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D.C.D.C.D.C.D.C.D.C.
GENERAGENERAGENERATORSGENERAGENERATORSTORSTORSTORS
C H A P T E R
LearLearLearLearLearning Objectivning Objectivning Objectivning Objectivning Objectiveseseseses
➣➣ ➣➣➣ Generator Principal ➣➣ ➣➣➣ Simple Loop Generator ➣➣ ➣➣➣^ Practical Generator ➣➣ ➣➣➣^ Yoke ➣➣ ➣➣➣ Pole Cores and Pole Shoes ➣➣ ➣➣➣^ Pole Coils ➣➣ ➣➣➣^ Armature Core ➣➣ ➣➣➣ Armature Windings ➣➣ ➣➣➣^ Bushes and Bearings ➣➣ ➣➣➣^ Pole-pitch ➣➣ ➣➣➣ Conductor-Coil and Winding Element ➣➣ ➣➣➣^ Coil-span or Coil-pitch ➣➣ ➣➣➣ Pitch of a Winding ➣➣ ➣➣➣^ Back Pitch ➣➣ ➣➣➣^ Front Pitch ➣➣ ➣➣➣ Resultant Pitch ➣➣ ➣➣➣^ Commutator Pitch ➣➣ ➣➣➣^ Single-layer Winding ➣➣ ➣➣➣ Two-layer Winding ➣➣ ➣➣➣^ Degree of Re-entrancy of an Armature Winding ➣➣ ➣➣➣ Multiplex Winding ➣➣ ➣➣➣^ Lap and Wave Winding ➣➣ ➣➣➣^ Simplex-lap Winding ➣➣ ➣➣➣ Numbering of Coils and Commutator Segments ➣➣ ➣➣➣^ Simplex Wave Winding ➣➣ ➣➣➣ Dummy or Idle Coils ➣➣ ➣➣➣^ Uses of Lap and Wave Windings ➣➣ ➣➣➣ Types of Generators ➣➣ ➣➣➣^ Brush Contact Drop ➣➣ ➣➣➣^ Generated E.M.F. or E.M.F. Equation of a Generator ➣➣ ➣➣➣^ Iron Loss in Armature ➣➣ ➣➣➣^ Total loss in a D.C. Generator ➣➣ ➣➣➣^ Stray Losses ➣➣ ➣➣➣^ Constant or Standing Losses ➣➣ ➣➣➣^ Power Stages ➣➣ ➣➣➣^ Condition for Maximum Efficiency
Generator converts mechanical energy into electrical energy using electromagnetic induction
Ç
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26.1. Generator Principle26.1. Generator Principle26.1. Generator Principle 26.1. Generator Principle26.1. Generator Principle
An electrical generator is a machine which converts mechanical energy (or power) into electrical energy (or power).
The energy conversion is based on the principle of the production of dynamically (or motionally) induced e.m.f. As seen from Fig. 26.1, whenever a conductor cuts magnetic flux, dynamically induced e.m.f. is produced in it according to Faraday’s Laws of Electromagnetic Induction. This e.m.f. causes a current to flow if the con- ductor circuit is closed.
Hence, two basic essential parts of an electrical generator are ( i ) a magnetic field and ( ii ) a conductor or conductors which can so move as to cut the flux.
26.2. Simple Loop Generator26.2. Simple Loop Generator26.2. Simple Loop Generator 26.2. Simple Loop Generator26.2. Simple Loop Generator
ConstructionConstructionConstructionConstructionConstruction
In Fig. 26.1 is shown a single-turn rectangular copper coil ABCD rotating about its own axis in a magnetic field provided by either permanent magnet is or electromagnets. The two ends of the coil
Fig. 26.
are joined to two slip-rings ‘ a ’ and ‘ b ’ which are insulated from each other and from the central shaft. Two collecting brushes (of carbon or copper) press against the slip-rings. Their function is to collect the current induced in the coil and to convey it to the external load resistance R. The rotating coil may be called ‘armature’ and the magnets as ‘field magnets’.
