Mathematical Model Of Process Research Articles

Analysis of the sintering process of the sintering charge in a high layer. Report 1. Fuel combustion and dissociation of limestone

Communication 1 provides a brief overview of theoretical works on the creation of mathematical models of the sintering process, ranging from simplified balance models to the three-dimensional dynamic model. A modern three-dimensional mathematical model is adapted from industrial data on the agglomeration of a sinter mix in a bed 700 mm high with a bed of sinter at the sinter plant No. 5 of PJSC “MMK”. Changes in the device circuit diagram of sinter plan, the actual temperature of the mix, segregation of fuel along the height of the bed, the mode of intensive ignition of the mix in the ignition hearth with diffusion burners, the unevenness of the sintering process across the width of the pallets, additional heating of the bed after the hearth with air from a linear cooler, the actual degree of throttling of the vacuum chambers of the sinter machine, heat exchange in pallets are taken into account. The process of a combustion zone of solid fuel formation under the ignition hearth has been analyzed, and an increase in its height during the sintering process in a high bed has been established, that due to the segregation of mix and fuel along the height of the bed and the consumption of oxygen for the oxidation of FeO above this zone. The processes of limestone dissociation and melting of the mix zones formation and their development during the sintering process are considered

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.

Diagnostics of the technical condition of wells drilled through freshwater horizons using active thermometry

Relevance. Recently, ESG (Environment, Social, Governance) principles have been given an important role in the agenda of oil and gas companies – this is an actively developing global trend in the modern business environment. One of its key aspects is a responsible attitude to the environment, increasing the priority of solving environmental problems arising from the extraction of hydrocarbons. A significant environmental problem is, in particular, pollution of freshwater horizons during oil production due to their poor-quality insulation during well cementing. At the same time, in the space of the well behind the casing, there is a flow of borehole fluid to freshwater horizons, which has a negative impact on the environmental situation in this region. In this regard, monitoring the technical condition of wells crossing freshwater horizons is an important and urgent task. Object. An operational well drilled through freshwater horizon, in which geophysical studies are carried out by the method of active thermometry – local heating of the casing section is carried out and the dynamics of the temperature field in it is studied. Aim. To identify qualitative patterns and obtain quantitative estimates of the effect of the fluid flow in the space behind the casing (column space) on the temperature field in the casing. Methods. Numerical mathematical modeling of thermal and hydrodynamic processes in a well using the software package Ansys Fluent (ANSYS Academic Research CFD license, agreement with Bashkir State University dated 06/15/2020). Results. The authors have studied the influence of a plane-parallel horizontal fluid flow of the freshwater horizon on the azimuthal temperature distribution of the casing string during induction heating. It is shown that in the case of leakiness of the cement ring in the interval of the freshwater horizon, an inhomogeneity of the azimuthal temperature distribution of the column is observed, reaching a value of few more K. The authors carried out the simulation of induction heating in the well with liquid column flow to the interval of the freshwater horizon. It is shown that the sign indicating the overflow is the occurrence of a temperature disturbance area vertically above the induction heating interval with a length of more than 1 m. In general, the results of the performed studies show the informativeness of the active thermometry method in relation to the diagnosis of the technical condition of wells drilled through freshwater horizons.

Advanced Statistical Approach for the Mathematical Modeling of Transfer Processes in a Layer Based on Experimental Data at the Boundary

Advanced Statistical Approach for the Mathematical Modeling of Transfer Processes in a Layer Based on Experimental Data at the Boundary

A new strategy to produce calcium carbide-acetylene from integrated multi-level low carbon construction driven by biomass

