To connect up rightly the inductors on an armature so as to produce a desired result is a simple matter in the case of ring winding, for bipolar or multipolar machines. It is a less easy matter in the case of drum winding, especially for multipolar machines. Often there are several different ways of arriving at the same result, and the fact that methods which are electrically equivalent may be geometrically and mechanically different makes it desirable to have a systematic method of treating the subject.
The elementary arrangement of drum and disc armatures has already been considered, which is sufficient explanation for small armature coils of only a few turns of wire, but in the case of larger machines which require many coils, further treatment of the subject is necessary.
For example, in order to direct the winder how to make the connections for, say a four pole machine having 100 bars spaced around its armature, some plain method of representing all the connections so that they may be easily understood is necessary. From this the workman finds out whether he is to connect the front end of bar No. 1 across to 50 or across a quarter of the circumference to 24, or across three quarters of it to bar 75. Again, he ascertains to which bar he is to connect the back1 end of the bar, and how the bars are to be connected to the commutator.
Winding Diagrams and Winding Tables.—In the construction of armatures, instructions to winders are given in the form of diagrams and tables. In the tables the letters F and B stand for front and back, meaning toward the front end, and from the front end respectively. The letters U and D stand for up and down.
Fig. 254.—End of ring winding for a four pole machine. An end view is simply a view showing the arrangement of the armature inductors and connections looking from the front or commutator end. A developed view of the above winding is shown in fig. 257.
There are three kinds of winding diagram:
1. End view diagram;
2. Radial diagram;
3. Developed diagram.
The end view is simply a view showing the arrangement of the armature inductors and connections looking from the front or commutator end, such as shown in fig. 254.
In the radial diagram the inductors of the armature are represented by short radial lines, while the end connectors are represented by curves or zigzags, those at one end of the armature being drawn within, those at the other end, without the circumference of the armature. With the radial diagram it is easier to follow the circuits and to distinguish the back and front pitch of the winding.
Fig. 255.—Partial sketch of a four pole machine laid on its side. If the observer imagine himself placed at the center, and the panorama of the four poles to be then laid out flat, the developed view thus obtained would appear as in fig. 256.
The developed diagram is a mode of representation, originally suggested by Fritsche of Berlin, in which the armature winding is considered as though the entire structure had been developed out of a flat surface. This is best explained by aid of figs. 255 and 256.
If in fig. 255, which represents an armature core and a four pole field, wires a and c be placed parallel to the axis of the armature to represent two of the armature inductors, and moved along the air gap space clockwise past the S poles, they will cut magnetic lines inducing electromotive forces in the directions indicated. To attempt to show a large number of inductors in a drawing of this kind would be unintelligible. Accordingly, the observer is considered as being placed at the center of the armature, and the panorama of the four poles surrounding him to be then laid out flat or "developed" as in fig. 256.
The faces of the N and S poles are shaded obliquely for distinction. By choosing the proper directions for these oblique lines, a piece of paper having a narrow slit to represent the wire may be laid over the drawing of the pole and when moved, as indicated by the dotted arrows to the right, the slit in passing over the oblique lines will cause an apparent motion in the direction in which the current in reality tends to flow. It is easily remembered which way the oblique lines must slope, for those on the N pole slope parallel to the oblique part of the letter N.
Lap Winding and Wave Winding.—In winding armatures there are two distinct methods employed, known respectively as lap and wave winding. The distinction arises in the following manner: Since the inductors, in passing a north pole generate electromotive forces in one direction, and in passing a south pole generate electromotive forces in the opposite direction, it is evident that an inductor in one of these groups ought to be connected to one in nearly a corresponding position in the other group, so that the current may flow down one and up the other in agreement with the directions of the electromotive forces. The order followed in making these connections gives rise to lap and wave windings.
Fig. 256.—Developed view of the four pole field shown in perspective in fig. 255.
Ques. What is lap winding?
Ans. One in which the ends of the coils come back to adjacent segments of the commutator; the coils of such a winding lap over each other.
Ques. What is a wave winding?
Ans. One in which the coil ends diverge and go to segments widely separated, the winding to a certain extent resembling a wave.
Fig. 257.—Development of ring winding of four pole machine shown in fig. 254. The dead wire or inactive inductors on the inside of the ring are shown in dotted lines, the full lines representing the active portion of the winding.
