Constructional Features of DC Machines - 2 | Basic Electrical Technology - Electrical Engineering (EE) PDF Download

Developed diagram 

Instead of dealing with circular disposition of the slots and the commutator segments, it is always advantageous to work with the developed diagram of the armature slots and the commutator segments as elaborated in figure 35.9.  In the figure 35.9, actual armature with 8 slots and 8 commutator segments are shown.

Imagine the structure to be cut radially along the line XX’O and unfolded along the directions shown to make it straight. It will result into straight and rectangular disposition of the slots and commutator segments.  

 Lap winding 

Suppose we want to make a lap winding for a P = 4 pole D.C machine having a total number slots S = 16.  So coil span is 16/4 = 4.  Commutator pitch of a progressive lap winding is y_c = +1.  In figure 35.9 only the slots and commutator segments are shown in which it is very difficult to show the coil sides and hence coil connections.  To view the coil sides / coils, we must look below from above the slots as depicted in figure 35.10. Once we number the slots, the numbering of the coil sides gets fixed and written.  The upper coil side present in slot number 1 is shown by firm line and named 1 while lower coil side is shown by a dashed line (just beside the upper coil side) and named as 1'.

Let us now see how coils can be drawn with proper termination on the commutator segments.  Since the coil span is 4, the first coil has sides 1 and 5' and the identification of the coil can be expressed as (1 - 5').  Let us terminate coil side 1 on commutator segment 1. The question now is where to terminate coil side 5'? Since the commutator pitch yc is +1, 5' to be terminated on commutator segment 2 (= yc +1). In D.C armature winding all coils are to be connected in series. So naturally next coil (2 - 6') should start from commutator segment 2 and the coil side 6' terminated on segment 3 as shown in figure 35.11. It may be noted that in a lap winding there exist a single coil between any two consecutive commutator segments. 

 It can be seen that the second coil 2 - 6' is in the lap of the first coil 1 - 5', hence the winding is called lap winding.  The winding proceeds from left to right due to our assumption that yc = +1.  Such a winding is called progressive simplex lap winding.  It can be easily shown that if y_c is chosen to be -1, the winding would have proceeded from right to left giving rise to a retrogressive lap winding.  One can make first a winding table and then go for actual winding.  By now it is clear that to go ahead with winding, two information are essential; namely the number of coil sides of a coil and the number of commutator segments where the free ends of the coil sides will be terminated.  In a winding table (look at figure 35.12) these two information are furnished.

 The complete progressive lap winding is shown in figure 35.13.  To fix up the position of the brushes, let us assume the instant when slots 1,2,3 and 4 are under the influence of the north pole which obviously means slots 5 to 8 are under south pole, slots 9 to 12 are under north pole and slots 13 to 16 under south pole. The poles are shown with shaded areas above the active lengths (coil sides) of the coils.  Considering generator mode of action and direction of motion from left to right (i.e., in clockwise direction of rotation of the cylindrical armature), we can apply right hand rule to show the directions of emf  in each coil side by arrows as shown in figure 35.13.  EMF directions are also shown in the simplified coil connections of the figure 35.12.  The emfs in the first four coils (1 - 5', 2 - 6', 3 - 7' and 4 - 8') are in the clockwise directions with 8' +ve and 1 -ve.  In the same way, 5 is +ve, 12' is –ve; 16' is +ve and 9 is –ve; 13 is +ve and 4' is –ve.  Therefore, two +ve brushes may be placed on commutator segment numbers 5 and 13.  Two numbers of –ve brushes may be placed on commutator segment numbers 1 and 9.  Two armature terminals A₂ and A₁ are brought out after shorting the +ve brushes together and the –ve brushes together respectively.  Thus in the armature 4 parallel paths exist across A₂ and A₁.  Careful look at the winding shows that physical positions of the brushes are just below the center of the poles.  Also worthwhile to note that the separation between the consecutive +ve and the –ve brushes is one pole pitch (16/4 = 4) in terms of commutator segments. 

