scholarly journals Mathematical model of orientation of a ferromagnetic particle in magnetic field

2018 ◽  
Vol 224 ◽  
pp. 02041
Author(s):  
Eugene Masyutkin ◽  
Vasilii Masyagin ◽  
Boris Avdeyev
Keyword(s):  
Magnetic Field ◽  
Mathematical Model ◽  
Homogeneous Magnetic Field ◽  
System Of Differential Equations ◽  
Medium Resistance ◽  
The Moment ◽  
Fourth Order Method ◽  
Driving Torque ◽  
The Mathematical Model ◽  
Angle Of Rotation

A mathematical model of the rotational motion of a particle with pronounced ferromagnetic properties, due to the moment of forces from the side of an external homogeneous magnetic field is deduced in the article. The basis of the model is the equation for the moment of forces effecting on a solid body. The driving torque is the magnetic moment, calculated through the strength of the external field and the magnetization of the material. The counter–torque is the moment of medium resistance, which mainly depends on the viscosity of the medium in which the simulated body is located. The dependences of the angle of rotation and angular velocity on time are determined. The mathematical model is represented as a system of differential equations. The developed mathematical model was solved by a Runge – Kutta fourth order method. The obtained results are presented in the form of graphs.

scholarly journals DEVELOPMENT OF MATHEMATICAL MODEL OF THE CONTROL SYSTEM OF LINKS OF THE SNAKE LIKE ROBOT

2016 ◽  
Vol 2 (1) ◽  
pp. 150-154
Author(s):  
Гладышев ◽  
Andrey Gladyshev ◽  
Алейников ◽  
Andrey Aleynikov ◽  
Афонин ◽  
...  
Keyword(s):  
Differential Equation ◽  
Mathematical Model ◽  
Control System ◽  
Transfer Function ◽  
Transfer Functions ◽  
Modular Control ◽  
The Moment ◽  
External Forces ◽  
The Mathematical Model ◽  
Angle Of Rotation

The mathematical model of a modular control system of links of the snake like robot for realization of the wave movement considering the moments of the external forces created by adjacent links and external indignations is given in work. As model of the electric drive of a direct current the differential equation of the second order connecting tension of u(t) given on the electric motor, the moment of loading of Mn (t) and an output angle of rotation of a shaft θ(t) is used. Transfer functions of separate links are calculated, and transfer function of a control system in general is received.

The Function of Magnetic Field in a Magnetic-Electrochemical Compound Polishing

2010 ◽  
Vol 97-101 ◽  
pp. 4141-4145 ◽  
Author(s):  
Li Min Shi ◽  
Er Liang Liu ◽  
Yong Jiang Niu ◽  
Yu Quan Chen
Keyword(s):  
Magnetic Field ◽  
Mathematical Model ◽  
Concentration Polarization ◽  
Electrochemical Reaction ◽  
Charged Particles ◽  
Polishing Process ◽  
Electrical Field ◽  
Movement Model ◽  
The Mathematical Model ◽  
The Magnetic Field

Traditionally, the magnetic field is always vertical to the electrical field in a magnetic-electrochemical compound polishing.The magnetic field is set to parallel the electrical field in this paper. The mathematical model of the charged particles movement in a magnetic field is established through the analysis of its movement process when using Coulomb laws and Lorentz force. Through constructing the velocity formulation and loci formulation, the function of the magnetic field is proved. Because of the magnetic field, the concentration polarization of electrochemical reaction can be reduced more and the electrochemical reaction can be accelerated easily than the traditional polishing in which the magnetic field is vertical to the electrical field. Finally, to verify the model, the magnetic-electrochemical compound polishing process has been tested and the results, compared with those obtained from the model, have shown the movement model is reasonable and the analysis to function of magnetic field is correct.

scholarly journals Modeling and Analysis of Magnetic Nanoparticles Injection in Water-Oil Two-Phase Flow in Porous Media under Magnetic Field Effect

Geofluids ◽  
2017 ◽  
Vol 2017 ◽  
pp. 1-12 ◽  
Author(s):  
Mohamed F. El-Amin ◽  
Ahmed M. Saad ◽  
Amgad Salama ◽  
Shuyu Sun
Keyword(s):  
Magnetic Field ◽  
Mathematical Model ◽  
Porous Media ◽  
Magnetic Nanoparticles ◽  
Additional Term ◽  
Flow In Porous Media ◽  
Phase System ◽  
Two Phase ◽  
The Mathematical Model ◽  
Nanoparticles Suspension

In this paper, the magnetic nanoparticles are injected into a water-oil, two-phase system under the influence of an external permanent magnetic field. We lay down the mathematical model and provide a set of numerical exercises of hypothetical cases to show how an external magnetic field can influence the transport of nanoparticles in the proposed two-phase system in porous media. We treat the water-nanoparticles suspension as a miscible mixture, whereas it is immiscible with the oil phase. The magnetization properties, the density, and the viscosity of the ferrofluids are obtained based on mixture theory relationships. In the mathematical model, the phase pressure contains additional term to account for the extra pressures due to fluid magnetization effect and the magnetostrictive effect. As a proof of concept, the proposed model is applied on a countercurrent imbibition flow system in which both the displacing and the displaced fluids move in opposite directions. Physical variables, including water-nanoparticles suspension saturation, nanoparticles concentration, and pore wall/throat concentrations of deposited nanoparticles, are investigated under the influence of the magnetic field. Two different locations of the magnet are studied numerically, and variations in permeability and porosity are considered.

