Page 49 - Electric Machinery Fundamentals

l NTRODUCTION TO MACHLNERY PRINCIPLES 25

Notice that as the magnetizing intensity is increased, the relative perme-
ability first increases and then starts to drop off. The relative permeability of a typ-
ical ferromagnetic material as a function of the magnetizing intensity is shown in
Figure 1-IOd. This shape is fairly typical of all ferromagnetic materials. It can
easily be seen from the curve for ILr versus H that the assumption of constant rel-
ative permeability made in Examples 1- 1 to 1-3 is valid only over a relatively
narrow range of magnetizing intensities (or magnetomotive forces).
In the following example. the relative permeability is not assumed to be
constant. Instead, the relationship between B and H is given by a graph.

Example 1-5. A square magnetic core has a mean path length of 55 cm and a cross-
2
sectional area of 150 cm . A 200-turn coil of wire is wrapped around one leg of the core. The
core is made of a material having the magnetization curve shown in Figure l- lOc.
(a) How much current is required to produce 0.012 Wb of flux in the core?
(b) What is the core's relative permeability at that current level?
(e) What is its reluctance?

Solution
(a) The required flu x density in the core is

B = 1'. = 1.012 Wb = 0.8 T
A 0.015 01'
From Figure l- lOc, the required magnetizing intensity is
H = 11 5 A· turnslm
From Equation (1- 20), the magnetomotivc force needed to produce this magnetizing
intensity is
'if= Ni = H(
= (115 A -tums/m)(0.55 m) = 63.25 A -turns
so the required current is
. g 63.25 A • turns
t= N= 200 tums 0.3 16A
(b) The core's permeability at this current is

B 0.8T
}L = Ii = 115 A . turns/m 0.00696 Him
Therefore, the relative permeability is

= .l': = 0.00696 Him = 5540
jJ., "" 4" X 10 7 Him
(c) The reluctance of the core is
'if 63.25 A • turns
'R = ¢ = 0.012 Wb = 5270 A ' turnslWb