A highly efficient and clean biomass energy-based calcium carbide-acetylene production system, including low-carbon energy supply, solid waste recycling and cascade utilization of waste heat, has been developed for the conventional energy-intensive and highly polluting fossil fuel-dependent calcium carbide industry. This system supplies the carbide-acetylene production plant with energy from the gasification of biomass and converts the plant's solid waste carbide slag into the calcium feedstock required by the plant. The waste heat from the plant's high-temperature exhaust gases is recycled and used via the multi-stage heat exchange, so that the energy cascade conversion and utilization is achieved. A simulation model of the plant is created in Aspen Plus, and a mathematical model for the biomass gasification process and cycle compensation of the calcium source through the Fortran language is written and embedded. When calculating the carbon consumption and CO2e emissions of the system, it was found that the carbon consumption and CO2e emissions of the conventional process were 5.43 t Coal·t−1C2H2 and 2.25 t CO2e·t−1C2H2, respectively. However, the carbon consumption of the new process was reduced by 65.19%, and carbon emissions by 27.24% in comparison. The energy analysis shows that the energy efficiency of the system is 36.21% for the conventional process and 44.82% for the new processes. The exergy analysis of the effective energy shows that the exergy efficiency of the new process is 73.20%, which is 52.98% better than that of the conventional process. Introduction of an index, the levelized income of acetylene product (LIOA), to characterize the product income of the system. When the price of acetylene is between 2.23 $/kg and 4.19 $/kg, the LIOA for the conventional and the new processes are 1.41 $/kg to 3.38 $/kg and − 1.28 $/kg to 0.68 $/kg, respectively. It is worth noting that the critical price (PCC2H2) for products generating net revenue from the new process is 3.17 $/kg. This study is of great importance for the development of a low-carbon biomass-coupled calcium carbide-acetylene process.

Modeling of Non-Stationary Mass Transfer Process in Groundwater

Purpose. Infiltration of contaminated water and accidental spills of chemically hazardous substances into groundwater lead to the formation of large zones of man-made pollution in aquifers. Therefore, it is important to develop protection systems against groundwater pollution. To analyze the effectiveness of such protection systems at the design stage, it is necessary to have scientifically based information on the dynamics of changes in groundwater contamination zones. Such information can be obtained using the method of mathematical modeling. The study aims to create a numerical model for calculating the non-stationary process of geomigration when using chemical protection of groundwater from pollution. Methodology. To describe the dynamics of groundwater flows, two filtration equations are considered, which allow mathematical modeling of the filtration process both for solving planned problems and for solving problems of specialized filtration. A two-dimensional geomigration equation was used to analyze changes in groundwater quality. This equation takes into account the convective transfer of impurities in the filtration flow, dispersion, and the intensity of impurity infiltration into the groundwater flow. This equation is also used to calculate the movement of the neutralizer in groundwater. The numerical integration of the filtration equation was performed using finite difference methods. An implicit splitting scheme was used to numerically integrate the geomigration equation. Findings. A fast-applicable numerical model for calculating groundwater dynamics has been built. The model is also a platform for solving another important task – the calculation of geomigration processes. A numerical model for calculating the unsteady-state geomigration process is proposed, which makes it possible to assess not only the process of formation of contamination zones in the groundwater flow, but also to determine the effectiveness of the method of neutralizing the impurities in the groundwater flow. Originality. Effective numerical models for rapid assessment of changes in groundwater dynamics and quality under the influence of anthropogenic sources have been developed. These models take into account a set of important physical factors that affect the process of geomigration and the process of neutralizing the impurity in the groundwater flow. Practical value. A computer program has been developed that allows determining the effectiveness of the process of neutralizing an aggressive impurity in groundwater by a computational experiment to protect it from anthropogenic pollution.

Competitive Adsorption of Aqueous Cd(II) and Pb(II) Solutions onto Silicas Synthesized with Saponin as Template Agent

