Calculation of the magnetic circuit


For what calculation of the magnetic circuit is necessary?

Problem of calculation in most cases is opredeleyony the magnetizing force of Iw necessary to excite in the magnetic conductor the certain magnetic flux or the certain magnetic induction in some site of the magnityony chain (most often in the air interval).

Схема расчета магнитных цепей

Scheme of calculation of magnetic circuits.

Calculation is conducted on the basis of the Ampere law according to which the sum of magnetic tension on certain sites of the magnetic circuit is equal to the magnetizing force:

N1ll + H1l1 +... + Hklk +... + Hnln =? Hklk = Iw,  at (k=n, k=1)

Here is called magnetic tension proizvedeyony field gradient Nk at length of the respective site, i.e. Hklk.

The magnetic circuit is divided whenever possible into the small number n of sites, within each of which it is possible to accept the nayopryazhennost of H and induction In constants (in fig. 1 п = 3). Then, if the magnetic flux F is set, for one of uchastyok having S1 section magnetic induction of B1 = ф is defined: S1

Схема магнитной цепи с магнитным зазором

Figure 1. The scheme of the magnetic circuit with magnet gap.

And on the basis of value of magnetic induction B1 by means of the magnetization curve of ferromagnetic material of this uchastyok of the core the strength of H1 corresponding to induction of B1 (fig. 2) is defined. For the second site it is necessary to find in the same order at first V2=F:S2, and then on H2 namagnichiyovaniye curve. The value of strength for all n of sites of the magnetic circuit consistently is defined by such way.

If in the magnetic circuit there is the air interval (or the nonferromagnetic site), then the section of the way of the flow in air can be accepted equal to the section of the site adjoining ферромагнитно­го. Therefore, induction is equal to induction on this neighboring site in the air interval of Vv. On the basis of this induction we define magnetic field strength. Usually in air it turns out quite big: Nv = Vv:µ 0,

Because of the fact that magnetic conductivity of air µвоз =µ0 is otyonositelno small and therefore for initiation of a little znayochitelny induction big field gradient is necessary.

Length of each of sites of the magnetic circuit should be considered length of the way of the flow, i.e. length of the average magnetic line.

After the magnetic tension of Hl for all sites of the chain is determined, using the Ampere law, podschityyovay the necessary magnetizing force: H1l1 + H2l2+ … + Hvlv =Iw

Or, if the number of rounds of the coil, then I= is known (H1l1 + H2l2+ … + Hvlv): w

When calculating it is useful to pay attention that the most part of the magnetizing force is spent for the malenyyoky air interval.

График определения напряженности поля

Figure 2. Schedule of definition of field gradient.

If it is necessary to solve the return problem, to determine the magnityony flow or induction by the set magnetizing Iw force, then calculation becomes complicated a little because distribution of strength of N between certain sites of the magnetic circuit is unknown, and it depends on unknown magnetic induction. For this reason the problem should be solved by selection or by means of creation of the magnetic characteristic of the ustroystyov. It is necessary to be set by some probable value магнитно­го the flow F' (or induction for one of sites) and to rasschiyotat as it was made higher, the magnetizing Iw force', necessary for excitation of this flow. The Iw value received in such way' should be compared with the preset value of Iw. If Iw' significantly differs from Iw, then it is necessary to repeat calculation, having set by new value of the flow F"; on the basis of this calculation to find new Iw value", etc.

The curve of dependence of the flow F from the magnetizing force I w, constructed by means of such calculations executed primeryono for five values F will represent the magnityony characteristic of the chain. By means of such harakteyoristika it is easy to define the flow corresponding to any znayocheniye of the magnetizing force.

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