Analytical Dependences Research Articles

The Use of Fresnel Lenses in LED Sources of Local Illumination to Оptimize the Distribution of Illumination of the Working Plane

For widely used LED sources there is a sharp decrease in the illumination of the working plane from the center to the edge. The purpose of this study was to analyze the effectiveness of Fresnel lenses usage as a fairly simple and technological element to increase the uniformity of illumination created by LED lamps of local lighting.A method has been developed for calculating of the distribution of illumination created by the combination of “LED matrix – Fresnel lens” when the distance between the lens and the matrix is less than the focal length of the lens. Comparison of the calculation results and experiments for the case when the lens is located at a distance of 50 cm from the working plane indicates the correctness of the developed calculation method. This made it possible to use this technique to solve the problem of improved uniformity of illumination distribution in the working plane of local lighting LED sources.It was found that the change in the distance between the matrix and the lens in the range of 0.5–1.5 cm affects the maximum illumination and its uniformity to a lesser extent than the change in focal lengths in the range of 10–100 cm. Analytical dependences of the uniformity of the working surface illumination as a function of the Fresnel lens focal length and its distance to the LED matrix were obtained for three cases. In the first case one lens is used for the entire matrix while the axes of symmetry of the light intensity curves of LEDs are parallel to the axis of the lens. In the second case one lens is also used for the entire matrix, but the continuations of the axes of symmetry of the light intensity curves pass through the front focus of the lens. In the third one an individual Fresnel lens is used for each LED. It is established that for all three cases dependencies have almost the same character. Therefore, the choice of using one of these three options may be due to manufacturability, cost-effectiveness, thermal stability, and other considerations.Calculations using the above-mentioned analytical dependences made it possible to determine values of the parameters of the “LED matrix – Fresnel lens” system at which the indicators of illumination and uniformity meet the standards’ requirements.

Analytical Dependence of the Probability of Masking Objects on the Density and Dispersion of the Aerosol

With the existing method for evaluating the effectiveness of masking objects with aerosols, two parameters are used: the length and width of an invisible smoke screen with a probability of at least 50 %. Both parameters were obtained during the practical tests of aerosol masking means. However, they are insufficient for assessing the masking ability of an aerosol cloud as a spatial formation. The purpose of this work is to reveal the analytical dependence of the probability of objects masking on the density and dispersion of the aerosol. Мaterials and methods. An extended approach was used to estimate the probability of masking at any theoretical value of the flux density (integral concentration, g/m2) of aerosol along the line of sight, taking into account its dispersion, by calculating the formation of a probability field from 5 to 95 % over the entire spatial structure of the aerosol cloud. The method used is the simulation on a PC of the dependence of the share of space occlusion for the observer (the eyepiece of an optical device) by aerosol particles of a given dispersion and flux density, which we took as the probability of masking. Discussion. It is shown in the article, that the resulting analytical expression as a result of processing the accumulated simulation results on a PC fully corresponds to the Bouguer-Lambert-Beer law, which is a generalization of many years of practical field and laboratory experiments with aerosols in the air and dispersed particles in solutions. The obtained probability values allow us to obtain a generalized efficiency criterion in the form of a new concept - the reduced masking zone. This term is mathematically analogous to the reduced impact zone, which is used to assess damage caused by munitions. Conclusion. For a full assessment of the effectiveness of aerosol countermeasures, the reduced masking zone must be calculated for all possible lines of sight (observation of an object): horizontally, vertically, and along inclined paths. This condition reflects the method of using modern weapons such as Javelin anti-tank systems, which are aimed at the target mainly horizontally, and the final trajectory before the impact is a «hill». The theoretical difference between the values of vertical and horizontal masking screens, obtained by the authors using a new method for calculating the parameters of an aerosol cloud, is presented in the illustrations to the article.

Parameters of the deep loader of the mole drainage gun

The purpose of the study is to substantiate the parameters of the deep-loader of the mole-drainage gun. A diagram of a mole-drainage gun is given. The main working parts of the mole drainage tool are a deep loader, a knife, a rope and a drainer. Analytical dependences are obtained for determining the main parameters and traction resistance of the deep-loader of the mole-drainage gun. Theoretical studies have established that for high-quality loosening of the soil with minimal traction resistance, the height of the deep digger should be 90 cm, the width of its chisel is 7 cm, the angle of the chisel to the horizon is within 26-320, the length of the chisel is 11.5 cm, and the sharpening angle is 250. Installing a knife on a deep-loader increases the density of the dredge wall by 1.45-1.48 times, the depth of the dredge laying by 1.15 times, while the traction resistance of the mole-drainage gun decreases by 12.9%.

