Analytical Dependences Research Articles

Calculation of horizontal collective drainage pipelines of reclamation systems in the presence of a ground water level slope

The purpose of this work is to develop a methodology for calculating the parameters of pressure horizontal collective drainage pipelines of reclamation systems that operate in the presence of a ground water level slope.
 The presented materials are based on the results of personal analytical studies of the main mathematical dependencies, which describe the pressure liquid flow in horizontal collective perforated pipelines, which operate in the presence of the ground water level slope.
 System of two differential equations, which describe the liquid motion in a drainage pipeline with variable flow rate and the conditions of liquid entry from the surrounding soil through the walls of the pipe in filtration mode, is considered. The explored pipeline is laid in the presence of the ground water level slope. By introducing new variables, the original system and its solution is presented in a dimensionless form.
 In this case the solution of the system depends on the value of three main factors: the resistance factor of the collecting drainage pipeline "ζl"; the generalized parameter "A", which comprehensively takes into account the structural and filtering characteristics of the stream; the ground water level slope «І». The analysis used the concept of an infinitely long drainage pipeline, which operates in the presence of the ground water level slope, or, what is the same, an inclined pipeline with an infinite filtering capacity of the side surface walls. Relatively simple and easy-to-use analytical dependencies were obtained on the basis of the conducted analysis. They allow to calculate the nature of the flow rate variations and pressure drop along the length.
 Corresponding graphic dependencies were constructed to simplify the calculations. It is shown that the value of the geometric slope of the ground water level, along with the resistance factor and the generalized parameter, significantly affects the calculated parameters of such pipelines.

Аппроксимация статической упругой линии несущего каната при тяговом расчете однопролетных мобильных канатных дорог

During the operation of cargo and passenger aerial ropeways, carrying-traction ropes are subject to natural sagging under the influence of their own weight, transported cargo or passenger cabins, wind and temperature effects. The ability to model the geometric shape of a rope, taking into account the conditions and operating modes of ropeways, is necessary when designing and modeling work processes in the rope system, optimizing the design and characteristics of the drive and tension mechanisms. This article presents a method for determining the analytical dependence approximating the configuration of the static elastic line of the carrying-traction rope, in relation to the problem of trac-tion calculation of single-channel single-span mobile ropeways. The peculiarity of the proposed approach is to take into account the inequality of the tension forces of the carrying-traction rope at the ends of the span, which makes it possible to more adequately reflect the real situation.

Effective electrical conductivity of random resistor networks generated using a Poisson–Voronoi tessellation

We studied the effective electrical conductivity of dense random resistor networks (RRNs) produced using a Voronoi tessellation when its seeds are generated by means of a homogeneous Poisson point process in the two-dimensional Euclidean space. Such RRNs are isotropic and in average homogeneous; however, local fluctuations of the number of edges per unit area are inevitable. These RRNs may mimic, e.g., crack-template-based transparent conductive films. The RRNs were treated within a mean-field approach. We found an analytical dependency of the effective electrical conductivity on the number of conductive edges (resistors) per unit area, nE. The effective electrical conductivity is proportional to nE when nE≫1.

Study of the effect of refrigeration treatment modes on the duration of the poultry meat cooling process

Currently, more and more attention is paid to the quality of food products and especially products that are sold in a chilled state. This is due to the fact that these products have a limited shelf life and to a greater extent must retain all quality characteristics. At the same time, refrigeration processes bear the main burden in terms of energy consumption, and therefore directly affect the cost and quality of the product. In this regard, reasonable refrigeration regimes are an integral part of production. This paper presents a study of various ways of cooling chicken meat, with the simulation of various parameters of the process of heat removal in the refrigerator. The studies were carried out on an operating experimental facility at various temperatures and air speeds, both simple air cooling and air-drop cooling were carried out. In the course of the study, the duration and dependences of the temperature of the cooled sample and the drying of the product on the mode of refrigeration were established. As a result of mathematical processing for the most optimal mode, analytical dependences of the shrinkage value of the test sample were obtained.As a result of the research, the most appropriate mode of refrigeration treatment of chicken meat was recommended, which allows to reduce the weight loss of products during the cooling process.