The aim of the research was to prepare silica adsorbents using an environmentally friendly pathway, a template synthesis with saponin biosurfactant as a structure-directing agent. The adsorbents prepared in this way exhibit improved adsorption properties while maintaining environmental innocuousness. For the preparation of porous silica, the biosurfactant template sol–gel method was used with tetraethoxysilane as a silica precursor. The silica adsorbents were analyzed by FTIR spectroscopy, nitrogen adsorption–desorption and SEM/EDX microscopy, TEM/HRTEM microscopy, and thermogravimetric analyses. Batch tests were carried out to remediate Pb(II)/Cd(II) ions in single/binary aqueous solutions, and the effect of the surfactant on the adsorption properties was assessed. The optimal adsorption parameters (pH, contact time, initial concentration of metal ions) have been determined. The adsorption was fitted using Langmuir and Freundlich adsorption isotherms and kinetic models. Mathematical modeling of the retention process of Pb(II) and Cd(II) ions from binary solutions indicated a competitive effect of each of the two adsorbed metal ions. The experimental results demonstrated that saponin has the effect of modifying the silica structure through the formation of pores, which are involved in the retention of metal ions from aqueous solutions and wastewater.

Calculation algorithm for electromagnetic wave processes in multi-wire intersystem ETL

The nature of the transient process and the magnitude of the overvoltages are determined by a large number of factors in the HV/EHV AC transmission networks. The paper presents the study of mathematical modelling of electromagnetic wave processes in long-distance electric transmission line (ETL). The mathematical model is based on electromagnetic processes occurring on distributed parameter lines that are characterized by specific derivatives of the system of differential equations. The application of a spline-interpolation technique enables the calculation of currents and voltages at the nodes of the scheme, which obtains the unknown coordinates of the overhead line mode at the beginning of the ETL to solve the transmission line equation. The following results are derived from computer simulations of transients during switching on. With a simulation model, the importance of intelligent control of shunt reactor (SR) and ungrounded reactor (UR) was demonstrated and considered for a 500 kV power networks.

Application of artificial intelligence to chronic kidney disease mineral bone disorder.

The global derangement of mineral metabolism that accompanies chronic kidney disease (CKD-MBD) is a major driver of the accelerated mortality for individuals with kidney disease. Advances in the delivery of dialysis, in the composition of phosphate binders, and in the therapies directed towards secondary hyperparathyroidism have failed to improve the cardiovascular event profile in this population. Many obstacles have prevented progress in this field including the incomplete understanding of pathophysiology, the lack of clinical targets for early stages of chronic kidney disease, and the remarkably wide diversity in clinical manifestations. We describe in this review a novel approach to CKD-MBD combining mathematical modelling of biologic processes with machine learning artificial intelligence techniques as a tool for the generation of new hypotheses and for the development of innovative therapeutic approaches to this syndrome. Clinicians need alternative targets of therapy, tools for risk profile assessment, and new therapies to address complications early in the course of disease and to personalize therapy to each individual. The complexity of CKD-MBD suggests that incorporating artificial intelligence techniques into the diagnostic, therapeutic, and research armamentarium could accelerate the achievement of these goals.

CONSTRUCTIONS OF THE PROTECTIVE STRUCTURES UNDER THE CONDITIONS OF HIGH-SPEED IMPACT

The stability of the building is characterized by the depth of penetration of the punch into the body of the structures, as well as their local damage due to the impact load. There was accumulated experience of mathematical modeling of the impact processes of solid bodies on various targets. The range of deformations changes of the reinforced concrete elements ("slab"), which corresponds to the high-speed interaction at the moment of punching by a solid body ("impactor") with an initial impact speed of up to 1000 m/s, as well as the determination of their dynamic nature of deformation require comprehensive justification. The analytical solution of the mathematical system of equations describing the movement of the impactor, as well as the state of the impactor and the slab during their interaction can be applied in a limited range. Therefore, the assessment of the local effect of the impact can be carried out on the basis of the results of experimental studies using empirical formulas, as well as numerical methods of modeling the work of bodies taking into account their elastic-plastic characteristics. The ANSYS software package was used in the conducted research, which implements a system of mathematical equations that describe the movement and state of the "impactor-slab" during their interaction. Based on the results of the performed numerical modeling, it was established that the tested slabs with the use of combined reinforcement - mesh and dispersed metal fiber - are not penetrated by the impactor, part of the sample remains intact. At the same time, the final speed of the impactor in these slabs is up to 35.0% less than in the slabs with the mesh reinforcement. The penetration depth decreased up to 20.0%. The experience of dispersion strengthening of the concrete indicates the inhibition of cracking in the fiber concrete elements, which makes it expedient for usage in the combined reinforced constructions of the protective structures, capable of withstanding the dynamic impacts under conditions of high-speed impact. Further development of the of technological concretes studies is needed for their possible use in barrier structures of protective structures.