Angular Pitch or Spread of Drum Coils.—Before taking up the winding as a whole, the form of the individual coil should be considered. Fig. 260 shows an end view of one coil in position on a drum armature of a multipolar machine. The two slots X and Y contain the sides of the coil and the distance between them on the surface of the drum is called the angular pitch or spread of the coil. Theoretically this is equal to the pitch of the poles, represented by the angle M, which is the angle between the pole centres.
Figs. 258 and 259.—Wooden armature core and winding table for practice in armature winding. By using strings of different colors to represent the various coils, the path of each coil is easily traced when the winding is completed, as in fig. 263.
For instance, on a four pole machine the pitch would be 90°, on a six pole machine, 60°, etc. Usually the angular pitch of the coil is made just a little less than the pole pitch of the machine, in order to shorten the end connections of the coils from slot to slot. However, if the angular pitch be made too small trouble will be encountered in commutation.
In addition to the angular pitch there is the commutator pitch which relates to the distance around the commutator bridged by the ends of the coil. Thus, if the commutator segments were numbered consecutively 1, 2, 3, etc., and the commutator pitch say is 10, it would signify that one end of the coil was connected to segment 1 and the other end to segment 11; the ends of the next coil in order then would be connected to segments 2 and 12, in each case there would be ten segments between the two segments connecting with the coil ends.
Fig. 260.—End view of drum armature of a multipolar machine showing one coil in position to illustrate the angular pitch or spread of drum coils.
Parallel or Lap Drum Winding.—In order to avoid much of the difficulty usually experienced by students of drum winding, the beginner should construct for himself a wooden armature core upon which he can wind strings of various colors, or wires with distinctive insulation, to represent the numerous coils that are used on real armatures. A few windings attempted in this way will make clear many points that cannot be so easily grasped from a written description.
The type of drum core best adapted for this work is the slotted variety as shown in fig. 258, as it will facilitate the winding. The core as shown in the illustration has twelve slots and six commutator segments, the number of each required for the example of lap winding indicated in the winding table fig. 259.
In making the wooden core, the slots may be formed by nailing a series of thin strips around a cylindrical piece of wood, thus avoiding the trouble of cutting grooves. In the illustrations the commutator segments are shortened (leaving no room for brushes) in order to show the connections as clearly as possible.
Fig. 261.—Developed view of a typical lap winding. From the figure it is seen that at the back of the armature each inductor is united to one five places further on, that is, 1 to 6, 3 to 8, etc., and at the front end of the winding, after having made one "element," as for example d-7-12-e, then forms a second element e-9-14-f which "laps" over the first, and so on all around until the winding returns on itself.
Ques. Describe the simple lap winding fig. 259.
Ans. As given in the table, it consists of six loops of wire presenting twelve inductors on the cylindrical surface of the core or drum. In the table, six wires are shown, having distinctive and varied insulation so as to readily distinguish the different coils. Opposite these are letters and figures designating the path and connections of each coil.
Ques. What is the path of the first coil?
Ans. According to the table it is:
A — 1 — 6 — B
that is, one end of the wire is connected to commutator segment A (fig. 262) and then wound to the back of the drum through slot 1, across the back of the drum to slot 6, returning through this slot, and then connected with commutator segment B.
Fig. 262.—Skeleton view of wooden armature core showing in position the first two coils of the winding indicated in the table fig. 259.
Ques. Describe the path of the second coil.
Ans. The second coil, having the block insulation, is wound according to the table, in the order:
B — 3 — 8 — C
that is, beginning at segment B, thence to back of drum through slot 3, across the back to slot 8, returning through this slot and ending at segment C.
The completed winding of the first two coils are shown in fig. 262, the drum being shown in dotted lines so that all of each coil may be visible.
Fig. 263.—View of completed winding as indicated in the table fig. 259. Thus the path of the first coil, according to the table is A-1-6-B which means that the coil begins at segment A of the commutator, rises to slot 1, and proceeds through the slot to the back of the drum; thence across the back to slot 6, through the slot and ending at segment B. The other coils are wound in similar order as indicated in the table.
Ques. How are the remaining coils wound on the drum?
Ans. Each of the succeeding coils are wound as indicated in the table, the last connection being made to segment A, the one from which the winding started.
Ques. What is the general form of the completed winding?
Ans. It may be considered simply as a wire wound spirally around the drum, with loops brought down to the commutator segments, and ending at the segment from which the start was made.
The completed winding as indicated by the table is shown in fig. 263. Here the path of each coil is easily distinguished by means of the varied insulations although in part hidden by the drum. Fig. 264 shows a developed view of the winding.