WWWor WWororororkingkingkingkingking
Imagine the coil to be rotating in clock-wise direction (Fig. 26.2). As the coil assumes successive positions in the field, the flux linked with it changes. Hence, an e.m.f. is induced in it which is
Cut-away view of dc generator
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As before, the coil ends are joined to these segments on which rest the carbon or copper brushes. It is seen [Fig. 26.6 ( a )] that in the first half revolution current flows along (ABMNLCD) i.e. the brush No. 1 in contact with segment ‘ a ’ acts as the positive end of the supply and ‘ b ’ as the negative end. In the next half revolution [Fig. 26.6 ( b )], the direction of the induced current in the coil has reversed. But at the same time, the positions of segments ‘ a ’ and ‘ b ’ have also reversed with the
Fig. 26.4 Fig. 26. result that brush No. 1 comes in touch with the segment which is positive i.e. segment ‘ b ’ in this case. Hence, current in the load resistance again flows from M to L. The waveform of the current through the external circuit is as shown in Fig. 26.7. This current is unidirectional but not continu- ous like pure direct current.
Fig. 26.6 Fig. 26. It should be noted that the position of brushes is so arranged that the change over of segments ‘ a ’ and ‘ b ’ from one brush to the other takes place when the plane of the rotating coil is at right angles to the plane of the lines of flux. It is so because in that position, the induced e.m.f. in the coil is zero. Another important point worth remembering is that even now the current induced in the coil sides is alternating as before. It is only due to the rectifying action of the split-rings (also called commutator) that it becomes unidirectional in the external circuit. Hence, it should be clearly under- stood that even in the armature of a d.c. generator, the induced voltage is alternating.
26.3.26.3. 26.3.26.3.26.3. Practical GeneratorPractical GeneratorPractical GeneratorPractical GeneratorPractical Generator
The simple loop generator has been considered in detail merely to bring out the basic principle
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underlying construction and working of an actual generator illustrated in Fig. 26.8 which consists of the following essential parts :
1. Magnetic Frame or Yoke 2. Pole-Cores and Pole-Shoes 3. Pole Coils or Field Coils 4. Armature Core 5. Armature Windings or Conductors 6. Commutator 7. Brushes and Bearings Of these, the yoke, the pole cores, the armature core and air gaps between the poles and the armature core or the magnetic circuit whereas the rest form the electrical circuit.
Fig. 26.
26.4.26.4.26.4.26.4.26.4. YYYYYokokokokokeeeee
The outer frame or yoke serves double purpose : ( i ) It provides mechanical support for the poles and acts as a protecting cover for the whole machine and
( ii ) It carries the magnetic flux produced by the poles.
In small generators where cheapness rather than weight is the main consideration, yokes are made of cast iron. But for large machines usually cast steel or rolled steel is employed. The modern process of form- ing the yoke consists of rolling a steel slab round a cy- lindrical mandrel and then welding it at the bottom. The feet and the terminal box etc. are welded to the frame afterwards. Such yokes possess sufficient mechanical strength and have high permeability.
26.5.26.5.26.5.26.5.26.5.^ PPPPPole Corole Corole Corole Corole Cores and Pes and Pes and Pes and Pes and Pole Shoesole Shoesole Shoesole Shoesole Shoes
The field magnets consist of pole cores and pole shoes. The pole shoes serve two purposes
Yoke
Shaft
Commutator
Lugs
Brushes
Field Poles Yoke
Field Winding Armature Conductors
Feet
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26.6.26.6. 26.6.26.6.26.6.^ Pole CoilsPole CoilsPole CoilsPole CoilsPole Coils
The field coils or pole coils, which consist of copper wire or strip, are former-wound for the correct dimension (Fig. 26.13). Then, the former is removed and wound coil is put into place over the core as shown in Fig. 26.14. When current is passed through these coils, they electromagnetise the poles which produce the necessary flux that is cut by revolving armature conductors.