Automated Study of Electrophysical Properties of Polymeric and Composite Materials

The use of secondary resources and composites in modern polymer materials would make it possible to reduce the cost and change the physical and mechanical properties of the packaging material. The use of composites to impart new properties to polymers complicates the implementation of technologies for the production of products from them, which prevents the improvement of product quality. This is due to the lack of an accumulated database and methods of predictive determination of the obtained properties of composite materials and polymers produced with the use of secondary raw materials. (Research purpose) The research purpose is testing the methodology of automated determination of electrophysical parameters of polymer and composite thermoplastic materials. (Materials and methods) A resonant method of monitoring the electrophysical parameters necessary for an energy-efficient method of high-frequency electrothermal heating of polymers has been substantiated. We selected and modified with the installation of an automated monitoring and data collection system cumeter with a working chamber from a standard cell, retrofitted with a heating system and thermal insulation. (Results and discussion) The results of the use of an automated process of control and determination of electrophysical parameters of polymer and composite materials based on polypropylene, polyethylene with a composite of titanium dioxide were presented. The method of establishing analytical dependencies for calculating the correction coefficient when calculating the effect of thermal insulation material (dielectric cardboard) and air gap in the working capacitor on the even electrophysical parameters of the polymer and composite under study was shown. (Conclusions) The possibility of conducting automated studies to determine the dielectric properties of polymer and composite materials using the developed automated control system for the process of control, transmission, processing, visualization and storage of information about the dielectric properties of ε, ε», tgδ polymer and composite materials was substantiated. The heating temperature ranges of polymer and composite materials PP H030 GP/3 TS and 1060PE were identified in automatic mode in order to organize the most energy-efficient operating modes of high-frequency electrical equipment.

Технологические режимы раздачи и обжима при локальном нагреве

The processes of spread and reduction of a heated rough piece under visco-plasticity conditions are viewed. The ratio for force stress calculating in operations, damage to the material of the rough pieces is obtained. In the branches of special en-gineering, high-strength alloys based on titanium and aluminum are used. In the branches of special engineering, high-strength alloys based on titanium and aluminum are used. These alloys have mechanical properties anisotropy. Processing of these alloys is difficult. For this reason, the pressure treatment operation is performed with heating of the deformation zone. The material in the deformation zone exhibits viscous properties. Deformation hardening and softening (stress relaxa-tion) of the material take place simultaneously. Besides, the lower the deformation rate, the greater the softening. In this regard, a constitutive equation representing these processes is found. The factor of hardening and softening creates condi-tions for reducing the power mode of pressure treatment operations and increasing the degree of primary part forming. Stress relaxation calculation with the help of analytical dependencies is necessary at the stage of expansion and pressing development. The calculated ratios are recorded as a function of the speed of these operations. In this case, the specified deformation (the change in the degree of forming) is taken into account, adjusted depending on the speed and mechanical characteristics of the bearing alloy anisotropy. The calculated ratios are obtained under conditions of a flat voltage scheme, which corresponds to expansion and pressing. Stress equilibrium equation and yield condition of anisotropic material are used. The joint solutions of this equation and yield conditions determine values of the meridional and circumferential stress-es arising in the piece part material. The values of the stresses allow calculating the forces of operations. It is shown that the speed of expansion and pressing and mechanical properties anisotropy affect the damage to the material of the «green body». Dependences for the calculation of damage are obtained on the basis of energy and deformation strength criteria. These dependencies allow predicting the quality of products. It is also shown that anisotropy affects the technological modes of expansion and pressing. As the anisotropy coefficient increases, the stresses and forces of operations decrease. Calculations of stresses, forces and material damage in the process of expansion of anisotropic titanium alloy VT14 at 875 ℃ are made.