Characteristics of operational control reliability of aircraft functional systems and avionics suites

The operational control system (OCS) of civil aircraft (A/C) airborne equipment is an important component of its technical operation system (TOS). Operational control is an integral part of the technical operation process. It makes it possible to assess the technical conditions (TC) of the objects to be monitored in various states of airborne equipment operation, aircraft preparation for flight, various types of maintenance and recovery. The main property of operational control is the reliability of control. The key task of operational control is not only to determine the type of technical condition, but also to quantify the correctness or erroneousness of decision-making. Control reliability characteristics (CRC) are quantitative indicators of the degree of objectivity in decision-making. Depending on the level of task details, it is necessary to distinguish the control reliability characteristics of units, functional systems (FS) and avionics suites for various means of operational control: built-in test equipment (BITE), on-board self-contained, ground-onboard and ground systems. The choice of the control reliability characteristics is based on the system analysis and the mathematical apparatus of logic, probability theory and mathematical statistics. Rational sets of technical states and decision-making about the technical conditions of functional systems and avionics suites are formed. Based on these sets, three groups of control reliability characteristics were identified. The first group consists of conditional probabilities of transitions in the operational control process under various types of control. The second group consists of unconditional probabilities of transitions in the operational control process under various types of control. The third group consists of a posteriori decision-making probability in the operational control process under various types of control. Analytical dependences for calculating the control reliability characteristics of three groups for functional systems and avionics suites and relationships between them are determined. The air-conditioning system was used to calculate the reliability of the control.

CONTRIBUTION TO THE DESIGN OF INVERTER CONVERTERS FOR HEATING AND WELDING AT HIGHER FREQUENCIES

The paper shows a significant contribution to analytical calculations of half-bridge and full-bridge inverter parameters, aiming to facilitate the operating process itself while designing systems like these. Attempts have been made within the well-known literature to precisely calculate the waveforms of characteristic currents and voltages of the inverter. Due to its complexity, exact explicit analytical forms have yet to be found, but instead, approximate forms were found. Large formulae for inverter currents and voltages prevented them from being used as an inverter project solution. The paper deals with simple analytical dependences for inverters, with a necessary accuracy from the aspect of engineering practice, that can also be directly implemented into calculations for characteristic inverter components and parameters. To confirm the new analytical expressions and method, the paper presents two interesting inverters that can be applied.

Determining the energy of impact of a railroad rolling stock wheelset when derailing over reinforced concrete sleepers using impact trace parameters

The object of research is reinforced concrete sleepers that are subjected to the impact of a wheel in a railroad rolling stock. A procedure is given to theoretically estimate the energy at the impact of a wheel into a reinforced concrete sleeper when a rolling stock wheelset derails. Experimental studies of the geometric parameters of impact traces that occur on reinforced concrete sleepers, depending on the height of the center of mass of the striker above the impact site, were conducted. Based on the results of the experiments, the average geometric parameters of the impact traces were obtained. It was established that the dependence of impact traces on the height of the center of mass of the striker above the place of impact into the reinforced concrete sleeper has a non-linear distribution. Experimental studies of the effect of the location of the reinforced concrete sleeper base on the geometric parameters of impact traces were conducted. It was established that the location of the reinforced concrete sleeper on a solid base and on crushed stone ballast does not exert a significant effect on change in the geometric parameters of impact traces. The obtained experimental values are within the limits of 3σ determined for the rigid abutment of the sleeper. It was established that when testing a reinforced concrete sleeper in a crushed stone box, the amount of energy depends on the height of the striker. At a height of 0.95 m, the amount of energy absorbed by the sleeper together with the ballast was 475 J, and at a height of 1.42 m – 710 J. Analytical dependences were obtained between the length of the face of the impact trace and the amount of absorbed energy, as well as the depth along the direction of the force and the amount of absorbed energy. It was established that the length of the impact trace has an extremum, which does not allow recommending this parameter for estimating the amount of absorbed energy for energy values E<200 J. To determine the amount of energy absorbed by the sleeper, it is recommended to use the parameter of the depth of the impact trace

