scholarly journals INVESTIGATION OF MATHEMATICAL MODEL OF A VIBRATING MIXER WITH A FREEZERY PENDULUM MECHANISM

2021 ◽  
pp. 124-135
Author(s):  
Oleh Tsurkan ◽  
Yurii Polievoda ◽  
Dmytro Prysyazhniuk
Keyword(s):  
Mathematical Model ◽  
Effective Means ◽  
Influential Factors ◽  
Dynamic State ◽  
Double Pendulum ◽  
Regression Equations ◽  
Lagrange Equations ◽  
Important Place ◽  
Dispersed Systems ◽  
Advantages And Disadvantages

An extensive review of vibrating mixers, identified their advantages and disadvantages. The application of the action of low-frequency oscillations on the process of mixing bulk inhomogeneous products is substantiated. All considered schemes of vibrating mixers, as well as designs in which mixing devices are driven by vibration-pulse transducers (in which the energy of the main or master system is used to create the technological motion of the driven system) can be attributed to energy-saving technological equipment. The article describes the design, the principle of operation of the developed vibrating mixer with a double pendulum freewheel mechanism for driving the agitator blades in rotational motion. The calculation scheme and laws of motion of this system in the form of Lagrange equations of the second kind (mathematical model) are presented. Using the obtained 2nd order multiple regression equations, recommendations were determined regarding the main parameters of the operating mode of the studied vibration mixing process. Analyzing the results of vibration mixing of bulk inhomogeneous raw materials, we can say that the most influential factors in determining the natural oscillation frequency of the system pendulum, which is one of the main objectives of our study is spring stiffness, spring attachment distance from axis of rotation, rotation angles, pendulum weight, length and the moment of inertia. The paper proves that among various forms of mechanical action on dispersed systems in technological processes vibration action occupies an important place as one of the most effective means to create the necessary dynamic state of dispersed systems.

Methodology of Estimation of Fire Separation Distances between Construction Facilities by Calculation

2020 ◽  
Vol 1006 ◽  
pp. 93-100
Author(s):  
Vadym Nizhnyk ◽  
Yurii Feshchuk ◽  
Volodymyr Borovykov
Keyword(s):  
Mathematical Model ◽  
Heat Flux ◽  
Linear Regression ◽  
Ignition Temperature ◽  
Oil Products ◽  
Regression Equations ◽  
Fire Load ◽  
Literary Sources ◽  
Tabular Method

Based on analysis of appropriate literary sources we established that estimation of fire separation distances was based of two criteria: heat flux and temperature. We proposed to use “ignition temperature of materials” as principal criterion when determining fire separation distances between adjacent construction facilities. Based on the results derived while performing complete factorial we created mathematical model to describe trend of changing fire separation distances depending on caloric power of fire load (Q), openings factor of the external enclosing structures (k) and duration of irradiation (t); moreover, its adequacy was confirmed. Based on linear regression equations we substantiated calculation and tabular method for the determination of fire separation distances for a facility being irradiated which contains combustible or otherwise non-combustible façade and a facility where liquid oil products turn. We developed and proposed general methodology for estimation of fire separation distances between construction facilities by calculation.

Development of a Mathematical Model for a Workpiece Heating and Cooling in a Protective Medium while Treatment under Pressure

2021 ◽  
Vol 410 ◽  
pp. 115-122
Author(s):  
Victoria V. Devyatiarova ◽  
Eugenia E. Balakhnina ◽  
Lilya M. Valeeva
Keyword(s):  
Mathematical Model ◽  
Cross Section ◽  
Arbitrary Shape ◽  
Thermal Conductivity Coefficient ◽  
Regression Equations ◽  
Heating And Cooling ◽  
Temperature Problem ◽  
Protective Medium ◽  
Computer Calculations ◽  
The Mathematical Model

