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did so with finite difference method along with determining the dynamic reaction with FEM. calculated the magnetic force using the finite element method, while Lefevre et al. Boules analytically predicted the flux density in permanent magnet machine. The problem of magnetically generated vibration has been addressed by other investigators. Their efforts resulted in torque calculation at several different locations based on the quasi-static magnetic field, which were verified by experiments. compared the several different methods to calculate the torque. Initially, papers mainly focused on the calculation of the torque as the output of motor. The analysis of magnetic force has been addressed by a number of investigators. These problems are particularly serious when the forcing frequencies match one or more of the structural resonant frequencies in the machine.
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Therefore, since the magnetic force increases approximately with the square of magnetic flux, the forces arising from designs using rare earth magnets are significantly greater than those from conventional magnet designs. Neodymium and other rare earths have greater retentivity, coercive force and maximum energy product than traditional ferrite magnets. Vibration is induced in permanent magnet DC motors and generators as shown in Figure 1, by traveling magnetic forces. Magnetic force analysis is important in determining not only the torque as the output of motor, but also the source of vibration in machine itself. In this paper the magnetic flux density, the magnetic force and the torque of a real three dimensional brushless DC motor are simulated using Maxwell 3 D V 11.1. The magnetic force can be calculated from the flux density by finite element methods and the Maxwell stress tensor in cylindrical coordinates. Keywords: Brushless DC Motor, Finite Element Analysis, Maxwell 3 D V 11.1Īs permanent magnet motors and generators produce torque, vibration occurs through the small air gap due to the alternating magnetic forces created by the rotating permanent magnets and the current switching of the coils. This page uses Creative Commons Licensed content from Wikipedia ( view authors).1Isfahan University of Technology, Isfahan, Iran.Įmail: January 8 th, 2009 revised February 4 th, 2009 accepted February 18 th, 2009. The relationship is given by Faraday's law:Īnd is the principle behind an electric generator.
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Outside of the magnet, the field lines will go from north to south.Ī change of magnetic flux through a loop of conductive wire will cause an emf, and therefore an electric current, in the loop. The direction of the magnetic-flux-density vector is by definition from the south to the north pole of a magnet (within the magnet).
#Magnetic flux equation free
Note that this indicates the presence of electric monopoles, that is, free positive or negative charges. Where E is the electric field intensity, is the free electric charge density, (not including dipole charges bound in a material), and is the permittivity of free space. In other words, the magnetic flux through any closed surface must be zero there are no free "magnetic charges".īy way of contrast, Gauss's law for electric fields, another of Maxwell's equations, is This equation, in combination with the divergence theorem, provides the following result: We know from Gauss's law for magnetism that Where is the magnetic flux and B is the magnetic flux density. The SI unit of magnetic flux is the weber, and the unit of magnetic flux density is the weber per square meter, or tesla. This law is a consequence of the empirical observation that magnetic monopoles do not exist or are not measureable. Gauss's law for magnetism, which is one of the four Maxwell's equations, states that the total magnetic flux through a closed surface is zero. More generally, magnetic flux is defined by a scalar product of the magnetic field density and the area element vector. The flux through an element of area perpendicular to the direction of magnetic field is given by the product of the magnetic field density and the area element. Magnetic flux, is a measure of quantity of magnetism, taking account of the strength and the extent of a magnetic field.
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