DETERMINATION OF THE MOMENT OF INERTIA OF THE FLYWHEEL MASSES, TAKING INTO ACCOUNT THE DEPENDENCE OF FORCES ON SPEED

The article discusses the performance characteristics of machines with a common criterion for all characteristics – the same work per cycle. The conclusion of analytical dependences characterising the movement of the electric drive in the transient mode is given, that is, taking into account the influence of var- ious quantities included in the equation of motion on the magnitude of the moment of inertia of the flywheel masses, with different types of load and different coefficients of unevenness of rotation. The zones of influence of the slope steepness of the mechanical characteristic MD(ω) on the required value of the moment of inertia are determined. It is shown that the values of the moment of inertia for aggregates with a smooth load are less than for aggregates with a sharply varying load, and that taking into account the influence of the dependence of MD(ω) on the required value of the moment of inertia J at large values of the coefficient of unevenness of motion δ is more necessary than at small values δ.

Математическое моделирование при управлении системами противопожарной защиты объектов

The problem of reliability of fire protection systems at the production stage and at the design stage is considered. Mathematical modeling of processes aimed at ensuring the safe evacuation of people in case of fire, taking into account the coefficient of compliance of the technical solution used in the methodology for calculating the amount of individual fire risk. The structural constructions of fire protection systems are analyzed with a demonstration of methods for assessing the reliability and structural significance of various structural constructions of fire protection systems on the basis and example of statistical data. To determine the coefficient of compliance of the fire alarm system, in the form of probabilities of effective operation of the fire alarm system, the following parameters are taken into account: the probability of effective operation of the fire alarm system, smoke protection system, and emergency warning system. The performance statistics of the SOUE for the period from 2013 to 2021 are graphically shown. It is shown that the resulting probability of effective operation of the SPS is determined by the structural design, and the corresponding formulas and examples are given. The dependences of the efficiency of the functioning of the SPZ on the efficiency of the SOUE for various structural arrangements have been constructed. Dependencies of the performance of the SDR were constructed based on statistical data. Analytical and graphical dependences of the reliability of the SOUE on the reliability of the SPS for various structural constructions are derived. Depending on the task being solved, the reliability (as well as efficiency) of the fire protection system can be controlled, while the reliability of the fire safety protection system can be determined depending on the required fire risk. Thus, one of the most important measures that minimizes individual risk should be considered to be increasing the efficiency of each of the subsystems included in the SDR, including the SOUE, as well as optimizing the structural design of the SDR.

Методика применения переменных нормативов при разработке плана формирования поездов

Purpose: The train formation plan is a fundamental technological document that affects the rational organization of the operational work of railways of JSCo “Russian Railways”. The amount of operating costs, the stability of the operation of stations, sections and transport hubs depends on its correct development. The existing practice assumes the use of the average values of its design parameters when calculating the train formation plan, without taking into account their variable nature. In this case, it is not always possible to guarantee that the optimal decision is taken on the organization of car traffic. The purpose of the article is to describe a method for taking into account the variable nature of the design parameters of the train formation plan, which will increase the stability of its individual assignments to the unevenness of operational work. Methods: Methods of theoretical analysis are used, existing analytical dependencies are described, which allow determining the calculated parameters of the train formation plan. Fuzzy set theory and its natural extension, fuzzy mathematics, have been used to describe the variable nature of the calculated parameters. To make an optimal decision on the adjustment of individual assignments of the train formation plan, the methods of decision-making theory have been used, namely, the Bellman-Zadeh method of decision-making in fuzzy conditions. Results: Calculation formulas have been obtained that allow determining the design parameters of the train formation plan in conditions of uneven operational work directly, without using auxiliary tables and graphs, having information only about the fluctuations of the car traffic of a specific purpose of the formation plan. A method has been developed for determining the threshold value of the car traffic, optimal in conditions of unevenness. Practical significance: Taking into account the variable nature of the design standards of the train formation plan during its development will increase the stability of its specific assignments, reduce operating costs for its implementation during the life cycle, reduce the number of operational adjustments.

