Environmental Engineering Reference
In-Depth Information
torque per ampere. This means that the spacial displacement from flux field and
armature current sheet must be maintained orthogonal:
ds
¼
rd
q
Z
¼
2
I
Z
2
p
r
A
x
¼
S
r
¼
2
p
rL
ð
5
:
5
Þ
B
z
Z
2
p
r
cos
ðbÞ
g
s
¼
A
x
B
z
cos
ðbÞ¼
B
z
Z
2
p
r
2
p
rL
¼
B
z
ZL
cos
ðbÞ
F
¼ g
s
S
r
¼
T
¼
Fr
¼
BZLr
cos
ðbÞ
Deviation from orthogonality between field flux distribution and armature
current sheet results in a loss in torque and torque ripple components. The brushed
dc machine, which the reader is no doubt familiar with, has
N
b
torque pulsations per
mechanical revolution of the armature, where
N
b
is the number of commutator
segments. The number of torque pulsations is the same regardless of the number of
magnetic poles in the brushed dc machine. The mechanical angle of the armature,
b
, is inversely proportional to the number of commutator segments so that the
following holds:
p
/
N
b
, where this range defines the peak-to-peak
torque pulsation magnitude according to (5.5). The common 12-bar commutator
has a torque ripple magnitude of
p
/
N
b
<
b
<
(Nm)
D
T
T
pk
¼
1
cos
p
N
b
ð
5
:
6
Þ
For the example of 12 segments, (5.6) predicts a variation in torque of (1
0.966)
¼
3.4%. However, if only eight commutator bars are used, the pulsation torque increases
to 7.6%. Of course, if only two segments are used, the torque ripple is 100%.
Regardless of technology, the purpose of any electric machine used for hybrid
propulsion is to develop the highest level of torque for a given current in the smallest
package possible. Torque and power density are absolutely essential in order to
maximize performance without incurring excessive weight and its attendant impact
on fuel economy. As (5.5) shows, torque production depends on as high a level of
flux in the machine as possible for a given magnitude of current (ampere-turns) and a
value of rotor radius and length that meets vehicle packaging constraints.
Each electric machine technology, when coupled with its electronic commu-
tator, the power electronics inverter, has relative merits and disadvantages. The
