The purpose of the study is to develop an identification method of a specific implementation of the elements of the measuring part (intermediate converters, analog filters) and partially computational-logical part (digital filters) of a microprocessor relay protection by the signal actuation time, which, unlike the existing approaches allows to identify and exclude the delays introduced by the executive protection elements. The method of directed graphs is used to form a mathematical model of the measuring part of the microprocessor relay protection. The solution formed as a result of differential equations is implemented using the method of analog implicit continuous integration. The time delays introduced by the input protection circuits are determined as follows: identical signals are fed to the terminal and the mathematical model of protection; signal actuation time is recorded, where the time starting point is the moment the input signal reaches the setpoint and the end point is the moment of the actuation signal occurrence. Having studied 144 different combinations of measuring part elements (intermediate converters, analog filters) and digital filters with a finite impulse response of microprocessor relay protection, the most “optimal” combination has been chosen, which features the least deviation from the response time of a real device in all studied modes as compared with other combinations. The proposed identification method of input circuit elements of microprocessor (numerical) protection is the main way to bring the model closer to a real device. It also enables to receive a table of “typical” response times of protections with the different structure of the measuring part and depending on the specific type of protection terminal choose in practice a predetermined “optimal” internal composition of protection used when setting up protection using their mathematical models.

The purpose of the paper is to develop a methodology for modeling railway power supply systems equipped with a set of devices implemented on the base of smart grid technologies. The research is carried out using the Fazonord software package designed for modeling the modes of railway power supply systems in phase coordinates. The calculation model is implemented for the power supply system of a two-track section with five traction substations. The results obtained show that reliable and high-quality power supply of train traction and non-traction consumers can be ensured on the basis of the integrated use of active Smart Grid elements, such as a phase number converter, active harmonic conditioner, controlled reactive power source, and a distributed generation unit. Computer simulation allows to establish that in the absence of reactive power sources there are noticeable voltage fluctuations on 10 kV buses of non-traction consumers; the asymmetry is approaching the limit of normally acceptable values; disabling of the active filter results in the increase of the total harmonic coefficient of voltages up to 16%; if the entire complex of active devices is available, the high quality of electrical energy is achieved; the phase number converter is robust and features low sensitivity to the errors in parameter setting; voltage deviations caused by the limited variation range of reactive power in the reactive power source are short-term and do not exceed the values acceptable in practice. Thus, on the basis of Smart Grid technologies, distributed generation units can be connected directly to the traction network using a phase number conversion device formed according to the reciprocal Steinmetz circuit. Elimination of harmonic distortions created by rectifier electric locomotives is carried out by means of an active conditioner of higher harmonics. A controlled reactive power source can be used to maintain voltage levels.

The purpose of this work is to study the self-starting of induction motors for the auxiliary needs of power plants and substations as well as the mutual influence of motors on each other under short-term voltage dips and after voltage recovery on the buses to which these motors are connected. The object of the research is the operating VIII section with the capacity of 0.4 kV of the auxiliary service system with 9 induction motors of the heat and power plant no.1 in the city of Dushanbe (Republic of Tajikistan). Simulation modeling was carried out in the software package Electrical Transient Analyzer Program (USA) using algebraic and simplified differential equations to determine the values of indicators of static and dynamic stability of auxiliary needs of power plants and substations. As a result of modeling, the values of indicators of static and dynamic stability of the auxiliary needs system of power stations are determined. Based on the results obtained the margins of static and dynamic stability of auxiliary needs of power plants and substations are constructed and the conditions for implementing the optimal self-start, which allow to ensure uninterrupted operation of responsible mechanisms with induction motors at voltage dips are determined. The developed methods for studying the self-starting of power plant and substation auxiliary need induction motors ensures more accurate determination of the values of static stability voltages and dynamic stability time. The developed simulation model allows to specify and determine the success of induction motor self-starting in the systems of power plant and substation auxiliary needs. The developed methods are recommended for more precise selection of operating values for relay protection and automation as well as technological protection in the systems of auxiliary needs of power plants and substations with induction motors for more reliable operation of the main and auxiliary technological equipment.

