The Mathematical Model of an Electrodynamic Geophone

Vestnik MEI ◽  
2021 ◽  
Vol 3 (3) ◽  
pp. 33-40
Author(s):  
Nikolay Yu. Gavryushin ◽  
◽  
Pavel A. Dergachev ◽  
Pavel A. Kurbatov ◽  
◽  
...  
Keyword(s):  
Mathematical Model ◽  
Output Signal ◽  
Active Vibration Control ◽  
Signal Amplitude ◽  
Graphical Form ◽  
Practical Implementation ◽  
Shake Table ◽  
Buried Objects ◽  
Complex Mathematical Model ◽  
The Mathematical Model

Electrodynamic geophones are applied in seismic prospecting, seismology and security systems. Devices with a similar design can be used as a generator in devices for energy storage, in active vibration control systems, and for detection of shallow-buried objects, including mines. To control the quality of geophones and verify the constancy of their characteristics during the manufacture, it is necessary to measure their frequency response on a shake table. The mathematical model of the geophone developed by JSC Scientific Research Engineering Institute (Balashikha, Moscow region) installed on a shake table is considered. The geophone schematic design is given, and the sequence of its operation is described. The approach of dividing an electromechanical system into several subsystems with subsequently uniting them into a resulting model is used for developing the geophone overall mathematical model. Detailed descriptions of the electrical, magnetic, and mechanical subsystems are presented. The assumptions used in compiling the overall mathematical model describing the geophone operation on the shake table are listed. A system of equations describing the interaction of the subsystems is compiled. Detailed descriptions of the resulting mathematical model, each of its element, and the interface included in its composition are presented. To estimate the developed mathematical model, the results obtained from the calculations on it are compared with the results from testing two experimental samples in the geophone operating frequency band from 10 to 100 Hz. For better clarity, the obtained results are compared in graphical form. The comparison has shown that the discrepancy between the results does not exceed 5% by the output signal amplitude. From the viewpoint of practical implementation, the developed mathematical model can be used in designing new geophones with other parameters, for example, with another natural frequency, or with a higher value of the output signal. It can also be used to develop more complex mathematical models containing a geophone. The accomplished study became a basis for elaborating a more complex mathematical model of a geophone with two natural frequencies in the operating band.

The Mathematical Model for the Generation of the Cylindrical Gear With Curved Cycloidal Teeth

2007 ◽  
Author(s):  
Iulian Stanasel ◽  
Adrian Ghionea ◽  
Ionut Ghionea ◽  
Petru Ungur ◽  
Oana Stanasel
Keyword(s):  
Mathematical Model ◽  
Production Costs ◽  
Reference Plane ◽  
Practical Implementation ◽  
Work Piece ◽  
Special Device ◽  
Technological Parameters ◽  
Cylindrical Gear ◽  
Processing Machine ◽  
The Mathematical Model

The performed studies regarding the cylindrical gears with curved teeth or in V showed that a uniform distribution of the load on the flanks is hard to realise, generally being necessary later finishing processing or modifying the gear by camber or flanking, which suppose supplementary expenses. On the basis of these mentions and taking into account the advantages of curved bevel gear, the purpose of this paper is to present an original study regarding the mathematical model for generation of a curved cylindrical gear with high performances. The cycloidal gear was chosen after a technical and an economical study regarding on the possibility of practical implementation with the lowest production costs using a special device, adapted on a Phauter processing machine of cylindrical gear. This was the main reason for choosing a cycloidal profile from several types of curved teeth (cycloidal arc, circle arc, Archimede’s spiral, involute arc). So, the main aim of the paper is to determine the equations of the flanks of cylindrical wheel with curved teeth in oblong cycloidal arc, in order to establish if the technical generation is possible. The curved cylindrical teeth with cycloidal flanks is generated by rolling with straight mobile line and continuous division by using a milling cutter with 1, 2, 3, 6 groups of knifes equidistantly placed, fixed on an adaptable device on a Phauter processing machine. The two curves which define the flank are simultaneously generated by correlated motions, and the flanks of the wheel part result as a roll of successive positions of generating hook materialized by the cutting edge of the tool. The shape of the contact curve between the conjugated surfaces of generating element and the wheel part can be obtained if you are taking into account the kinematic condition. Using this condition you can determine the relationship between the kinematic, geometric and technological parameters. The line of the flanks is studied in the reference plane and in parallel planes with this, and the profile of the flanks is determined in perpendicular planes on the work piece axis. Based on the parametric equations it was made the simulation program in MATLAB that indicates that this gears can be obtained, and constitutes the first step in practical manufacturing of this kind of gears. By analyzing the obtained shape they result useful conclusions for the manufacturing of the involute-tooth gear with curved oblong cycloidal arc. On the other hand, using Solid Edge it was made the spatial modeling of the cylindrical gear with curved cycloidal teeth that allows next FEA studies regarding on the contact and bending stress.