Comparative analysis of experimental data on the sublimation of uranium carbonitrides and uranium-zirconium carbonitrides at high temperatures

The review is devoted to a comparison of new experimental data on the sublimation of uranium-zirconium carbonitrides with di erent contents of carbon, nitrogen, and oxygen impurities at high temperatures (1700- 2300 K), obtained by us in the past 2 years, with data of previous works presented in the literature on the sublimation of uranium carbonitrides, obtained by us and by other authors using mass spectrometry and some other methods of thermodynamic analysis. The main attention is paid to the consideration of the composition of the gas phase and the analytical dependences of the partial pressures of its components on temperature, as well as the chemical mechanism and heats of sublimation. The main feature of the sublimation process of all materials based on uranium carbonitride (both pure and doped with zirconium) is its incongruent nature, due to the loss of nitrogen, which leads to a shift in their compositions towards the phase with higher carbon content. The chemical mechanisms of sublimation of carbonitrides of both types are considered, according to which oxygen impurities in these materials lead to the appearance of oxide components UO, UO2 and CO in the gas phase and additional release of nitrogen. The introduction of zirconium into uranium carbonitride and an increase in the carbon content in it lead to a decrease in the partial pressures of uranium monoxide and nitrogen, which increases the thermal stability of this innovative fuel material.

Analytical dependence of burnup on enrichment of prospective fuel and parameters of reactors fuel campaign

The paper is devoted to the definition of an analytical expression for estimating the burnup depth of nuclear fuel depending on its enrichment level, the periodicity of refueling, thermal stressthermal stress and the duration of the time period between refueling (reactor campaign) in a wide range of changes in key parameters for different types of thermal neutron reactors. The analytical expressions obtained in the work for the burnup depth are compared with numerous neutron physics calculations and experimental data from different authors for uranium fuel enrichment up to 9%. Calculations of the fuel share of the cost of electricity of nuclear power plants with PWR type reactors were performed and its sensitivity to changes in burnup depth and enrichment of fuel, the refueling periodicity, as well as to market prices for natural uranium, conversion, enrichment, fabrication of fuel assemblies and SNF handling were determined.

RESISTANCE OF COMPRESSED CONCRETE TO LONG-TERM LOADS

This article deals with the main regularities and features of compressed concrete deformation under the action of long-term loads. The main efforts are aimed at establishing an analytical dependence on determining the long-term strength level of compressed concrete. A critical analysis of the currently existing dependencies based on its calculation was carried out. These studies are based on the general provisions and hypotheses of the previously developed energy model of concrete and reinforced concrete deformation.The defining hypothesis of the specific potential energy invariance of the concrete ultimate deformation (destruction) and its independence from the loading mode of the concrete itself was used. The specific potential energy of compressed concrete deformation at the moment of its destruction under three loading modes is considered: instantaneous dynamic, standardized short-term and long-term. The level of compressed concrete long-term strength is related to the dynamic increase factor limit values (DIFu) under the instantaneous loading mode. In turn, the compressed concrete dynamic increase factor is functionally related to the generally recognized coefficient of compressed concrete standardized elastic-plastic properties under a short-term loading regime. In this way, the functional dependence of the level of compressed concrete long-term strength was obtained not only on its standardized elastic-plastic characteristics, but also on the rate of concrete deformation or on the rate of its loading. The evaluation of the proposed methodology for determining the level of compressed concrete long-term strength is reduced to a comparison of the relevant theoretical calculations results with the various researchers’ published experimental data.

Theoretical and experimental study of heat and mass transfer, evaporation and ignition drops of monoatomic ethanol/butanol binary mixture in cold air

The study evaporation process results of lower alcohols' single drops (ethanol, butanol and their binary mixtures) with an initial droplet size of 1.5-2.5 mm in air at room temperature and atmospheric pressure are presented. To describe the heat and mass transfer of the fuel mixture's drops with different initial composition, prognostic evaluation of dynamics' changes fuels drops size, composition and temperature during their evaporation are proposed. Taking into account the temperature dependence of the heat of vaporization, an analytical dependence for evaluating the drop surface temperature of one-component evaporating fuels is proposed. Comparative analysis of the calculated model's data allowed to suggest a possible evaporation mechanism of multi-component fuel mixtures droplets and to explain some peculiarities in the behavior of the main characteristics this process. It is shown that the thermocouple wires qualitatively affects the behavior with time of temperature and droplet size. Formula for the drop's temperature during evaporation into account the influence of thermocouple are presented.

