Electrical Machines

D.C. Motors

Introduction
D. C. motors are seldom used in ordinary applications because all electric supply companies furnish alternating current However, for special applications such as in steel mills, mines and electric trains, it is advantageous to convert alternating current into direct current in order to use d.c. motors. The reason is that speed/torque characteristics of d.c. motors are much more superior to that of a.c. motors. Therefore, it is not surprising to note that for industrial drives, d.c. motors are as popular as 3-phase induction motors. Like d.c. generators, d.c. motors are also of three types viz., series-wound, shunt-wound and compoundwound. The use of a particular motor depends upon the mechanical load it has to drive.
D.C. Motor Principle
A machine that converts d.c. power into mechanical power is known as a d.c. motor. Its operation is based on the principle that when a current carrying conductor is placed in a magnetic field, the conductor experiences a mechanical force. The direction of this force is given by Fleming’s left hand rule and magnitude is given by;
F = BIl newtons
Basically, there is no constructional difference between a d.c. motor and a d.c. generator. The same d.c. machine can be run as a generator or motor.
Working of D.C. Motor
Consider a part of a multipolar d.c. motor as shown in Fig. (4.1). When the terminals of the motor are connected to an external source of d.c. supply:
(i) the field magnets are excited developing alternate N and S poles;
(ii) the armature conductors carry ^currents. All conductors under N-pole carry currents in one direction while all the conductors under S-pole carry currents in the opposite direction.
Suppose the conductors under N-pole carry currents into the plane of the paper and those under S-pole carry currents out of the plane of the paper as shown in Fig.(4.1). Since each armature conductor is carrying current and is placed in the magnetic field, mechanical force acts on it. Referring to Fig. (4.1) and applying Fleming’s left hand rule, it is clear that force on each conductor is tending to rotate the armature in anticlockwise direction. All these forces add together to produce a driving torque which sets the armature rotating. When the conductor moves from one side of a brush to the other, the current in that conductor is reversed and at the same time it comes under the influence of next pole which is of opposite polarity. Consequently, the direction of force on the conductor remains the same.
DC motor 

Types of D.C. Motors

Like generators, there are three types of d.c. motors characterized by the connections of field winding in relation to the armature viz.:
(i) Shunt-wound motor in which the field winding is connected in parallel with the armature [See Fig. 4.4]. The current through the shunt field winding is not the same as the armature current. Shunt field windings are designed to produce the necessary m.m.f. by means of a relatively large number of turns of wire having high resistance. Therefore, shunt field current is relatively small compared with the armature current.
shunt wound motor
(ii) Series-wound motor in which the field winding is connected in series with the armature [See Fig. 4.5]. Therefore, series field winding carries the armature current. Since the current passing through a series field winding is the same as the armature current, series field windings must be designed with much fewer turns than shunt field windings for the same m.m.f. Therefore, a series field winding has a relatively small number of turns of thick wire and, therefore, will possess a low resistance.
(iii) Compound-wound motor which has two field windings; one connected in parallel with the armature and the other in series with it. There are two types of compound motor connections (like generators). When the shunt field winding is directly connected across the armature terminals [See Fig. 4.6], it is called short-shunt connection. When the shunt winding is so connected that it shunts the series combination of armature and series field [See Fig. 4.7], it is called long-shunt connection
series wound motor
The compound machines (generators or motors) are always designed so that the flux produced by shunt field winding is considerably larger than the flux produced by the series field winding. Therefore, shunt field in compound machines is the basic dominant factor in the production of the magnetic field in the machine.