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.

Multi-mode Optimization of Diesel Engine Turbocharging

The thermogasdynamic engine system consisting of a number of subsystems of varying complexity is considered. The solution to the optimization problem in general is carried out by a multi-step iterative process of exchanging information between the levels repeatedly with refinement for all successive iterations of the initial data. Mathematical models of gas-dynamic processes in the flow section in variable modes, the simulation model of a gas turbine engine, and the model of multi-mode optimization of a gas turbine engine have been developed. The optimization of general-mode parameters is carried out in the space of points each of which reaches a minimum expression for the mode parameters.

Can physics-informed neural networks beat the finite element method?

Partial differential equations (PDEs) play a fundamental role in the mathematical modelling of many processes and systems in physical, biological and other sciences. To simulate such processes and systems, the solutions of PDEs often need to be approximated numerically. The finite element method, for instance, is a usual standard methodology to do so. The recent success of deep neural networks at various approximation tasks has motivated their use in the numerical solution of PDEs. These so-called physics-informed neural networks and their variants have shown to be able to successfully approximate a large range of PDEs. So far, physics-informed neural networks and the finite element method have mainly been studied in isolation of each other. In this work, we compare the methodologies in a systematic computational study. Indeed, we employ both methods to numerically solve various linear and nonlinear PDEs: Poisson in 1D, 2D and 3D, Allen-Cahn in 1D, semilinear Schrödinger in 1D and 2D. We then compare computational costs and approximation accuracies. In terms of solution time and accuracy, physics-informed neural networks have not been able to outperform the finite element method in our study. In some experiments, they were faster at evaluating the solved PDE.

Analysis of the influence of uneveneity of the sintering process of the barch on the operation of the sintering machine

Literature data on the unevenness of temperature and composition of the gas leaving the sintering bed across the width and length of it and their influence on the productivity of sinter machines are considered. An analysis of the technologies reasons for the unevenness of the sintering process was carried out. It is shown that the reasons for the width of the pallets include the distribution of the mix bed in the loading bin, air leaks into the ignition hearth, the wall effect at the side plates of the pallets, the shape and angle of inclination of the sides relative to the grates. Along the length of the sinter machine, the unevenness of gas flow and composition is due to a decrease in the gas-dynamic re-sistance of the bed during the sintering process, segregation of the mix and fuel along the height of the bed, completion of bed drying and gaps between pallets. Using an adapted mathematical model of the sintering process, a comparison was made of the parameters of the basic (non-uniform) and calculated uniform operating modes of the AKM-312 sinter machine of the Steel Plant NLMK. I It has been established that with the vertical installation of the pallet sides accepted in the calculations that an increased gas flow rate at the periphery of the bed is accompanied by an increase in gas temperature with a corresponding decrease in the suction before exhausters. It was found that during the transition from the base to the uniform mode of operation of the sinter machine, the gas temperature in front of the exhausters decreased from 99.6 to 85.1 °C, the suction increased from 13.54 to 14.26 kPa, and in the collecting collector – by 1.15 kPa. The productivity of the sinter machine increased by 4.1%. When installing pallet sides vertically, the effectiveness of increasing the height of the layer on its periphery instead of compacting it and constructive solutions has been justified. Its increase provided an additional productivity of the sinter machine by 1.8%, a total of 5.9%. It has been shown that due to the simultaneous increase in gas temperature over the entire width of the bed in the final period of the sintering process, with a uniform operating mode of the sinter machine, the maximum gas temperature at the end of the process increases with a lower one – in front of the exhausters. From the point of view of the capabilities of exhausters in terms of the created suction, the accepted representation of their gas-dynamic characteristics at a temperature of 150 °C, which is possible only with a high level of unevenness of the sintering process, is not reasoned

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.