Fig. 264.—Developed view of the winding shown in perspective in fig. 263.
Ques. What condition must obtain in winding an even number of coils?
Ans. The wire must not be wound around the drum to diametrically opposite positions, as for instance 1 to 7 in fig. 265.
Ques. Why is this?
Ans. The reason will be clearly seen by attempting the winding on the wooden core. A winding of this kind on the drum fig. 258, would proceed as follows:
A | — | 1 | — | 7 | — | B |
B | — | 3 | — | 9 | — | C |
C | — | 5 | — | 11 | — | D |
In order now to continue winding in a regular way, the wire from segment d should pass to the rear of the armature along space 7, but this space is already occupied by the return of the first coil. Continuing the winding from this point, it would be necessary to carry the wire from segment d to 6 or 8, resulting in an unbalanced winding.
Fig. 265.—Lap winding for bipolar machine, with uneven number of coils; in this case the rear connectors may be made directly across a diameter as shown.
Ques. How is a symmetrical winding obtained having an even number of coils?
Ans. The inductors, in passing from the front to the rear of the armature, fig. 263, must occupy positions 1, 3, 5, 7, 9, 11, and the even numbered positions will then serve as the returns for these wires.
In the example here shown there are six coils, comprising twelve inductors and six commutator segments; it should be noted, however, that if there were an uneven number of coils, the rear connections could be made directly across a diameter as shown in fig. 265, which would give a symmetrical winding.
With ten slots as shown in the figure, the drum would be wound, for a bipolar machine, according to the following table:
A | — | 1 | — | 6 | — | B |
B | — | 3 | — | 8 | — | C |
C | — | 5 | — | 10 | — | D |
D | — | 7 | — | 2 | — | E |
E | — | 9 | — | 4 | — | F |
Fig. 266.—Developed view of a typical wave winding. This winding, instead of lapping back toward the commutator segment from whence it came, as in lap winding, turns the other way. For instance, d-7-12 does not return directly to e, but goes on to i, whence another element i-17-4-e continues in a sort of zigzag wave.
Ques. Are coils such as shown in figs. 263 and 265 used in practice?
Ans. No, for practical use each coil would consist of several turns, the diagram then merely indicates the end connections and slots for the several turns of each coil.
Series or Wave Drum Winding.—In this mode of winding, the inductors are arranged around the armature so that they do not turn back, thus describing a zigzag or wave-like path; that is, the coil ends instead of connecting with adjacent segments of the commutator, are attached to segments more or less remote.
Ques. Describe the circuits of a simple or simplex wave winding.
Ans. Only two sets of brushes are required for such a winding, but as many brushes as there are poles can be used.
Fig. 267.—Five coil wave winding for a four pole machine. In this winding only two brushes are used, there being only two paths through the armature.
Ques. For what service are wave windings adapted?
Ans. They are generally used on armatures designed to furnish a current of high voltage and low amperage.
An example of wave drum winding for a four pole machine is shown in fig. 267. For simplicity, very few coils are taken, there being only five as shown in the illustration. To make the winding, one strip should be removed from the wooden core and the others spaced equally around the cylindrical surface. This will give ten slots, the number required for the five coils. The winding is indicated in the following table:
A | — | 1 | — | 4 | — | C |
B | — | 3 | — | 6 | — | D |
C | — | 5 | — | 8 | — | E |
D | — | 7 | — | 10 | — | A |
E | — | 9 | — | 2 | — | B |
Accordingly the first coil starting at segment A, is carried to the back of the drum through slot 1, thence across the back and returning through slot 4, ending at segment C the starting point of the second coil. Each coil is wound on in similar manner, the last coil ending at segment A, the starting point of the first coil. A developed view of the winding is shown in fig. 268.
Double Windings.—In the various drum windings thus far considered, each coil had its individual slots, that is, no two occupied the same two slots. This arrangement gave twice the number of slots as commutator segments.
Fig. 268.—Developed view of the five coil wave winding shown in fig. 267.
In a double winding there are as many segments as slots, each of the latter containing two inductors, comprising part of two coils.
The Siemens Winding.—In winding drum armatures for bipolar dynamos of two horse power or less, and especially for very small machines as used in fan or sewing machine motors, a form of winding, known as the Siemens winding, which is shown in fig. 271, is largely used. It consists in dividing the surface of the armature core in one equal number of slots, say 16, and using a 16 part commutator.
