Статьи журнала - Siberian Aerospace Journal
Все статьи: 330
Optimization control actions for the electrolytic method of aluminium production
Статья научная
The most common indicator of the aluminium production process managing efficiency is the cost of the metal production, but this concept includes a lot of components. First, this is the cost of raw materials and electricity in this region, as well as the labour cost per ton of products, consumption coefficients of raw materials and energy, capital costs for construction and repairs, waste disposal cost, environmental payments, etc. At the same time, there is no single functional of the process quality, depending on technological parameters, that is, the problem of complete and relatively strict mathematical process optimization as a whole is currently not solvable, not only because of its volume, but because of the lack of a complete efficiency model. In this study, particular efficiency criteria are considered, the improvement of which is aimed at the optimization model of control actions developed by the authors, which are selected based on the possible levers of the current automated process control system (APCS) for aluminium electrolysis. All tests were carried out on Virtual cell software without transfer to a real control object.
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Optimization the position of the spacecraft instrument panel mounting points based on modal analysis
Статья научная
The paper presents optimization of the location of interface points of the spacecraft instrument panel using modal analysis, as well as a quasi-static calculation of the panel under study, confirming effective-ness of proposed changes in the panel design. The instrument panel is a three-layer honeycomb structure consisting of two aluminum plates and a honeycomb filler. Cellular panels have a number of advantages: a small weight of the structure, high rigidity, specific strength. Using finite element modeling, the range of natural frequencies and vibration patterns of the instrument panel was determined, which made it possible to determine optimal location of the panel fixing points to the spacecraft body to increase the lower limit of natural frequency range and increase its carrying capacity.
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Optimizing the readability of tests generated by symbolic execution
Статья научная
Taking up about half of the development time, testing remains the most common method of software quality control and its disadvantage can lead to financial losses. With a systematic approach, the test suite is considered to be complete if it provides a certain amount of code coverage. At the moment there are a large number of systematic test generators aimed at finding standard errors. Such tools generate a huge number of difficult-to-read tests that require human verification which is very expensive. The method presented in this paper allows improving the readability of tests that are automatically generated using symbolic execution, providing a qualitative reduction in the cost of verification. Experimental studies of the test generator, including this method as the final phase of the work, were conducted on 12 string functions from the Linux repository. The assessment of the readability of the lines contained in the optimized tests is comparable to the case of using words of a natural language, which has a positive effect on the process of verification of test results by humans.
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Parameters of rocket engine chambers, obtained by selective laser melting
Статья научная
When designing and testing a low-thrust rocket engine (LTRE), one of the most important tasks is to ensure the quality of materials, which, in turn, affects the reliability of the product. Currently, additive technologies for manufacturing parts from metals are actively developing. This direction is relevant for rocket and space technology products to reduce weight and increase the reliability of products. The article presents the results of studies of the chemical composition and mechanical characteristics of the material of the low-thrust rocket engine demonstrator chamber, manufactured by selective laser melting from metal powder. The properties of products made from Inconel 718 metal powder were studied. Samples were made and the chemical, mechanical and structural characteristics of the material were studied. Based on the test results, two LTRE samples were printed. LTRE chambers were tested for vibration loads, strength and tightness. Increased porosity and roughness of the test material of the engine chamber were noted. When analyzing a number of parameters of the selective laser melting technology, an experimental selection of printing parameters was carried out and the most significant factors affecting the print quality (surface roughness and porosity) were identified. Based on the results of the work carried out, four groups of controlled printing parameters were identified that affect the properties of the resulting material. The work also provides recommendations on printing modes and characteristics to obtain the highest quality parts.