The Effect of Surface Kinetics in Fracture Acidizing

1974 ◽  
Vol 14 (04) ◽  
pp. 385-395 ◽  
Author(s):  
L.D. Roberts
Keyword(s):  
Experimental Data ◽  
Mathematical Model ◽  
Mass Transfer ◽  
Reaction Rates ◽  
Graphical Form ◽  
Mixing Coefficient ◽  
Acid Reaction ◽  
The Mathematical Model ◽  
Plate System ◽  
Acid Leakoff

Abstract A mathematical model is developed that yields the distance to which live aid may penetrate into a fracture under conditions in which the over-all reaction kinetics. The model is solved by an explicit finite-difference method, and the results are presented in graphical form. An example design presented in graphical form. An example design calculation is given for HC1 reaction in a dolomite fracture. Experimental data are presented for acid flow in limestone and dolomite laboratory - prepared fracture systems 4.1 t 9.7 ft long, at 71, 190, and 290F. From these experiments was determined a parameter appearing in the mathematical model-termed the effective mixing coefficient. The mixing coefficient has a minimum in the low Reynolds number region, indicating that rectilinear laminar flow is approached more closely just before the flow becomes turbulent. The mixing coefficient also appears to be dependent upon temperature in the laminar flow region. The mathematical solutions given in this paper are applicable to situations in which the over-all rate of acid reaction is not determined solely by mass transfer. Introduction Acids are widely used in the hydraulic fracturing of reservoirs to stimulate wells. Roughly speaking, the purpose of the acid is to selectively react with and dissolve portions of the fracture wall so that a finite fluid conductivity remains when the well is returned to production. One important variable that must be known in designing these acid fracturing treatments is the distance to which acid will penetrate the fracture before completely reacting penetrate the fracture before completely reacting and becoming spent. This distance is usually termed the acid penetration length and is an essential part of the information needed for predicting productivity after acidizing. Other important design variables include the dynamic fracture geometry and the residual fracture conductivity. Because of its importance in predicting stimulation ratios, acid penetration into a fracture has been studied by several investigators. Both static tests and dynamic tests have been used to predict acid reaction rates in fractures. It seems predict acid reaction rates in fractures. It seems reasonable that a dynamic acid reactor test will be useful for predicting acid spending rates, since the mass transfer rate in an actual fracture may be approached in this type of test. One experimental apparatus used for acid flow tests in parallel plate system such as that used by Barron et al. plate system such as that used by Barron et al. and by Williams and Nierode. In these tests, acid is pumped at a known flow rate through a fracture of known geometry and the inlet and outlet acid composition is measured. From the resulting information it is possible to predict acid penetration in a real fracture with the aid of a mathematical model having experimentally determined parameters. We present here the results of an investigation of the use of mathematical model for predicting acid spending a fracture. Using Williams and Nierode's approach to calculating acid penetration, we have extended their method to allow for the fact that the surface reaction rates of several acid-rock systems (e.g., HC1-dolomite) may be finite compared with the rate of mass transfer to the surface. Experimental data are presented for determining the parameters appearing in the mathematical model and a sample calculation illustrates its use. MATHEMATICAL MODEL FOR ACID FRACTURING The mathematical model presented here is a modification of that introduced by Williams and Nierode to allow for the occurrence of finite reaction rates. This modification makes it possible to calculate theoretical penetration distances for acid featuring when reaction kinetics are important as in the case of the HC1-dolomite reaction. Since an analytical solution of the model is not possible, a finite-difference method was developed and is presented in Appendix A. presented in Appendix A. The model for acid formula is fracturing is presented in Fig. 1. Here the acid leakoff velocity, presented in Fig. 1. Here the acid leakoff velocity, is assumed constant over the fracture length. SPEJ p. 385