In the Siemens winding, the end of the wire used at the start is to be connected to the first commutator bar, but must be fastened to the armature core out of the way so as not to interfere with the winding of the coils.
If eight turns of wire be required to fill a slot with one layer, then the wire is carried from front to back and bent aside so as to clear the shaft; after passing across the back or pulley end of the armature, it is wound in the diametrically opposite section and brought to the front, then across the commutator end and up close to the beginning of the coil.
Fig. 269.—Series connected wave wound ring armature for a four pole machine. The coils are so connected that only two brushes are necessary.
Since eight turns are to be used, the process of winding is continued until the section is full and the end of the coil will lie in a position ready to begin the next section. Sometimes the wire is cut at this part of the coil leaving 3 or 4 inches projecting for connecting to the commutator bar 2, or next to the first bar where the winding was started.
The usual practice is, however, to make a loop of the wire of sufficient length to make the connection to the commutator and it has the advantage that since all of the coils on the armature are joined in series, the ending of one coil is joined to the beginning of the next which avoids making mistakes in making the commutator connections.
If the ends be cut they should be marked "beginning" and "end" to avoid trouble, because if they get mixed, it will be necessary to test each coil with a battery and compass needle in order to determine the polarity produced and find which is the beginning of the coil and which the end. With 32 ends of the wire projecting from the end of the armature, it is confusing and mistakes are often made in the connections, so that one or more coils may oppose each other which would reduce the voltage.
After the surface of the armature is covered with one layer it will be noticed that the number of leads from the coils to the commutator bars is only one-half the number of bars and that they lie on one-half of the armature.
In order to complete the winding the first layer should be insulated and the second layer wound on. The beginning of the new coil will be directly over the first coil put on, but the beginning of the new coil will be diametrically opposite the beginning of the first coil wound.
The winding is now continued section by section and as each coil is finished a loop or pair of leads is left to connect to each bar. When the last coil is wound, its end will be found lying next to the wire used in starting and should be joined to it and finally connected to bar number one where the start was made.
Fig. 270.—Developed view of the series connected wave wound ring armature shown in fig. 269.
With the winding and commutator connected, all of the coils are in series and the beginning of the first coil joins the end of the last coil.
If a pair of brushes be now placed on the commutator at opposite points the current will flow into the bar and then divide between the two leads connected to it, half of the current flowing around one side and the other half flowing around the other half of the armature or in other words, the two halves of the armature are joined in parallel.
Ques. What is the objection to the Siemens winding just described?
Ans. It produces an unsightly head where the wires pass around the shaft and requires considerable skill to make it appear workmanlike.
Ques. How may this be avoided?
Ans. By using the chord windings of Froehlich or Breguet, which are improvements over the Siemens in appearance and are more easily carried out.
Fig. 271.—End view of an armature, showing the distinction between Siemens' winding and chord winding.
Chord Winding.—In cases where the front and back pitches2 are so taken that the average pitch differs considerably from the value obtained by dividing the number of inductors by the number of poles, the arrangement is called a chord winding.
In this method each coil is laid on the drum so as to cover an arc of the armature surface nearly equal to the angular pitch of the poles; it is sometimes called short pitch winding.
Ques. What is the difference between the Siemens winding and the chord winding?
Ans. This is illustrated in fig. 271, which shows one end of an armature. In the Siemens winding, a wire starting, say at A, crosses the head and enters the slot marked B. If it enters slot C it is a chord winding.
Ques. Describe a chord winding.
Ans. The winding is started in the same manner as described in the Siemens method, only instead of crossing the head and returning in the section diametrically opposite, the section A C, fig. 271, next to it is used for the return of the wire to the front end. Leads for connecting to the commutator are left at the beginning and end of each section as before stated and the only difference between the two methods will be noticed when the first layer is nearly complete in that two sections lying next to each other have no wire in them. This will cause the winder to think he has made a mistake, but by continuing the winding and filling in these blank spaces in regular order when the two layers are completed, all the sections will be filled with an equal number of turns and there will be the required number of leads from the coils to connect up to the commutator bars.
Ques. How many paths in the chord winding just described?
Ans. Two.
Multiplex Windings.—An armature may be wound with two or more independent sets of coils. Instead of independent commutators for the several windings, they are combined into one having two or more sets of segments interplaced around the circumference. Thus, in the case of two windings, the brush comes in contact alternately with segments of each set. The brush then must be large enough to overlap at least two segments, so as to collect current from both windings simultaneously. Both windings then are always in the circuit in parallel.
