6. A calculation of magnetic circuit and determination of o.C. Current of asynchronous machine in traction mode
At the calculation of magnetic circuit a magnetizing current is determined, stipulating MMF of asynchronous motor. For this purpose it is necessary to calculate MMF of magnetic circuit as a sum of magnetic voltage drops across separate areas of magnetic circuit of asynchronous machine: air-gaps, tooth areas, backs of armature and rotor :
F∑ = Fδ + Fz1 + Fj1 + Fz2 + Fj2
where Fz1 and Fz2 − magnetic voltage drops respectively in the toothes of stator and rotor; Fj1 and Fj2 − magnetic voltage drops respectively in the back of stator and rotor.
The value of magnetic flux is determined also in an air-gap:
Фδ0 = kЕ0∙Uph1/(4ksh∙kw1∙wph1∙f), (52) where kЕ0 = 1/(1 + kσ0), kσ0 = Хs1/Хm = I0m Хs1/(Uph1 – I0m Хs1) – a dispersion factor of flux linkage of primary circuit, approximately accepted equal to kЕ0 = 0,95÷0,97; I0m – magnetizing current in the o.c. mode.
Magnetic induction in the air-gap of motor in the o.c. mode is
Вδ0 = [Фδ0/(αi∙li∙τ]∙104 = [1,57∙Фδ0/(li∙τ)]∙104. (53)
Calculation of magnetic voltage drops in stator and air-gap is made in accordance with methodology, expounded in § 2.6 [1]. Magnetic voltage drops in the toothes of rotor at straiht and trapezoid toothes is calculated also in accordance with § 2.6 [1].
In case of application of "squirrel-cage" round slots are used on a rotor (fig. 9, а). At the calculation of MMF of toothes the following values are determined:
rating width of tooth
bz2 = π[Dr − 2(hlm2 + d/3)]/z2 − 0,94d;
tooth step of rotor
tz2 = π∙Dr / z2
coefficient, taking into account the increase of induction in rotor toothes relativly to induction in an air-gap
kz2 = tz2∙l1 / (ksf∙bz2∙l2)
where l1 and l2 − active length of stator and rotor; at l1 = l2
kz2 = tz2 / (ksf∙bz2)
magnetic induction in rotor toothes is
Bz2 = kz2∙ Вδ;
length of magnetic line of force in rotor toothes is
Lz2 = 2d
MMF of rotor toothes (on the poles pair)
Fz2 = Hz2∙Lz2,
where Hz2 is determined by the curve of magnetizing.
MMF of rotor back is determined:
Fj2 =Hj2∙Lj2,
where Lj2 = π∙Dr,av / 2p; Dr,av = Dr – 2hz2 – hj2; hj2 − height of rotor back; Hj2 − field intensity in the rotor back.
The value of hj2 is determined by a formula
hj2 = [(Dr – 2hz1 – Di2) / 2] − 2∙nax,v∙dax,v / 3,
where Di2 − internal diameter of rotor (bore for a shaft); nax, v − number of rows of axial vent channels; dax, v − diameter of axial of a vent channel; in the absence thereof of vent a member 2∙nax,v∙dax,v / 3 equals to the zero.
The value of the field intensity is determined by induction in the armature back
Bj2 = Фδ0∙104/(2Sj2),
where Sj2 = hj2∙ksf∙l2 − area of cross-section of rotor back.
At the calculation of MMF of rotor back of bipolar machines it is accepted, that a magnetic flux passes also through the shaft of motor, but induction in a yoke remains unchanging along a pole pitch. Intensity Нj2 is determined by the basic magnetizing curve. In this connection for the rotor back of bipolar motor it is accepted
hj2 = (Dr – 2hz2)/2, Lj2 = 2hj2
At the calculation of asynchronous machine one has to set oneself the value of αi. After implementation of calculation it is necessary to specify the value of αi. As researches show, the value of αi substantially depends on the saturation of tooth areas and backs of stator and rotor. If designate ratio of MMF of toothes, backs and MMF of air-gap by coefficients
kμz = (Fz1 + Fz2) / Fδ; kμb = (Fj1 + Fj2) / Fδ,
t
hat
for determination of
αi
it is possible
to take advantage Fig.
12 of
curves, shown
on a fig. 12.
A value of curve shape coefficient of the field ksh depends on a value αi (fig. 13).
T
otal
MMF
of magnetic circuit
F∑
allows to define the magnetizing current
value (reactive
constituent of o.c.
current)
I0m = 1,11∙p∙F∑/m1∙wph1∙kw1), (54)
Fig. 13 where m1 − number of stator winding phases.
At m1 = 3
I0m = 0,37∙p∙F∑/( wph1∙kw1) (55)
After determination of magnetizing current a checking of
dispersion coefficient of flux kσ0 is made:
kσ0 = I0m∙Хs1 / (Uph1 – I0m∙ Хs1).
If values of coefficients αi, ksh, kσ go away with accepted at the beginning of calculation, then it is necessary again to make the calculation of magnetic circuit and magnetizing constituent of primary current.
Current of idling
I0 = √(I20m + I20a), (56)
where I0a = Р0/(m1∙Uph1) − active constituent of o.c. current, Р0 − losses of the synchronous idling, Р0 = Pst + m1∙I20∙r1; Рst − losses in steel.
Power-factor of the synchronous idling
cosφ0 = I02 / I0.
Coefficient of saturation
kμ = F∑0 / Fδ.
Constituent of magnetizing current on air-gap (А)
Iδ = I0m / kμ
Constituent of magnetizing current on steel
Ist = I0m (F∑0 − Fδ) / F∑ = I0m (1 – 1/ kμ).