The purpose of the paper is to study the energy and operational parameters of a belt conveyor under two starting methods: direct and frequency. Taking into account the non-linearity of the mathematical description of belt conveyor mechanical part and induction motor drive, the analysis of starting modes is carried out by the method of nonlinear differential calculus where equivalent masses are replaced with the discrete ones. The calculations are performed on the models using MATLAB. It is found out that the use of a frequency converter for the conveyor allows to reduce the maximum current by 4.7 times when starting the motor; by 2.5 times the maximum moment; by 1.52 times the maximum moment of resistance forces on the motor shaft; by 8.68 times the maximum value of power losses in stator windings; by 10.2 times the total power losses; by 2.9 times the power consumed from the network; by 3.4 times the amount of energy losses in the stator windings; by 3 times the total energy losses; by 1.25 times the energy consumed from the network; by 3 times the maximum acceleration of the belt; by 3 times the overshooting values during transients by the values of leading tension forces of the belt on various sections of the conveyor; by 1.875 times the transients duration in terms of the leading tension forces of the belt on different sections of the conveyor. The developed mathematical model of the belt conveyor makes it possible to obtain quantitative estimates of energy and operational parameters of the installation under two starting methods: direct and frequency. The use of frequency start-up of the conveyor allows to decrease motor energy losses by 3 times. It also reduces motor heating as well as decreases the maximum values of belt tension forces on various sections of the conveyor by more than three times.

The purpose of this work is to develop a multi-agent model of an integrated energy supply system in the AnyLogic simulation software and to conduct a research on the operation and interaction of objects in this system using the obtained model. A multi-agent approach is proposed to study integrated energy supply systems as it enables to carry out a detailed research of interaction and coordination mechanisms of various elements and subsystems (energy sources, transport subsystems, active consumers, etc.) of the object under investigation. The model is implemented in AnyLogic simulation software that supports designing, development and documenting of the created models, carrying out computer experiments, parameter optimization according to some criterion that enables visualization of the mechanisms of interaction and connection between the agents. A multi-agent model of the integrated power supply system has been developed. Agent state diagrams that take into account the operation of its elements have been created and the principles of their interaction and coordination have been analyzed. The structure of the developed model of an integrated power supply system contains four types of agents and connections between them. An experiment has been conducted on the basis of the developed model, in which the optimal solution was found for energy supply of consumers. The results of the conducted computational experiment show that the specified conditions and restrictions are met; messages and parameters are correctly transmitted between the agents and the agents perform the assigned functions in the system. The results obtained will allow to model real power supply systems of any complexity in order to study the properties and improve the efficiency of these systems. The developed model enables the possibility to model complex processes in an integrated energy supply system which relate to production, transport, distribution and consumption of energy.

The purpose of the study is to analyze the practical implementation of high-voltage electrical equipment technical state estimation subsystems as a part of solving the lifecycle management problem based on machine learning methods and taking into account the effect of the adjacent power system operation modes. To deal with the problem of power equipment technical state analysis, i.e. power equipment state pattern recognition, XGBoost based on gradient boosting decision tree algorithm is used. Its main advantages are the ability to process gapped data and efficient operation with tabular data for solving classification and regression problems. The author suggests the formation procedure of correct and sufficient initial database for high-voltage equipment state pattern recognition based on its technical diagnostic data and the algorithm for training and testing sets creation in order to improve the identification accuracy of power equipment actual state. The description and justification of the machine learning method and corresponding error metrics are also provided. Based on the actual states of power transformers and circuit breakers the sets of technical diagnostic parameters that have the greatest impact on the accuracy of state identification are formed. The effectiveness of using power systems operation parameters as additional features is also confirmed. It is determined that the consideration of operation parameters obtained by calculation as a part of the training set for high-voltage equipment technical state identification makes it possible to improve the tuning accuracy. The developed structure and approaches to power equipment technical state analysis supplemented by power system operation mode data and diagnostic results provide an information link between the tasks of technological and dispatch control. This allows us to consider the task of power system operation mode planning from the standpoint of power equipment technical state and identify the priorities in repair and maintenance to eliminate power network “bottlenecks”.

