Environmental Engineering Reference
In-Depth Information
where
L
m
is the magnet length in the direction of magnetization (along rotor
radius). A number of refinements are generally made to (5.14) to account for stator
slotting (Carter coefficient), rotor curvature, magnet fringing and leakage, and
other non-ideal factors. For the purpose of this development, (5.14) is sufficient.
Because rotor magnets have finite interpolar gap (if made from a ring magnet),
or an intentional circumferential gap to minimize the magnet material and to
develop a desired flux pattern, it is necessary to calculate the fundamental com-
ponent of the magnet produced flux density for a given arc segment of material.
The arc segment length is taken as the ratio of magnet pitch,
t
m
, to stator pole pitch,
t
s
. For this discussion, the magnet to pole pitch ratio is
a
m
. From this consideration,
the fundamental component of magnet flux density in the airgap becomes,
from (5.14):
2
a
m
4
p
B
g
sin
p
B
g
1
¼
ð
5
:
15
Þ
The back-emf according to Faraday's law is due to the rate of change of total
flux linking the stator coils. In the M/G development under consideration, the stator
coils in a phase are assumed to be all connected in series. The total flux per pole
is now
f
p
¼ p
D
si
P
a
m
s
1
hB
g
s
1
¼
0
:
97
0
:
7
< a
m
<
0
:
9
ð
5
:
16
Þ
where
D
si
is the stator bore diameter,
s
1
the stacking factor of stator laminations,
h
the stator stack length and
a
m
¼
0.8 typically.
The speed voltage induced into the stator coils is composed of a stack up of
individual coil turn emfs having various angular relations to the composite voltage
due to their placement in slots, whether the coils are full pitched over a pole or short
pitched, and whether the stator slots are skewed, or more practically, whether the
rotor magnets are skewed in the axial direction. Derivations for distribution, pitch
and skew factors can be found in many texts on machine design. For the purpose
here it is important to realize that the winding factor,
k
w
, is less than unity. The
SPM internal emf is now
r
2
p
fk
w
N
s
f
p
3
2
E
0
¼
ð
V
rms
, line-to-line)
ð
5
:
17
Þ
k
w
¼
k
d
k
p
k
s
N
s
¼
PN
c
where
N
c
is the number of turns per coil, per phase, per pole, and
N
s
is the total
turns in series per phase.
It is still not possible to evaluate the M/G power capability since the variables
for machine reactance (speed times inductance) listed in (5.13) are not known.
Therefore, the next step in the design of the SPM machine is a determination of the
