Lap Winding

 Lap winding

we know that,
coil span = S/P
where, S=Number of slots
            P=Number of poles

Assuming we want to design a lap winding for 4 pole DC machine having a total number slots, S=16

Coil span = 16/4 = 4

we also know that Commutator pitch for lap winding, Yc = ± 1

• The upper coil side present in slit number 1 is shown by firm line and named 1 while lower coil side is shown by a dashed line and named as '1' .
• Since, coil span = 4, the first coil has sides 1 and 5 and coil can be identified as (1-5'). If we terminate coil 1 on commutator segment 1, so where to terminate coil side 5'.
• Since commutator pitch is ±1 , 5' should be terminate on commutator segment 2(=Yc + 1).  DC armature winding, all coils are to be connected in series. So naturally next coil (2-6') should start from 2 and end in slot 6.
• Coil (2-6') lies in the lap of (1-5'), hence winding is called lap winding. the winding proceeds from left to right due to our assumption Yc = 1. such a winding is called as progressive simplex lap winding.
• If Yc  = -1, winding progresses from right to left, giving rise to retrogressive lap winding.
• To place brushes assume slots (1-4) are under influence of north pole and slots (5-8) are under South pole, (9-12) are under north pole and (13-16) are under south pole.
• Also, assume armature rotates from left to right i.e. in clockwise direction since current is shown upwards (assuming B is coming out) so by motional emf rule 1 is negative and 5' is positive (in terms of emf polarity).
• In lap winding there may be circulating currents due to unbalance of emf in different parallel paths. As each parallel path undergoes different poles.
• So, 1 is negative, 8' is positive, 5 is positive, 12' is negative, 16' is positive and 9 is negative, 13 is positive and 4' is negative.

Because pole pitch = 16/4 = 4 poles, so after each 4 commutator segments direction of magnetic field with respect of conductor rotation reverses.

• So 2 positive brushes can be connected to 5 and 13. two negative brushes to 1 and 9.
• So for armature current there are 4 parallel paths as 2 paths originate from each commutator segment and these are set of 2 brushes for each polarity.
• Distance between a positive and negative brush is pole pitch = S/P.

Each terminal carries current equal to armature current which gets equally divided into two brushes connected to that terminal. Each brush is connected to one commutator segment which itself is connected to two conductors so current gets further divided into two equal parts. So current per conductor is Ia/4. So, we can say current gets divided into 4 parallel paths which is same as number of poles.

Hence, number of parallel paths (A) = number of poles (P).