The purpose of the work is to identify complex transient heat flow paths in the combustion chamber of engine, significantly improve the models of diesel engine heat flow, and study the effect of aluminum oxide coating by the galvanic plasma method on short-term and long-term reactions of the piston head. The analysis of operation of aluminum alloy coated diesel engine piston is carried out using a modified quasi-steady method and a finite element method. A thermodynamic analysis is presented using energy and state equations with corresponding gas heat transfer. Time-dependent boundary conditions are set on the gas-blown surfaces of 2D finite element transition models of combustion chamber components. It is shown that this methodology can reveal complex transient paths of the heat flow in engine combustion chambers and distribution details of heat losses in various cooling media. Numerical simulation has shown that the maximum temperature increase relative to the uncoated piston is 64.3% for the coating thickness of 0.13 mm. Tests have shown that the coatings can endure up to 280 thermal cycles. It is found out that predictions of numerical simulation are in good agreement with the results of experiments conducted with repaired pistons. The experimental operation of Cummins КТА 38 engines at Chernogorsk and Vostochno-Beysk coal mines has shown that the engine equipped after repair with the piston coated with aluminum applied by the galvanic plasma method has been in operation for 2 years and 3 months, whereas its set overhaul period is 18,000 hours. Therefore, the proposed methodology allows to reduce temperature variations in the piston and, thereby increase the service life of engine pistons coated with the use of the thermal barrier coating technology.

The purpose of the paper is to diagnose the state of a power transformer by determining its equivalent circuit parameters by means of synchronized vector measurements of currents and voltages in the transformer normal operation mode without shutdowns, which makes it possible to increase the reliability of relay protection operation. A cost-effective method for proactive diagnostics of power transformers is proposed. Through monitoring of additional parameters (short circuit resistance, active and inductive resistance of the positive sequence, active and inductive resistance of the negative sequence) it can increase the speed and accuracy of detecting possible internal short circuits arising due to winding damage or high-voltage transformer bushings without diagnosed transformer disconnection from the network. The method allows to estimate the transformer health index and serviceability by the difference between the calculated parameters of the equivalent circuit and the passport values of the parameters. Having conducted the damage cause dependent analysis of the number of power transformer damages, the authors determined total economic losses that include the losses caused by equipment damage and losses caused by the interruptions in consumer power supply. The total economic losses for a power transformer with a rated power of 63 MVA amounted to 10687402 rubles. It is shown that the diagnostic system expands the possibilities of analyzing the transformer state in operating modes, allows to prevent the approaching of the damage moment and occurrence of sudden accidents as well as minimizes the expected damage from shutdowns and equipment failure. A hardware and software complex is proposed for the diagnostics of power transformer internal damage. The given main characteristics of the proposed hardware and software complex include the number of measuring channels, accuracy class, sampling frequency, and others. The results of the work expand the possibilities of analyzing the transformer state in the operating mode and can be used in the world practice of creating various monitoring systems designed to identify the defects developing in transformers caused by winding deformation.

The purpose of the paper is to create a control system of edge quality under finishing machining of parts by elastic polymer abrasive tools, which are effective in surface conditioning and rounding of part edges. The principle of the system approach is used for a formalized description of the system characterized by the mutual interaction between the subsystems that form it. Consideration is given to the control system of these finishing operations design in order to ensure the required quality (in terms of surface roughness, size and geometric accuracy of edges) and optimal process performance under a large variety of tool designs and shapes of the processed surfaces and their mutual arrangement. The system includes input parameters, state space (subroutines) and output data. The input parameters of the system include equipment, workpiece and tool. The state space includes subsystems of mathematical interaction models of tool and surface and forces on the basis of which the mathematical models of material removal, roughness formation, power consumption, tool wear, and cutting zone temperature operate. The information from these subsystems is transmitted to the subsystem for optimizing finishing operation parameters. An algorithm for designing finishing technological operations is presented. It consists of source data input to the system, analysis of operation functional capability, decisions on the possibility of changes in the input data, control action formation, designing of operation, organization of preparation for operation execution, control of operation execution results for the compliance with the requirements of normative and technical documentation and finishing operation implementation in mass production. The developed system provides optimal tools and processing modes as a result of fulfillment of its functions. When this information is implemented in the manufacturing process of parts, the required quality indicators (surface roughness, size and geometric accuracy of edges) are provided as well as the optimal process performance.