Losses in a D.C. Motor

The losses occurring in a d.c. motor are the same as in a d.c. generator  (i) copper losses (ii) Iron losses or magnetic losses (iii) mechanical losses As in a generator, these losses cause (a) an increase of machine temperature and (b) reduction in the efficiency of the d.c. motor.
The following points may be noted:
(i) Apart from armature Cu loss, field Cu loss and brush contact loss, Cu losses also occur in interpoles (commutating poles) and compensating windings. Since these windings carry armature current (Ia),
Loss in interpole winding = Ia 2× Resistance of interpole winding
Loss in compensating winding = Ia 2× Resistance of compensating winding
(ii) Since d.c. machines (generators or motors) are generally operated at constant flux density and constant speed, the iron losses are nearly constant.
(iii) The mechanical losses (i.e. friction and windage) vary as the cube of the speed of rotation of the d.c. machine (generator or motor). Since d.c. machines are generally operated at constant speed, mechanical losses are
considered to be constant.

Commutation in D.C. Motors

Since the armature of a motor is the same as that of a generator, the current from the supply line must divide and pass through the paths of the armature windings.
In order to produce unidirectional force (or torque) on the armature conductors of a motor, the conductors under any pole must carry the current in the same direction at all times. This is illustrated in Fig. (4.10). In this case, the current flows away from the observer in the conductors under the N-pole and towards the observer in the conductors under the S-pole. Therefore, when a conductor moves from the influence of N-pole to that of S-pole, the direction of current in the conductor must be reversed. This is termed as commutation. The function of the commutator and the brush gear in a d.c. motor is to cause the reversal of current in a conductor as it moves from one side of a brush to the other. For good commutation, the following points may be noted:
(i) If a motor does not have commutating poles (compoles), the brushes
must be given a negative lead i.e., they must be shifted from G.N.A.
against the direction of rotation of, the motor.
(ii) By using interpoles, a d.c. motor can be operated with fixed brush
positions for all conditions of load. For a d.c. motor, the commutating
poles must have the same polarity as the main poles directly back of
them. This is the opposite of the corresponding relation in a d.c.
generator.
Note. A d.c. machine may be used as a motor or a generator without changing the commutating poles connections. When the operation of a d.c. machine changes from generator to motor, the direction of the armature current reverses. Since commutating poles winding carries armature current, the polarity of commutating pole reverses automatically to the correct polarity.





commutation in dc motors

Armature Reaction in D.C. Motors

As in a d.c. generator, armature reaction also occurs in a d.c. motor. This is expected because when current flows through the armature conductors of a d.c. motor, it produces flux (armature flux) which lets on the flux produced by the main poles. For a motor with the same polarity and direction of rotation as is for generator, the direction of armature reaction field is reversed.
(i) In a generator, the armature current flows in the direction of the induced e.m.f. (i.e. generated e.m.f. Eg) whereas in a motor, the armature current flows against the induced e.m.f. (i.e. back e.m.f. Eg). Therefore, it should be expected that for the same direction of rotation and field polarity, the armature flux of the motor will be in the opposite direction to that of the generator. Hence instead of the main flux being distorted in the direction of rotation as in a generator, it is distorted opposite to the direction of rotation. We can conclude that:
Armature reaction in a d.c. generator weakens the jinx at leading pole tips and strengthens the flux at trailing pole tips while the armature reaction in a d. c. motor produces the opposite effect.
(ii) In case of a d.c. generator, with brushes along G.N.A. and no commutating poles used, the brushes must be shifted in the direction of rotation (forward lead) for satisfactory commutation. However, in case of a d.c. motor, the brushes are given a negative lead i.e., they are shifted against the direction of rotation.
With no commutating poles used, the brushes are given a forward lead in a d.c. generator and backward lead in a d.c. motor.
(iii) By using commutating poles (compoles), a d.c. machine can be operated with fixed brush positions for all conditions of load. Since commutating poles windings carry the armature current, then, when a machine changes from generator to motor (with consequent reversal of current), the polarities of commutating poles must be of opposite sign.
Therefore, in a d.c. motor, the commutating poles must have the same
polarity as the main poles directly back of them. This is the opposite of
the corresponding relation in a d.c. generator.

