08 Airgap MMF - Airgap MMF MMF from Double Layer Lap...

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Airgap MMF MMF from Double Layer Lap Winding MMF from Concentric Winding MMF from Salient Poles MMF Wave
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Part 1 - MMF from Double Layer Lap Winding
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Airgap MMF for a Full Pitch Winding (1) Ni a F 2 2 Ni a F F a is the MMF of one half of the magnetic circuit.
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Airgap MMF for a Full Pitch Winding (2)
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Airgap MMF for a Full Pitch Winding (3) d Ni d Ni F a a a a a  cos ) 2 ( cos 2 2 2 2 / 2 / 2 / 3 2 / 1 i N 2 4 a a i N cos 2 4 1 F
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Airgap MMF for a Full Pitch Winding (4) Extended to multi-pole case P Ni P Ni PP ( ( 2 ) 2 / /( ) 2 / () 2 / /( ) 2 / 3 (  d Ni d Ni d d P F ae ae ae ae a a a a a ) cos( ) ( ) cos( 2 ) 2 cos( ) 2 ( ) 2 cos( 2 ) 2 / /( 2 2 / 2 / 2 / 3 2 / ) 2 / /( ) 2 / 2 / /( ) 2 / ( 1 Define a ae P i N 2 4 2 2 2 2 a a P i N 2 cos 2 4 1 F a ae P 2
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Harmonics of MMF for a Full Pitch Winding Assume ( ( P ) 2 cos( ) cos( ... 5 , 3 , 1 a ah ae ah ah h ah a h F h F F F F s( s( 2 2 /2 / 3 Ni Ni  ,... 17 , 13 , 9 , 5 , 1 for , 2 4 2 sin 4 ) cos( ) 2 ( ) cos( 2 2 2 / h h i N h N d h d h F ae ae ae ae ah  ,... 19 , 15 , 11 , 7 , 3 for , 2 4 2 h h i N i h
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Fractional Pitch Winding (1) Fractional Pitch Full Pitch a axis m a axis N turns per coil N=2N c turns N turns per coil N=2N c turns c c
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Fractional Pitch Winding (2) 3 4 2 i N c 3 and 2 conductors from a F m a axis 2 i N c 2 2 2 2 2 2 ae 2 2 4 and 1 conductors from a F i N c N turns per coil N=2N c turns 1 2 2 2 i N c 2 2 2 2 2 2 ae 2 2 c a F i N c  i N c 2 2 2 2 2 2 ae 2 2
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Fractional Pitch Winding (3) a F i N c 2 2 2 2 ae  ... 5 , 3 , 1 h ah a F F i N c 2 2 2 ) 2 cos( ) cos( a ah ae ah ah P h F h F F h d h i N d h i N F ae ae c ae ae c ah sin ) cos( ) ( ) cos( 2 2 2 / 2 / 2 / 2 / pitch factor for the i h N c 2 4 2 sin h k ph h th harmonic
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Distributed Winding (1) Full Pitch
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Distributed Winding (2) Fractional Pitch (exaggerated end turns) 2 3 m a axis a 2 m m m a m P 2 a axis q=2 q=4 q coils per group
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Distributed Winding (3) m   1 ... 1 , 0 ... 5 , 3 , 1 , 1 ... 1 , 0 , q h ah q a a F F F 2 3 m 2 1 1 ... 1 , 0 ... 5 , 3 , 1 ) 2 1 ( cos q q h ae ah q h F  where a ... 1 , 0 ... 5 , 3 , 1 ) 2 1 ( cos ae h ah q h F ph c ah k h i N F 4 a axis h q h ae h 2 1 Let
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Distributed Winding (4) jh jqh j qq h j j h j q h e e e e e h h h h 1 Re Re ] Re[ ) cos( 11 ) ( 1
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08 Airgap MMF - Airgap MMF MMF from Double Layer Lap...

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