THE USE OF REFRACTED WAVES IN SURFACE-CONSISTENT PROCEDURES OF DYNAMIC CORRECTION

2019 ◽  
pp. 4-13
Author(s):  
K. A. Khemraev
Keyword(s):  
Mathematical Model ◽  
Ray Tracing ◽  
Dynamic Correction ◽  
Buried Objects ◽  
Factor Decomposition ◽  
The Mathematical Model ◽  
The Given ◽  
Refracted Waves ◽  
Three Factor

In the given paper a three factor decomposition of the field of refracted waves is considered with help of ray-tracing. Due to the fact that the solution obtained on the basis of the mathematical model is unstable, a condition is proposed that regularizes the solution. The possibility of applying the considered mathematical model is demonstrated in case of refraction and buried objects.

Simulation Study of Active Vibration Control of Cantilever Beam by Using State and Output Feedback Control Laws

2013 ◽  
Author(s):  
S. M. Khot ◽  
Nitesh P. Yelve ◽  
Raj Nair
Keyword(s):  
Mathematical Model ◽  
Feedback Control ◽  
Vibration Control ◽  
Output Feedback ◽  
Active Vibration Control ◽  
Output Feedback Control ◽  
Full Model ◽  
Control Laws ◽  
Active Vibration ◽  
The Mathematical Model

Undesired noise and vibrations have a detrimental effect in many areas. Hence the control of vibrations has become a relevant technological challenge. Active vibration control of structures using smart materials especially is in vogue. It involves sensing the motion of the structure using sensors, generating a control signal using a controller and applying a control force on the structure using actuators. To design the control system of any vibrating structure, the mathematical model of the system is required. However, it is not possible, to theoretically construct the model of complex structures. On the other hand, it is relatively simpler to model such systems in an Finite Element (FE) environment like ANSYS©. This paper deals with the extraction of the mathematical model of a cantilever beam from its FEA model. This procedure of extraction is applicable to any mechanical system under dynamics study. Then again, the matrices thus formed are usually very large and require a lot of computational time to process. Hence an attempt is made to construct the reduced model of the system which approximates the actual model to the desired extent. In this paper, the full model of the beam is reduced by discarding those modes which do not contribute to the overall response on the basis of their dc gains in MATLAB©. It is found that the frequency and transient responses of the full and reduced models match closely. Hence the reduced model may be used to represent the system instead of the full model with reasonable accuracy. Design of controller is attempted using the theory of state and output feedback control laws. The controller is modeled by calculating the optimal control gain by formulating an algorithm to solve the equations involved. The transient and frequency responses of the controlled full model and reduced models are then plotted. The procedure for designing controller described in this paper may be extended to any real world system.

scholarly journals MATHEMATICAL MODELLING OF IMMUNE PROCESSES AND ITS APPLICATION

2020 ◽  
Vol 13 (5) ◽  
pp. 5-18
Author(s):  
N. I. ARALOVA ◽  
Keyword(s):  
Mathematical Model ◽  
Immune Response ◽  
Blood Flow ◽  
Blood Circulation ◽  
Moving Objects ◽  
Scientific School ◽  
Blood Flows ◽  
Theory Of Optimal Control ◽  
Complex Mathematical Model ◽  
The Mathematical Model

The aim of the study was to develop a mathematical model to research hypoxic states in case of simulation of an organism infectious lesions. The model is based on the methods of mathematical modeling and the theory of optimal control of moving objects. The processes of organism damage are simulated with the mathematical model of immune response developed by G.I. Marchuk and the members of his scientific school, adapted to current conditions. This model is based on Burnet’s clone selection theory of the determining role of antigen. Simulation results using the model are presented. The dependencies of infectious courses on the volumetric velocity of systemic blood flow is analyzed on the complex mathematical model of immune response, respiratory and blood circulation systems. The immune system is shown to be rather sensitive to the changes in blood flow via capillaries. Thus, the organ blood flows can be used as parameters for the model by which the respiratory, immune response, and blood circulation systems interact and interplay.