Torque and Speed of a D.C. Motor

For any motor, the torque and speed are very important factors. When the torque increases, the speed of a motor increases and vice-versa. We have seen that for a d.c. motor;
N = K (V- IaRa)/ Ф = K Eb/ Ф…………………………………………….(i)
Ta α ФIa…………………………………………………………………………(ii)
If the flux decreases, from Eq.(i), the motor speed increases but from Eq.(ii) the motor torque decreases. This is not possible because the increase in motor speed must be the result of increased torque. Indeed, it is so in this case. When the flux decreases slightly, the armature current increases to a large value. As a result, in spite of the weakened field, the torque is momentarily increased to a high value and will exceed considerably the value corresponding to the load. The surplus torque available causes the motor to accelerate and back e.m.f (Ea=PФZN/60A)to rise. Steady conditions of speed will ultimately be achieved when back e.m.f. has risen to such a value that armature current[Ia = (V- Ea)/ Ra]develops torque just sufficient to drive the load.
Illustration
Let us illustrate the above point with a numerical example. Suppose a 400 V
shunt motor is running at 600 r.p.m., taking an armature current of 50 A. The armature resistance is 0.28 Ω. Let us see the effect of sudden reduction of flux by 5% on the motor.
Initially (prior to weakening of field), we have,
Ea = V-IaRa= 400 – 50 × 0.28 = 386 volts
We know that Eb α Ф N. If the flux is reduced suddenly, Eb α Ф because inertia
of heavy armature prevents any rapid change in speed. It follows that when the flux is reduced by 5%, the generated e.m.f. must follow suit. Thus at the instant of reduction of flux, E’b = 0.95 × 386 = 366.7 volts.
Instantaneous armature current is
I’a=(V- E’b)/ Ra =(400-366.7)/0.28=118.9A
Note that a sudden reduction of 5% in the flux has caused the armature current to increase about 2.5 times the initial value. This will result in the production of high value of torque. However, soon the steady conditions will prevail. This will depend on the system inertia; the more rapidly the motor can alter the speed, the sooner the e.m.f. rises and the armature current falls.

Speed of a D.C. Motor

Eb = V-IaRa
But Eb=PФZN/60A
PФZN/60A  = V- IaRa
Or  N = (V- IaRa)/ Ф ×  60A/ PZ
Or N = K (V- IaRa)/ Ф
But         V- IaRa = Ea
Therefore N= K Eb/ Ф
Or N α Eb/ Ф
Therefore, in a d.c. motor, speed is directly proportional to back e.m.f. Eb and inversely proportional to flux per pole Ф.
Speed Relations
If a d.c. motor has initial values of speed, flux per pole and back e.m.f. as N11 and Eb1 respectively and the corresponding final values are N22 and Eb2 then,
N1 α Eb1/ Ф1 and N2 α Eb2/ Ф2
Therefore N2/ N1 = (Eb2/ Eb1) ×( Ф1 / Ф2)
(i) For a shunt motor, flux practically remains constant so that Ф1 = Ф2.
therefore  N2/ N1 = Eb2/ Eb1
(ii) For a series motor, Ф α Ia prior to saturation.
therefore N2/ N1 = (Eb2/ Eb1) × (Ia1/Ia2)
where Ia1 = initial armature current
Ia2 = final armature current
Speed Regulation
The speed regulation of a motor is the change in speed from full-load to no-load and is expressed as a percentage of the speed at full-load i.e.
% Speed regulation = [( N.L. speed - F.L.speed)/F.L.speed ] × 100
=[(No -N)/N] × 100
where No = No – load .speed
N = Full – load speed 

Shaft Torque (Tsh)