The paper reviews and develops the mathematical model of plastic flow during the hot-forming processes. A flat non-stationary temperature problem for a cross-section of a long solid (rolled product) of arbitrary shape with different heat transfer conditions along the perimeter of the cross-section was considered. Equations for calculation of the thermal conductivity coefficient and heat capacity of tungsten billets were obtained in the temperature range of 700 - 1500°C, based on the literature data. Analytical dependences in form of regression equations were obtained, allowing for computer calculations of physical specifications of 11x11 mm VA grade tungsten billets in form of temperature functions with accuracy sufficient for practical calculations.

scholarly journals Analysis of e-mail tools for educational purposes

2020 ◽  
Vol 8 (1) ◽  
pp. 50-61
Author(s):  
Stanislav Proichev ◽  
Hanna Chemerys
Keyword(s):  
Comparative Analysis ◽  
Effective Means ◽  
Effective Communication ◽  
Scientific Work ◽  
Educational Institutions ◽  
Educational Services ◽  
Email Marketing ◽  
Advantages And Disadvantages ◽  
E Mail

Based on the analysis of scientific work was to determine the popularity and development of email marketing as one of the effective means of communication. Here are the main benefits of email marketing. The study found that email marketing allows effective communication between educational institutions and future recipients of educational services. There is a need to identify appropriate and effective tools for Internet mailing. The work is devoted to analyzing and exploring the functionality of mailing tools and constructors for email creation. During the study, the concept of "letter constructor" was defined. A comparative analysis was performed describing the main features, advantages and disadvantages of Stripo, Tilda, Makemail, Beefree, and Mailchimp, Unisender, E-sputnik, SendPulse mail designers. The appropriate combination of tools for mailing for educational purposes is determined.

scholarly journals World Experience in Creating Mathematical Models of Air Springs: Advantages and Disadvantages

2021 ◽  
pp. 25-42
Author(s):  
A. Y Kuzyshyn ◽  
S. A Kostritsia ◽  
Yu. H Sobolevska ◽  
А. V Batih
Keyword(s):  
Mathematical Model ◽  
Finite Element ◽  
Mathematical Models ◽  
Dynamic Behavior ◽  
High Speed ◽  
Vertical Direction ◽  
Rolling Stock ◽  
Air Spring ◽  
Advantages And Disadvantages ◽  
Mechanical Models

Purpose. Taking into account the production and commissioning of modern high-speed rolling stock, the authors are aimed to analyze the currently created mathematical models describing the dynamic behavior of the air spring, systematize them and consider the advantages and disadvantages of each model type. Methodology. For the analysis, a comparative chronological method was used, which makes it possible to trace the development of several points of view, concepts, theories. In accordance with the adopted decision equations, the existing models of air springs were divided into three groups: mechanical, thermodynamic and finite-elements. When analyzing mathematical models, the influence of a number of parameters on the dynamic behavior of the air spring, such as disturbing force frequency, heat transfer, nonlinear characteristics of materials, the shape of the membrane, etc., was considered. Findings. A feature of mechanical models is the determination of input parameters based on the analysis of experimental results, requires access to complex measuring equipment and must be performed for each new model of an air spring separately. Unlike mechanical models, which allow taking into account the damping effect of an air spring in the horizontal and vertical direction, thermodynamic models are mainly focused on studying the dynamic behavior of an air spring in the vertical direction. The use of the finite element method makes it possible to most accurately reproduce the dynamic behavior of an air spring, however, it requires significant expenditures of time and effort to create a finite element model and perform calculations. Originality. Mathematical models of the dynamic behavior of an air spring are systematized, and the importance of their study in conjunction with a spatial mathematical model of high-speed rolling stock is emphasized. Practical value. The analysis of the mathematical models of the dynamic behavior of the air spring shows the ways of their further improvement, indicates the possibility of their use in the spatial mathematical model of the rolling stock in accordance with the tasks set. It will allow, even at the design stage of high-speed rolling stock, to evaluate its dynamic characteristic and traffic safety indicators when interacting with a railway track.