MATHEMATICAL MODELING OF BLOOD FLOW IN A POROUS VESSEL HAVING DOUBLE STENOSES IN THE PRESENCE OF AN EXTERNAL MAGNETIC FIELD

2011 ◽  
Vol 04 (02) ◽  
pp. 207-225 ◽  
Author(s):  
J. C. MISRA ◽  
A. SINHA ◽  
G. C. SHIT
Keyword(s):  
Mathematical Modeling ◽  
Magnetic Field ◽  
Mathematical Model ◽  
Blood Flow ◽  
Shear Stress ◽  
External Magnetic Field ◽  
Volumetric Flow Rate ◽  
Hematocrit Level ◽  
Flow Through ◽  
The Mathematical Model

In this paper, a mathematical model has been developed for studying blood flow through a porous vessel with a pair of stenoses under the action of an externally applied magnetic field. Blood flowing through the artery is considered to be Newtonian. This model is consistent with the principles of ferro-hydrodynamics and magnetohydrodynamics. Expressions for the velocity profile, volumetric flow rate, wall shear stress and pressure gradient have been derived analytically under the purview of the model. The above said quantities are computed for a specific set of values of the different parameters involved in the model analysis. This serves as an illustration of the validity of the mathematical model developed here. The results estimated on the basis of the computation are presented graphically. The obtained results for different values of the parameters involved in the problem under consideration, show that the flow is appreciably influenced by the presence of magnetic field and the rise in the hematocrit level.

scholarly journals INVESTIGATION OF THE INFLUENCE OF PRESSING BELTS TENSION OF THE BACK CIRCUIT OF PRESS - SELECTIVE PR-1.5

2018 ◽  
Vol 13 (2) ◽  
pp. 76-76
Author(s):  
Валерий Белов ◽  
Valeriy Belov ◽  
Леонид Рыбаков ◽  
Leonid Rybakov ◽  
Светлана Овчукова ◽  
...  
Keyword(s):  
Mathematical Model ◽  
Experimental Studies ◽  
Field Research ◽  
Test Protocol ◽  
Optimal Value ◽  
The Stability ◽  
The Moment ◽  
The Mathematical Model ◽  
Elastic Characteristics

A brief analysis of suspension mechanisms and ways to improve the quality of press harvesting for flax harvesting is considered. By researching the mathematical model, the authors prove the possibility of increasing the stability of the elastic characteristics of the suspension mechanisms by changing the angle between the levers or changing the geometry of the structure, for example, the attachment point of a two-arm lever. Particular attention is drawn to the new term “reduced rigidity” of the suspension mechanism. Using this notion and the method of its determination, the authors recommend determining the optimal value of the reduced stiffness of the suspension in the way of mathematical modeling and using this indicator as the main optimization parameter. The results of theoretical and experimental studies were presented by the authors in the form of elastic characteristics of the suspension mechanisms. When conducting a study of the mathematical model, it is suggested to take into account the condition of equality of the maximum values of the moments of forces from the action of the tension forces of the belts or the mass of the working element and the moment of forces acting on the side of the tension springs. During the research of the suspension mechanism, the actual dimensions of the PR-1.5 baler design were adopted. At the same time, we briefly describe the design of the improved tensioning mechanism of a baler for flax harvesting. A rather detailed analysis is given by the authors of the obtained elastic characteristics of the suspension mechanism. Some new features of the elastic characteristics of the suspension mechanism that have not been previously detected are described. To confirm the correctness of the reasoning, the authors implemented their research in a real press-picker and conducted field research that confirmed the possibility of improving the quality of the upgraded version of the machine. To confirm the results of the research, the authors presented a fragment of the field test protocol. The task is solved, uniformity of the roll density is ensured and its density is increased.

scholarly journals Procedure for selecting optimal geometric parameters of the rotor for a traction non-partitioned permanent magnet-assisted synchronous reluctance motor

2021 ◽  
Vol 6 (8 (114)) ◽  
Author(s):  
Borys Liubarskyi ◽  
Dmytro Iakunin ◽  
Oleh Nikonov ◽  
Dmytro Liubarskyi ◽  
Vladyslav Vasenko ◽  
...  
Keyword(s):  
Magnetic Field ◽  
Mathematical Model ◽  
Finite Element ◽  
Permanent Magnets ◽  
Geometrical Parameters ◽  
Synchronous Reluctance Motor ◽  
Reluctance Motor ◽  
Electromagnetic Momentum ◽  
Conditional Optimization ◽  
Angle Of Rotation