INFLUENCE OF OPERATIONAL LOADS ON BALLASTING PARAMETERS OF UNDERWATER CROSSINGS OF TRUNK OIL AND GAS PIPELINES

The trunk oil and gas pipelines are under operational loads affecting the strength and reliability of the structure. The most significant effect of loads is manifested at pipeline crossings across rivers. The stability of underwater pipeline design position and thus its reliability is achieved by ballasting with the required intensity. The current regulatory document SP 36.13330.2012 provides for the required intensity determination, taking into account the water buoyancy force and pipeline crossing along the longitudinal profile of the transition. At the same time, it should be noted that ensuring pipeline bending along the longitudinal profile of the crossing with the use of ballasting of the required intensity also depends on the internal forces acting in the pipeline wall during operation. However, this document does not take into account operational loads when determining the required ballasting intensity. In addition, ballasting with the ensuring pipeline bending along the longitudinal profile of the crossing leads to the occurrence of bending stresses, in some cases quite high, which affect the level of total stresses, strength and reliability of the structure. In many cases, water occupies only part of the concave section of the pipeline at crossings. Taking into account the above conditions and features, studies of the ballasting of underwater crossings of trunk oil and gas pipelines were carried out.
 The aim of the work is to obtain analytical dependences of the ballasting intensity and bending stress in an underwater pipeline at different altitude water levels at the transition from operational loads and geometric characteristics of the crossing.
 The research method is a theoretical study of the stress-strain state of an underwater pipeline under the action of operational loads and weights.
 The dependences of ballasting intensity with weights of the underwater pipeline on the operational loads and the geometric characteristics of the transition at different elevations of the water level at the transition are obtained, and the highest bending stresses in the pipeline wall at the underwater crossing are determined. Recommendations to reduce the total longitudinal stress level in an underwater pipeline are given.

ОПРЕДЕЛЕНИЕ ТОЧЕК БИФУРКАЦИИ В ФУНКЦИОНИРОВАНИИ СИСТЕМЫ «ПОЧВА – РАСТЕНИЕ – ВОЗДУХ»

To date, a number of mathematical models of plant growth, developed by domestic and foreign scientists, are known. However, the issues of determining the bifurcation points that arise during the functioning of “soil-plant-air” system have not been sufficiently considered. In relation to the issues considered in the article, the bifurcation point is a critical state of the “plant” subsystem, at which it becomes unstable with respect to fluctuations in natural and climatic conditions (drought, frost, prolonged rains, etc.) and there is uncertainty in the development of plants (further growth or their death), as well as the intensive growth of plants as a result of the corresponding technological operations. For control and operational management of the formation of agricultural crops, it is desirable to know the bifurcation points determined by the biological time of plant growth and extreme weather situations. Therefore, the main goal of research is the analytical determination of bifurcation points observed during the vegetation of plants. The “plant” subsystem at the bifurcation point can be simultaneously in two or more states. As a result of the analysis of the obtained analytical dependences of various possible states of “soil-plant-air” system, it is proposed to subdivide bifurcations into negative and positive ones. A method has been obtained for determining bifurcation points during the functioning of “soil-plant-air” system. Under natural and climatic conditions, critical situations can arise with insufficient incoming substances to “soil-plant-air” system, such as light supply, moisture supply, heat supply, food supply and gas supply of plants. As a result of analytical studies, bifurcation points were determined in “soil-plant-air” system, depending on the radiation balance (R) formed on the underlying surface, slopes of different exposure and steepness, and coefficients characterizing light, moisture, heat, food and gas supply plants.

Dependence analysis for calculating the theoretical stress concentration factor in a butt welded joint

Determination of the theoretical stress concentration factor in a butt welded joint by different methods is considered. The results obtained on the basis of analytical dependencies and the finite element method are compared with varying the geometric parameters of the joint. The most accurate dependencies are established for determining the theoretical stress concentration factor for a different number of parameters in a given range of their values. Keywords: butt welded joint, theoretical stress concentration factor, analytical dependencies, finite element method. manshula@mail.ru, a.shlepetinskiy@reph.ru

Deformations of a three-dimensional model of a trihedral double lattice rod tower

Introduction. The calculation of deformations of spatial structures, as a rule, is carried out numerically on the basis of the finite element method. With the development of computer mathematical systems for regular systems an opportunity to obtain analytical solutions appeared. Such solutions can be used as test ones to evaluate numerical solutions and for preliminary calculation of a structure at design stage. The task has been set to derive deformation dependences of a spatial truss under various loads from its size and number of panels.
 
 Materials and methods. The truss of the tower structure is statically determined. The calculation of force values in the bars is performed by cutting out nodes in a Maple symbolic mathematics system. The Maxwell – Mohr formula is used to determine the displacement of a node at the top of the frame, considering only the longitudinal deformations of the rods. From the generalization of a series of analytical solutions for trusses with consecutively increasing number of panels onto an arbitrary number of panels the sought formula is derived by the induction method.
 