scholarly journals COMPARATING ANALYSIS OF COORDINATE SEARCH METHODS EFFICIENCY FOR THE OPTIMAL SOLAR PANEL POSITION FINDING

2019 ◽  
pp. 77-84
Author(s):  
M. O. Slabinoga ◽  
N.B. Klochko ◽  
O. S. Krynytskyi ◽  
Yu. M. Kuchirka
Keyword(s):  
Experimental Data ◽  
Mathematical Model ◽  
Solar Panel ◽  
Surveillance Systems ◽  
Solar Panels ◽  
Search Methods ◽  
Optimal Position ◽  
Advantages And Disadvantages ◽  
Rosenbrock Method ◽  
Efficiency Of Algorithms

The work is devoted to the investigation of the effectiveness of the coordinate search methods for solving the problem of finding the position of the solar panels, in which the greatest power of the produced current is achieved. The existing solutions in the market of sun surveillance systems (solar trackers) are analyzed. The advantages and disadvantages of such systems are presented in comparison with fixed panels. It is proposed to improve the hardware and software for research of the solar panels efficiency, developed by the authors and highlighted in the previous works, by integrating the program realization of the algorithm of coordinate search of the maximum power of solar panels into the existing. For this purpose, the efficiency of three algorithms for coordinate search of the maximum, namely, the method of coordinate ascending, the Huck-Jeeves method and the Rosenbrock method, was studied in three parameters. Experiments were carried out on data obtained both experimentally using the lab stand for solar panel efficiency research, and by generation using mathematical model of the solar panel efficiency dependance on the angle of radiation, described in previous works. TThe results of experiments are analyzed, which showed a fundamental difference between the work of coordinatewise search algorithms on a mathematical model and experimental data. The main indicators of the efficiency of algorithms are substantiated on the basis of the meteorological conditions in which the measurement was carried out for the formation of experimental data. Conclusions are drawn regarding the efficiency of using these coordinate-based search methods for solving the problem of finding the optimal position of solar panels. Further prospects for research on this topic and the possibility of using coordinate-wise search methods in software of solar panels with a biaxial orientation on the position of the Sun are given.

scholarly journals Modeling and Optimal Controller Based on Disturbance Detector for the Stabilization of a Three-link Inverted Pendulum Mobile Robot

Electronics ◽  
2020 ◽  
Vol 9 (11) ◽  
pp. 1821
Author(s):  
Luis Alfonso Jordán-Martínez ◽  
Maricela Guadalupe Figueroa-García ◽  
José Humberto Pérez-Cruz
Keyword(s):  
Mathematical Model ◽  
Mobile Robot ◽  
Nonlinear Model ◽  
Direct Current ◽  
Inverted Pendulum ◽  
Experimental Tests ◽  
Optimal Controller ◽  
Stabilization Problem ◽  
Lagrange Equations ◽  
Direct Measurements

This work presents the realization of a complicated stabilization problem for a three inverted pendulum links-based mobile robot. The actuators of the mobile robot are direct current motors that have tachometer couplings to measure both the position and speed of the wheels and links. Using direct measurements under load and analyzing the deceleration curve, the motor parameters are determined experimentally. A mathematical model of the robot is obtained via the Euler–Lagrange equations. Next, the nonlinear model is linearized and discretized. Based on this discrete LTI model, an optimal controller is designed. The states and disturbances are estimated using a robust detector. Both the controller and detector are implemented in the robot processor. Numerical simulations and experimental tests show a good performance of the controller despite the presence of disturbances.

scholarly journals Steady-State Steering Characteristics of Mathematical Model for Semitrailer Based on Variations in Camber Parameters

2020 ◽  
Vol 2020 ◽  
pp. 1-14
Author(s):  
Yi Wei ◽  
Shuilong He ◽  
Enyong Xu ◽  
Genge Zhang ◽  
Rongjiang Tang ◽  
...  
Keyword(s):  
Mathematical Model ◽  
Steady State ◽  
Test Data ◽  
Dynamic State ◽  
Model Parameters ◽  
Stability Factor ◽  
Camber Angle ◽  
Body Roll ◽  
Vehicle Test ◽  
Real Vehicle

