landscape-ecological balance, ecological zoning was carried out in the region, the degree of stability of steppe agricultural landscapes under anthropogenic influence was determined, based on mathematical model of erosion process, intensity of washout was calculated, environmental and economic losses arising in connection with violation were indicated, self-regulation of landscapes, environmental protection (antierosion) measures have been developed. The amount of residual flushing after they are carried out characterizes the effectiveness of reducing the water flows. Conclusions - field agrolandscapes of agricultural enterprises of the Akmola region, specializing in production of crop products, can be classified as anthropogenically disturbed with low degree of environmental stability, which is due to the significant plowing of their territory. One of the main factors of environmental destabilization in steppe agricultural entities is the spread of water erosion on slope arable land, environmental damage from which is confirmed by the loss of soil layer. The proposed measures to support landscape environmental stability can be applied when planning the use of land resources and developing on-farm land management projects.

Influence of connecting a new gas pipeline to the operating gas pipeline on the flow rate of production wells

In some cases, it is necessary to connect new line to the pipeline. From this point of view, in the presented work, serious changes occurring in the pipeline as a result of connecting a new gas pipeline to the operating gas pipeline are investigated. The changes occurring in the pipeline are transmitted to the formations, which causes a violation of the stable operation of the wells in the initial period. After a certain period of time, the dynamic processes formed in the system as a result of changes in the transport line become stationary. From this point of view, it is of great practical importance to consider the stationary state of the processes occurring in the system. Therefore, in the presented work, as a result of the addition of a new line to the pipeline, the change in the production of gas wells in stationary regime conditions is studied. The effect of these changes on the operating mode of the wells, the effect on the change in production of operational wells is studied. Taking into account the interaction of the layer-pipeline system, a mathematical model of the movement process of gas and gas-liquid mixture is established, using the equations of motion and continuity, the resulting system of related differential equations is solved. With the help of the obtained formulas, the pressure drop and production reduction for each well are calculated during the connection of the new line. Numerical calculations are performed using various practical values of system parameters and the obtained results are analyzed. Keywords: production; layer; pressure; pipeline; stationary state; gas-liquid mixture; motion and continuity equation.

Mathematical understanding (hermeneutic aspects of educational activities)

The article discusses the issues of mathematical understanding as an educational practice of identifying the algorithmic meanings of mathematical (mathematized) educational texts. The hermeneutic orientation towards following the “guiding thread of language” (G.-G. Gadamer), as it is shown, cannot be narrowed to the attitude towards natural languages inherent in humanitarian educational practices. The “common place” of mathematical understanding in educational practices is: some of created languages (of scientific communication) being consolidated around the mathematical installation are not reducible to its sign universality or educational generalizations. But it often turns out to be outside the field of view of practicing teachers, in a didactically abstract position. The article substantiates the possibility of rehabilitating the hermeneutic attitude in mathematical education in connection with its development and strengthening in understanding the prerequisites for the algorithmic solution of mathematical problems (the need for additional information, non-standard solution techniques, transfer of educational goal setting to the area of interdisciplinary relationships or life experience, etc.). The author shows and comments on the effectiveness of the hermeneutic approach in mathematics education using examples of solving problems in algebra, geometry and in constructing mathematical models of various physical processes.

Частная полумарковская модель как инструмент снижения сложности задачи оценивания устойчивости функционирования элементов информационной инфраструктуры, подверженной воздействию угроз

Decision-making on information infrastructure (II) security for its sustainable functioning in the face of threats requires a tool to assess the sustainability of its individual elements. The application of the semi-Markov model to assess the stability of the functioning of elements of II exposed to threats in a direct setting is associated with the increasing complexity of the description of the object of delineation (parametric space) in step progression from the number of the considered impacts, which reduces its practical significance. However, no studies have been found in the scientific literature to reduce the complexity of the semi-Markov model. The article presents an approach to reducing the complexity of modeling by adopting correct assumptions when forming the initial data. Given the conditions under which it is possible to take a series. It was a cost to limit the applicability of the model by significantly reducing the complexity of the modelling. The problem statement and the modified transition graph are given. The novelty of the problem statement is to take into account the limitations on the available resources for the restoration of functionality of the element. To explain the physical essence of the modeling process, a thought experiment with a model is introduced. To solve the problem, the following methods were used: a) expert methods for extraction of initial data; b) mathematical models of private semi-Markov processes; c) methods of transformation of Laplace; r) methods of planning of experiment. Illustrative examples and graphs accompany the task sequence demonstration. As a result of the experiment, the regularities of the studied process, the existence of which was proved formally. As a result of the experiment, the regularities of the studied process were revealed, the existence of which was officially proved. The results of the study broaden knowledge about the application of methods of Markov processes to assess the stability of the functioning of AI elements in relation to the conditions of the impact of threats.