In fact for a P polar machine using lap winding, number of parallel paths a = P.  Will it be advisable to put only a pair of brushes in the armature?  After all a pair of brushes will divide the armature into two parallel paths

Let, the total number of slots = S

The total number of poles = P 

∴ Total no. of commutator segments = S 

Total no. of coils = S ∵ double layer winding 

 No. of coils between two consecutive commutator segments = 1 ∵ simplex lap winding 

 Number of commutator segments between consecutive +ve and

  –ve brushes = S / P 

∴ Number of coils between the +ve and –ve brushes = S / P 

If only a pair of brushes is placed, then armature will be divided in to two parallel paths consisting of S/P coils in one path and coils in the other path.  So current distribution in the paths will be unequal although emf will be same.  A little consideration shows another pair of brushes can be put (figure 35.13) producing 4 identical parallel paths.  Therefore, in a lap winding number of brushes must always be equal to the number of poles.  Lap winding is adopted for low voltage, high current D.C Machines.  

Another example of Lap winding 

In figure (35.14), a 4-pole, lap winding for d.c machine armature is presented with 8 numbers of slots.  Armature winding of a d.c machine is double layer type which means that in each slot there will be two coil sides present.  The upper coil sides are numbered as 1, 2, 3…8 and the lower coil sides are marked as 1', 2', 3' ….8'.  Number of commutator segments are 8 and they are also numbered as 1,2,3…8.  Since two coil sides make a single coil and each slot is housing two coil sides, number of total coils that can be accommodated is also 8 (= number of slots).  It may be noted that coil ends of first, second, third,…eight coils are respectively, 1 - 1', 2 - 2', 3 - 3'…8 - 8'.  The spatial distance between two coil sides of a coil should be one pole pitch apart.  Now number of slots per pole isCoil side 1 of the first coil is put in slot number 1 and its other coil side 1' is placed in slot number 3.  The ends of the first coil 1 and 1' are terminated to commutator segments 1 and 2 respectively.  In the same way coil sides 2 and 2' of the second coil are placed in slot numbers 2 and 4 respectively.  Also its coil ends 2 and 2' are terminated on commutator segments 2 and 3 respectively.  Between commutator segments 1 and 3 we find that first and second coils are present and they are series connected by virtue of the termination of the ends 1' (of first coil) and 2 (of second coil) on the same commutator segment 2.  In the same fashion one can complete the connection of the third, fourth, … eighth coil.  End 8' of the eighth coil is finally terminated on commutator segment 1 where one end of the first coil was terminated at the beginning.  Thus we see that all the coils are connected in series via commutator segments in a closed circuit.

To fix up the position of the brushes consider an instant when there are two slots under each pole and the armature is rotating in the clock wise direction.  By applying right hand rule, we can find out the direction of the emfs induced in the conductors (i.e.,  or ⊗).  In order to show the direction of emfs in the coils more clearly, the coils have been shown spread out off the slots like petals in the figure (35.14).  If you start from any of the commutator segments and trace all the coils you will encounter as many clock wise arrows as the number of anti clockwise arrows.  Which simply confirms that total emf acting in the loop is zero.  Now the question is where to put the brushes?  In commutator segments 8 and 4 arrows converge indicating 2 brushes are to be placed there.  These two  

brushes externally joined together to give +ve armature terminal of the generator.  Similarly two brushes should be placed on segments 2 and 6 and joined together to give –ve terminal of the generator.  It is quite obvious now that across the armature terminals of the d.c generator 4 parallel paths exist.  In general for a p polar machine number of parallel paths a, will be equal to the number poles p.  Parallel paths and the coils with polarity of voltages are shown in the simplified diagram in figure (35.15).  Since lap winding provides more number of parallel paths, this type of winding is employed for large current and low voltage d.c machines.  For clarity each coil in the armature is shown to have single turn in figure (35.14)

Wave w inding

In this winding these coil sides of a coil is not terminated in adjacent commutator segments, i.e., y_c ≠ 1.  Instead yc is selected to be closely equal to two pole pitch in terms of commutator segments.  Mathematically y_c ≈ 2S/P.  Let us attempt to make a wave winding with the specifications S = 16 and P = 4.  Obviously, coil span is 4 and y_c = 8. 