To master the basic characteristics of steady-state cornering for a semitrailer, this paper summarises the current modelling methods for handling and stability and discusses their limitations. The classical linear mathematical model for a two-degree-of-freedom (DOF) handling and stability system is used to develop a new model. Analysis methods are proposed to introduce the influence of the camber angle and body roll into the model parameters. Thus, a mathematical model for the lateral stability of semitrailer with five DOFs is established. At the same time, a modified formula to calculate the stability factor of the semitrailer is developed with a MATLAB model to solve the dynamic state equation. The mathematical model, which considers the body roll and the changes in the camber angle caused by roll, compares the turning radius ratio and yaw rate as the evaluation index with the classical linear mathematical model of a two-DOF system. The vehicle parameters for three different types of semi-tractor trailers are used to calculate and compare two mathematical models for handling and stability using real vehicle test data. The results show that the new modelling and analysis method proposed in this paper has a high calculation accuracy and fast calculation speed, is clear and concise, and is consistent with the real vehicle test data. In addition, the accuracy of the new mathematical model for handling and stability and the improved stability factor are verified.

scholarly journals Liquid–liquid gravity displacement in a vertical fracture during drilling: Experimental study and mathematical model

2019 ◽  
Vol 38 (2) ◽  
pp. 533-554
Author(s):  
Dong Xiao ◽  
Yingfeng Meng ◽  
Xiangyang Zhao ◽  
Gao Li ◽  
Jiaxin Xu
Keyword(s):  
Mathematical Model ◽  
Drilling Fluid ◽  
Effective Means ◽  
Fluid Density ◽  
Shape Factors ◽  
Fracture Width ◽  
Factors Affecting ◽  
Double Substrate ◽  
Fracture Height ◽  
Liquid Displacement

Gravity displacement often occurs when drilling a vertical fractured formation, causing a downhole complexity with risk of blowout and reservoir damage, well control difficulty, drilling cycle prolongation, and increased costs. Based on an experimental device created for simulating the gravity displacement, various factors affecting the displacement quantity were quantitatively evaluated by simulating the fracture width, asphalt viscosity, drilling fluid density, and viscosity under different working conditions, and a liquid–liquid displacement law was obtained. Using the theories of rock mechanics, fluid mechanics, and seepage mechanics, based on conformal mapping, as well as a fracture-pore double substrate fluid flow model, we established a steady-state mathematical model of fractured formation liquid–liquid gravity displacement by optimizing the shape factors and using a combination of gravity displacement experiments to verify the feasibility of the mathematical model. We analyzed the influence of drilling fluid density, fracture height and length, and asphalt viscosity on displacement rate, and obtained the corresponding laws. The results show that when the oil–fluid interface is stable, the fracture width is the most important factor affecting the gravity displacement, and plugging is the most effective means of managing gravity displacement.

scholarly journals Mathematical model of pantograph cooperation with two degrees of freedom with a catenary system

2019 ◽  
Vol 294 ◽  
pp. 05005
Author(s):  
Marek Kaniewski ◽  
Michał Cichoński
Keyword(s):  
Mathematical Model ◽  
Discrete Model ◽  
Degrees Of Freedom ◽  
Variable Stiffness ◽  
System Model ◽  
Dynamic State ◽  
Rolling Stock ◽  
Two Degrees Of Freedom ◽  
Technical Specifications ◽  
Catenary System

The authors present a method of modeling pantograph cooperation with a catenary system by means of a computer program based on a pantograph discrete model with two degrees of freedom and a catenary system model as a focused mass that in the dynamic state has variable stiffness along the span. After performing the appropriate tests, the validation was carried out according to the proposed method in the PN EN 50318:2019-02 standard required in the Technical Specifications for the interoperability of the subsystem “Energy” and “Rolling stock -locomotives and passenger rolling stock” of the trans-European rail system in Europe.

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