Page 48 - Electric Machinery Fundamentals

24 ELECTRIC MACHINERY FUNDAMENTALS

nonlinearity accounts for many of the peculiar behaviors of machines that will be
explained in future chapters. We will use MATLAB to calculate solutions to prob-
lems involving the nonlinear behavior of real machines.

Example 1-4. Find the relative permeability of the typical ferromagnetic material
whose magnetization curve is shown in Figure I- lOe at (a) H = 50, (b) H = 100, (c) H =
500, aud (d) H ~ 1000 A • turns/m.

Solution
The permeability of a material is given by

and the relative permeability is given by

(1-23)
(
Thus, it is easy to determine the permeability at any given magnetizing intensity.
(a) At H ~ 50 A ' turns/m, B ~ 0.25 T, so
0.25 T
~ 0.0050 H/m
50 A • turns m
/
and
JL ~ 1'0 ~ 0.0050 Him ~ 3980
I f.Lo 41T X 10 7 Him
(h) AtH ~ 100A ' tums/m,B ~ o.n T, so
B
JL ~ -H ~ 100 ~.n T / ~ 0.0072 H/m
• turns m
and
~ 1'0 ~ o.oon H/m ~ 5730
f.Lr f.Lo 41TXI07H/m
(c) AtH ~ 500A'turns/m,B ~ 1.40T, so
~ Ii ~ l AO T ~ 0.0028 H/m
J.l. H 500 A • turns/m
and
JL ~ 1'0 ~ 0.0028 Him ~ 2230
r flo 41T X 10 7 Him
(d) At H ~ 1000 A • turns/m, B ~ 1.51 T, so
B 1.51 T
JL ~ H- ~ 1000 A / ~ 0.00151 H/m
• turns m
and
~ 1'0 ~ 0.00151 Him ~ 1200
Mr f.Lo 41T X 10 7 Hfm