Eddy current losses

Losses of energy during magnetization reversal

The Losses of energy during magnetization reversal with suitable examples and sketches are discuss here advanced.

If there is no linear relationship between magnetic induction and field strength, then assuming that the magnetic field is the same at all points of the normal plane, the energy density can be determined by integration from the magnetization curve. Dividing the integration loop into separate sections, starting from the zero value of induction, taking into account the symmetry of the hysteresis loop, we obtain

Losses of energy during magnetization reversal

Fig. 2.5

Each integral in expression (2.5) represents the area of ​​the figure bounded by the ordinate axis and the corresponding section of the hysteresis loop (Fig. 2.5). When magnetizing from zero to the maximum value of induction m B, specific energy equal to the area is expended. A decrease in the field strength from the maximum value 0 c m m HHBS 0 mH to zero reduces the specific energy of the field, i.e. causes a return of energy to the current source proportional to the area m m r mB H B BS. compaction of material and residual induction r Demagnetizing B to zero requires energy proportional to the area 0 r c r p B HBS. Thus, the specific energy spent in one full magnetization reversal cycle is

Losses of energy during magnetization reversal

those. corresponds to the area of the hysteresis loop in the corresponding scale H S bax along the axes of tension and induction h and b. The energy spent during magnetization reversal is released in the ferromagnet as heat.

The energy loss associated with magnetization reversal is also called the hysteresis loss. This name reflects the fact that in the absence of the hysteresis phenomenon (0), the magnetization reversal losses will be zero, because the area of the hysteresis loop will be zero.

Losses of energy during magnetization reversal

Fig. 2.6

The energy loss per magnetization reversal of the entire volume of the ferromagnet is determined by the area of the hysteresis loop constructed in the coordinates i and т, which is called the Weber-ampere characteristic. Indeed, for example, for the coil in Fig. 2.4

/ iH wi l ki == and / () B wS kΨ = Ψ = Ψ, i.e. the weber-ampere characteristic () f iΨ = is the dependence () () iB f H kf ki Ψ = ⇒ Ψ =, rebuilt taking into account the scale factors / li kw = and 1 / () kw SΨ = corresponding to the dimensions of a real ferromagnetic body . Then, in accordance with (2.3), the energy loss in the volume V is equal to lS

Based on experimental studies by Steinmetz, a formula was proposed for calculating power losses during symmetric magnetization reversal due to hysteresis

where 4 1.5 0.005 10− η = × … is the dimensionless coefficient characterizing the core material; f is the power frequency in Hz; V is the core volume in m3; m B is the maximum value of magnetic induction in the magnetization reversal cycle in T. The value of the power loss satisfactorily coincides with experience if

It should be noted that the magnetization reversal of a ferromagnet can occur not only as a result of a change in the direction of the external field associated with a change in the direction of the current in the coil, but also when the ferromagnet rotates in a constant magnetic field or when the field rotates relative to the ferromagnet. In this case, the magnetization reversal is called rotational. The losses due to hysteresis during rotational magnetization reversal at low values ​​of induction are almost the same as during cyclic reversal. However, with a maximum induction above 0.8 … 1.0 T, losses decrease and significantly differ from losses during cyclic magnetization reversal (Fig. 2.6).

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