 Results. An algorithm of derivation of formulas for the deflections of a building along two mutually perpendicular horizontal axes under the action of lateral uniformly distributed nodal loads is presented. Effort distribution patterns are obtained for the truss rods and analytical stress dependences of some rods on the number of panels are found. Linear asymptotics of the solutions for the number of panels and the points of extremum are found and computed.
 
 Conclusions. The considered model of the spatial statically determined tower truss allows deriving exact formulas for deformations under the action of various loads within the limits of the adopted model. It is possible to use derived formulas for a preliminary estimation of designed structure and to apply as test ones for numerical calculations. The extremum points and analytical expressions for asymptotes allow the derived formulas to be used for solving stiffness optimization problems of a structure.

Эффективная переработка полезных ископаемых определяется правильностью стратегии выбора техники и технологии при производстве работ. В современных условиях, когда необходимо наращивание производственной мощности действующих горно-обогатительных комбинатов, повышение производительности производства не может рассматриваться в отрыве от возможностей конкретного технологического оборудования. При решении вопросов повышения эффективности горно-обогатительного оборудования требуется особо уделять внимание оптимизации его взаимодействия в единой технологической схеме. Общеизвестно, что на горно-перерабатывающих

The efficiency of mineral processing is determined by the correct selection strategy for equipment and technology in the production process. In the present-day context, when it becomes necessary to increase the production capacity of existing mining and processing plants, enhancing the production capacity cannot be considered in isolation from the potential performance of the specific process equipment. When addressing the challenges associated with improving the efficiency of mining and processing equipment, special attention needs to be paid to streamlining its interaction within a unified process flowchart. It is generally known, that the bin storages at mining and processing facilities are intended to receive rock mass and secure batching and uniform supply of loose and lumpy materials from the bin to the downstream technological equipment. The bin storage parameters have to be defined with account of the properties of the materials to be used. The aim of this study is to develop an optimal design of the bin-and-feeder system that would ensure the material path close to the brachistochrone curve. Based on the presented analytical dependences, the main characteristics of releasing the mineral raw material from the bin-and-feeder systems have been established for the conditions of mining and processing plants. The received data can be used in further research to provide a mathematical model of material flow, as well as in the finding an optimal design of the bin. A complex approach that included a system scientific analysis and generalization of previously published studies was used in addressing the tasks set. An approach is suggested to develop a promising design of the bin-and-feeder system to deliver the mineral raw materials based on using the guides that would ensure the material flow as close to the brachistochrone curve as possible. This approach can be implemented in the bin-and-feeder systems for ore processing plants in order to reduce the energy consumption for the transportation and feeding of the mineral raw materials.

The Activity of a Solar-Type Star TOI-1422 and Mass Loss of the Atmosphere of the Planet TOI-1422b

The results of the analysis of the activity of a solar type star G2V TOI-1422 are presented and estimates of the loss of atmospheric matter of the planet TOI-1422b are made. The planet can be attributed to the type of hot Neptunes. Compared to other exoplanets of a similar mass range, it is expected that the planet has an extensive gas envelope. According to the long-term photometric survey of Kamogata Wide-field Survey (KWS) the TOI-1422 activity was analyzed and the existence of possible activity cycles of 1650–1680 days and 2450 days was suggested. The probable value of the rotation period P of the star lies in the range of 27 (+19, –8) days, observations of the KWS survey in the V filter indicate the most possible value for the period P = 32 days. Mass loss of the planet’s atmosphere is determined using an approximation formula corresponding to the model of atmospheric loss with an energy restriction. To estimate the flux of XUV photons analytical dependences were used linking the flux values and the parameter log R_{{{text{HK}}}}^{'}. Calculations have shown that the atmosphere matter loss of TOI-1422b is dot {M} = 9.4 times {{10}^{8}} g/s; considering the existing errors in determining the parameters of the atmosphere it lies in the range from 6.8 times {{10}^{8}} to 1.4 times {{10}^{9}} g/s, and considering the uncertainty in the value of the chromospheric activity index—from 8.3 times {{10}^{8}} to 1.1 times {{10}^{9}} g/s.