The torque which is available at the motor shaft for doing useful work is known as shaft torque. It is represented by Tsh. Fig. (4.9) illustrates the concept of shaft torque. The total or gross torque Ta developed in the armature of a motor is not available at the shaft because a part of it is lost in overcoming the iron and frictional losses in the motor. Therefore, shaft torque Tsh is somewhat less than the armature torque Ta. The difference Ta – Tsh is called lost torque.
shaft torque
Ta - Tsh =9.55 × iron and frictional losses/N
For example, if the iron and frictional losses in a motor are 1600 W and the
motor runs at 800 r.p.m., then,
Ta - Tsh =9.55 × 1600 /800 =19.1 N-m
As stated above, it is the shaft torque Tsh that produces the useful output. If the speed of the motor is N r.p.m., then,
Output in watts= 2πN Tsh/60
or Tsh =Output in watts /(2πN /60 ) N-m
or Tsh = 9.55 ×Output in watts /N     N-m
Brake Horse Power (B.H.P.)
W.D./revolution = force x distance moved in 1 revolution
F × 2π r = 2π×Tsh J
W.D./minute = 2π N Tsh J
W.D./ sec= 2πNTsh J/60 jS-1 or watt=2πNTsh J/(60 ×746) H.P.
Useful output power =2πNTsh J/(60 ×746) H.P.
or B.H.P. =2πNTsh J/(60 ×746)


Armature Torque of D.C. Motor

Torque is the turning moment of a force about an axis and is measured by the
product of force (F) and radius (r) at right angle to which the force acts i.e.
D.C. Motors torque
T = F × r
In a d.c. motor, each conductor is acted upon by a circumferential force F at a distance r, the radius of the armature (Fig. 4.8). Therefore, each conductor exerts a torque, tending to rotate the armature. The sum of the torques due to all armature conductors is known as gross or armature torque (Ta).
Let in a d.c. motor
r = average radius of armature in m
l = effective length of each conductor in m
Z = total number of armature conductors
A = number of parallel paths
i = current in each conductor = Ia/A
B = average flux density in Wb/m2
Φ = flux per pole in Wb
P = number of poles
Force on each conductor, F = B i l newtons
armature torque
Torque due to one conductor = F × r newton- metre
Total armature torque, Ta = Z F r newton-metre
= Z B i l r
Now i = Ia/A, B = Φ/a where a is the x-sectional area of flux path per pole at
radius r. Clearly, a = 2πr l /P.
Ta = Z × (Ф/a)×( Ia/A)×l×r
Ta = Z × (ФP/2πr l)×( Ia/A)×l×r = Z Ф IaP/(2πA) N-m
or Ta = 0.159Z Ф Ia(P/A) N-m……………………………………(i)
so Ta
Ta α Ф Ia
Hence torque in a d.c. motor is directly proportional to flux per pole and
armature current.
(i) For a shunt motor, flux Φ is practically constant.
Ta α  Ia
(ii) For a series motor, flux Φ is directly proportional to armature current Ia
provided magnetic saturation does not take place.
Ta α Ia2
up to magnetic saturation
Alternative expression for Ta
Eb = PФZN/60A
(60×Eb) /N= PФZ/A
From Eq.(i), we get the expression of Ta as:
Ta =0.159×(60× Eb/N)× Ia
Ta =9.55×( EbIa/N)

Voltage & Power Equation of D.C. Motor

Let in a d.c. motor (See Fig. 4.3),
V = applied voltage
Eb = back e.m.f.
Ra = armature resistance
Ia = armature current
Since back e.m.f. Eb acts in opposition to the applied voltage V, the net voltage across the armature circuit is V- Eb. The
armature current Ia is given by;
Ia = (V – Eb)/ Ra
or V = Eb + IaRa ……………………………..(i)
This is known as voltage equation of the d.c. motor.
voltage equation
Power Equation
If Eq.(i) above is multiplied by Ia throughout, we get,
VIa = EbIa +I2aRa
VIa= electric power supplied to armature (armature input)
EbIa = power developed by armature (armature output)
I2aRa = electric power wasted in armature (armature Cu loss)
Thus out of the armature input, a small portion (about 5%) is wasted as a I2aRa and the remaining portion EbIa is converted into mechanical power within the armature.
Condition For Maximum Power
The mechanical power developed by the motor is Pm= EbIa
Now Pm=VIa -I2aRa
Since, V and Ra are fixed, power developed by the motor depends upon armature current. For maximum power, dPm/dIa should be zero.
dPm/dIa = V – 2IaRa
or IaRa = V/2
Now, V = Eb + IaRa =Eb + V/2
therefore Eb=  V/2
Hence mechanical power developed by the motor is maximum when back e.m.f. is equal to half the applied voltage.
Limitations
In practice, we never aim at achieving maximum power due to the following reasons:
(i) The armature current under this condition is very large—much excess of rated current of the machine.
(ii) Half of the input power is wasted in the armature circuit. In fact, if we take into account other losses (iron and mechanical), the efficiency will be well below 50%.