PROBABILISTIC ANALYSIS OF MULTICHANNEL BUS ARBITRATORS OF COMPUTER NETWORK INTERFACES

Probabilistic analysis was conducted on the functioning algorithms of bus arbiters within the ‘Common Bus’ interface of computer networks. The research employed the theory of random impulse flows as its apparatus. Analytical dependencies were derived to calculate the average waiting time for service requests from network subscribers. The first-come-first-serve and round-robin service algorithms provided better service uniformity than priority algorithms. Keywords: algorithm, service, request–impulse, interface, bus arbiter, common bus.

MODELS OF EXTINGUISHING AGENT MOVEMENT IN AIR SPACE

A system of linear differentiated equations, which takes into account the resistance of the air medium and the presence of wind, is used to formalise the movement of an extinguishing agent. Furthermore, using the integral Laplace transform allows the construction of a structural and dynamic scheme that reflects the process of supplying an extinguishing agent to the fire. Such a structural and dynamic scheme opens up opportunities for building a simulation model of the extinguishing agent movement using the Simulink mathematical visual modelling package. This simulation model provides for the determination of the current coordinates of the extinguishing agent and the speed of its movement to the fire. The parameters of this simulation model are the initial velocity of the extinguishing agent, the height from which it is supplied, the resistance of the air environment, the angle of supply of the extinguishing agent, and the presence of wind. We used the Simulink package to simulate the process of the extinguishing agent supply to the fire. Data sets were obtained for the time of the extinguishing agent supply to the maximum range, for the maximum supply range, and for the value of the extinguishing agent velocity at the maximum range. We have noted that for small angles of the extinguishing agent, there is a slight increase in the time of its supply to the maximum range by no more than 3.0% with a threefold increase in the resistance of the air medium and regardless of the variation in the value of the initial speed of the extinguishing agent supply. The analytical dependence of the time of supplying an extinguishing agent to the maximum range on the rate of its supply is obtained. In particular, the time of the extinguishing agent supply to the maximum range at small angles lies within (0.66÷0.88) s, which is quite significant for low-inertial fire extinguishing systems, the inertial properties of which are characterised by time parameters. This circumstance necessitates considering the time of supplying an extinguishing agent to the fire when solving problems of analysis and synthesis of fire extinguishing systems. This factor can be accounted for through the transfer function of the lagging link. The time parameter of such a transfer function is equivalent to the time of supplying the extinguishing agent to the fire. Keywords: extinguishing agent, delivery range, travel speed.

Stress stateofa composite tractive element with cable rigidity variable over length considering bending on a drum with curved generatrix

Purpose. Establishment of dependencies for parameters of a stress-strain state of a composite tractive element taking into account bending of a rope with cable rigidity variable over length on a drum with a curved generatrix. Research methodology. Development of a method for calculating the influence of a complex of factors on a stress-strain state of a rope by constructing and solving a model of a stress-strain state of a composite tractive element with cable tensile rigidity variable over length, cable base breakages and a non-cylindrical drum shape, using the methods of mechanics of layered composite materials with soft and hard layers. Findings. Analytical dependencies are obtained in a closed form and allow determining the maximum quantitative indicators of a stress-strain state of a rope of a combined structure with a broken cable, rigidity different from the main cables and variable along rope length in a straight rope part and in a part of interaction with a curved drum of a hoisting machine. Analytical dependencies are established for determining the maximum angles of rubber shear between cables, which allows determining the dangerous tangential stresses in a tractive element for cases of flat rope tension, rope bending on a convex drum, and bending on a convex drum of a rope with cables of reduced tensile rigidity. The results of solving the problem of determining the distribution of forces in a rope with cables of different rigidity by the developed method absolutely coincide with the only possible distribution of forces in a sample of three cables, which allows considering the developed algorithm reliable to describe the mechanism of redistribution of forces between cables with different tensile rigidity, including in the event of cable breakage, and the obtained results are reliable. Scientific novelty. A method of calculating the influence of a complex of factors on a stress-strain state of a rope is developed. The dependencies of parameters of a stress-strain state of a composite tractive element are established, taking into account rope bending, which has cable base breakages and cable rigidity variable over length, on a drum with a curved generatrix. Practical significance. A method for determining the indicators of a stress-strain state of a composite tractive element, which has cable base breakages and cable rigidity variable over length, including for bending on a non-cylindrical drum, is developed. This makes it possible to increase the operational safety of a composite tractive element in hoisting and transporting machines, in particular at significant hoisting heights, and also contributes to justifying the use of a rope design as a stay rope in capital structures.

