Page 45 - Electric Machinery Fundamentals

lNTRODuc nON TO MACHINERY PRINCIPLES 2 1

g 200 A • lurns
<f> ~ "R ~ 751,000 A. turnslWb
~ 0.00266 Wb
Finally, the magnetic flux density in the motor's air gap is

B ~ 1'. ~ 0.000266 Wb 0.19T
A 0.0014 m'

Magnetic Behavior of Ferromagnetic Materials

Earlier in this section, magnetic penneability was defmed by the equation
B ~ ,uH (1- 21)
It was explained that the permeability of ferromagnetic materials is very high, up
to 6000 times the permeability of free space. In that discussion and in the examples
that followed, the permeability was assumed to be constant regardless of the mag-
netomotive force applied to the material. AlUlOUgh permeability is constant in free
space, this most certainly is not true for iron and other ferromagnetic materials.
To illustrate the behavior of magnetic permeability in a ferromagnetic ma-
terial, apply a direct current to the core shown in Figure 1-3, starting with 0 A and
slowly working up to the maximum permissible current. When the flux produced
in the core is plotted versus the magnetol1lotive force producing it, the resulting
plot looks like Figure I- lOa. This type of plot is called a saturation curve or a
magn.etization curve. At first, a small increase in the magnetomotive force pro-
duces a huge increase in the resulting flux. After a certain point, though, further
increases in the magnetomotive force produce relatively smaller increases in the
flux. Finally, an increase in the magnetomotive force produces almost no change
at all. The region of this figure in which the curve flattens out is called the satu-
ration region, and the core is said to be saturated. In contrast, the region where the
flux changes very rapidly is called the unsaturated region of the curve, and the
core is said to be unsaturated. The transition region between the unsaturated re-
gion and the saturated region is sometimes caIIed the knee of the curve. Note that
the flux produced in the core is linearly related to the applied magnetomotive
force in the unsaturated region. and approaches a constant value regardless of
magnetomotive force in the saturated region.
Another closely related plot is shown in Figure I-lOb. Figure I- lOb is a
plot of magnetic flux density B versus magnetizing intensity H. From Equations
(1- 20) and (1- 2Sb),
Ni g
H=- = - (1-20)
Ie Ie
(
q, = BA (1- 2Sb)
it is easy to see that magnetizing intensity is directly proportional to magneromotive
f orce and magnetic flux density is directly proportional toflux for any given core.
Therefore, the relationship between B and H has the same shape as the relationship