26.7.26.7. 26.7.26.7.26.7. ArArArmaArArmamamamaturturturturture Core Core Core Core Coreeeee
It houses the armature conductors or coils and causes them to rotate and hence cut the magnetic flux of the field magnets. In addition to this, its most important function is to provide a path of very low reluctance to the flux through the armature from a N -pole to a S -pole. It is cylindrical or drum-shaped and is built up of usually circular sheet steel discs or laminations approximately 0.5 mm thick (Fig. 26.15). It is keyed to the shaft. The slots are either die-cut or punched on the outer periphery of the disc and the keyway is located on the inner diameter as shown. In small machines, the armature stampings are keyed directly to the shaft. Usually, these laminations are perforated for air ducts which permits axial flow of air through the armature for cooling purposes. Such ventilating channels are clearly visible in the lami- nations shown in Fig. 26.16 and Fig. 26.17.
Fig. 26.13 Fig. 26. Up to armature diameters of about one metre, the circular stampings are cut out in one piece as shown in Fig. 26.16. But above this size, these circles, especially of such thin sections, are difficult to handle because they tend to distort and become wavy when assembled together. Hence, the circu- lar laminations, instead of being cut out in one piece, are cut in a number of suitable sections or segments which form part of a complete ring (Fig. 26.17).
Fig. 26.15 Fig. 26.
Laminators
Key way
Air holes (^) Air holes
Slot Teeth Key way
Wire
Exciting coils
Laminated pole core
Laminated pole shoe
Frame
Slot
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A complete circular lamination is made up of four or six or even eight segmental laminations. Usually, two keyways are notched in each segment and are dove-tailed or wedge-shaped to make the laminations self-locking in position.
The purpose of using laminations is to reduce the loss due to eddy currents. Thinner the laminations, greater is the resistance offered to the induced e.m.f., smaller the current and hence lesser the I^2 R loss in the core.
26.8.26.8.26.8. Ar 26.8.26.8.ArArArmaArmamamamaturturturturtureeeee WWWWindingsWindingsindingsindingsindings
The armature windings are usually former-wound. These are first wound in the form of flat rectangular coils and are then pulled into their proper shape in a coil puller. Various conductors of the coils are insulated from each other. The conductors are placed in the armature slots which are lined with tough insulating material. This slot insulation is folded over above the armature conductors placed in the slot and is secured in place by special hard wooden or fibre wedges.
26.9.26.9.26.9. 26.9.26.9. CommutatorCommutatorCommutatorCommutatorCommutator
The function of the commutator is to facilitate collection of current from the armature conduc- tors. As shown in Art. 26.2, it rectified i.e. converts the alternating current induced in the armature conductors into unidirectional current in the external load circuit. It is of cylindrical structure and is built up of wedge-shaped segments of high-conductivity hard-drawn or drop forged copper. These
Fig. 26.18 Fig. 26.
segments are insulated from each other by thin layers of mica. The number of segments is equal to the number of armature coils. Each commutator segment is connected to the armature conductor by means of a copper lug or strip (or riser). To prevent them from flying out under the action of centrifu- gal forces, the segments have V -grooves, these grooves being insulated by conical micanite rings. A sectional view of commutator is shown in Fig. 26.18 whose general appearance when completed is shown in Fig. 26.19.
26.10.26.10.26.10. Brushes and Bearings 26.10.26.10.Brushes and BearingsBrushes and BearingsBrushes and BearingsBrushes and Bearings
The brushes whose function is to collect current from commutator, are usually made of carbon or
Fig. 26.