THE ACTIVITY OF A SOLAR-TYPE STAR TOI-1422 AND MASS LOSS OF THE ATMOSPHERE OF THE PLANET TOI-1422b

The results of the analysis of the activity of a solar type star G2V TOI-1422 are presented and estimates of the loss of atmospheric matter of the planet TOI-1422b are made. The planet can be attributed to the type of hot neptunes. Compared to other exoplanets of a similar mass range it is expected that the planet has an extensive gas envelope. According to the long-term photometric survey of Kamogata Wide-field Survey (KWS) the TOI-1422 activity was analyzed and the existence of possible activity cycles of 1650-1680 days and 2450 days was suggested. The probable value of the rotation period P of the star lies in the range of 27 (+19, –8) days, observations of the KWS survey in the V filter indicate the most possible value for P = 32 days. Mass loss of the planet’s atmosphere is determined using an approximation formula corresponding to the model of atmospheric loss with an energy restriction. To estimate the flux of XUV photons analytical dependences were used linking the flux values and the parameter \(\log R_{{{\text{HK}}}}^{'}\). Calculations have shown that the mass loss of TOI-1422b is \(\dot {M} = 9.4 \times \) 108 g/s and taking into account the existing errors in determining the parameters of the atmosphere it lies in the range from 6.8 × 108 g/s to 1.4 × 109 g/s.

Methods for improving the efficiency of a small forklift with an on-board steering system

In the known scientific and technical literature, insufficient attention is paid to the study of the dynamic processes of wheeled vehicles with an on-board steering system. An overview of the operation of small-sized loaders is presented. The aim of this work is to improve the methodology for calculating the parameters of the turning process and the dynamic stability of a small-sized loader with a 4x4 wheel configuration. A single-axle nonlinear mathematical model with five degrees of freedom is presented. Based on the Lagrange equations of the second kind, analytical dependencies of the machine's motion were compiled. The following main parameters were varied during the modeling process: the mass of the load to be lifted, and the position of the center of mass of the entire machine, the height of the bucket above the bearing surface, and the initial speed of the loader. The 4th order Runge-Kutt numerical method was used to solve the composite mathematical model. When comparing the calculated and experimental oscillograms, they practically coincide in terms of the main form of oscillation and the nature of the change in traction force, with a discrepancy of 11%. When the loader turns as a result of sliding the running wheels on the bearing surface, the oscillatory process is undamped and close in nature to self-oscillations. In this case, the running wheels are detached from the bearing surface, and with an increase in the outreach and height of the load, the intensity of oscillations increases and, under certain circumstances, it is possible to lose machine stability or to hit the bucket bottom against the bearing surface. When the center of mass of the loader passes through the axle of the front wheels, the machine becomes unstable. This corresponds to the maximum angle of deviation of the center of mass forward. As a criterion for the stability of a loader during a turn, it is proposed to calculate the angle of deviation of its center of mass relative to the static position. At the maximum overhang of the bucket with a full load, its value should not exceed 170.

Dynamics of mechanical drives with ball overruning clutches

Problem. The possibilities of application and the principle of operation when turning on the new overrunning ball clutch are considered. Its design for the standard starter of cars and other vehicles must function during operation in various modes. The main goal of the work is to study the amount of change in the minimum and maximum time of turning on and off the proposed ball overrunning clutch, taking into account dynamic phenomena at the first stage of its operation. Methodology. The kinematic chain of the drive is considered as the functioning of an elastic system. It has been established that there is a higher probability of dynamic phenomena occurring in such systems during the rolling of the balls into the working grooves of the driven semi-coupling, so this process is considered in the paper. Results. The results of these studies improve the characteristics of unstable modes of operation of new clutches, which can be introduced into production after comprehensive studies of their loading capacity. When the clutch switches to another mode of operation, the oscillating phenomena of its elements are not completely excluded. Originality. Therefore, in order to improve the smoothness of the operation of such new clutches, the possibility of taking into account oscillatory phenomena is being considered. Practical value. Developed analytical dependencies for determining the minimum and maximum engagement time of the ball overrunning clutch are presented. The main parameters for further research of mechanical drives with overrunning ball clutches, for which the operating torque is known, have been obtained.

