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Armature winding types; lap winding sketch

Short answer

Lap winding has A=P parallel paths; wave winding has A=2; frog-leg combines both. For the 12-slot, 2-pole lap winding with 12 commutator segments, there are 24 conductors, back pitch 11, front pitch 9, and progressive lap gives commutator pitch 1. Two brushes are placed at the neutral axis.

Discuss the types of armature winding in dc machine in brief. Draw the sketch for lap winding in which number of slots = 12, number of poles = 2 and number of commutator segments = 12.

Types of armature winding

An armature winding consists of coils placed in slots and joined to the commutator segments. It is classified by how the coils are connected.

1. Lap winding

  • The end of a coil is connected to the commutator segment next to the one where the coil began, so successive coils overlap (lap back).
  • Number of parallel paths A=PA = P (number of poles).
  • Number of brushes = number of poles.
  • Needs equaliser rings to balance emf. Used for low voltage, high current machines.

2. Wave winding

  • A coil end is connected to a segment about one pole-pair pitch ahead, so the winding progresses like a wave around the armature.
  • A=2A = 2 always; only two brushes are needed (though PP may be used).
  • Gives higher emf with fewer turns. Used for high voltage, low current machines.

3. Frog-leg winding: a combination of lap and wave windings on the same armature. It is self-equalising, so separate equaliser rings are not needed.

Both lap and wave may be simplex, duplex or triplex, and progressive or retrogressive. Coils are normally double-layer (one side in the top of a slot, the other in the bottom).

Lap winding: 12 slots, 2 poles, 12 segments

Each slot has 2 coil sides (double layer), so the number of coils =12= 12 and conductors Z=24Z = 24.

  • Pole pitch =Z/P=24/2=12= Z/P = 24/2 = 12 conductors (6 slots). The coil is made slightly short of full pitch because yby_b must be odd.
  • Back pitch yb=11y_b = 11 (odd), front pitch yf=9y_f = 9 (for progressive lap yb−yf=2y_b - y_f = 2).
  • Commutator pitch yc=1y_c = 1 segment; A=P=2A = P = 2, so 2 brushes.
CoilTop conductorBottom conductorSegments
11 (slot 1, top)12 (slot 6, bottom)1 and 2
23 (slot 2, top)14 (slot 7, bottom)2 and 3
35 (slot 3, top)16 (slot 8, bottom)3 and 4
47 (slot 4, top)18 (slot 9, bottom)4 and 5
59 (slot 5, top)20 (slot 10, bottom)5 and 6
611 (slot 6, top)22 (slot 11, bottom)6 and 7
713 (slot 7, top)24 (slot 12, bottom)7 and 8
815 (slot 8, top)2 (slot 1, bottom)8 and 9
917 (slot 9, top)4 (slot 2, bottom)9 and 10
1019 (slot 10, top)6 (slot 3, bottom)10 and 11
1121 (slot 11, top)8 (slot 4, bottom)11 and 12
1223 (slot 12, top)10 (slot 5, bottom)12 and 1

Coil kk goes from conductor 2k−12k-1 to 2k+102k+10 and its finish is joined to the start of coil k+1k+1 at segment k+1k+1.

 Developed view (coil 1 and 2 shown)
      N                      S
   |--------|-------------|--------|
 slot 1 2 3 4 5 6 7 8 9 10 11 12
 coil 1: top of slot 1 --> bottom of slot 6
 coil 2: top of slot 2 --> bottom of slot 7
 ....
 seg:  1  2  3  4  5  6  7  8  9 10 11 12
 brushes (2): on segments under the neutral axes

Each brush covers a segment, so the coils form 2 parallel paths (6 coils in series per path).

✓ Answer checked by Claude Opus 5.5 (high effort)

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