Segment
Micanite V-ring
Riser or lug
End ring
Cummutator hub
Shaft
Commutator lugs Insulated copper segments
End clamp
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26.14.26.14. 26.14.26.14.26.14. Coil andCoil andCoil andCoil and WCoil andWWWWinding Elementinding Elementinding Elementinding Elementinding Element
With reference to Fig. 26.21, the two conductors AB and CD along with their end connections constitute one coil of the armature winding. The coil may be single-turn coil (Fig. 26.21) or multi- turn coil (Fig. 26.22). A single-turn coil will have two conductors. But a multi-turn coil may have many conductors per coil side. In Fig. 26.22, for example, each coil side has 3 conductors. The
Fig. 26.
Fig. 26.21 Fig. 26.22 Fig. 26. group of wires or conductors constituting a coil side of a multi-turn coil is wrapped with a tape as a unit (Fig. 26.23) and is placed in the armature slot. It may be noted that since the beginning and the end of each coil must be connected to a commutator bar, there are as many commutator bars as coils for both the lap and wave windings (see Example 26.1). The side of a coil (1-turn or multiturn) is called a winding element. Obviously, the number of winding elements is twice the number of coils.
26.15.26.15. 26.15.26.15.26.15. Coil-span or Coil-pitch (YCoil-span or Coil-pitch (YCoil-span or Coil-pitch (YCoil-span or Coil-pitch (YCoil-span or Coil-pitch (Y SSSSS )))))
It is the distance, measured in terms of armature slots (or armature conductors) between two sides of a coil. It is, in fact, the periphery of the armature spanned by the two sides of the coil. If the pole span or coil pitch is equal to the pole pitch (as in the case of coil A in Fig. 26.24 where pole- pitch of 4 has been assumed), then winding is called full-pitched****. It means that coil span is 180 electrical degrees. In this case, the coil sides lie under opposite poles, hence the induced e.m.fs. in them are additive. Therefore, maximum e.m.f. is induced in the coil as a whole, it being the sum of the e.m.f.s induced in the two coil sides. For example, if there are 36 slots and 4 poles, then coil span is 36/4 = 9 slots. If number of slots is 35, then Y (^) S = 35/4 = 8 because it is customary to drop fractions. If the coil span is less than the pole pitch (as in coil B where coil pitch is 3/4th of the pole pitch), then the
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winding is fractional-pitched. In this case, there is a phase difference between the e.m.fs. in the two sides of the coil. Hence, the total e.m.f. round the coil which is the vector sum of e.m.fs. in the two coil sides, is less in this case as compared to that in the first case.
26.16.26.16.26.16.26.16.26.16. Pitch of aPitch of aPitch of aPitch of aPitch of a WWWWWinding (Y)inding (Y)inding (Y)inding (Y)inding (Y)
In general, it may be defined as the distance round the armature between two successive conduc- tors which are directly connected together. Or, it is the distance between the beginnings of two consecutive turns. Y = YB − YF ........for lap winding = YB + Y (^) F ........for wave winding In practice, coil-pitches as low as eight-tenths of a pole pitch are employed without much serious reduction in the e.m.f. Fractional-pitched windings are purposely used to effect substantial saving in the copper of the end connections and for improving commutation.
26.17.26.17.26.17.26.17.26.17. Back Pitch (YBack Pitch (YBack Pitch (YBack Pitch (YBack Pitch (Y BBBBB )))))
The distance, measured in terms of the armature conductors, which a coil advances on the back of the armature is called back pitch and is denoted by YB. As seen from Fig. 26.28, element 1 is connected on the back of the armature to element 8. Hence, YB = (8 − 1) = 7.
26.18.26.18.26.18.26.18.26.18. FrFrFrFrFront Pitch (Yont Pitch (Yont Pitch (Yont Pitch (Yont Pitch (Y FFFFF )))))
The number of armature conductors or elements spanned by a coil on the front (or commutator end of an armature) is called the front pitch and is designated by YF. Again in Fig. 26.28, element 8 is connected to element 3 on the front of the armature, the connections being made at the commutator segment. Hence, YF = 8 − 3 = 5. Alternatively, the front pitch may be defined as the distance (in terms of armature conductors) between the second conductor of one coil and the first conductor of the next coil which are connected together at the front i.e. commutator end of the armature. Both front and back pitches for lap and wave-winding are shown in Fig. 26.25 and 26.26.