Studying the system of diagnostic parameters of the hydraulic drive taking into account the measurement error

Problem. The article considers a methodology for improving the efficiency of operational performance of mobile machines due to the perfection of the hydraulic drive diagnostic system, which is determined by the improvement of design, manufacture, and operation. Goal. The modern development of diagnostic methods is carried out through the use of more accurate or non-contact measuring instruments, and the technical condition of most hydraulic units is determined by the size of the gaps in the joints of their parts. Methodology. The study of the relationship between structural and diagnostic parameters based on the mathematical model of the hydraulic drive made it possible to develop diagnostics of hydraulic units of mobile machines by measuring the determining diagnostic parameter (performance or pressure) at one point of the hydraulic drive, as well as to establish analytical dependencies that determine the error of diagnosing hydraulic units and its components under uncertainty of the values of the gaps in these hydraulic units. Results. The presented work continues research in this direction and establishes the properties of the system of diagnostic parameters, in which the pump speed is the determining parameter. Originality. The properties of the system of diagnostic parameters, in which the pump speed is the determining parameter, are established. The relationship between the standard and the investigated systems of diagnostic parameters is established. Practical value. The equations are obtained and the diagnostic errors of hydraulic units and the components of these errors are determined using these equations when diagnosing by pump speed under the condition of uncertainty in the values of pump clearances. The results are compared with a standard diagnostic system.

Investigation of the Interaction Process with the Environment of a Bulldozer Bladow with Variable Geometry

The purpose of the work is theoretical and experimental confirmation of rational parameters, a significant range of rational use and efficiency growth of bulldozers-terrasers due to the installation of a universal, adaptable to variable working conditions of the blade with a variable geometry of its profile. Experimental studies have confirmed the correctness of the assumptions made when deriving analytical dependencies for determining the volume of the accumulated ground prism, as well as the components of the horizontal resistance to cutting and digging with a blade with a variable geometry. The experimental and theoretical dependences obtained as a result of the research made it possible to develop a methodology for determining the main parameters of a blade with a variable geometry, taking into account functional limitations. The article shows the stages of theoretical and experimental results of checking the dependence of the counteraction forces (their horizontal and vertical components) on digging and generating a drawing prism of the material being developed on the defining parameters of the blade with variable geometry (angles of capture, tilt and cutting, blade width, etc.). The proposed method for determining the main parameters of the blade with variable geometry allows you to choose them taking into account the universal purpose of the blade, the results of the research, the existing geometric dependencies between the parameters and various functional limitations.

OPTIMIZATION OF CALCULATIONS OF BUILDING STRUCTURES

Building structures are very diverse in their shapes, sizes, loading conditions, etc. Their durability depends on many factors, including how accurately the design scheme reflects the actual conditions of its operation. Because no matter how precise and complex calculation methods are used, if an incorrect calculation scheme is calculated, then the results of such calculations will not reflect the true picture. Therefore, the problem of optimization of design schemes is of great scientific and practical importance. Optimization parameters depend on specific conditions. One of the existing approaches for finding optimal solutions is based on mathematical modeling, when the model is an analytical dependence of the objective function on dependent (controlled) variables, the numerical values and range of which are set based on the actual operating conditions of this structure. The compilation of such models and the performance of appropriate calculations require a deep understanding of the essence of the phenomenon and knowledge of the mathematical apparatus. Of the existing methods, the most common and developed is linear programming, when the model is a linear function and the variables in the constraint system are also linear. The idea of the method is technically implemented in the add-in "Search for a solution" for Microsoft Excel. With its help, you can find the optimal (maximum or minimum) numerical value of the objective function contained in one cell, taking into account restrictions on the values of dependent variables in other cells. Most often, this superstructure is used in solving optimization problems of the economy (simplex method, transport problem, etc.). In the public domain, there are very few results of using this approach in the calculations of building structures at the initial design stage. In the proposed work, an attempt was made to use this add-on in the problem of optimizing the geometric dimensions of a structure, when the numerical value of the bending moment in a particular section was chosen as the optimization criterion. It is appropriate to solve such a problem at the stage of drawing up the design scheme of the structure. Keywords: calculation scheme, line of influence, search for solutions

Modelling the parameters of accelerated move-ment of passenger cars in coordinated traffic