scholarly journals System of operational control of psychophysiological indicators of operators of hierarchical systems in making management decisions

Doklady BGUIR ◽  
2021 ◽  
Vol 19 (7) ◽  
pp. 72-79
Author(s):  
N. V. Pushkareva
Keyword(s):  
Mathematical Model ◽  
Selection Criterion ◽  
Test Methods ◽  
Graphical Form ◽  
Operational Control ◽  
Hierarchical Systems ◽  
Psychophysiological State ◽  
High Level ◽  
The Mathematical Model ◽  
Selection Of

A system of operational control of psychophysiological indicators of operators is presented. It includes a set of test methods for selecting psychologically compatible operators of high-responsibility systems. The selection of operators on a PC is carried out. The results of electronic protocols in narrative and graphical form are given. After that, the method of selecting psychologically compatible operators of highresponsibility systems is applied. It uses a mathematical model selection of PC-based operators using regression analysis. The coefficients of this model are taken as a selection criterion. The maximum permissible maximum criterion corresponds to the coefficient of the mathematical model of the work of operators with a relatively high level of professionally important qualities. And the maximum permissible minimum criterion corresponds to the coefficient of the mathematical model of the work of operators with a relatively average level of professionally important qualities. In future, the calculation is completed according to the developed algorithm for the selection of psychologically compatible operators. Operational control of the psychophysiological state (PFS) of operators is performed with the control support of marks from the target in optimal conditions using a hierarchical system of group tracking on the example of links of the automatic control system. As a criterion for assessing the stability of the PFS operators at the time of the control, the range of changes in the value of the RMS error when accompanying the control mark is taken.

scholarly journals MATHEMATICAL MODELING OF TECHNOLOGICAL MODES OF HEAT-PUMPING SYSTEMS FOR TECHNOLOGICAL PROCESSES

2021 ◽  
pp. 85-91
Author(s):  
Boris Kotov ◽  
Vladimir Grishchenko ◽  
Yuriy Pantsir ◽  
Igor Garasimchuk
Keyword(s):  
Mathematical Model ◽  
Automatic Control ◽  
Heat Pump ◽  
Material Balance ◽  
Heat Pumps ◽  
Practical Implementation ◽  
Industrial Complex ◽  
Energy Potential ◽  
The Mathematical Model ◽  
Heat Carriers

One of the ways to increase the energy efficiency of the process of heat supply of technological facilities and production facilities of the agro-industrial complex is the use of heat pumps. Their use allows to increase the energy potential of heat carriers. To optimize the mode parameters and create systems for automatic control of the heat pump installation, it is necessary to establish a relationship between the parameters of the processes occurring in the elements of the installation by creating a mathematical model of non-stationary thermal modes. In the analysis of recent studies and publications, it is established that the calculations of processes in heat pumps are presented mainly for stationary modes of operation without taking into account the dynamics of the condenser. If the dynamic modes of individual elements are given, then they are described by mathematical models of considerable complexity, which greatly complicates their practical implementation. In the article, the heat pump installation, as an object of modeling, is considered as a physical system, which consists of four series-connected elements: evaporator, condenser, compressor, throttle valve forming a closed circuit. The principle of operation of a simple heat pump installation is explained by the scheme and schedule of the theoretical cycle of the steam compressor heat pump. To simplify the mathematical model, certain assumptions were made: the change in the parameters of liquid, vapor and air varies in a straight line, the thermophysical characteristics of the material of heat exchangers, air and vapor flows, heat transfer coefficients do not depend on temperature and are average for the cycle. On the basis of thermal and material balance the corresponding differential equations which make mathematical model of dynamics of change of parameters of the heat exchanger have been made. The mathematical model is supplemented by a simulation model in the MatLAB / Simulink computer environment, as well as graphical interpretations of dynamic characteristics. The developed mathematical model of dynamics of thermal processes in the heat pump installation can be used for calculation of parameters of heating and cooling of streams of heat carriers and creation of system of automatic control of them.