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Parametric analysis of the anisogrid body of the spacecraft for cleaning the orbit of space debris
Статья научная
The article presents an approach to solving the problem of designing a spacecraft for cleaning the orbit of space debris (space garbage collector-KSM), the body of which is made in the form of a cylindrical mesh anisogrid shell. The design task is to select the optimal parameters of the anisogrid body of the KSM (the shape and cross-sectional area of the ribs, the number of annular and spiral ribs, material characteristics, etc.) that provide the necessary strength and stability of the structure with minimal weight. During the design process, a parametric analysis of the anisogrid housing of the space garbage collector was carried out. By varying the number and angle of inclination of unidirectional spiral ribs, we find the optimal design scheme that satisfies the specified safety and stability coefficients. Parametric analysis of the KSM body includes modeling of the main weight and strength parameters: determination of the stress-strain state of the structure, values of the body’s natural frequencies, determination of the bending margin from the longitudinal force, determination of the body mass. The analysis of the load-bearing capacity of the anisogrid housing of the space garbage collector was carried out by the finite element method using the MSC Nastran software package. A finite element mesh model was created from a two-node spatial finite element bundle. The disk attached to the end of the shell was modeled using a rigid finite element. The size of the final beam element for all shell models was the same and equal to 10 mm. During the parametric analysis, three variants of the mesh composite structure with a different number and angle of inclination of unidirectional spiral ribs were considered. Based on the results of parametric analysis of the spacecraft body, its geometric dimensions are determined and the mass of the spacecraft structure as a whole is minimized.
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Parametric analysis of the strength of a solid propellant rocket engine nozzle
Статья научная
The paper presents an approach to solving the problem of designing a solid propellant rocket engine (SPRE) nozzle using such a design feature as a carbon fiber insert plate. The design task is to select the optimal parameters of the plate shape and thickness, providing the required load-bearing capacity with minimal mass. During the design process, a parametric analysis of a SPRE nozzle with a carbon fiber insert plate was carried out. By varying the thickness of the plate, an optimal design scheme that corresponds to the specified safety and stability factors was selected. Parametric analysis of an insert plate made of a composite material includes modeling of its main weight and strength parameters: analysis of the stress-strain state of the structure, values of natural frequencies, determination of the buckling margin, and determination of a SPRE nozzle mass. The analysis of the load-bearing capacity of a SPRE nozzle with an insert plate made of a composite material was carried out by the finite element method using the SolidWorks Simulation software package. When conducting a parametric analysis, two variants of a SPRE nozzle with and without an insert plate were considered. According to the results of a parametric analysis of a SPRE nozzle, its geometric dimensions were determined and the structure mass was minimized.
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Статья научная
A mathematical model of the aircraft avionics thermal state describing the heat exchange of the onboard equipment housing with a honeycomb structure made of a carbon fiber composite, the process of heat transfer of the onboard equipment elements and the air is developed. The considered heat transfer process in a heterogeneous medium is described by the boundary value problem for the heat equation with boundary conditions of the third kind. To solve the direct problem of the onboard equipment housing with a honeycomb structure thermal state, the Monte- Carlo method on the basis of the probabilistic representation of the solution in the form of an expectation of the functional of the diffusion process is used. The inverse problem of the honeycomb structure heat exchange is solved by minimizing the function of the squared residuals weighted sum using an iterative stochastic quasigradient algorithm. The developed mathematical model of the onboard equipment in the unpressurized compartment thermal state is used for optimizing the temperature and airflow of the thermal control system of the blown onboard equipment in the unpressurized compartment of the aircraft.
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Статья научная
The analyzes of the requirements to 3D-configuration pipelines production at the rocket and space industry enterprises is done. A review of different approaches to pipe bending technology (with heat treatment and without heat treatment) is carried out. The object of the study is the bending process and a universal bending machine for pipelines’ production of complex configuration. The article is divided into four sections, which consider the key factors, causing directly the effectiveness of the technological operation of pipeline bending of a complex 3D-trajectory. An overview of no-temperature shaping of the pipeline is given in the first section. The requirements to the technology, excluding: corrugation, flattening, stretching and thinning of pipeline walls during their bending, are considered. The actual regulatory documents and industry aerospace standards, regulating production of pneumatic and hydraulic pipelines are given. An example of calculating the minimal allowable bend radius of the pipe, depending on the diameter and thickness of the pipe wall, is given. The requirements to unification of the pipe size production and gaps are listed. The dependence of the maximal allowable internal pressure in the pipeline is shown. The requirements to equipment, used in pipeline bending and to the design of the pipe bending machine are considered. In the second section, the possibilities of temperature influence on the pipe bending process are viewed. The analysis of patent and technical literature and six possible methods of effective thermal effects are presented: heating of the whole pipeline length, narrow zone heating of the bend pipe place, water cooling with nitrogen in the pipe, laser-cooling of atoms of the pipes, application of the petroleum products on the place of heating of the pipe and using of modern fillers inside the pipe to change its temperature. In the third section the tasks of the development of a universal bending machine are set; the system of the algorithm of the universal bending machine operation is considered; the system of algorithm of the bending machine operating with CNC is shown. The General functional scheme of the bending machine and the sequence diagram of the equipment operation is given.