Simulation of a Heat Transfer Mechanism in a Shell and Tube Coil Heat Exchanger

Statement of the problem. The mechanism of heat exchange between counterflow circuits in a shell-and-tube coil heat exchanger, inside which heating and heated coolants flow, is discussed. It is required to build computer models of the movement of coolants in different operating conditions, to simulate the mechanism of heat exchange in the countercurrent mode of movement of coolants in a shell-and-tube coil heat exchanger. This problem was solved in the Solidworks Flow Simulation software package. Results. A mathematical model of the heat exchange process in a shell-and-tube coil heat exchanger was obtained with visualization of the mechanisms of coolant movement inside the heating and heated circuits. Conclusions. Based on the simulation results, a comparison was made of various computer models of the apparatus obtained. The optimal design has been determined.

Investigation of the transient change of the cutting force during the milling of C45 and X5CrNi18-10 steel taking into account the dynamics of the electro-mechanical measuring system

The possible methods of determining the cutting force—due to the great practical importance of knowing the force—have long been and are still intensively studied areas of cutting theory. In milling, cutting is a series of successive short material removals. During force measurement in such cases, the transient process that can be detected at the beginning of the process can influence the nature of the entire cutting cycle. The present study reports on the research, the aim of which was to explore the dynamic process of cutting force measurement in intermittent cutting. The measurements were made during face milling of C-steel and highly alloyed steel (X5CrNi 18–10). The milling head contained a single insert, with which the disturbing interaction of the multiple cutting edges was eliminated. As a result of the work, a method suitable for examining the close relationship between the initial transient nature of the milling cycle and the decay, as well as a mathematical model for the decay process, was developed. The model was validated with cutting experiments and measurements. The achieved results can be used to better understand the process of chip removal and to determine the actual power requirements of milling works.

Physical Analysis and Mathematical Modeling of the Hydrogen Storage Process in the MmNi4.2Mn0.8 Compound.

The results of an experimental and mathematical study into the MmNi4.2Mn0.8 compound's hydrogen storage properties are presented in the present research. Plotting and discussion of the experimental isotherms (P-C-T) for different starting temperatures (288 K, 298 K, 308 K, and 318 K) were carried out first. Then, the enthalpy and entropy of formation (ΔH0, ΔS0) were deduced from the plot of van't Hoff. Following that, the P-C-T were contrasted with a mathematical model developed via statistical physics modeling. The steric and energetic parameters, such as the number of the receiving sites (n1, n2), their densities (Nm1, Nm2), and the energy parameters (P1, P2) of the system, were calculated thanks to the excellent agreement between the numerical and experimental results. Therefore, plotting and discussing these parameters in relation to temperature preceded their application in determining the amount of hydrogen in each type of site per unit of metal ([H/M]1, [H/M]2) as well as for the entire system [H/M] versus temperature and pressure besides the absorption energies associated with each kind of site (ΔE1, ΔE2) and the thermodynamic functions (free energy, Gibbs energy, and entropy) that control the absorption reaction.

Mathematical model for assessing the influence of vibrations for multicopter elements

The article discusses the problem of studying the probabilistic characteristics of vibrations of the propellermotor group of an unmanned aerial vehicle such as a multicopter. The results of the research are presented in the form of quantitative values of the vibration parameters of the propeller-motor group of the agrodrone at given values of the input parameters of the electric drive control system, taking into account the influence of external factors. It is shown that the values of the parameters characterizing the vibrations of the propeller-motor group of the agrodrone can be different depending on the operating modes of the engines and changes in external conditions.Based on the experimental studies carried out, sets of measured random vibration parameters were obtained, which made it possible, based on the application of mathematical statistics methods, to calculate the mathematical expectations and dispersions of the amplitudes and velocities of vibration processes. The obtained probabilistic characteristics make it possible to study emissions (crossing a given level) of processes, to evaluate the intensity and probabilistic characteristics of the process going beyond the given boundaries.A mathematical model of the vibration process is substantiated, which allows, on the basis of the obtained experimental data, to assess the influence of vibrations on the elements of equipment installed on a multicopter, to assess its performance and reliability, and to determine tolerances on equipment parameters. The computer modeling of the probabilistic characteristics of vibration processes clearly demonstrated the efficiency of the proposed research methodology.