This paper reports the construction of a mathematical model for determining the electromagnetic momentum of a synchronous reluctance motor with non-partitioned permanent magnets. Underlying it is the calculation of the engine magnetic field using the finite-element method in the flat-parallel problem statement. The model has been implemented in the FEMM finite-element analysis environment. The model makes it possible to determine the engine's electromagnetic momentum for various rotor geometries. The problem of conditional optimization of the synchronous reluctance motor rotor was stated on the basis of the rotor geometric criteria. As an analysis problem, it is proposed to use a mathematical model of the engine's magnetic field. Constraints for geometric and strength indicators have been defined. The Nelder-Mead method was chosen as the optimization technique. The synthesis of geometrical parameters of the synchronous reluctance motor rotor with non-partitioned permanent magnets has been proposed on the basis of solving the problem of conditional optimization. The restrictions that are imposed on optimization parameters have been defined. Based on the study results, the dependence of limiting the angle of rotation of the magnet was established on the basis of strength calculations. According to the calculation results based on the proposed procedure, it is determined that the optimal distance from the interpole axis and the angle of rotation of magnets is at a limit established by the strength of the rotor structure. Based on the calculations, the value of the objective function decreased by 24.4 % (from −847 Nm to −1054 Nm), which makes it possible to significantly increase the electromagnetic momentum only with the help of the optimal arrangement of magnets on the engine rotor. The results of solving the problem of synthesizing the rotor parameters for a trolleybus traction motor helped determine the optimal geometrical parameters for arranging permanent magnets.

scholarly journals Calculation of magnetic devices cleaning coolants in the agro–industrial complex

2018 ◽  
Vol 224 ◽  
pp. 05003 ◽  
Author(s):  
Boris Avdeyev ◽  
Victor Prosvirnin ◽  
Roman R. Dema
Keyword(s):  
Fractional Composition ◽  
Initial Conditions ◽  
Homogeneous Magnetic Field ◽  
Magnetic Impurities ◽  
Industrial Complex ◽  
Particle Coagulation ◽  
Magnetic Devices ◽  
Medium Resistance ◽  
Cleaning Methods ◽  
The Mathematical Model

Traditional ways of cleaning of cooling lubricants in agrarian–industrial complex are considered in the article. Experimental data on the presence of magnetic impurities and its fractional composition as a result of parts machining on machines with the use of cooling lubricants are cited. Combined devices based on the combination of traditional methods for cleaning technical fluids have been used to intensify the cleaning process. The use of such combined cleaning methods is grounded, the forces effecting on the particles in the process of separation – coagulation forces, magnetic deposition, and medium resistance – are considered. The mathematical model of the coagulation process of two particles having similar size in a homogeneous magnetic field is made up. However, it is impossible to solve the obtained system even by a numerical method with unknown initial conditions. In this connection, the inverse problem is proposed. The physical significance of the effect of forces is as follows: a floccule consisting of two particles is destroyed under the effect of coagulation forces; the resistance of the medium prevents it. Its numerical solution allows finding the main dynamic characteristics of particle coagulation: the speed and distance from which they interact.

Kinetic Theory for Mixtures of Dilute Gases of Linear Rotating Molecules in an External Magnetic Field (Formal Theory)

1970 ◽  
Vol 25 (8-9) ◽  
pp. 1178-1190 ◽  
Author(s):  
H.H. Raum ◽  
W.E. Köhler
Keyword(s):  
Magnetic Field ◽  
Transport Theory ◽  
Formal Theory ◽  
Coupled System ◽  
Homogeneous Magnetic Field ◽  
Orthogonal Expansion ◽  
Local Conservation ◽  
Dilute Gases ◽  
Starting Point ◽  
The Moment

Abstract A transport theory is developed for mixtures of dilute gases consisting of linear rotating diamagnetic molecules in an external homogeneous magnetic field. This formalism is adequate for a treatment of the Senftleben-Beenakker effects for gas mixtures. Starting point is the system of linearized Waldmann-Snider equations. A complete scheme of orthogonal expansion tensors in velocity and rotational angular momentum is given, up to tensors of third rank and power. The moment method is applied to solve the coupled system of Waldmann-Snider equations and the resulting system of transport relaxation equations (TRE) is stated up to third rank tensor equations. The local conservation laws - linearized in the deviation from thermal equilibrium - are derivated from the TRE.

Probabilistic model of structural phase transition in perovskites

2021 ◽  
pp. 2150211
Author(s):  
S. H. Jabarov ◽  
R. T. Aliyev ◽  
N. A. Ismayilova
Keyword(s):  
Mathematical Model ◽  
Phase Transitions ◽  
Crystal Structures ◽  
Structural Phase ◽  
Random Variable ◽  
Structural Phase Transitions ◽  
The Moment ◽  
The Mathematical Model ◽  
First Time

In this work, the crystal structures and phase transitions of compounds with perovskite structure were investigated. The classification of structural phase transitions in perovskites was carried out, the most common crystal structures and structural phase transitions were shown. A mathematical model was constructed, a theorem was given and proved for the probability of a possible transition. The formulas [Formula: see text] and [Formula: see text] are given for the mathematical expectation and variance of random variable [Formula: see text], which is the moment when the stochastic process [Formula: see text] deviation from the boundary [0, [Formula: see text]] interval for the first time. According to the mathematical model, one of the trajectories of random processes corresponding to the phase transitions that occur in perovskites is constructed.

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