Fig. 26.25 Fig. 26.26 Fig. 26.
26.19.26.19.26.19.26.19.26.19. Resultant Pitch (YResultant Pitch (YResultant Pitch (YResultant Pitch (YResultant Pitch (Y^ RRRRR)))))
It is the distance between the beginning of one coil and the beginning of the next coil to which it is connected (Fig. 26.25 and 26.26). As a matter of precaution, it should be kept in mind that all these pitches, though normally
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26.23.26.23.26.23. Degr 26.23.26.23.DegrDegrDegree of RDegree of Ree of Ree of Ree of Re-entrant of ane-entrant of ane-entrant of ane-entrant of ane-entrant of an ArArArArArmamamamamaturturturturetureeee WWWWWindingindingindingindinginding
A winding is said to be single re-entrant if on tracing through it once, all armature conductors are included on returning to the starting point. It is double re-entrant if only half the conductors are included in tracing through the winding once and so on.
26.24.26.24.26.24. Multiple 26.24.26.24.MultipleMultipleMultiplexMultiplexxxx WWWWWindingindingindingindinginding
In such windings, there are several sets of completely closed and independent windings. If there is only one set of closed winding, it is called simplex wave winding. If there are two such windings on the same armature, it is called duplex winding and so on. The multiplicity affects a number of parallel paths in the armature. For a given number of armature slots and coils, as the multiplicity increases, the number of parallel paths in the armature increases thereby increasing the current rating but decreasing the voltage rating.
26.25.26.25.26.25. La 26.25.26.25.LaLaLap andLap andp andp andp and WWWWavWavavavaveeeee WWWWindingsWindingsindingsindingsindings
Two types of windings mostly employed for drum-type armatures are known as Lap Winding and Wave Winding. The difference between the two is merely due to the different arrangement of the end connections at the front or commutator end of armature. Each winding can be arranged progressively or retrogressively and connected in simplex, duplex and triplex. The following rules, however, apply to both types of the windings :
Multiplex Winding
Wave winding Lap winding
( i ) The front pitch and back pitch are each approximately equal to the pole-pitch i.e. windings should be full-pitched. This results in increased e.m.f. round the coils. For special pur- poses, fractional-pitched windings are deliberately used (Art. 26.15). ( ii ) Both pitches should be odd, otherwise it would be difficult to place the coils (which are former-wound) properly on the armature. For exmaple, if YB and YF were both even, the all the coil sides and conductors would lie either in the upper half of the slots or in the lower
21 22 23 24 (^1 2 3 4 5 6 )
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half. Hence, it would become impossible for one side of the coil to lie in the upper half. Hence, it would become impossible for one side of the coil to lie in the upper half of one slot and the other side of the same coil to lie in the lower half of some other slot. ( iii ) The number of commutator segments is equal to the number of slots or coils (or half the number of conductors) because the front ends of conductors are joined to the segments in pairs. ( iv ) The winding must close upon itself i. e. if we start from a given point and move from one coil to another, then all conductors should be traversed and we should reach the same point again without a break or discontinuity in between.
26.26.26.26. 26.26.26.26.26.26. Simplex Lap-windingSimplex Lap-windingSimplex Lap-windingSimplex Lap-windingSimplex Lap-winding*
It is shown in Fig. 26.25 which employs single-turn coils. In lap winding, the finishing end of one coil is connected to a commutator segment and to the starting end of the adjacent coil situated under the same pole and so on, till and the coils have been connected. This type of winding derives its name from the fact it doubles or laps back with its succeeding coils. Following points regarding simplex lap winding should be carefully noted :
1. The back and front pitches are odd and of opposite sign. But they cannot be equal. They differ by 2 or some multiple thereof. 2. Both YB and YF should be nearly equal to a pole pitch. 3. The average pitch YA = 2
Y B +^ YF. It equals pole pitch = Z P .
