Environmental Engineering Reference
In-Depth Information
AP and AN for the respective coil sides, P for positive magnetomotive force (mmf)
when a positive current flows into that slot.
Solution:
The reader can verify the mmf waveform in the spacial direction
(
x
-direction) by plotting out the current amplitudes beneath a particular row. Be
careful to take into account the current sign and slot conductor clocking orientation.
Time
BN
AP
CN
BP
AN
0.001
0.002
0.003
0.004
0.005
0.006
0.007
0.008
0.009
0.01
0.011
0.012
0.013
0.014
0.015
0.016
0.017
0.018
0.019
0.02
0.021
0.022
0.023
−49.691
−23.121
6.696
35.573
59.454
74.984
79.982
73.747
57.153
32.532
3.342
−26.317
−52.281
−70.901
−79.563
−77.050
−63.715
−41.431
−13.328
16.647
44.284
65.701
77.890
29.451
54.765
72.387
79.842
76.083
61.638
38.536
10.021
−19.901
−47.029
−67.550
−78.585
−78.581
−67.541
−47.014
−19.884
10.039
38.552
61.650
76.089
79.841
72.380
54.752
79.142
77.886
65.691
44.269
16.629
−13.346
−41.446
−63.726
−77.055
−79.561
−70.893
−52.267
−26.301
3.360
32.549
57.166
73.754
79.983
74.978
59.442
35.557
6.679
−23.138
49.691
23.121
−6.696
−35.573
−59.454
−74.984
−79.982
−73.747
−57.153
−32.532
−3.342
26.317
52.281
70.901
79.563
77.050
63.715
41.431
13.328
−16.647
−44.284
−65.701
−77.890
−29.451
−54.765
−72.387
−79.842
−76.083
−61.638
−38.536
−10.021
19.901
47.029
67.550
78.585
78.581
67.541
47.014
19.884
−10.039
−38.552
−61.650
−76.089
−79.841
−72.380
−54.752
The two colour shaded blocks are approximately the PM span. For example, in
the
t
¼
1 ms row (top row) and for the case where radian frequency is 377 rad/s, the
north magnet pole is just left of the CN conductors and the south magnet pole just
approaches the CN conductors. The reader can verify that the mmf over each
magnet is given by
mmf
N
¼
X
ð
BN
I
B
þ
AP
I
A
Þ
; mmf
S
¼
X
ð
BP
I
B
þ
AN
I
A
Þ
mmf
N
¼
40
ð
49
:
69
Þþ
40
ð
29
:
45
Þ¼
3,165
:
6
At
mmf
S
¼
40
ð
49
:
29
Þ
40
ð
29
:
45
Þ¼
3,165
:
6
At
The stator windings produce an mmf of proper polarity to cause the rotor to
spin in the counterclockwise direction, as seen by the left shifting of the magnet
pole shaded areas above as the time evolves towards 20 ms.
