This preview shows page 1. Sign up to view the full content.
EEL 3216 Introduction to Power Systems
Homework # 6
SOLUTIONS
46. The flux density distribution over the surface of a twopole stator of radius r and
length l is given by
cos(
)
Mm
BB
t
Z
D
±
Prove that the flux density under each pole face is
2
M
rlB
I
Solve first specifically for a 2pole and then for a 4pole machine and generally for a P
pole machine
SOLUTION
(a)
P = 2: Seen from the rotor the flux density becomes time independent
cos( )
M
, since the rotor spins with the mechanical angular velocity
Z
m
. The
flux penetrating an infinitesimal small area
dd
Al
r
²²
is
d
cos( )d
M
lrB
DD
and the total flux under each pole face is the aerial integral of
this
d
. In a 2pole machine one pole face (e.g. one north pole) reaches over 180
q
from
D
= 90
q
to
D
= 90
q
(assuming the peak flux density B
M
at
D
= 0). Therefore, the total
flux becomes
2
2
2
2
cos( )d
sin( )
sin(
) sin(
)
2
22
MM
M
M
rlB
rlB
rlB
rlB
S
SS
ID
±
±
ªº
This is the end of the preview. Sign up
to
access the rest of the document.
This note was uploaded on 02/01/2012 for the course EEL 3216 taught by Professor Brooks during the Spring '08 term at FSU.
 Spring '08
 BROOKS
 Flux

Click to edit the document details