The purpose of the work is to adjust the cutting modes for the manufacturing process of the Cover-Bracket part, which are set in accordance with the recommendations of the electronic catalog CoroPlus ToolGuide by the tool manufacturer Sandvik. This correction is required in order to improve the dynamic stability of machining. The problem of cutting mode adjustment is solved through the use of the methods of numerical simulation of the tool-workpiece system dynamics with regard to the resonances in the Femap engineering analysis program with Nastran. Recommendations are given for cutting modes taking into account the technical capabilities of the machine-tool and tooling, as well as the volume of the material removed with no reference for the dynamic properties of the tool and machine-tool. It is shown that at the 7th and 8th technological transitions the resonant vibrations are observed in the milling tool-workpiece system and the ratio of forces on the cutting edges of milling tools changes up to 245%, which leads to their uneven wear and decreases machining quality. It is found out that the oscillations of the processing forces can be represented as a sum of several harmonics of the rotational and tooth mesh frequencies. The results obtained show that the problem of deviation from the resonant frequencies can be solved not only by lowering the spindle speed, but also by changing the manufacturing process. Recommended change in the sequence of the technological transitions 7 and 8 allows to avoid resonance frequencies without reducing the performance level and machine at the maximum permissible cutter speed of 18,000 rpm. Under this approach, the first harmonics of the tooth mesh frequencies will be outside the resonant zone. In the future, it is planned to supplement the model with the dynamic characteristics of the machine-tool, tool and equipment.

The purpose of the article is to establish experimentally the effect of material inhomogeneity on the characteristics of strength (σ_в, σ_0.2) and plasticity (δ) on example of a rolled steel sheet. Uniaxial tensile testing was carried out on flat samples of hot-rolled sheet made of St3 alloy cut in three directions relative to rolling: along, across and at the angle of 450. The heterogeneity of structure was established by studying the fracture surface of the destroyed samples after tensile testing. A metallographic research and micromechanical testing (measurement of microhardness) of sections parallel to the fracture surface were carried out as well. The uniaxial tensile testing of flat samples resulted in obtaining the values of the characteristics of strength (σ_в, σ_0.2) and plasticity (δ). The analysis of fracture patterns, microstructure and microhardness values of the material allowed to reveal the structural heterogeneity caused by the presence of fibrous ness and a banded ferrite-pearlite structure oriented along the deformation direction. The formation reason of the latter was the presence of oriented non-metallic inclusions - elongated plastic sulfides. The study determined that the material under investigation features the anisotropy of mechanical properties and structural heterogeneity. The values of the ultimate strength (σ_в) and yield strength (σ_0.2) decrease from the longitudinal direction to the transverse direction (relative to the rolling direction) and vice versa (from the transverse to longitudinal direction) in the first case probably due to the influence of non-metallic inclusions (plastic sulfides) and, as a result, the banded ferrite-pearlite structure; in the second case due to the influence of fiber direction. The values of the relative elongation (δ) decrease from the longitudinal direction to the direction at an angle of 450 and then increase to the transverse direction as a result of different hardening of the material during plastic deformation. This is proved by the obtained microhardness values of the investigated sections and the values of the maximum applied loads during the tensile test. The obtained values are obviously the result of the influence of fiber orientation relative to the existing maximum tensile stresses.