Weighing logistics: on the issue of accuracy of determining the weight of the transported goods

Methods. The results are obtained with the following methods: the method of abstractions in determining the essence of the category of «social justice»; general to specific method in establishing the unity of the existing concepts of social justice; standard methods of sociological research in determining the value system of the Ukrainians towards social justice. Results. As a result of the conducted research, the possible value of financial losses during the sale of such goods as sand, wheat, fodder corn, food corn, iron ore pellets, titanium ore, and rolled ferrous metals was determined. These losses can range from hundreds to tens of thousands of hryvnias. The list of available offers of electronic scales for weighing goods on land was analyzed, the value of error when weighing with automobile and wagon scales was determined. The possibility of describing the error using a logarithmic equation has been demonstrated, which proves that the relative weighing error decreases as the mass increases. The equation formula was found by the analytical economic-mathematical method using Microsoft Excel spreadsheets. Based on the use of the properties of the dispersion of weighing, a logistical and organizational method of increasing the accuracy of weighing has been developed, which consists in several repeated weighings and determining the resulting weight as the arithmetic mean of all attempts. A formula was developed to determine the optimal number of repeated weighings to increase accuracy, taking into account the cost of one weighing and losses during a single weighing. The method of weighing cargo on water was analyzed, its limitations were revealed and the need for its improvement was indicated in terms of taking into account such factors as water salinity, through which the draft of the vessel is measured. An analytical dependence has been developed to determine the weight of the goods loaded onto the vessel by its draft depending on the salinity of the water in which the vehicle is located. Novelty. In the process of analyzing exporters’ losses during product weighing, logistical and organizational measures have been developed that are guaranteed to reduce losses. Practical value. Techniques are proposed that will reduce the exporter’s losses when weighing goods both on land and at sea, which will allow adjusting the size of the weighing error with available devices.

Theoretical aspects of the genesis of composites: Dependence of properties on the history of formation

AbstractStudies of the last decades have brought the results of modern natural science into technology of composite materials of the widest range. The methods of percolation theory have become constructive tools for studying the structure of composites, for the purposeful creation of materials with desired properties. In this paper, a computer model of the processes of self‐organization of percolation clusters has been created. The model considers such problems with self‐organization, in which the properties of a percolation cluster are also determined by the history of the system's development. To study the structure and properties of such systems, a three‐dimensional continuum percolation problem with interacting elements is solved in the model. Iterative algorithms for the motion and interaction of particles and clusters, leading to the formation of percolation systems, have been developed. Their structure and properties have been studied, a number of standard parameters have been calculated, and the dependence of the structure and properties of clusters on the rate of system generation, degree of self‐organization, and characteristic values of the correlation length has been studied; analytical dependences of a number of parameters of percolation systems are obtained.

PLASTIC DEFORMATION WITH OPEN STITCHING. CONCAVITY OF THE UPPER END OF THE WORK PIECE

A theoretical description of the formation of concavity at the upper end of the work piece at the beginning of the piercing process is obtained. The established analytical dependences make it possible to calculate the maximum depth of the resulting concavity. The high accuracy of the calculated data is confirmed by comparison with known experimental data.