Electric discharge process modelling when piston pins recovery in internal combustion engines

Introduction. The relevance of the topic of the presented article is determined by the improvement of the technology for repairing and restoring machine parts. Currently, the technology of restoring piston pins of internal combustion engines (ICE) by a high-energy method of plastic deformation of metal using the energy of a high-voltage pulse discharge in a liquid is widely used – the electrohydraulic effect, and on its basis electrohydraulic processing. The purpose of the article is to increase the efficiency of the method of restoring piston pins of internal combustion engines due to the use of the electrohydraulic distribution method.Materials and methods. The research methods such as the analysis of the degree of influence of the electrical parameters of the electrohydraulic distribution process on the amount of deformation of the piston fingers depending on the relevant material were used. The article discusses a mathematical model of the electric discharge process when restoring piston pins. The calculation method determines the modes and parameters of the process of electrohydraulic distribution of piston pins while maintaining their fatigue life, static strength and wear resistance.Results. In this work, the degree of influence of the electrical parameters of the electrohydraulic distribution process on the amount of deformation of the piston pins, depending on the product material used, is established. A mathematical model of the electric discharge process during the restoration of piston pins has been developed, and based on them, the modes and parameters of the process of electrohydraulic distribution of piston pins have been determined while maintaining their fatigue life, static strength and wear resistance.Discussion and conclusions. The studies have shown that exploding wires made of iron, copper, and tungsten are not effective in restoring piston pins with an internal radius of up to 10 mm. The pressure in the case of their use does not exceed 100 MPa. Exploding Al wires with a diameter of less than one millimeter have the greatest effect. In this case, the inductance of the circuit should be minimal, because this provides the largest share of the energy released in the discharge channel from all stored in the capacitor. This ensures the highest pressure in the channel. Based on the same considerations, the capacity should be limited to a range of 3-12 UF. This method can be applied to the restoration of other car parts.

A mathematical model of the copper plating process in restoration of road transport equipment parts

Introduction. The use of restored parts of motor vehicles makes it possible to reduce the financial costs of repairing equipment. The cost of the restored parts should not exceed 50% of the cost of the new part. Increasing the productivity (deposition rate) of an electrolytic copper coating during the restoration of parts of motor vehicles requires taking into account the technological and economic aspects of the restoration process. The study of the factors (deposition conditions) that most affect the deposition process of the copper coating, the analysis of the experimental results and its statistical processing made it possible to optimize the technology of restoration of copper parts to create the most appropriate deposition modes with maximum productivity, thus reducing the cost of restoration of parts of motor vehicles. The purpose of the research is to develop a mathematical model of the effect of deposition conditions (electrolyte temperature, cathode current density) and electrolyte composition (concentration of copper sulfate and sulfuric acid) on the performance of the deposition process of copper coating, for further development of the most productive technology for restoring collectors of electric motors of motor vehicles.Materials and methods. The studies on equipment that allows obtaining the necessary data with the required accuracy were carried out. Mathematical processing using modern statistical data processing tools that excluded possible errors, providing to obtain the dependence of factors with the necessary accuracy was carried out.Results. In the course of studies of copper sulfate electrolytes to obtain an electrolytic copper coating, with the further development of technology for the restoration of automotive parts, it became necessary to determine the effect of deposition conditions – “factors” (cathode current density, electrolyte temperature, copper sulfate concentration, sulfuric acid concentration) on the deposition rate – “response”. It was found that the factor “cathode current density” and the combination of factors “cathode current density” and “sulfuric acid concentration” are the most significant. The deposition conditions in order to obtain the most productive technology for restoring collectors of electric motors of motor vehicles by depositing a copper coating have been optimized. According to the obtained model, the optimal values of the deposition conditions for obtaining the maximum deposition rate are the electrolyte temperature of 35...40 ° C, the cathode current density of more than 5 A/Dm2, the concentration of copper sulfate 200...250 g/l, the concentration of sulfuric acid 40...70 g/l.