Q. Draw the developed diagram of a simplex progressive 2 layer lap winding for a 4 pole generator with 12 coils clearly indicating the position of brushes.

Sol.  No. of commutator segments = no. of coils, C = 12, Twelve coils have 24 coil - sides. For two coil - sides per slots,

                Total no. of slots = 24/2 = 12

                Back pitch,      y_b = 2C/P ± K = 24/4 ± 1 = 7 or 5

                For progressive lap winding,

                    Y_w = y_b - y_f = +2

                     y_f = 5 for y_b = 7

            or y_f = 3 for y_b = 5

        It is desirable that y_b + y_f/2 should be as nearly equal to pole pitch as it possible. In view of this, y_b = 7 and y_f = 5 should be chosen for this commutator machine, because 7 +5/2 = pole pitch in terms of coil - sides (= 24/4 coil - sides per pole).

                     For probressive simplex lap winding, commutator pitch,

                             Y_c = +1

For drawing the winding diagram in radial form, 12 commutator or segments, 12 slots and 24 coils sides are first drawn. Now segment 1 is connected to top coil - sides 1 and then to bottam coil - sides 8 (1 + y_b = 1 +7). Note that the coil - sides 1 and segment 1 are so numbered tha the coils resemble a lap coil. Since y_C = 1, the coil - sides 8 is connected to segment 2 (1 + y_C = 1 +1).Bottom couil - side is now connected to top coil - sides 3 (8-y_f = 8-5), then to bottom coil - sides 10 (3 +7), then to top coil - side 5 (10-5), then to bottom is helpful in drawing this winding diagram.

        + y_b                    -y_f                 +y_b           -y_f             +y_b

         (1 - → 8) - →      (3 - →   10)  - →       (5 - →   12)- →

     (7  → 14) → (9 → 16) →         (11 → 18) →             (13 → 20)   →

    (15 → 22) → (17 → 24)(19 → 26 or 26-24, i.e. 2) → (26 → y_f or 21 → 21+y_b, i.e. 4) → (28 - y_f i.e. 23 → 6) → 1

                In the winding table (1→8) means that the top coil - side 1 is, connected to bottom coil - side 8 to form one coil. Same is true for all other coils. Note that winding table does not contain any no, greater than 24 ( = total no. of coil - sides). Each coil - sides is used only once in the winding table and the winding closes on itself (starting from 1 and ending on 1)

        In this machine with 12 slots and 4 pole, 3 slots are assumed to be under the effect of each pole. For example, 3 slots with coil - side 7 to 12 under the adjacent S pole and so on. Direction of e.m.fs. and current in the coil - sides under N pole are indicated by, cross and those under S pole denoted by dot. Now the directions of currents can be marked by noting that current flows from segments to cross - marked coil - sides and to the segments from dot - marked coil - sides.

                                               A careful examination of winding reveals that current leave at the commutator segments, 1, 7 and the current enter at the commutator segments 4, 10. Thus four brushes A, B, C, D can be placed in contact with segments 1, 4, 7, 10 respectively. Brushes A and C have the same polarity. These can, therefore, be joined together, similarly brushes C and D can be joined. Armature power can be handled at the terminals marked E, F. If E and F are given are negative and positive polarities respectively; the machine works as motor with the direction of rotation anti - clockwise.

           From brushes A, one parallel path is through coils a, b, c to brush B and the second parallel path is through coils l, k, j to brush D. From brush C, one parallel path is through coils f, e, d to brush B and the second parallel path through coils g, h, I, o brush D. These parallel path at any instant. There are thus four parallel paths for a 4 - pole machine - in general, for a simplex lap winding, no. of parallel paths A is equal to the no. of poles P, i.e. A = P. Expression ΦZN/60 (P/A) reveals tha the generated e.m.f. in lap connected machine (equal to Φ.ZN) is independent of the no. of poles.