Problem. In order to fine-tune the coordination plan to the specific traffic conditions on the road network segment selected for coordination, it is necessary to determine the time for vehicles to travel between synchronized traffic lights. Such models should be based on accelerated rather than uniform moving, and a parameter estimation method should be developed to form them. Goal. Development of a new method for estimating the parameters of a linear model of decreasing acceleration, which allows estimating them in specific driving conditions based on knowledge of two quantities: the length of the link and the random time of its overcoming in free driving conditions. Methodology. Using the functional relationships between travel time, acceleration, speed, and distance, known from kinematics, we have moved to a new sequence of actions to select the type and estimate the parameters of the model that relates the acceleration and speed of a car. For this purpose, using the obtained analytical dependence between time and distance travelled, which contains unknown model parameters, it is possible to find the values of these coefficients by minimising the sum of squares of the difference between the calculated and actual lengths of the link. Results. Based on the search for the minimum square of deviations between the actual and calculated values of the link length, the method of estimating the parameters of the model of accelerated movement of cars at a start from a standstill, based on the results of observations in Kharkiv and Vinnitsa, led to coefficients similar to existing models. The average steady-state speed is estimated at 53.14 km/h. Originality. The presented methodology contains the new transition method from actual times of link passing to parameters of linearly decreasing acceleration model. Practical value. The developed method allows fine-tuning the offsets of the traffic light cycles in the coordination plan to the specific traffic conditions on the road network segment selected for coordination based on actual times of link passing.

Forecasting of financial risks of decline in profit and profitability of companies in the retail industry on the basis of correlation and regression analysis of macroeconomic factors

Aim. Development and realization of the innovative approach to forecasting of financial risks of profit and profitability decrease of retail industry companies on the basis of correlation and regression analysis of macroeconomic factors.Tasks. To identify and substantiate the macroeconomic risk factors of decrease in the retail trade turnover of the Russian companies of the retail industry; to develop a methodology of construction and build regression dependence of the total turnover of the companies of the retail trade industry in the Russian Federation (RF) on the macroeconomic factors; to define parameters of the analytical dependence of the retail trade turnover of the leading Russian retailers on the macroeconomic factors; to reveal and argue the position concerning the restrictions of application of correlation and regression analysis.Methods. The authors applied a systematic approach, providing a comprehensive study of the impact of macroeconomic factors on financial risks of profit and profitability reduction, as well as the correlation and regression analysis, methods of mathematical statistics and econometrics.Results. The methodology of estimation and forecasting of financial risks of profit and profitability decrease of the retail industry companies under the influence of external macroeconomic risk factors based on the use of the regression dependence of the retail industry companies turnover on the selected and grounded macroeconomic factors built in the present article is offered.Conclusions. The methodology of building regression dependences of retail turnover on external macroeconomic factors and the methodology of assessing the impact of these factors on the financial risks of reduced profit and profitability indicators proposed in the study are a methodological basis for forecasting changes in the results and efficiency of economic activities of companies in the retail industry and developing preventive measures aimed at reducing the financial risks of such companies. The quantitative assessments of the impact of macroeconomic factors on the retail turnover of leading Russian retailers obtained in the work allow to identify the most significant external macroeconomic risk factors for each of the companies and give a reasonable forecast of changes in retail turnover, profit and profitability indicators of these companies under the influence of macroeconomic factors.

Justification of the method for determining the reliability of the operator of a mobile fire fighting installation

The object of research is the operator of a mobile fire installation; the subject of research is the operator’s characteristics, particularly his reliability. The method of determining the reliability of a mobile fire installation operator as a functional element of a dynamic system is substantiated. Operator failure is interpreted as the output of its frequency characteristics beyond permissible limits. Analytical dependences for variations of the operator’s frequency characteristics on variations of its parameters – transmission coefficient, delay time, and time constant are constructed. The amplitude and phase reliability of the operator of a mobile fire installation are determined using the Laplace functions, the arguments of which are the permissible values of variations in the frequency characteristics of the operator and variations of its parameters. Determination of variations of operator parameters is carried out by the instrumental method using the operator’s activity monitoring system. The test effect on the operator of a mobile fire installation is carried out in the form of a rectangular pulse that formalizes the change in the position of the combustion cell at a priori a given distance over a priori predetermined time. A signal characterizing the operator’s response to the test impact is determined using the Laplace integral transform. Measuring the parameters of this signal allows you to determine the variations in operator parameters that are used to determine its reliability. It is shown that for variations of operator parameters, the values of which are 10.0 % with RMS deviations of 3.3 %, with a probability of 0.8715 the amplitude-frequency and phase-frequency characteristics at the time of its control will not differ from their nominal values by more than 5.0 %. The requirements regarding the reliability of the operator’s activity control system are determined