scholarly journals Examination of the Unmanned Aerial Vehicle

2019 ◽  
Vol 24 ◽  
pp. 01006
Author(s):  
Lucjan Setlak ◽  
Rafał Kowalik
Keyword(s):  
Mathematical Model ◽  
Pid Controller ◽  
Control Program ◽  
Practical Implementation ◽  
Research Subject ◽  
Electronic Components ◽  
Computing Power ◽  
Interdisciplinary Field ◽  
Aerial Vehicle ◽  
The Mathematical Model

The contemporary interdisciplinary field of knowledge, which is the robotics used in unmanned aerial vehicles, is developing very dynamically. In view of the above, the authors of this paper have set themselves the following thesis: it is possible to build a flying mobile robot based on a controller with low computing power and a simple PID controller, and in this respect they undertook to prove it. The examined object in real experiments was the Quadrocopter. The article discusses the tasks implemented during the design and practical implementation of a remotely controlled flying unit. First, a mathematical model describing the dynamics of the UAV movement was defined. Then, electronic components were selected to allow the quadrocopter to fly. The board has a central unit in the form of the ATmega644PA microcontroller. In the following, the process of programming subsequent elements that make up the quadrocopter control program was carried out. The control system for stabilizing the machine requires information about the location of the quadrocopter in space. This is accomplished by a measurement module containing an accelerometer and a gyroscope. In addition, the quadrocopter needs information about the potential operator's commands. In the final part of the article, based on the analysis of the research subject, the mathematical model created and the necessary simulation tests carried out in this area, practical conclusions were presented.

scholarly journals Developing a System to Support Banks in Making Investment Decisions when Organizing Project Financing

2020 ◽  
Vol 15 ◽  
Keyword(s):  
Mathematical Model ◽  
System Development ◽  
Investment Decision ◽  
Investment Decisions ◽  
Software Implementation ◽  
Practical Implementation ◽  
Project Financing ◽  
The Russian Federation ◽  
The Republic ◽  
The Mathematical Model

The article deals with the development of an information system providing support for making investment decisions by Ziraat Bank in organizing project financing of innovative projects implemented within the machinebuilding cluster of the Republic of Tatarstan and its affiliated entities in the Russian Federation. A set of requirements for such a system was formulated and an appropriate mathematical model developed. The software implementation of the mathematical model was carried out in the Ziraat Bank's investment decision support system. An algorithm for system development was proposed, the practical implementation of which was performed using the theory of oriented graphs along with the schedule theory.

scholarly journals Thermal protection implementation of the contact overheadline based on bay controllers of electric transport traction substations in the mining industry

2021 ◽  
Vol 251 ◽  
pp. 738-744
Author(s):  
Dmitry Lantsev ◽  
Vladimir Frolov ◽  
Sergej Zverev ◽  
Dirk Uhrlandt ◽  
Jiří Valenta
Keyword(s):  
Mathematical Model ◽  
Thermal Protection ◽  
Mining Industry ◽  
Practical Implementation ◽  
Electric Transport ◽  
Contact Erosion ◽  
Traction Substations ◽  
Digital Protection ◽  
Microcontroller Unit ◽  
The Mathematical Model

The article presents the principle of thermal protection of the contact overheadlineand substantiates the possibility of practical implementation of this principle for rail electric transport in the mining industry. The algorithm for the implementation of modern digital protection of the contact overhead line as one of the functions of the controller is described. A mathematical model of thermal protection is proposed, which follows from the solution of the heat balance equation. The model takes into account the coefficient of the electrical networktopology, as well as the coefficient of consumption of the current-carrying core of the cable, which determines the reduction in the conducting section from contact erosion and the growth of oxide films. Corrections for air flows are introduced when receiving data from an external anemometer, via telemechanics protocol. The mathematical model was tested by writing a real thermal protection program in the C programming language for the bay controller, based on the circuitry of which is the STM32F407IGT6 microcontroller for the microcontroller unit. Verification tests were carried out on a serial bay controller in 2020. The graphs for comparing the calculated and actual values of temperatures, with different flow rates of the current-carrying conductor of the DC cable, are given. To obtain data, telemechanics protocols IEC 60870-104 and Modbus TCP, PLC Segnetics SMH4 were used.

Sign in / Sign up

Export Citation Format

Share Document