The Eddy current losses with suitable examples and sketches are discuss here advanced.When the magnetic flux penetrating continuous conducting bodies undergoes changes, then in accordance with the law of electromagnetic induction, electromotive forces are induced and electric currents appear. The electric charges that form these currents move along closed circuits in planes normal to the direction of the magnetic flux and resemble the trajectories of particles in vortex flows. This similarity was the reason for the name of their eddy currents.

It should be noted that eddy currents are generated regardless of whether the body is in a stationary magnetic flux, the magnitude of which varies with time, or whether it moves relative to the magnetic flux. In both cases, in accordance with the Lenz rule, eddy currents create effects that inhibit the changes that cause these currents to appear. If currents occur in a body in a stationary alternating magnetic flux, then they excite their own magnetic field, which tends to weaken the change in the main magnetic flux that caused them. When a conducting body moves in a constant magnetic field, eddy currents create a force that impedes movement.

Fig. 2.7

From the picture of the distribution of eddy currents in Fig. 2.7, but it is seen that the demagnetizing effect will be unequal in different parts of the cross-section of the rod. The central part is covered by the largest number of eddy current circuits; therefore, their MDS in the center is maximum. On the surface of the same MDS eddy currents is zero. Therefore, the demagnetization in the center will be maximum and the magnetic flux will be distributed unevenly over the cross section, increasing from the center to the edges. This phenomenon will be expressed more sharply, the greater the frequency of the magnetic flux, as well as the magnetic permeability, conductivity and thickness of the rod. At high frequencies, magnetic flux is distributed only in a very thin surface layer.

Under conditions of operation at low frequencies, the demagnetization and braking manifestations of eddy currents, as well as the associated energy loss, are usually negligible. More significant are losses in the form of heat from their flow. Therefore, it is precisely these losses that are called eddy current losses.

Let us determine the losses from the flow of eddy currents in the rod in Fig. 2.7, b, which is penetrated by an alternating magnetic flux Φ directed along the axis of the rod. Let the width of the rod significantly exceed its thickness. In the body of the rod, we single out a hollow cylinder of width b, height h, and wall thickness spaced x from the center. Then the magnetic flux bd dx xΦ, penetrating the cylinder, the EMF induced in it x E and the resistance along the current path x r will be equal to:

where: f k – coefficient of shape of the EMF curve; f is the frequency of the current in the winding in Hz; m B is the maximum induction in T; γ is the specific conductivity of the rod material; – the amplitude of the magnetic flux in Wb. Φmaxx The power released in the form of heat in an elementary cylinder can be defined as

and full power –

Where

Is a coefficient proportional to the conductivity and squared thickness of the rod, and V = bhd is the volume of the rod.

The energy converted to heat by eddy currents can be very large. Therefore, all structural elements of electrical machines penetrated by an alternating magnetic flux are made of sheets isolated from each other, the thickness of which is selected depending on the frequency. The higher the frequency, the thinner the sheets should be at the same value of specific losses in order to reduce the thickness d to compensate for their increase associated with the growth of f. The separation of the magnetic circuit into plates is called “batching”, from it. Schichte – layer. It runs along the direction of the magnetic flux. Separate core plates are insulated from each other by varnish or scale that occurs on their surface during heat treatment.

Since the losses are proportional to the square of the thickness of the plates, it would seem that they can be reduced to an arbitrarily small value. However, with an increase in the number of plates with the same dimensions of the structure, the total insulation thickness increases and the steel section decreases. This leads to an increase in magnetic induction and a corresponding increase in not only losses from eddy currents, but also from hysteresis. Therefore, the choice of plate thickness is made taking into account many factors. For elements of machines subject to alternating magnetization reversal with frequencies not exceeding 100 Hz, electrical steel 0.35 and 0.5 mm thick is used.

Fig. 2.8

The second way to reduce eddy current losses is to increase the resistivity of the material. To this end, silicon is included in electrical steel. At 2 … 3.5% of the silicon content, eddy current losses are reduced by 4 … 5 times.

Power f P is consumed from the source of electrical energy supplying the coil. With negligible losses in the coil winding, exciting the magnetic field, and in the absence of losses on magnetization reversal, i.e. if a non-magnetic body is in the magnetic field, the power of the eddy current losses corresponds to the active component of the current Ia and can be defined as

The decrease in the magnetic flux caused by the demagnetizing effect of the eddy currents is compensated by a corresponding increase in the reactive current of the coil exciting the magnetic field. In practice, this increase in reactive power consumption is negligible and is usually neglected.

Reference

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