The purpose of the work is to provide conditions for machined workpiece surface quality control based on the use of gas-magnetic supports in machine-tool systems (on example of the 3K227A internal grinding machine). To model the trajectory of tool and workpiece mutual movement the methods of nonlinear dynamics are used. The literature data on the problem are analyzed and experimental studies are carried out. Based on the considered issues of controlling the dynamic stability of technological systems under machining by means of contactless controlled gas-magnetic supports of spindle units, a scheme for adaptive control of the machine-tool system is proposed. It allows in many respects to eliminate external mechanical effects on the technological system, internal vibrations caused by drives and moving parts, as well as to compensate temperature deformations of the spindle unit frame and body. An adaptive control system based on gas-magnetic supports of the spindle assembly and the workpiece, as well as the control systems of the position of workpiece and tool (on example of 3K227A internal grinding machine) are demonstrated in action. The gas-magnetic support control system developed at Komsomolsk-na-Amure State Technical University makes it possible to set the position of the rotor axis with the accuracy of 0.1 microns. The study results obtained lead to the conclusion that the control of two adaptive links on the gas-magnetic supports, i.e., the spindle assembly of the tool and the spindle assembly of the workpiece, allows to achieve a rotation accuracy of up to 0.2 microns. The methods of nonlinear dynamics make it possible to construct an attractor (trajectory) of the tool tip movement in the real time, which provides a possibility to affect the input parameters of the machining process and thereby to control the output parameters. In addition to this, the control system of machine-tool system dynamic stability is applicable to other processing types as well, including edge cutting machining.

The purpose of the study is to conduct experiments in order to determine the possibility of technogenic goldbearing raw material cyanidation using ultra-low concentrations of NaCN. Experiments are carried out on the cyanidation of three samples of technogenic raw materials of different composition. The first sample consists of pyrite cinders (Au – 1.8-2.3 g/t, Ag – 13-22 g/t, Fe – 48.52%, Cu – 0.15-0.30%, Zn – 0.3–0.6%). The second sample is represented by the aged tailings of copper-zinc flotation (sample I) with the content of Au – 0.8 g/t, Ag – 7.0 g/t, Fe – 17.2%, Cu – 0.212%, Zn – 0.207%. The next object is the copper-zinc flotation tailings of a concentration plant (sample II), with the following content of Au – 1.22 g/t, Ag – 15.2 g/t, Cu – 0.13%, Zn – 0.23%. It is recommended to use an aqueous wash from nonferrous metals with subsequent lime treatment as a preliminary processing of pyrite cinders. Cyanidation is carried out at different consumptions of reagent: from 0.075 to 3 kg/t. The experiments have shown that gold recovery in this range of NaCN consumption varies from 42.9 to 44.2%; moreover, a decrease in the reagent consumption allows to reduce the concentration of non-ferrous metal ions in cyanidation solutions. Before cyanidation sample I has also been subjected to aqueous wash to remove acid and non-ferrous metals. NaCN consumption varies from 0.25 to 2.2 kg/t. In this case the extraction of gold amounts to 36.6–46.4%. Cyanidation of tailings (sample II) is carried out in the range of 0.15–1.2 kg/t of NaCN. Gold recovery varies from 24.1 to 30.9%. The cyanidation technology of technogenic raw materials in the field of ultra-low concentrations of sodium cyanide is promising, since it provides acceptable gold recovery under low reagent consumption. For further research in the field of development of an extraction technology of valuable components, the flotation tailings of copper-zinc production (sample II) are chosen as a promising object. It is planned to carry out semiindustrial tests, calculate technical and economic indicators and develop process regulations.