Construction of D.C. Machines

 

A D.C. machine consists mainly of two part the stationary part called stator and the rotating part called stator.
The stator consists of main poles used to produce magnetic flux ,commutating poles or interpoles in between the main poles to avoid sparking at the commutator but in the case of small machines sometimes the interpoles are avoided and finally the frame or yoke which forms the supporting structure of the machine.
The rotor consist of an armature a cylindrical metallic body or core with slots in it to place armature windings or bars,a commutator and brush gears
The magnetic flux path in a motor or generator is show below and it is called the magnetic structure of generator or motor.

Let us check the parts in detail

Frame

Frame is the stationary part of a machine on which the main poles and commutator poles are bolted and it forms the supporting structure by connecting the frame to the bed plate.The ring shaped body portion of the frame which makes the magnetic path for the magnetic fluxes from the main poles and interpoles is called Yoke.

Yoke

Why we use cast steel instead of cast iron for the construction of Yoke?
In early days Yoke was made up of cast iron but now it is replaced by cast steel.This is because cast iron is saturated by a flux density of 0.8 Wb/sq.m where as saturation with cast iron steel is about 1.5 Wb/sq.m.So for the same magnetic flux density the cross section area needed for cast steel is less than cast iron hence the weight of the machine too.If we use cast iron there may be chances of blow holes in it while casting.so now rolled steels are developed and these have consistent magnetic and mechanical properties.

End Shields or Bearings

If the armature diameter does not exceed 35 to 45 cm then in addition to poles end shields or frame head with bearing are attached to the frame.If the armature diameter is greater than 1m pedestral type bearings are mounted on the machine bed plate outside the frame.These bearings could be ball or roller type but generally plain pedestral bearings are employed.If the diameter of the armature is large a brush holder yoke is generally fixed to the frame.

 

Field Poles

In early stages or say in the case of small machines the poles were cast integral to the yoke.But nowadays we use completely laminated pole or solid steel poles with laminated pole shoes.

Why we use laminated field poles?

We use laminated field poles because the surface of armature is not uniform since it has got notches or slots.And so when it rotates through the field produced by the pole shoes there may be pulsations in the field and this varying field could produce an eddy current inside the field pole.So to avoid this we use laminated field poles.

How laminated field poles reduce eddy current ?

The laminated field poles allows only the eddy current to pass through the length of lamination not through the entire body of pole ie from lamination to another laminations.These lamination are held together by means of a rivet.The outerside of the laminations are curved to fit closely to the inner frame.
The field coils are supported by the pole shoe and it spread out the flux in the airgap and owing to its large cross-section it reduces the magnetic reluctance.

How the pole shoe is attached to the yoke?

Generally two methods are employed for attaching pole shoes to the yoke.In the case of small pole shoes,poles is drilled and tapped to receive pole bolts but for large size a circular or rectangular pole bar is fitted or passed through the pole.This pole bar is drilled and tapped and the pole bolts passing through laminations is screwed int o the tapped bar.


Commutating poles /Interpoles

Interpoles or commutating poles are similar to that of main poles and has got a core which terminates with in a poleshoe.it is constructed in various shapes and the coils are mounted on the core.It is usually spaced in between two two main poles and bolted to yoke.Interpoles are usually made of solid steel but for the machines with varying loads sheet steel is used for construction.Interpoles are used to reduce spark while commutation.