4. Commutator pitch YC = ±1. (In general, YC = ± m ) 5. Resultant pitch YR is even, being the arithmetical difference of two odd numbers, i.e. , Y (^) R = YB − YF. 6. The number of slots for a 2-layer winding is equal to the number of coils ( i.e. half the number of coil sides). The number of commutator segments is also the same.
***** However, where heavy currents are necessary, duplex or triplex lap windings are used. The duplex lap winding is obtained by placing two similar windings on the same armature and connecting the even- numbered commutator bars to one winding and the odd-numbered ones to the second winding. Similarly, in triplex lap winding, there would be three windings, each connected to one third of the commutator bars.
Simplex lap winding
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21 to (21 + 9) = 30 → 30 to (20 − 7) = 23 23 to (23 + 9) = 32 → 32 to (32 − 7) = 25 25 to (25 + 9) = 34 = (34 − 32) = 2 → 2 to (34 − 7) = 27 27 to (27 + 9) = 36 = (36 − 32) = 4 → 4 to (36 − 7) = 29 29 to (29 + 9) = 38 = (38 − 32) = 6 → 6 to (38 − 7) = 31 31 to (31 + 9) = 40 = (40 − 32) = 8 → 8 to (40 − 7) = 33 = (33 − 32) = 1 The winding ends here because we come back to the conductor from where we started. We will now discuss the developed diagram which is one that is obtained by imagining the armature surface to be removed and then laid out flat so that the slots and conductors can be viewed without the necessity of turning round the armature in order to trace out the armature windings. Such a developed diagram is shown in Fig. 26.31.
Fig. 26. The procedure of developing the winding is this : Front end of the upper side of coil No. 1 is connected to a com- mutator segment (whose number is also 1). The back end is joined at the back to the 1 + 9 = 10th coil side in the lower half of 5th slot. The front end of coil side 10 is joined to commutator segment 2 to which is connected the front end of 10 − 7 = 3 i.e. 3rd coil side lying in the upper half of second armature slot. In this way, by travelling 9 coil sides to the right at the back and 7 to the left at the Fig. 26.
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front we complete the winding, thus including every coil side once till we reach the coil side 1 from where we started. Incidentally, it should be noted that all upper coil sides have been given odd numbers, whereas lower ones have been given even numbers as shown in the polar diagram (Fig. 26.32) of the winding of Fig. 26.31. Brush positions can be located by finding the direction of currents flowing in the various conduc- tors. If currents in the conductors under the influence of a N -pole are assumed to flow downwards (as shown), then these will flow upwards in conductors under the influence of S -pole. By putting proper arrows on the conductors (shown separately in the equivalent ring diagram), it is found that commu- tator bars No. 1 and 9 are the meeting points of e.m.fs. and hence currents are flowing out of these conductors. The positive brushes should, therefore, be placed at these commutator bars. Similarly, commutator bars No. 5 and 13 are the separating points of e.m.fs. hence negative brushes are placed there. In all, there are four brushes, two positive and two negative. If brushes of the same polarity are connected together, then all the armature conductors are divided into four parallel paths.
Fig. 26. Division of conductors into parallel paths is shown separately in the schematic diagram of Fig. 26.34. Obviously, if I (^) a is the total current supplied by the generator, then current carried by each parallel path is I (^) a /4. Summarizing these conclusions, we have
1. The total number of brushes is equal to the number of poles. 2. There are as many parallel paths in the armature as the number of poles. That is why such a winding is sometimes known as ‘multiple circuit’ or ‘parallel’ winding. In general, number of parallel paths in armature = mP where m is the multiplicity (plex) of the lap winding. For example, a 6-pole duplex lap winding has (6 × 2) = 12 parallel paths in its armature. 3. The e.m.f. between the +ve and −ve brushes is equal to the e.m.f. generated in any one of the parallel paths. If Z is the total number of armature conductors and P the number of poles, then the number of armature conductors (connected in series) in any parallel path is Z/P.
o
p
a b c d e f g
j i h
k
l
m
n
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Fig. 26.
