ABSTRACT
These large magnetic moments allow atoms within small volumes of the material to orient themselves locally such that the magnetic moments of the atoms within these volumes are aligned in the same direction. Such volumes, which contain locally oriented atoms, are called magnetic domains or, more simply, domains, and the length of a typical domain in one direction is of the order of 10-3 to 10-5 m. If a volume of ferromagnetic material such as iron in the demagnetized state is considered, the domains will be present but the direction of the magnetic moment of the various domains will
14. 5 MAGNETIC HYSTERESIS LOSS
(14.1)
Solving eq. (14.1) for i, we obtain
(14.2)
dt (AN) dB
dt volts (14.3)
Substituting eqs. (14.2) and (14.3) into eq. (14.4) yields
dB HL dJ = AN dt N dt = ALH dB joules (14.5)
and
J = AL f H db joules (14.6) As the current i is increased, the energy supplied to the field as the
flux density changes from Be, corresponding to point e, to Ba , corresponding to point a, is
Ba
e
(14.7)
( Ba Bd ~
e b
joules (14.8)
and the energy released, Jout, from Fig. 14.3b is equal to
( Bb Bd ~
a e
joules (14.9)
Ph f 3 P = - = f H dB watts/meter hv V
(14.11)
(14.12)
where
Bm = maximum value of flux density
::iy b )'
The Magnetic Circuit
r= ~ ohms z dx
(14.14)
<p = 2Bxy webers
(14.15)
(14.16)
But again, y = 1, and
cp = 2Bx webers (14.17)
e r watts
Substituting eqs. (14.15) and (14.17) into eq. (14.18) yields
and P e is equal to
watts
(14.18)
(14.19)
(14.20)
and
( dB)2 = B2 (d Sin(wt)\2 = 2B2 2 t dt m dt") w m cos w 2
volts
(14.21)
(14.22)
(14.23)
However, the mean value of cos2 wt over a cycle is equal to 0.50. Then eq. (14.21) becomes
m 6p
(14.24)
14. 7 NO-LOAD CORE LOSS
1. Fundamental core loss a. Hysteresis loss b. Eddy-current loss
2. Rotational core loss a. High-frequency rotor-surface and stator-surface losses b. High-frequency rotor-tooth and stator-tooth pulsation losses
(14.25)
where
Kt = empirical fundamental tooth factor, which is close to 1. 0, dimensionless
maximum flux density, watts/meter3, watts/centimeter3, or watts/ inch3
Pet = eddy-current loss/unit volume in the stator teeth, based on statortooth maximum flux density, watts/meter3, watts/centimeter3, or watts/inch3
Kc = empirical fundamental core factor, which is close to 1. 0, dimensionless
V c = volume of stator core, meters3, centimeter3, or inches3 Phc = hysteresis loss/unit volume in the stator core, based on stator-core
maximum flux density, in watts/meter3, watts/centimeter3, or watts/ inch3
P ec = eddy-current loss/unit volume in the stator core, based on statorcore maximum flux density, watts/meter3, watts/ centimeter3, or watts/inch3
14. 8 LOAD LOSS
~ ,.... c· n
Chapter 14
numeric (14.26)
As discussed in Section 14.6, it is necessary to laminate magnetic cores of polyphase induction motors and to provide some amount of insulation on the surface of the steel laminations. Until about the middle of this century, this was accomplished by applying various formulations of organic varnish. Although the varnish buildup could be controlled to some extent by controlling the viscosity of the varnish, the buildup was typically in the range 0.012 to 0.018 mm (or 0.0005 to 0.0007 in. /side). However, some buildups exceeded this range. For punchings with a thickness of 0.5 mm (0.020 in.) and using a conservative value of varnish buildup of 0.015 mm, the buildup would constitute about (2)(0.015)/0.5 = 0.06 per unit, or 6%, of the overall core length, not including radial air ducts. This amount of buildup corresponds to (0.06)(40) = 2.4 cm, for a 40-cm solid stack length, or to approximately 0.90 in. for a 15-in. solid stack length.