Ques. What is the effect of a multiplex winding?
Ans. It reduces the tendency to sparking, because only half of the current is commutated at a time, and also because adjacent commutator bars belong to different windings.
Fig. 272.—A progressive wave winding. If the front and back pitches of a wave winding be such that in tracing the course of the winding through as many coils as there are pairs of poles, a segment is reached in advance of the one from which the start was made, the winding is said to be progressive. The figure shows three coils of a winding having 18 inductors. From the definition, the number of coils to consider to determine if the winding be progressive is equal to the number of poles divided by 2, which in this case is equal to 2. These coils are shown in the figure as follows: A—1—4—F and F—11—14—B. The second coil ends at segment B which is in advance of segment A from which the winding began, indicating that the winding is progressive. Fig. 272 is given simply to illustrate the definition of a progressive winding, and not to represent a practical winding.
Ques. Does an accident to one winding disable the machine?
Ans. No, it simply reduces its current capacity.
Ques. Can multiplex windings have more than two windings?
Ans. Yes, there may be three or four windings.
Ques. What is the objection to increasing the number of windings?
Ans. It involves an increased number of inductors and commutator segments, which is undesirable in small machines, but for large ones might be allowable.
Fig. 273.—A retrogressive wave winding. If the pitches be such that in tracing the winding through as many coils as there are pairs of poles, the first segment of the commutator is not encountered or passed over, the winding is said to be retrogressive. The number of coils to consider is two, as follows: A-1-4-D and D-7-10-G. The second coil ends at G, hence, since the segment A where the start was made has not been reached or passed over the winding is retrogressive. Fig. 273 is given simply to illustrate the definition of retrogressive winding, and not to represent a practical winding.
When there are two independent windings the arrangement is called duplex, with three windings, triplex, and with four, quadruplex.
Ques. What loss is reduced with multiplex windings?
Ans. In these windings, the division of what otherwise would be very stout inductors into several smaller ones, has the effect of reducing eddy current loss.
Ques. For what service are machines with multiplex windings specially adapted?
Ans. Multiplex windings are used in machines intended to supply large currents at low voltages, such as is required in electrolytic work.
Number of Brushes Required.—The number of places on the commutator at which it is necessary or advisable to place a set of collecting brushes can be ascertained from the winding diagrams. All that is necessary is to draw arrows marking the directions of the induced electromotive forces. Wherever two arrow heads meet at any segment of the commutator, a positive brush is to be placed, and at every point from which two arrows start in opposed directions along the winding, a negative brush should be placed.
Ques. How many brushes are required for lap windings and ordinary parallel ring windings?
Ans. There will be as many brushes as poles, and they will be situated symmetrically around the commutator in regular order and at angular distances apart equal to the pole pitch.
It should be noted that the number of brush sets does not necessarily show the number of circuits through the armature.
Ques. How many brushes are required for wave windings?
Ans. If arrows be drawn marking the direction of the induced electromotive forces to determine the number of brushes, it will be found that only two brushes are required for any number of poles.
Ques. What is the angle between these two brushes?
Ans. It is the same as the angle between any north and south pole.
For instance, in a ten pole machine with wave winding the pitch between the brushes may be any of the following angles:
360 / 10 | = | 36° |
3 * 36° | = | 108° |
5 * 36° | = | 180° |
Figs. 274 and 275.—Right and left hand windings. These consist respectively of turns which pass around the core in a right or left handed fashion. Thus in fig. 274, in passing around the circle clockwise from a to b, the path of the winding is a right handed spiral. In fig. 275, which shows one coil of a drum armature, if a be taken as the starting point, in going to b, a must be connected by a spiral connector across the front end of the drum to one of the descending inductors such as M, from which at the back end another connector must join it to one of the ascending inductors, such as S, where it is led to b, thus making one right handed turn.
Sometimes with lap winding it is desirable to reduce the number of brushes. In fig. 276, is shown the distribution of currents in a four pole lap wound machine having four brushes and generating 120 amperes. In each of the four circuits the flow is 30 amperes, and the current delivered to each brush is 60 amperes. If now two of the brushes be removed, the current through each of the remaining two will be 120 amperes, while internally there will be only two circuits as shown in fig. 277. It should be noted, however, that these two circuits do not take equal shares of the current since, though the sum of the electromotive forces in each circuit is the same, the resistance of one is three times that of the other, giving 90 amperes in one and 30 amperes in the other, as indicated in the figure. If no spark difficulties occur in collecting all the current with only two brushes, the arrangement will work satisfactorily, but the heat losses will be greater than with four brushes.
