Figure 8-12 shows a lap-winding coil. The conductors shown on the left side lie in the top side of the rotor slot. Those on the right side lie in the bottom half of another slot approximately one pole pitch away. At any instant the sides are under adjacent poles, and voltages induced in the two sides are additive.

Other coil sides fill the remaining portions of the slots. The coil leads are connected to the commutator segments, and this also connects the coils to form the armature winding. This is shown in Fig. 8-13.
The pole faces are slightly shorter than the rotor core.

Almost all medium and large dc machines use simplex lap windings in which the number of parallel paths in the armature winding equals the number of main poles. This permits the current per path to be low enough to allow reasonable-sized conductors in the coils.

Windings. Representations of dc windings are necessarily complicated. Figure 8-14 shows the lap winding corresponding to the Gramme-ring winding. Unfortunately, the nonproductive end portions are emphasized in such diagrams, and the long, useful portions of the coils in the core slots are shown as radial lines.

Conductors in the upper layers are shown as full lines, and those in the lower layers as dotted lines. The inside end connections are those connected to the commutator bars. For convenience, the brushes are shown inside the commutator.

Note that both windings have the same number of useful conductors but that the Gramme-ring winding requires twice the number of actual conductors and twice the number of commutator bars. Figure 8-15 shows a 6-pole simplex lap winding. Study of this reveals the six parallel paths between the positive and negative terminals. The three positive brushes are connected outside the machine by a copper ring T# and the negative brushes by T#.

The two sides of a lap coil may be full pitch (exactly a pole pitch apart), but most machines use a short pitch (less than a pole pitch apart), with the coil throw one-half slot pitch less than a pole pitch. This is done to improve commutation.

Equalizers. As shown in Fig. 8-15, the parallel paths of the armature circuit lie under different poles, and any differences in flux from the poles cause different voltages to be generated in the various paths. Flux differences can be caused by unequal air gaps, by a different number of turns on the main-pole field coils, or by different reluctances in the iron circuits.

With different voltages in the paths paralleled by the brushes, currents will flow to equalize the  voltages. These currents must pass through the brushes and may cause sparking, additional losses, and heating. The variation in pole flux is minimized by careful manufacture but cannot be entirely avoided.

To reduce such currents to a minimum, copper connections are used to short-circuit points on the paralleled paths that are supposed to be at the same voltage. Such points would be exactly two pole pitches apart in a lap winding.

Thus in a 6-pole simplex lap winding, each point in the armature circuit will have two other points that should be at its exact potential. For these points to be accessible, the number of commutator bars and the number of slots must be a multiple of the number of poles divided by 2.

These short-circuited rings are called “equalizers.” Alternating currents flow through them instead of the brushes. The direction of flow is such that the weak poles are magnetized and the strong poles are weakened. Usually, one coil in about 30% of the slots is equalized. The crosssectional area of an equalizer is 20% to 40% that of the armature conductor.

Involute necks, or connections, to each commutator bar from conductors two pole pitches apart give 100% equalization but are troublesome because of inertia and creepage insulation problems. Figure 8-15 shows the equalizing connections behind the commutator connections. Normally they are located at the rear coil extensions, and so they are more accessible and less subject to carbon-brush dust problems.

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