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Статья научная
The article proposes an approach to developing the architecture of a service-oriented information processing system, modeling and process control. The system, which is being developed, is a tool for identifying, predicting and controlling discrete-continuous processes. Its mathematical apparatus is based on nonparametric algorithms of identification and control. The software architecture includes the following main modules: the module for processing data, modeling and forecasting output process variables and the process control module. The first module includes data preprocessing algorithms: normalization, centering and analysis of outliers and omissions. The modeling module is an algorithm for research and recovery dependencies between process variables, process identification using nonparametric estimation of the regression function from observations. The last module is an implementation of nonparametric dual control algorithms. Control devices built on the basis of these algorithms perform functions of both object control and its study. The article discusses the application of architectural solutions based on two proven approaches in the field of software development: the composite approach and the service- oriented approach.. The main principles of composite architecture as a set of software systems with many characteristics that perform a specific task and service-oriented architecture as a modular approach to software development are described. The advantages of the applied composite service-oriented architecture over other variants of software architecture for control systems are shown, in particular, monolithic software architecture is compared with composite service-oriented architecture. This means that a researcher can use a single operation, which is a logically isolated, repeated task related to the production process of the enterprise. At the same time, it is necessary to ensure positive results when integrating with existing software products of enterprises which greatly complicates and requires the development of new components, as well as support for the "inherited" parts of the system.
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Piecewise approximation based on nonparametric modeling algorithms
Статья научная
In this research the issue of inertialess processes modeling is under study. The main modeling algorithm is the non-parametric recovery algorithm of the regression function. The algorithm allows to build a process model under conditions of low a priori information. This feature may be particularly important in modeling processes of large dimensions prevailing in the space industry. One important feature of the algorithm for nonparametric estimation of the regression function is that the accuracy of modeling using this algorithm highly depends on the quality of the observations sample. Due to the fact that in processes with large dimensions of input and output variable vectors observation sampling elements are in most cases unevenly distributed, the development of modifications to improve the quality of mod-eling is relevant. The modification of the nonparametric dual algorithm based on piecewise approximations has been devel-oped. According to the proposed modification, the process area is divided into sub-areas and a non-parametric esti-mate of the regression function for each of these sub-areas is recovered. The proposed modification reduces the impact of some observation sampling features, such as sparseness or voids in observation samples on the quality of the built model. The computational experiments were carried out, during which a comparison was made between the classical algorithm of non-parametric estimation of regression function and the developed modification. As the computa-tional experiments have shown, with uniform distribution of the sample elements of observations, the developed modification does not lead to the improvement of the quality of modeling. With a substantial uneven distribution of the observations sample elements, the developed modification resulted in a 2-fold improvement in the quality of the simulation. The results suggest that the proposed modification can be used to model complex technologi-cal processes, including those in the space industry.
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Plasmotron for coating internal surfaces of component parts
Статья научная
Plasma spraying is one of technologically appropriate, productive and effective methods of applying protec-tive coatings to component parts produced by aerospace, metallurgical and other industries, objects exposed to high temperatures, dynamic loads, aggressive media, etc. Plasma spraying makes it possible to apply quite a va-riety of materials, such as metals, oxides, carbides, nitrides, etc. to different surfaces. Certain problems may arise, though, in applying protective coatings to the inner surfaces of cylinders and complex parts of small size (about 100 mm). These complexities depend on the dimensions of the plasma generator proper. There are no home-produced small-size plasma torches, they are all imported from other countries. That causes certain prob-lems with delivery, to say nothing of very high commercial price. One of the ways to improve the situation is to develop small-size plasmatrons capable of applying high-quality coatings to the internal surfaces of limited-size parts; that may significantly reduce expenses through import substitution. The effectiveness of the proposed device is in working out a method of applying high-quality coatings to the inner surfaces of orifices as small as 60 mm in diameter (operating a plasmatron of smaller size), as well as in significant cost reduction due to domestic production. Sample calculations show that the price of that plasma-tron type will not exceed 0.5 million rubles.