Armature

The armature consists of a core and winding.Due to the good magnetic properties of iron it is used as the armature core.Iron is also a good conductor of electricity so the rotation of iron core in the magnetic field could produce a current in the core and this current called eddy current cause the wastage of energy as heat.To reduce eddy current the core is made of thin laminations.These laminations are made up of low loss silicon steel of of 0.4 to 0.5 mm thick and insulated with varnish.
In small machines armature laminations are fitted to the shaft and clamped tightly between the flanges.These flanges also acts as a support for the armature winding.One end of flange rests against a shoulder on the shaft,the laminations are fitted and then end is pressed on the shaft and retained by a key.
The core(except small size is divided into number of packets by radial ventilation spacers.The spacers are usually ‘I’ sections welded to thick steel laminations and arranged to pass centrally down each tooth.
Armature Lamination for small machine
For small machines the punching is made on the same piece which is built directly on the shaft and ventilation holes are provided to pass air into ventilating ducts.
Armature lamination for medium size machine
Medium size machines are machines having more than four poles,these machines are built on a spider.The spider may be fabricated and the lamination about 100cm are punched in one piece and keyed directly to spider.
Armature lamination for large machine
For large type of machines segmental lamination is employed since thin lamination may get distorted or become wavy when assembled together.Hence instead of being cut into one piece it is cut into a number of segments or sections which forms a complete ring.A complete circular ring could be made of 4,6 or even 8 segmental sections or laminations.Usually two key ways are notched in each segments and are dove tailed or wedge shaped to make the laminations self locking in position.

Armature Windings

The armature windings are placed or housed in the slots grooved on the surface of armature and and are so spaced such that one coils side or say a conductor of coil comes under north pole and the other coilside or second conductor comes under south pole.
Generally in D.C. machines two layer windings with diamond shaped coil is used.The coils are usually former wound.
How the coils are kept in position?
In small machines armature coils are held i position by means of band of steel wire which is wound under tension along core length.In large machine wedges of fiber or wood is used to keep the coils in position ie in the slots and use the wire band to overhang the coil.
Factors affecting armature winding
Armature winding plays an important role in the conversion of energy fro one form to another in electrical machines.The factors which should be given care while designing a winding is that the weight and material should be optimum or best for the high efficiency of machine.It should have necessary mechanical,electrical and thermal strength to meet the machine requirements and a life span about 16 to 20 years.It should be able to maintain the current collection at the commutator side without sparking.
Equilizer Rings
Equalizer connections or equilizer rings are located under the over hang on the commutator side.Equilizer rings could be also accommodated in the other end of armature.Equilizer rings are used to get uniform voltage.

Commutator

A commutator converts alternating voltage into direct voltage.A commutator is a cylindrical structure built up of segments made of hard drawn copper.These segments separated from each other and from frame by means of mica strips.These segments are connected to the winding by means of risers .The risers have air spaces between one another or that the air is drawn across the commutator there by keeping the commutator cool.The components of a commutator is shown below

The general appearance of commutator when completed and commutator and armature assembly is shown below.


Brush Gear

We use brush gear to collect or feed current from a rotating commutator.A brush gear consists of following parts.
  1. Brushes
  2. Brush Holders
  3. Brush studs or Brush holder arm
  4. Brush Rocker
  5. Current collecting busbars


Brushes

The brushes used for machines are divided into five classes according to the material with which it is made they are
  1. Metal Graphite brush
  2. Carbon Graphite brush
  3. Graphite brush
  4. Electro – Graphite brush
  5. Copper brush
The maximum current density at brush contact varies from 0.5A/sq.cm to 23A/sq.cm for copper.For large current machines working at low voltage copper brushes are employed.Lubrication should be done properly else it may cut the commutator rapidly leading to high wear and tear.Graphite and carbon graphite brushes are self lubricating and therefore it is used very widely.
Even for soft brushes there is wear but it takes place gradually.Though the mica segments between the commutator doesn’t wear easily but it reduces the effective contact with the segments and it may result in sparking and damage to the commutator.So to reduce this the micas ‘undercut’ a level below the commutator surface using a narrow milling cutter.


