Abstract
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.
Highlights
A problem statementThe use of magnetic properties of materials has found wide application in electrical engineering, and in machine building and mining and processing complex
Let’s write down rotation of the magnetic particle placed in constant magnetic field and caused by its orientation along magnetic field line by means of the differential equation for the moment of forces affecting on a particle
The considered model of rotary motion of a spherical ferromagnetic particle represents an angle of rotation and the angular speed arising at affect of magnetic field on a particle
Summary
The use of magnetic properties of materials has found wide application in electrical engineering, and in machine building and mining and processing complex. As well–known examples of the use of devices based on permanent magnets or electromagnets, it is possible to bring electromagnets for moving massive metal objects, magnetic plates similar in operating principle to the function of the vice grip, magnetic and electromagnetic couplings, magnetic bearings, solenoid valves and cranes of the linear and rotary drive, magnetostrictive devices, separation of ferromagnetic impurities from cooling lubricants, removing of cutting or grinding products in metal processing, etc. One should include a huge number of various displacement sensors, torsion sensors, angle of rotation sensors, limit switches sensors, level gauges, based on the change in the force of attraction / rotation of the magnet or electrical resistance under external influence in a special group. The main advantage of using magnetic forces is a good fixation index, as well as relatively small device sizes
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