scholarly journals МЕТОД ПОПЕРЕДНЬОГО ФОРМУВАННЯ ОСНОВНИХ ПАРАМЕТРІВ ПІД ЧАС ГЛИБОКИХ МОДІФІКАЦІЙНИХ ЗМІН У ЛІТАКАХ ТРАНСПОРТНОЇ КАТЕГОРІЇ

2018 ◽  
pp. 62-67
Author(s):  
Дмитрий Васильевич Тиняков ◽  
Виктор Иванович Рябков
Keyword(s):  
Mathematical Model ◽  
Mathematical Models ◽  
Long Range ◽  
Structural Members ◽  
Wing Area ◽  
Middle Range ◽  
Mass Increment ◽  
Passenger Aircraft ◽  
The Mathematical Model ◽  
The Relationship

The method of a preliminary development of main performances during deep variation in variants of a transport category aircraft, that is, when changing a wing area and a powerplant output, has been proposed. The main performance of any aircraft on the stage of its modifying is takeoff mass to, its value depends on structural members’ masses, in which modifications changes are present. The method is based on the com-parative evaluation of take-off mass increments of a basic aircraft and it’s variant. That allows qualitatively and quantitatively to evaluate the specific value of the take-off mass increment of an airplane variant depending on engineering and economical requirements changes. Also, it is obvious that changes in the combination of performances their changes in the process of an aircraft variant creation, move the solution of an existence equation at new point, which corresponds to a new takeoff mass. The analysis of the method was implemented on the example of the regional passenger aircraft variant with two turboprop engines. The method of a preliminary development of main performances of a transport category aircraft subject to deep modification, i.e. when changing a wing area or a powerplant output, is proposed. The mathematical model for the estimation of the takeoff mass increment, depending on requirement groups realized in modifications, is developed by using the models of calculation of required mass (due to change of modification) and available mass (constant for a base variant). Statistical equations for the preliminary estimation of a takeoff mass increment, that create the relationship between the constituent masses and the takeoff mass for a regional aircraft, are used. For middle-range and long-range airplanes an adjustment is needed. The proposed method and the mathematical models allow at a preliminary designing stage of an airplane variant not only typical required quantitative change in structure, but the necessary changes of a wing area and a powerplant output to satisfy the required engineering and economical requirements, which aircraft and air-lines’ markets dictate.

Temperature Influence on Performance of Oxidation Ponds

1991 ◽  
Vol 24 (5) ◽  
pp. 85-96 ◽  
Author(s):  
Qingliang Zhao ◽  
Zijie Zhang
Keyword(s):  
Mathematical Model ◽  
Temperature Influence ◽  
Field Scale ◽  
Experiment Data ◽  
Computer Technique ◽  
Oxidation Pond ◽  
Optimum Model ◽  
Oxidation Ponds ◽  
The Mathematical Model ◽  
The Relationship

By means of simulated tests of a laboratory–scale oxidation pond model, the relationship between BOD5 and temperature fluctuation was researched. Mathematical modelling for the pond's performance and K1determination were systematically described. The calculation of T–K1–CeCe/Ci) was complex but the problem was solved by utilizing computer technique in the paper, and the mathematical model which could best simulate experiment data was developed. On the basis of experiment results,the concept of plug–ratio–coefficient is also presented. Finally the optimum model recommended here was verified with the field–scale pond data.

scholarly journals NECESSITY TO IMPROVE THE MATHEMATICAL MODEL OF FREIGHT CARS TO STUDY CASES OF ITS DERAILMENTS

2020 ◽  
pp. 442-451
Author(s):  
А.V. Batig ◽  
A. Ya. Kuzyshyn
Keyword(s):  
Mathematical Model ◽  
Mathematical Models ◽  
Computer Experiment ◽  
Rolling Stock ◽  
Software Systems ◽  
Freight Car ◽  
The Stability ◽  
The Many ◽  
The Impact ◽  
The Mathematical Model