Brush Holders & Brush Rockers

Usually we use box type brush holders in all D.C. machines.At the outer end of arm a brush box is provided which is open at top and the bottom is attached.The brush is pressed to the commutator by means of a clock spring and this pressure could be adjusted by a level arrangement in the spring.The brush is connected to a flexible conductor called pigtail.The flexible conductor may be attached to the brush by a screw or may be soldered.
Brush boxes are generally made of bronze casting or sheet brass.For small machines working on low voltage commutation conditions are easy and galvanized steel boxes are employed.There are individual and multiple brush holders available on the market.In multiple brush holders a number of single brush holders are built into one long assembly.

Brush Rockers

Brush holder are connected or fixed to brush rockers with bars.The brush rockers arranged concentrically round the commutator.Cast iron is is usually used for brush rockers.

Armature Shaft Bearings

For small machines roller bearings are used at both ends. For large machines roller bearings are used at driving end and ball bearings at non driving or commutative end.Sometimes pedastal bearings are also used for large machines.The bearings are housed in the endshield.The figure below shows a pedestal bearing.

Important terms regarding armature winding

Armature Windings
The mean­ing of the following terms used in connection with armature winding should be clearly kept in mind.
Pole-pitch
It may be variously defined as :
i) The periphery of the armature divided by the number of poles of the generator i.e. the distance between two adjacent poles.
ii) It is equal to the number of armature conductors (or armature slots) per pole. If there are 48 conductors and 4 poles, the pole pitch is 48/4 = 12.
Conductor
The length of a wire lying in the magnetic field and in which an e.m.f. is induced, is called a conductor (or inductor) as. for example, length AB or CO in Fig. 26.21
Coil and Winding Element
With reference lo 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 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 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.
Coil-span or Coil-pitch (YS)
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 pilch (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 arc 36 slots and 4 poles, then coil span is 36/4 = 9 slots. If number of slots is 35. then Ys = 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 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
Pitch of a Winding (Y)
In general, it may be defined as the distance round the armature between two successive conduc­tors which are directly connected together. Or, it is the distance between the beginnings of two consecutive turns.
Y   = YB – YF ………… for lap winding
= YB + YF —— 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.
Back Pitch (YB)
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 I is connected on the back of the armature to clement 8. Hence. YB = (8 – 1) = 7.
Front Pitch (YF)
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 clement 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 ie. commutator end of the armature. Both front and back pitches for lap and wave-winding are shown in Fig. 26.25 and 26.26.
Resultant Pitch (YR)
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 stated in terms of armature conductors, are also sometimes given in terms of armature slots or commutator bars because commuta­tor is, after all, an image of the winding
Commutator Pitch (YG)
It is the distance (measured in commu­tator bars or segments) between the segments to which the two ends of a coil arc connected. From Fig. 26.25 and 26.26 it is clear that for lap winding. YG is the difference of YB and Yf whereas for wavewinding it is the sum of YB and Yf Obviously, commutator pitch is equal to the number of bars between coil leads. In general. Yc equals the ‘plex’ of the lap-wound armature. Hence, it is equal to 1, 2,3,4 etc. for simplex-, duplex, triplex-and quadruplex etc. lap-windings.

Back or Counter E.M.F.