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Point defects in nematic liquid crystal materials with conical anchoring at the interface
Статья научная
The topological point defects in nematic liquid crystal materials have been studied. The method of oblique light incidence has been proposed to determine an azimuthal director angle of an achiral nematic as well as a chiral nematic (cholesteric). The idea of the method is based on the dependence of the optical phase difference between ordinary and extraordinary light beams on the azimuthal director angle at the layer center at oblique incidence of light on a structure in which the polar director angle of a nematic liquid crystal is not equal to 0° or 90° (conical boundary conditions). It has been shown that the phase difference reaches a maximum at a zero azimuthal angle at the center of the layer regardless of the total twist angle of the director. The developed method has been used to analyze topological defects formed in the nematic and cholesteric layers under conical boundary conditions at the interface. The director field distributions of nematic and cholesteric near the surface point defects (boojums) with topological charges m = +1 and m = –1 have been drawn based on the experimental data. The proposed method of oblique light incidence can be used to analyze a wide class of the achiral and chiral liquid crystal media of various types: smectics, nematics, and cholesterics with tilted or hybrid boundary conditions.
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Статья
During the period of active lifetime in different types of orbits, spacecraft (SC) are exposed to various factors of outer space. The main factor influencing the performance of radio-electronic equipment is the ionizing radiation of outer space. The main effect associated with the impact of ionizing radiation of outer space on the SC (dose effects), in its physics, is determined by the radiation dose absorbed in the components of the electronic component base (ECB) and construction materials during the entire lifetime. This effect explains the failures in the operation of radio-electronic equipment due to the degradation of the parameters of the used ECB products and materials. Calculation of levels of exposure to absorbed doses depending on various parameters of the orbit is a necessary and important task for ensuring the SC functioning during a given lifetime, since calculations of radiation resistance are based on the levels of exposure in orbit. Carrying out calculations taking into account the SC and onboard equipment (OBE) design features is the key problem from the point of view of minimizing mass protection and the scope of tests of critical ECB products. In addition to taking into account the design of the SC and the OBE, an important aspect when calculating the radiation resistance is taking into account the relative position of the OBE in the SC. The paper considers the possibility of unifying the requirements for radiation resistance for SC with dif-ferent operating orbits and lifetime, as well as the possibility of carrying out a unified calculation without taking into account the design features of the SC, OBE and relative position within the SC.
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Статья научная
This paper presents an overview of the current technical problem related to two-phase spacecraft thermal control systems and possible technical applications of thermal energy recovery in the organic Rankine cycle as an integral part of thermal management systems. The design solution involves the integration of a steam microturbine behind an evaporator radiator. The microturbine is a tangential supply device and a radially centripetal impeller of low speed nst<40. In this area, there is no reliable data on the design and energy of both the supply device and the impeller. The energy (loss of enthalpy) of the supply device mainly determines the transport of the swirling flow to the impeller and, as a result, the circumferential operation on the turbine. A prototype of a radial microturbine has been developed and presented in order to evaluate the design of the flow part of both the supply device and the impeller. As a result of the analysis, the main determining hydrodynamic areas necessary for hydrodynamic analysis and mathematical elaboration of the flow calculation algorithm with an assessment of energy losses are identified: the flow of a swirling flow of a radial-annular slit; axial-annular slit and tangential supply device. The first two algorithms assume computational modeling, the model of energy losses in a tangential supply device is not amenable to analytical modeling because it includes a sequence (or compatibility) of flows under boundary conditions defined as “local resistances”: the sudden expansion, reversal of the flow, together with a section of radially circumferential flow, the mutual influence of these boundary conditions assumes only an expe rimental assessment of energy losses in a tangential supply device through the loss coefficient of local resistance in the range of changes in geometric and operating parameters. As a result of experimental studies, a database has been proposed on the loss coefficient of tangential microturbine supply devices in the field of the practical range of the existence of operating and design parameters.
