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AEM & Devices Lab Classes 7 02 2011.docx
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1.2. Electromagnets with external forward armature travel

The most widespread forms of electromagnets of this type are electromagnets, presented on fig 1.3. As it follows from pictures, in examined cases there are two identical basic air-gap, in this connection a full electromagnetic force F is determined by a formula

F = 2F0 = 2∙5,1∙B02 S0 / μ0,

Fig. 1.3, a where В0 − induction in a basic air-gap, Wb/сm2; S0equivalence cross-section of each of basic gaps, сm2.

So, MMF, being on both gaps, determined so:

(wI)0 = φ (wI)П = 2∙δ0B0 / μ0,

where φ − coefficient, taking into account of MMF drop in steel and non-working gaps.

Induction В0 with a glance of possible in exploitation lowering of MMF (w∙I)п = χ∙w∙I, where χ ≤ 1, equals to: B0 = μ0∙φ∙χ∙w∙I / 2δ0

Permissible MMF w∙I of electromagnet coils is determined coming from its operation mode, terms of heating and presence of two coils, having a cooling surface 2Scl.

a) Continuous running duty of Fig. 1.3, b electromagnet

For this mode next correlations, similar to got before, are correct. Resistance of one coil :

R = 10-4∙ρ∙π∙(1 + n)∙dc∙w / 2Sm

where w − total number of loops of both coils; Sm – cross-section of wire metal, equals to :

Sm = 2fap∙m∙n∙ dc2 / w.

So, general losses in resistance of electromagnet are equal to:

P = 2R∙I2 = 10-4∙ρ∙π(1 + n)∙w2∙I2 / fap∙m∙n∙dc

On the other hand, Р is determined from correlation

Θper = P / 2h∙Scl = P / [2h∙(Sex + α∙Sin)].

Substituted Р and Scl from (1.5) into the formula Θper, we will define the value of MMF of electromagnet:

wI = 2√[104fapm2n(1 + 2n + α)∙hΘperdc3 / ρ(1 + n)]

the value of electromagnetic force

F = 8∙104∙μ0∙φ2∙ε2∙χ2fap ∙τ2m2n∙(1+ 2n + α)∙hΘperdc5/ [ρ(1 + n) δ02],

and key size of a core

dс = 5√{[103∙ρ∙(1 + n)∙Fδ02 / [φ2∙ε2∙χ2fap∙τ2m2n∙(1+ 2n + α)∙hΘper]}

Designating, as well as before,

C1 = [2∙103∙ρ(1+n)] / [φ2∙χ2fapτ2m2n(1+2n+α)∙hΘper], we will get accordingly:

F = 2dc5 / (C1∙ δ02) (1.42)

and dc = 5[C1F∙δ02 / 2ε2] (1.43)

Transformation of the last formula gives dependence

F / δ03 = 2ε2∙χ5 / C1, (1.44)

facilitating, as it was explained before, determination of dc = χ∙δ0. Thus under F they understand full force of electromagnet. In this case we determine:

  1. MMF of coils

w∙I = (9∙103dc / φ∙χ∙τ)∙√(dc / C1) (1.45)

2) cross-section of wire

Sm = [2.82∙ρ∙(1 + n)∙dc2 / (φ∙χ∙τ∙U)]∙√(dc / C1) (1.46)

3) number of coil loops

w = U∙√[103fapn / ρ∙(1 + n)∙(1 + 2n + α)∙hΘperdc) ] = C2U∙√(C1 /dc) (1.47)

4) induction in a working air-gap

B0 = (0,396∙10-4F) / (τ∙ε∙dc)

approximately by a formula

B0(4∙10-5 / τ∙ 5C1) ∙√(F3/ δ04)

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