Fig. 276.—Distribution of armature currents in a four pole lap wound dynamo having four brushes and generating 120 amperes.
Ques. Are more than two brushes ever used with wave winding?
Ans. It is sometimes advisable to use more than two brushes with wave windings, especially when the current is very large.
For instance, in the case of a singly re-entrant3 simplex wave winding for an eight pole machine, whenever any brush bridges adjacent bars of the commutator, it short circuits one round of the wave winding and this round is connected at three intermediate points to other bars of the commutator. Hence, if the short circuiting brush be a positive brush, no harm will be done by three other positive brushes touching at the other points. If these other brushes be broad enough to bridge across two commutator bars, they may effect commutation, that is, three rounds instead of one undergoing commutation together.
Number of Armature Circuits.—It is possible to have windings that give any desired even number of circuits in machines having any number of poles.
Fig. 277.—Showing effect of removing two of the brushes in fig. 275. If no spark difficulties occur in collecting the current with only two brushes, the arrangement will work satisfactorily, but the heat losses will be greater than with four brushes.
Ques. How many paths are possible in parallel?
Ans. For a simplex spirally wound ring, the number of paths in parallel is equal to the number of poles, and for a simplex series wound ring, there will be two paths. In the case of multiplex windings the number of paths is equal to that of the simplex winding multiplied by the number of independent windings.
In large multipolar dynamos it is, as a rule, inadvisable to have more than 100 or 150 amperes in any one circuit, except in the case of special machines for electro-chemical work. Such considerations are factors which govern the choice of number of circuits.
Equalizer Rings.—These are rings resembling a series of hoops provided in a parallel wound armature to eliminate the effects of "unbalancing," by which the current divides unequally among the several paths through the armature. By means of leads, equalizer rings connect points of equal potential in the winding and so preserve an equalization of current.
Fig. 278.—Rear view of armature of a large dynamo built by the General Electric Co., showing equalizer rings.
Ques. In multipolar machines what points are connected by equalizer rings?
Ans. Any two or more points in the winding, that during the rotation, are at nearly equal potentials.
If there were perfect symmetry in the field system, no currents would flow along such connectors; however, owing to imperfect symmetry, the induction in the various sections of the winding may be unequal and the currents not equally distributed.
Drum Winding Requirements.—There are several conditions that must be satisfied by a closed coil drum winding:
1. There cannot be an odd number of inductors;
An odd number of inductors would be equivalent to not having a whole number of coils. The even numbered inductors may be regarded as the returns for the odd numbered inductors.
2. Both the front and back pitches must be odd in simplex windings.
3. The average pitch should be approximately equal to the number of inductors divided by the number of poles.
This condition must obtain in order that the electric pressures induced in inductors moving simultaneously under poles of opposite sign, will be added. The smallest pitch meeting this condition would stretch completely across a pole face, while the largest would stretch from the given pole tip to the next pole tip of like polarity.
The choice of front and back pitch for a given number of inductors should, with lap and wave windings in general, comply with the following conditions:
1. All the coils composing the winding must be similar, both mechanically and electrically, and must be arranged symmetrically upon the armature.
2. Each inductor of a simplex winding must be encountered once only, and the winding must be re-entrant.
3. Each simplex winding composing a multiplex winding must fulfill the requirement for a simplex winding.
4. A singly re-entrant multiplex winding must as a whole satisfy the requirement for a simplex winding.
In addition to the above requirements for lap and wave windings in general, lap windings must comply with the following conditions:
1. The front and back pitches must be opposite in sign;
2. The front and back pitches must be unequal;
If they be equal, the coil would be short circuited upon itself.
3. The front and back pitches must differ by two;
4. In multiplex windings, the front and back pitches must differ by two multiplied by the number of independent simplex windings composing the multiplex winding;
5. The number of slots on a slotted armature may be even or odd;
6. The number of inductors must be an even number; it may be a multiple of the number of slots;
In the case of wave windings the several conditions to be fulfilled may be stated as follows:
1. The front and back pitches must be alike in sign;
2. The front and back pitches may be equal or they may differ by any multiple of two.
They are usually made nearly equal to the number of inductors divided by the number of poles.