One of the most important problems that pose a serious threat to the functioning of railways is the problem of freight cars derailment. However, according to statistics, the number of cases of the derailments of freight cars in trains annually grows. Тo prevent such cases, the necessary preventive measures are developed, and to study the causes of their occurrence, a significant number of mathematical models, programs and software systems created by leading domestic and foreign scientists. Studies of such mathematical models by the authors of this work have led to the conclusion that they are not sufficiently detailed to the extent that it is necessary for analyze the reasons of its derailment. At the same time, an analysis of the causes of the rolling stock derailments on the railways of Ukraine over the past five years showed that in about 20 % of cases they are obvious, and in 7 % of cases they are not obvious and implicitly expressed. The study of such cases of rolling stock derailment during an official investigation by the railway and during forensic railway transport expertises requires the use of an improved mathematical model of a freight car, which would allow a quantitative assessment of the impact of its parameters and rail track on the conditions of railway accidents. Therefore, taking into account the main reasons that caused the occurrence of such railroad accidents over the last five years on the railways of Ukraine, the article selected the main directions for improving the mathematical model of a freight car, allowing to cover all the many factors (explicit and hidden) and identify the most significant ones regarding the circumstances of the derailment rolling stock off the track, established on the basis of a computer experiment. It is proposed in the mathematical model of a freight car to take into account the guiding force, the value of which is one of the main indicators of the stability of the rolling stock. The authors of the article noted that not taking into account the influence of the guiding forces on the dynamics of the freight car can lead to an erroneous determination of the reasons for the rolling stock derailment or even to the impossibility of establishing them.

scholarly journals METHODS OF FORMULATING AND SOLVING OPTIMIZATION PROBLEMS OF CUTTING LOGS OF LARGE SIZE BY BAR-SAWING METHOD WITH CUTTING OUT ONE BAR AND FIVE PAIRS OF SIDE EDGING BOARDS WITH SUBSEQUENT SAWING LUMBER FOR EDGED BOARDS

2017 ◽  
Vol 7 (1) ◽  
pp. 137-150
Author(s):  
Агапов ◽  
Aleksandr Agapov
Keyword(s):  
Mathematical Model ◽  
Objective Function ◽  
Optimization Problem ◽  
Optimization Problems ◽  
Target Function ◽  
Cross Sectional ◽  
Optimization Task ◽  
Cutting Out ◽  
The Mathematical Model ◽  
The Relationship

For the first time the mathematical model of task optimization for this scheme of cutting logs, including the objective function and six equations of connection. The article discusses Pythagorean area of the logs. Therefore, the target function is represented as the sum of the cross-sectional areas of edging boards. Equation of the relationship represents the relationship of the diameter of the logs in the vertex end with the size of the resulting edging boards. This relationship is described through the use of the Pythagorean Theorem. Such a representation of the mathematical model of optimization task is considered a classic one. However, the solution of this mathematical model by the classic method is proved to be problematic. For the solution of the mathematical model we used the method of Lagrange multipliers. Solution algorithm to determine the optimal dimensions of the beams and side edging boards taking into account the width of cut is suggested. Using a numerical method, optimal dimensions of the beams and planks are determined, in which the objective function takes the maximum value. It turned out that with the increase of the width of the cut, thickness of the beam increases and the dimensions of the side edging boards reduce. Dimensions of the extreme side planks to increase the width of cut is reduced to a greater extent than the side boards, which are located closer to the center of the log. The algorithm for solving the optimization problem is recommended to use for calculation and preparation of sawing schedule in the design and operation of sawmill lines for timber production. When using the proposed algorithm for solving the optimization problem the output of lumber can be increased to 3-5 %.

scholarly journals Analysis on Present Mathematical Model for Predicting the Crop Production

2020 ◽  
Vol 9 (12) ◽  
pp. 168-170
Keyword(s):  
Mathematical Model ◽  
Mathematical Models ◽  
Real World ◽  
Crop Production ◽  
Ghg Emissions ◽  
Data Set ◽  
Factors Affecting ◽  
The Government ◽  
The Mathematical Model ◽  
Government Website