When the armature of a d.c. motor rotates under the influence of the driving torque, the armature conductors move through the magnetic field and hence e.m.f. is induced in them as in a generator The induced e.m.f. acts in opposite direction to the applied voltage V(Lenz’s law) and in known as back or counter e.m.f. Eb. The back e.m.f.  Eb (= P Φ ZN/60 A) is always less than the applied voltage V, although this difference is small when the motor is running under normal conditions.
Consider a shunt wound motor shown in Fig. (4.2). When d.c. voltage V is applied across the motor terminals, the field magnets are excited and armature conductors are supplied with current. Therefore, driving torque acts on the armature which begins to rotate. As the armature rotates, back e.m.f. Eb is induced which opposes the applied voltage V. The applied voltage V has to force current through the armature against the back e.m.f.  Eb . The electric work done in overcoming and causing the current to flow against Eb is converted into mechanical energy developed in the armature. It follows, therefore, that energy conversion in a d.c. motor is only possible due to the production of back e.m.f. Eb.
Net voltage across armature circuit = V – Eb
If  Ra is the armature circuit resistance, then, Ia = (V – Eb)/ Ra
Since V and Ra are usually fixed, the value of Eb will determine the current drawn by the motor. If the speed of the motor is high, then back e.m.f. Eb (= P Φ ZN/60 A) is large and hence the motor will draw less armature current and viceversa.
back emf
Significance of Back E.M.F.
The presence of back e.m.f. makes the d.c. motor a self-regulating machine i.e., it makes the motor to draw as much armature current as is just sufficient to develop the torque required by the load.
Armature current,Ia = (V – Eb)/ Ra
(i) When the motor is running on no load, small torque is required to overcome the friction and windage losses.  Therefore, the armature current Ia is small and the back e.m.f. is nearly equal to the applied voltage.
(ii) If the motor is suddenly loaded, the first effect is to cause the armature to slow down. Therefore, the speed at which the armature conductors move through the field is reduced and hence the back e.m.f. Eb falls. The decreased back e.m.f. allows a larger current to flow through the armature and larger current means increased driving torque. Thus, the driving torque increases as the motor slows down. The motor will stop slowing down when the armature current is just sufficient to produce the increased torque required by the load.
(iii) If the load on the motor is decreased, the driving torque is momentarily in excess of the requirement so that armature is accelerated. As the armature speed increases, the back e.m.f. Eb also increases and causes the armature current Ia to decrease. The motor will stop accelerating when the armature current is just sufficient to produce the reduced torque required by the load.
It follows, therefore, that back e.m.f. in a d.c. motor regulates the flow of armature current i.e., it automatically changes the armature current to meet the load requirement


Compound Generators in Parallel

Under-compounded generators also operate satisfactorily in parallel but overcompounded generators will not operate satisfactorily unless their series fields are paralleled. This is achieved by connecting two negative brushes together as shown in Fig. (3.16) (i). The conductor used to connect these brushes is generally called equalizer bar. Suppose that an attempt is made to operate the two generators in Fig. (3.16) (ii) in parallel without an equalizer bar. If, for any reason, the current supplied by generator 1 increases slightly, the current in its series field will increase and raise the generated voltage. This will cause generator 1 to take more load. Since total load supplied to the system is constant, the current in generator 2 must decrease and as a result its series field is weakened. Since this effect is cumulative, the generator 1 will take the entire load and drive generator 2 as a motor. Under such conditions, the current in the two machines will be in the direction shown in Fig. (3.16) (ii). After machine 2 changes from a generator to a motor, the current in the shunt field will remain in the same direction, but the current in the armature and series field will reverse. Thus the magnetizing action, of the series field opposes that of the shunt field. As the current taken by the machine 2 increases, the demagnetizing action of series field becomes greater and the resultant field becomes weaker. The resultant field will finally become zero and at that time machine 2 will shortcircuit machine 1, opening the breaker of either or both machines.
compound generators in parallel
When the equalizer bar is used, a stabilizing action exist? and neither machine tends to take all the load. To consider this, suppose that current delivered by generator 1 increases [See Fig. 3.16 (i)]. The increased current will not only pass through the series field of generator 1 but also through the equalizer bar and series field of generator 2. Therefore, the voltage of both the machines increases and the generator 2 will take a part of the load.





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