The purpose of the article is to assess the application possibility of methane of various conversion methods (СО₂, Н₂О, О₂) for combined reduction of iron and non-ferrous metals (nickel, copper, lead and zinc) from B₂O₃-CaO-Fe₂O₃-МеО oxide melts in the temperature range of 1273–1673 K. Thermodynamic modeling is carried out using a technique, which allows to estimate the variations in phase compositions depending on the amount of the reducing agent induced. The technique differs from the known ones by sequential calculation cycles with the removal of the formed gases and the metal phase from the working fluid composition. It is found that regardless of gas composition the process goes on in several stages. In the case of the combined reduction of iron and nickel (lead or zinc), the first stage is reduction of Fe₂O₃ to Fe₃O₄ and FeO. The content of Fe₂O₃ decreases, while the contents of FeO and Fe₃O₄ increase (at the end of the stage the content of Fe₃O₄ reaches its maximum value). At the second stage, there is the transition of Fe₃O₄ → FeO when the values of the contents of Fe₂O₃ and Fe₃O₄ decrease to negligible values. The third stage features the manifestation of the metallic phase. In the case of the combined reduction of iron and copper, the process can be divided into three stages according to the variations of the content of iron oxides, and into two stages according to the variations of the content of CuO and Cu₂O. The first stage of iron reduction ends at the moment when the content of magnetite reaches its maximum value, the second stage finishes when the metallic phase appears. The first stage of copper reduction includes the transition of CuO to Cu₂O and achievement of the maximum value of Cu₂O content. The second stage includes the reduction of copper from Cu₂O. A gas with the increased content of hydrogen, which corresponds to methane steam reforming is shown to be the most effective reducing agent. The results obtained make it possible to predict the parameters of the metal reduction process during oxide systems bubbling by methane conversion products. The results will be useful for the development of technologies for selective reduction of metals.

The purpose of this paper is to conduct the research on hydrochloric acid cleaning of gold-containing cathode deposits from the impurities of heavy non-ferrous metals and mathematical processing of the experimental data obtained by the method of dispersion analysis. The atomic absorption method is used to study the chemical composition of the cathode deposits. The method of dispersion analysis is used to process experimental data. The composition of cathode deposit impurities is studied using x-ray spectral microanalysis. The study of the chemical composition of cathode deposits has shown that their main components are gold, silver, copper, lead, as well as non-metallic impurity compounds (CaO, SiO₂, etc.). It is found that the optimal concentration of hydrochloric acid for cleaning gold-containing cathode deposits from heavy non-ferrous metals is 371 kg/m₃; the degree of copper transition to solution is 69.06%, lead – 93.9%. The calculation of the expected mass fraction of precious metals in the alloyed gold demonstrates an increase in the mass fraction of gold by 14.08%, silver – by 17.46%. The study of the chemical composition of cathode deposits has also revealed that the main impurities that affect their subsequent processing are copper and lead. The latter fall into the ingot of alloyed gold, which is the target product of gold-bearing ore processing and complicate subsequent refining. The dispersion analysis of experimental data shows that solvent concentration significantly affects the transition degree of heavy non-ferrous metals to the solution starting from the value of 20.1 kg/m₃. It is shown that the proposed method allows to increase the content of precious metals in the alloyed gold by 31.54%, as well as to perform maximum transition of copper and lead to the solution. The use of acid leaching of impurities from cathode deposits obtained by cyanide-sorption technology is one of the promising directions for improving the quality of gold-containing alloys and hence the reduction of the cost of refining services.