India is a worldwide agriculture business powerhouse. Future of agriculture-based products depends on the crop production. A mathematical model might be characterized as a lot of equations that speak to the conduct of a framework. By using mathematical model in agriculture field, we can predict the production of crop in particular area. There are various factors affecting crops such as Rainfall, GHG Emissions, Temperature, Urbanization, climate, humidity etc. A mathematical model is a simplified representation of a real-world system. It forms the system using mathematical principles in the form of a condition or a set of conditions. Suppose we need to increase the crop production, at that time the mathematical model plays a major role and our work can be easier, more significant by using the mathematical model. Through the mathematical model we predict the crop production in upcoming years. .AI, ML, IOT play a major role to predict the future of agriculture, but without mathematical models it is not possible to predict crop production accurately. To solve the real-world agriculture problem, mathematical models play a major role for accurate results. Correlation Analysis, Multiple Regression analysis and fuzzy logic simulation standards have been utilized for building a grain production benefit depending model from crop production. Prediction of crop is beneficiary to the farmer to analyze the crop management. By using the present agriculture data set which is available on the government website, we can build a mathematical model.

Walking Stability Analysis of Multi-Legged Crablike Robot over Slope

2013 ◽  
Vol 572 ◽  
pp. 636-639
Author(s):  
Xi Chen ◽  
Gang Wang
Keyword(s):  
Mathematical Model ◽  
Stability Analysis ◽  
Stability Criterion ◽  
Stability Margin ◽  
Static Stability ◽  
Matlab Simulation ◽  
And Performance ◽  
The Stability ◽  
The Mathematical Model ◽  
The Relationship

This paper deals with the walking stability analysis of a multi-legged crablike robot over slope using normalized energy stability margin (NESM) method in order to develop a common stabilization description method and achieve robust locomotion for the robot over rough terrains. The robot is simplified with its static stability being described by NESM. The mathematical model of static stability margin is built so as to carry out the simulation of walking stability over slope for the crablike robot that walks in double tetrapod gait. As a consequence, the relationship between stability margin and the height of the robots centroid, as well as its inclination relative to the ground is calculated by the stability criterion. The success and performance of the stability criterion proposed is verified through MATLAB simulation and real-world experiments using multi-legged crablike robot.

BASIC MATHEMATICAL MODELS AND AN APPROXIMATE METHOD OF FILTRATION THEORY

2021 ◽  
pp. 25-31
Author(s):  
Alla A. Mussina
Keyword(s):  
Mathematical Model ◽  
Porous Media ◽  
Mathematical Models ◽  
Heterogeneous Porous Media ◽  
Effective Management ◽  
Filtration Theory ◽  
New Device ◽  
Scientific Papers ◽  
The Mathematical Model ◽  
Inhomogeneous Liquids

The article defines the basic concepts of filtration theory and provides an overview of the existing mathematical models of inhomogeneous liquids in porous media. The paper considers the Stefan problem. The number of scientific papers devoted to the study of porous structures has recently increased. This is primarily due to the fact that the prob-lems of oil and uranium production have been identified, and the solution of environmental problems is overdue. Therefore, a new device is needed to develop models of liquid filtration. With the advent and development of computer technology, it has become easier to solve problems that require numerical methods for their solution. Understanding the movement of fluids and the mechanism of dissolution of rocks under the action of acids in heterogeneous porous media is of great importance for the extraction and production of oil and the effective management of these processes. The article examines the mathematical model of the theory of isothermal filtration. Possible variants of the solva-bility of the model are shown. The research scheme consists of the output of a mathematical model, the formulation of the problem, one variant of the solution of the problem, the algorithm of the numerical method of solving the problem.