Figure' 35.14: Lap winding, polar diagram

The first coil is (1 - 5') and is terminated on commutator segments 1 and 9.  The second coil (9 - 13') to be connected in series with the first and to be terminated on commutator segments 9 and 1 (i.e., 17').  Thus we find the winding gets closed just after traversing only two coils and it is not possible to carry on with the winding. Our inability to complete the wave winding will persist if 2S remains a multiple of P.  It is because of this reason expression for commutator pitch yc, is modified to yc = 2(S ± 1)/P.  In other words, number of slots, should be such that 2(S ± 1) should be multiple of P.  It can be shown that if +ve sign is taken the result will be a progressive wave winding and if –ve sign is taken the result will be retrogressive wave winding. 

Figure 35.15: Parallel paths across armature terminals

An example

We have seen that for 4-pole wave winding, choice of S = 16 is no good.  Let us choose number of slots to be 17 and proceed as follows: 

No. of poles, P = 4 

 No. of slots, S = 17 

 Windi ng pitch, y_c  =  2(S +1) / P choosing +1 for progressive winding 

∴ yc = 2(17 + 1) / 4 = 9 

 Coil span = S / P ≈  4 

Once coil span and the commutator pitch yc are calculated, winding table, shown in figure 35.16(a) can be quickly filled up. Series connection of all the coils are also shown in figure 35.16(b).  Directions of induced emfs are shown after assuming slots 1 to 4 and 9 to 12 to be under north pole; slots 5 to 8 and 13 to 16 to be under south pole.  Since S/P is not an integer slot 17 has been assumed to be in the neutral zone.  It is interesting to note that polarity of the induced emf reverses after nearly half of coils are traversed.  So number of armature circuit parallel paths are two only.  It is because of this reason wave winding is preferred for low current, large voltage d.c machines. 

Figure 35.16: Wave winding table and coil connections

In figure 35.17 are shown only two coils to explain how winding proceeds.  Important thing to be noted from this figure is that the first coil (1 - 5') starts from commutator segment one and ends on commutator segment 10, where from the second coil (10 - 14') starts and finally gets terminated on commutator segment 2.  In other words between any two consecutive commutator segments 2 coils are present.  This statement can be generalized as: for a P polar simplex wave winding, between any two consecutive commutator segments P/2 coils will be present.  A look at those two coils suggest that the winding progresses like a wave – hence the name wave winding.  Figure 35.18 shows  the completed wave winding where the directions of induced emfs in the coil sides are also shown.

That the number of parallel paths in a simplex wave winding is always 2 can be established mathematically as follows. 

  Let, the total number of slots = S

 The total number of poles = P

∴ total no. of commutator segments  = S 

Total no of coils = S ∵ double layer winding

 No. of coils between two consecutive commutator segments = P/2 ∵ simplex wave

 Number of commutator segments between consecutive +ve & 

-ve bru shes = S /P

∴ Number of coils between the +ve & -ve brushes = (S/P) × (P/2) 

= S/2  

Thus, a pair of brush divides the armature into two parallel paths.  From the direction of emfs –ve brush can be placed on commutator segment 9 and the +ve brush can positioned touching commutator segments 13 and 14.  In a wave winding since number of parallel paths are 2, theoretically a pair of brushes is sufficient for armature independent of the number of poles of the machine.  However for relatively large armature current one can put additional brushes such that total number of brushes are equal to P thereby reducing the size of the brushes.  For the 4 polar winding that we are considering, additional +ve brush can be placed over commutator segments 4 and 5 and another –ve brush can be placed over commutator segments 17 and 1 as shown with dotted boxes in figure 35.18.