In this research, we investigate the process of X-ray radiometric separation of both raw materials (quartz, carbonaceous reducing agent) used for silicon smelting in ore-smelting furnaces and the resulting smelting products. The research objects were quartz from the Aktas field (Kazakhstan), coal from the Shubarkol field and silicon metal of various grades smelted at the Tau-Ken Temir LLP (Karaganda, Kazakhstan). X-ray diffraction analysis was performed using a Philips powder diffractometer. To determine the SiO₂ and Fe₂O₃ content, an ARL PERFORM’X X-ray fluorescence spectrometer was used. To remove impurities, a СРF1-150М single-strand radiometric separator was used. We found that the radiometric separation of original quartz samples with the Fe₂O₃ content of ~ 0.1–0.15% produces pure quartz with the Fe₂O₃ content of ≤ 0.05% and a yield of 65–70%. Provided that the Fe₂O₃ content in the original quartz sample does not exceed 0.5%, concentrates with the Fe₂O₃ content of 0.05% and a yield of 35–55% can be obtained. The yield of pure quartz with the Fe₂O₃ content of 0.01% does not exceed 15–20%. The use of radiometric separation is established to reduce the amount of phosphorus in the final product by 2–3 times. This method is effective for obtaining coal concentrates of varying ash content (2.0, 4.1 and 7.3%); the resulting concentrated product obtained with a yield of 25% contains 1.5% of ash. Separation of silicon metal (with the initial iron content of 1.2–1.5%) yields a product matching silicon grade 773 (product yield ~ 50%), 553 (~ 35%) or 441 (20%). It is concluded that radiometric separation allows the content of impurities in quartz, silicon metal and coal ash to be reduced, thus facilitating the production of higher-grade silicon.

The purpose of the paper is to study the physical and chemical features of high-quality iron concentrate precipitation from nitric acid leaching solutions of low-grade copper-sulfide raw materials, and to obtain a highly profitable product which is suitable for direct processing at ferrous metallurgy enterprises. To conduct the experiments on obtaining impurity rich and depleted iron concentrate a hydrolytic precipitate containing 54.6% iron and numerous impurities obtained as a result of processing of nitric acid leaching solutions of rough copper sulfide concentrate from the Zhezkazgan deposit is used. Analytical studies of initial materials and resulting products of the processes under investigation are conducted using the modern certified methods including the x-ray spectral, x-ray phase, atomic absorption analysis, mass spectrometry method with inductively coupled plasma. We have obtained a high-quality iron concentrate containing minimal amounts of silicon, aluminum, phosphorus and sulfur as well as partial and generalized equations that give an idea of the influence of the studied factors on the indicators of the iron concentrate production process. The apparent activation energy of the process has been calculated – 46.77 kJ/mol. It probably indicates the presence of diffusion complications caused by the formation of solid products passivating the surface of the material being dissolved. The principal possibility of obtaining high-quality iron concentrate from processing poor copper-sulfide concentrate middlings of the Zhezkazgan deposit is shown. The mathematical processing of experimental data has resulted in the determination of equations that characterize the degree of influence of the studied factors on the process indicators. It is found out that the production process of the saleable iron concentrate proceeds in the mode of diffusion restrictions. It is the first time, when multivariate generalized dependencies are obtained for the process under consideration and their analytical transformations are performed. These methods can be used to study the analogous processing of similar metallurgical raw materials.

The purpose of the article is to develop and substantiate the principles of an energy model of an industrial reverberatory furnace taking into account chemical composition and properties of natural gas as well as to calculate the furnace thermal efficiency in order to estimate its industrial performance. To conduct the research mathematical calculations are performed based on the data of chemical and physical analysis of flue gases and chimney temperature using standard graphs of excess air and enthalpy values of flue gas components. The measurement of the amount of waste pollutants is carried out using MRU Delta 65-3 gas analyzers, which identify the total amount of gases (O₂, CO, NO, H₂S) They determine the temperature, pressure (vacuum), calculate the content of CO₂ and installation efficiency as well. Aspen Hysys program is used to verify the mathematical model. The data on the properties of natural gas are obtained i ncluding the data on chemical composition, molecular weight, calorific value, excess air during combustion. The data on flue gases are also obtained, which include the data on the burnt gas components, molecular weights, enthalpy, calorific value, flue gases ratio at the temperatures from 94°C to 316°C. The chemical reactions of combustion given with the number of moles required and formed for each reaction are used to calculate the thermal efficiency of a reverberatory furnace for nickel alloys. The calculated data are confirmed by Aspen Hysys software. Based on the studies conducted, it is found that the variable having the greatest influence on the thermal efficiency is the low calorific value, since it depends on the composition of the natural gas. The proposed methods for calculating the thermal efficiency using a computer program are effective if an operator wants to evaluate the furnace operation efficiency on site.