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Prediction of formation of competing phases during the growth of Cr2GaC THIN FILMS ON MgO(111)
Статья научная
MAX-phases are a family of ternary layered compounds with the formal stoichiometry Mn+1AXn (n = 1, 2, 3...), where M is a transition d-metal; A is a p-element (for example, Si, Ge, Al, S, Sn, etc.); X is carbon or nitrogen [1]. Layered triple carbides and nitrides of d-and p-elements (MAX-phases) exhibit a unique combination of properties characteristic of both metals and ceramics, which makes their application as various coatings in space industry very promising. Obtaining the desired properties of the MAX-phases depends on the technological conditions of material synthesis. This requires thorough theoretical modelling of the elements’ interaction at the interface. Concurrent growth of competing phases along with the MAX-phase may occur due to the favorability of competing phases’ formation and may also be promoted by lower energy interfaces with the substrate in comparison with a MAX-phase. In this work, we study thermodynamic favorability of competing phases and Cr2GaC MAX-phase depending on the chemical composition of the atomic flow. To study these compounds, it was necessary to consider the Cr-Ga-C system. According to the effective heat of formation model, each reaction of a certain phase formation can be characterized by enthalpy [2]. To find out the most favorable phases, it was necessary to calculate the enthalpy of all possible reactions. Thus, the task was to sort through all possible reactions between pure elements available in various ratios, in particular, in the ratio corresponding to the given MAX-phase stoichiometry, i.e. Cr:Ga:C=2:1: 1. Moreover, it is considered that the density of near-coincidence sites [3,4] for interfaces between MAX-phase, thermodynamically favourable competing phases and MgO(111) surface shows a role of the interface in the determination of the structural quality of the MAX-phase thin film grown on MgO(111).
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Pressure measurement inside non-sealed equipment bay of the geostationary spacecraft
Статья научная
The equipment of the non-sealed spacecraft is functioning during the operation phase in the envi-ronment that includes the equipment bay inherent atmosphere. JSC “ISS” together with MAI have developed and implemented in software a mathematical model for the pressure dynamics estimation of the equipment bay inherent atmosphere and for the design parameters selection and construction of the ventilation openings of the non-hermetic equipment bay. The pressure drop dynamics estimation of the equipment bay inherent atmosphere was also carried out according to the developed model. A block of the pressure sensors (joint development of ISS and Novosibirsk State University) was in-tegrated into the geostationary spacecraft for the in-situ pressure measurement inside the non-hermetic equipment bay during the operation. This block consists of two sensors: a semiconductor sensor based on MEMS- technology (micro-electromechanical system) and an inverse magnetron sen-sor with the cold cathode. The pressure sensor unit provides the pressure measurement from 790 up to 1∙108 mm Hg. The authors present the results of pressure measurements inside the non-hermetic equipment bay during the first six months of the spacecraft operation on the geostationary orbit. This article also compares the in-situ pressure measurement results and the calculated pressure drop obtained using the mathematical model for the non-hermetic equipment bay spacecraft.
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Production of finly despersed powder from graphite by electrolysis
Статья научная
Multifunctional coating is a multi-layer structure applied to the surface of an aircraft to protect it from external influences. The main tasks of the multifunctional coating are: restoration of properties, overall dimensions, mass of the surface of the product, which were violated under operating conditions; changing the initial physical, mechanical and chemical properties of the product surface to ensure the specified operating conditions. Today multifunctional coatings based on micro glass spheres with applied tungsten are widely used in aerospace engineering. However, this coating has a number of disadvantages: the coating layers heterogeneity; the composition contains a harmful and dangerous component – a fluorone dye. In this article it is suggested to replace the main component of a multifunctional coating with finely dispersed graphite powder obtained by electrolysis. For this purpose, the equipment based on the principle of a diaphragm electrolyzer was constructed. The main elements of the device are a stainless steel cathode and a graphite anode immersed in an aqueous solution. As a result of anodic processes, a finely dispersed graphite powder was obtained. The average particle size of the resulting graphite particles is 4 microns. This finely dispersed graphite powder can be used as the main component of a multifunctional coating in aircraft, since it has an even homogeneous structure, as well as higher values of the main mechanical properties of a multifunctional coating.