Design and Implementation of Digital Asthma Diagnosis System

2019 ◽  
Vol 14 (3) ◽  
pp. 1-15
Author(s):  
Qinghua Yao ◽  
Xiantao Yang
Keyword(s):  
Mathematical Model ◽  
Mutation Rate ◽  
Forced Expiratory Volume ◽  
Digital Signals ◽  
Respiratory Parameters ◽  
The Mathematical Model ◽  
The Relationship ◽  
Objective Indicators ◽  
Signal Conditioning Circuit

In this article, the MSP430F149 is the microcontroller (MCU), and a pressure sensor, MPX5100AP, is used to measure body measurement of maximal forced expiratory volume (FEV) and peak expiratory flow rate (PEFR). The two analog signals are processed by the signal conditioning circuit, and then the corresponding digital signals are acquired by the MCU. With the related operations of multiple respiratory parameters, a built-up time of respiration signal mutation rate values and the determination of the mutation rate, a mathematical model is built among FEV, PEFR and the rate of variation. The mathematical model of the system is analyzed, and the relationship between the detection results and the degree of airway obstruction is established. Finally, the patient's condition analysis results are given directly on the LCD, which provided the objective indicators for the medical treatment of the disease.

scholarly journals Diagnostics of supercapacitors

2018 ◽  
Vol 182 ◽  
pp. 01009 ◽  
Author(s):  
Valeriy Martynyuk ◽  
Oleksander Eromenko ◽  
Juliy Boiko ◽  
Tomasz Kałaczyński
Keyword(s):  
Mathematical Model ◽  
Mathematical Models ◽  
Methodological Approach ◽  
Frequency Dispersion ◽  
Technical Condition ◽  
Transient Processes ◽  
Nonlinear Frequency ◽  
Diagnostic Reliability ◽  
General Reliability ◽  
The Mathematical Model

The paper represents the mathematical model for diagnostics of supercapacitors. The research objectives are the problem of determining a supercapacitor technical condition during its operation. The general reliability of diagnostics is described as the methodological and instrumental reliabilities of diagnostics. The instrumental diagnostic reliability of supercapacitor includes the probabilities of errors of the first and second kind, α and β respectively. The methodological approach to increasing the reliability of supercapacitor diagnostic has been proposed, in terms of multi-parameter supercapacitor diagnostic by applying nonlinear, frequency dependent mathematical models of supercapacitors that take into account nonlinearity, frequency dispersion of parameters and the effect of transient processes in supercapacitors. The more frequencies, operating voltages and currents are applied in the supercapacitor diagnostics, the more methodological reliability of diagnostics will increase in relation to the methodological reliability of supercapacitor diagnostics when only one frequency, voltage and current are applied.

scholarly journals Modeling and Optimization of Bidirectional Clamping Forces in Drilling of Stacked Aluminum Alloy Plates

Materials ◽  
2020 ◽  
Vol 13 (12) ◽  
pp. 2866
Author(s):  
Jintong Liu ◽  
Anan Zhao ◽  
Piao Wan ◽  
Huiyue Dong ◽  
Yunbo Bi
Keyword(s):  
Mathematical Model ◽  
Finite Element ◽  
Aluminum Alloy ◽  
Clamping Force ◽  
Practical Application ◽  
Element Simulation ◽  
Theory Of Plates ◽  
Plates And Shells ◽  
The Mathematical Model ◽  
The Relationship

Interlayer burrs formation during drilling of stacked plates is a common problem in the field of aircraft assembly. Burrs elimination requires extra deburring operations which is time-consuming and costly. An effective way to inhibit interlayer burrs is to reduce the interlayer gap by preloading clamping force. In this paper, based on the theory of plates and shells, a mathematical model of interlayer gap with bidirectional clamping forces was established. The relationship between the upper and lower clamping forces was investigated when the interlayer gap reaches zero. The optimization of the bidirectional clamping forces was performed to reduce the degree and non-uniformity of the deflections of the stacked plates. Then, the finite element simulation was conducted to verify the mathematical model. Finally, drilling experiments were carried out on 2024-T3 aluminum alloy stacked plates based on the dual-machine-based automatic drilling and riveting system. The experimental results show that the optimized bidirectional clamping forces can significantly reduce the burr heights. The work in this paper enables us to understand the effect of bidirectional clamping forces on the interlayer gap and paves the way for the practical application.

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