As shown in Fig. 26.35, conductor AB is connected to CD lying under S -pole and then to EF under the next N -pole. In this way, the winding progresses, pass- ing successively under every N -pole and S -pole till it returns to a conductor A ′ B ′ lying under the original pole. Because the winding progresses in one direction round the armature in a series of ‘waves’, it is known as wave winding. If, after passing once round the ar- mature, the winding falls in a slot to the left of its starting point (as A ′ B ′ in Fig. 26.35) then the winding is said to be retrogressive. If, how- ever, it falls one slot to the right, then it is progressive.
Assuming a 2-layer winding and supposing that conductor AB lies in the upper half of the slot, then going once round the armature, the winding ends at A ′ B ′ which must be at the upper half of the slot at the left or right. Counting in terms of conductors , it means that AB and A ′ B ′ differ by two conductors (although they differ by one slot).
From the above, we can deduce the following relations. If P = No. of poles, then YB = back pitch YF = front pitch
then YA = 2
Y B +^ YF = average pitch ; Z = total No. of conductors or coil sides
Then, YA × P = Z ± 2 YA = Z 2 P
±
Since P is always even and Z = PYA ± 2, hence Z must always be even. Put in another way, it
means that Z 2 P
± must be an even integer.
The plus sign will give a progressive winding and the negative sign a retrogressive winding.
Points to Note :Points to Note :Points to Note :Points to Note :Points to Note :
1. Both pitches YB and YF are odd and of the same sign. 2. Back and front pitches are nearly equal to the pole pitch and may be equal or differ by 2, in which case, they are respectively one more or one less than the average pitch. 3. Resultant pitch YR = YF + YB. 4. Commutator pitch, YC = YA (in lap winding YC = ±1).
Also, YC = No. of Commutator bars 1 No. of pair of poles
±
5. The average pitch which must be an integer is given by
YA = 2 1 No. of Commutator bars 1 2 / 2 No. of pair of poles
Z Z P P
± + ± = =
It is clear that for YA to be an integer, there is a restriction on the value of Z. With Z = 32, this winding is impossible for a 4-pole machine (though lap winding is possible). Values of Z = 30 or 34 would be perfectly alright.
} nearly equal to pole pitch
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6. The number of coils i.e. NC can be found from the relation.
N (^) C =
2 2
PY A ±
This relation has been found by rearranging the relation given in (5) above.
7. It is obvious from (5) that for a wave winding, the number of armature conductors with 2 either added or subtracted must be a multiple of the number of poles of the generator. This restriction eliminates many even numbers which are unsuitable for this winding. 8. The number of armature parallel paths = 2 m where m is the multiplicity of the winding. Example 26.2. Draw a developed diagram of a simplex 2-layer wave-winding for a 4-pole d.c. generator with 30 armature conductors. Hence, point out the characteristics of a simple wave winding. (Elect. Engg-I, Nagpur Univ. 1991)
Solution. Here, YA =
30 2 4
± = 8 ***** or 7. Taking YA = 7, we have YB = YF = 7
Fig. 26. As shown in Fig. 26.36 and 26.37, conductor No. 5 is taken to conductor No. 5 + 7 = 12 at the back and is joined to commutator segment 5 at the front. Next, the conductor No. 12 is joined to commutator segment 5 + 7 = 12 ( (^) ∵ Y (^) C = 7) to which is joined conductor No. 12 + 7 = 19. Continuing this way, we come back to conductor No. 5 from where we started. Hence, the winding closes upon itself.
- If we take 8, then the pitches would be : Y (^) B = 9 and YF = 7 or Y (^) B = 7 and YF = 9. Incidentally, if Y (^) A = Y (^) C is taken as 7, armature will rotate in one direction and if Y (^) C = 8, it will rotate in the opposite direction.