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Prospects for the development of charger-discharge devices of spacecraft power supply systems
Статья научная
Power supply system (PSS) is designed to ensure uninterrupted autonomous power supply of on-board equipment in all modes and at all stages during the active life of spacecraft. Lots of PSS makes up a significant proportion of the mass spacecraft and improvement of specific energy characteristics of PSS leads to a synergistic effect when the mass and energy consumption resources available for the payload are simultaneously increased, which increases efficiency of spacecraft generally. The article considers the evolution of structural and circuit solutions for PSS spacecraft, its energyconverting equipment and the effect of these changes on energy-mass characteristics of PSS. It is shown that a significant effect on energy and mass characteristics of PSS provide structural and circuit design solutions for charging and discharging devices of energy-converting equipment and the choice of voltage value of recharging batteries (RB). The development of the element base, the creation of programmable digital devices capable of functioning under the influence of space factors and the emergence of new circuit design and management solutions for pulse converters that have occurred in the last decade opens up new opportunities for improvement of the PSS of spacecraft. In the article as a chagrining and discharging device of PSS a pulse voltage converter (PVC) with a new modulation strategy is reviewed, with the ability to reverse the flow of energy and the ability to work in a step-up mode with high efficiency. Its application as a single charger-discharge device (CDD) allows for a significant improvement in performance of CDD and PSS in general, such as efficiency, energy mass, reliability and a number of others. Ability of PVC to reverse the flow of energy and the possibility of working in a step-up mode opens up the possibility to abandon the use of RB with a voltage lower than the voltage at the main output of PSS and switch to using RB with an average discharge voltage close to the voltage at the main output of PSS. Such a structural and circuit design solution of CDD and RB will allow to increase efficiency of CDD up to 99 % and additionally improve energy and mass characteristics of PSS.
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Статья научная
Changing the low-voltage level of the output load power bus (27–28 V) in the power supply system (PSS) of the spacecraft (SC) to a high-voltage (100 V) allowed us to significantly reduce the SC mass in connection with the reduction in the mass of cables and energy converting equipment (ECE). However, a number of problems have arisen related to the difficulty of matching the increased voltage levels of energy sources and loads, taking into account the necessary level of reliability of the PSS. Therefore, the issues of choosing the PSS structure and methods for developing ECE are relevant and priority task facing their developers. To date, in the field of development and creation of high-voltage high-power PSS of SC, a promising direction is their design based on integrated ECE modules, in particular, on the basis of modules of charge-discharge regulators (CDR) of accumulator batteries (AB). In the article, a calculation and comparative analysis of the SC PSS structures with the connection of the CDR module to the solar battery (SB) bus and with the connection of the CDR module to the output load power bus is performed. In the course of analysis of the results obtained, it was found that both options for the PSS implementation can be optimal depending on the given curve of the SC load and the requirements for the PSS for specific energy, weightdimension and other characteristics. The final choice of the SC PSS structure should be made subject to the specific power of the ECE and the subsequent calculation of the weight-dimension characteristics of the alternative PSS. Simulation of two options for the implementation of the AB CDR module was carried out: a push-pull converter with one inductor and a Weinberg converter with a magnetically coupled inductor and an additional power diode. It is established that both investigated options can be used in the development and creation of the CDR module of the highvoltage PSS of spacecraft. However, the design of CDR module based on the Weinberg converter can significantly reduce the values of the used inductors and output capacitors subject to the required levels of output voltage ripple.
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Prospects of application of the combined storage space application
Статья научная
Combined energy storage systems are widely used as part of renewable sources in the manufacturing industry, transportation infrastructure, space engineering, and other industries. This trend is due to their higher reliability and efficiency than that of power supplies made of the same type of cells, which can be observed, in particular, in devices for space applications, where power cells are subject to higher requirements for the range of operating temperatures, as well as for input and output characteristics. The article describes the development of the structure of a portable combined energy storage device based on a block of supercapacitors and batteries with a charge and discharge control system, with a scalable (based on the components used) spectrum of input characteristics and a wide range of operating temperatures. The authors presented a mathematical model of a combined energy storage device developed in the Simulink environment, which makes it possible to assess the performance capabilities of the proposed structure by analyzing the different modes of operation of the circuit. Such a device can be used in conditions of extremely low charging currents. For example, if the solar panels are shaded or their spatial orientation is sub-optimal, high-capacity lithium-ion batteries cannot be charged correctly. Also, the advantages of combined electricity storage structures include their operability over a wide temperature range thanks to the ability of supercapacitors to retain their charge even at low temperatures. The article also shows the printed circuit assembly in the form of a 3D model obtained by designing the device circuit in Altium Designer 17 CAD; the results of research and performance testing of a physically implemented combined energy storage device are shown, which confirm its performance characteristics on the example of one of the component modules of the prototype satellite platform CubeSat; the article also provides recommendations for the possible application of such devices and highlights prospects for the application of combined energy storage devices in actuating elements of large flexible spacecraft.
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