## Monday, 30 December 2019 ## Fleming Left Hand Rule Statement

FLEMING LEFT HAND RULE STATEMENT:

The direction of force acting in the conductor carrying current and placed in a magnetic field can be found by using Flemings Left Hand Rule which states that “ Stretching out the first finger, middle finger and the thumb of the left hand such that they are at right angles to each other as shown in figure, if the first finger points towards the direction of magnetic field, the middle finger points towards the direction of current, then the thumb points out the direction of motion of the conductor”.

DC MOTOR

Basically there is no difference in the construction of a dc generator and dc motor. The only difference lies in the utilization of the machine. When the dc machine converts mechanical energy into electrical energy, it is termed as dc generator whereas when the dc machine converts electrical energy into mechanical energy, it is termed as dc motor. Both work on the similar principle. Whenever a conductor is placed in a magnetic field and mechanical motion to the conductor is given, emf is generator whereas in the motor due to the input of electric current, varying field is produced and when a conductor is placed in the varying magnetic field, a mechanical force is experienced by the conductor and the conductor is pushed away from the field. This mechanical energy is utilised to rotate the armature of the d.c. motor.

WORKING PRINCIPLE OF DC MOTOR :

For the sake of understanding the concept, consider a single polar motor as shown in Figure. The conductor is placed around the circumference of an armature such that it falls under the influence of uniform magnetic field. In Figure. The conductor does not carry any current and so the flux of the main pole does not get distorted and is in the direction shown in Figure. In the next Figure, the flux of the main pole is purposely omitted for the purpose of clear understanding of the flux produced by the current in the conductor. The current in the conductor travels from back to front and the direction of magnetic flux produced can be found by thumb rule. Fleming left hand rule states that keeping the thumb, forefinger and middle figure at right angles to each other, if the forefinger, and middle finger points out flux and direction of current, the thumb points out the direction of force experienced by the conductor.

In Figure, both the flux of the main pole and the flux produced by the current in the conductor are shown together. It will be seen that flux produced by the current in the conductor opposes the main flux on the right hand side and aid at the left hand side due to which the flux get elongated towards the left hand side of the conductor. Since the flux pattern towards left hand side of the conductor is in unstable position, it exerts a force on the conductor in the direction shown in Figure. Since the conductor is free to move over the shaft which is supported by bearings, the conductor moves giving way for the next conductor to occupy its place. As the second conductor also carries the current in the same direction as that of the first, it also experiences a force as before and moves in the forward direction giving its place for the third conductor. The cycle continues as long as the current exists in the conductor. If the direction of current in the conductor changes then the direction of force also changes. The magnitude of the force exerted is given by the equation :

F = BllSin θ Newtons

Where F is the force exerted on the conductor in Newtons

B is the flux density in Wb/m2
I is the current in the conductor in amperes
l is the effective length of the conductor in metres
Sin θ, is by which the magnitude of force depends on the position of the conductor in the magnetic field.

From the equation, it is seen that the force exerted on the conductor depends upon the flux density of the main pole and the current in the conductor. Greater the flux density of the main pole, greater is the force on the conductor and so greater is the speed of the motor. Again, greater is the current in the conductor, greater is the force on the conductor and greater is the speed of the motor.

## Saturday, 28 December 2019 ## Power Flow Diagram of DC Generator

POWER FLOW DIAGRAM OF DC GENERATOR

Power flow diagrams give the stages of power in the case of a dc generators showing clearly the losses that occur at various stages of generation of power. The input to a generator is mechanical power a hydel, steam, diesel or nuclear source in the form of rotational power. The power flow diagram is shown in figure below.

EFFICIENCY OF DC GENERATOR:

Efficiency, η = Output/Input

In the case of a dc generator the output is a known factor from which input can be found. Thus the formula gets modified as,

Efficiency, η = Output/[Output +  Losses]
= Output/[Output +  Copper loss + Stray losses]

The following three types of efficiencies can be determined for a DC generator.

(a) Mechanical efficiency (ηm)

ηm = B/A = Total watts generated in armature/ Mechanical power supplied
= EgIa/Output of driving engine

(b) Electrical efficiency (ηe)

ηe = C/B = Watts available in load circuit/Total watts generated
= VI/EgIa

(c) Overall or Commercial efficiency (ηc)

ηc = C/A = Watts available in load circuit/Mechanical power supplied
= VI/Output of driving engine

Overall efficiency can also be found by

ηc = ηm x ηe

CONDITIONS FOR MAXIMUM EFFICIENCY:

Let the generator,

Output = VI watts
Input = Output + Losses

The losses comprises of constant losses and variable losses.

Constant Losses (WC) = Stray losses + Shunt Field copper losses

In the case of shunt field,
Field copper losses = Ish2 Rsh

The variable losses occur in the armature winding and series field winding and are equal to
I2aRa + I2seRse

Therefore,

Generator Input = Output + Variable losses + Constant losses
= VI + I2aRa + I2seRse + WC

η = Output/Input
= VI/( VI + I2aRa + I2seRse + WC)

Since shunt field current (Ish) is supplied by armature. Ia > 1 but in practice the shunt field current is negligible as compared to line current. Therefore Ia = I (approx).

η = Output/Input = VI/(VI + I2Ra + WC)

Dividing numerator and denominator by VI,

η = 1/{1 + (IRa/V + WC/VI)}

Efficiency shall be maximum when the denominator is minimum. Differentiating the denominator with respect to I and equating to zero.

d/dI(IRa/V + WC/VI) = 0

We get,

Ra/V – WC/VI2 = 0
Or Ra/V = WC/VI2
Or I2Ra = WC

That is, when the variable losses is equal to constant losses, the efficiency of a DC generator is maximum. The load current corresponding to maximum efficiency is given by,

I2Ra = WC

Or I = (WC/Ra)

## Thursday, 26 December 2019 ## Losses in DC Generators

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Losses in DC Generators:

The total losses in DC generators fall under the following three categories:

(a) Copper losses
(b) Magnetic losses
(c ) Mechanical losses

The difference between the power input and power output is called power loss, Ii is essential to consider the power loss for the following reasons

(a) The temperature rise of the generator is due to the heat developed within it and is proportional to the losses. Greater the heat developed, greater is the temperature rise and greater is the loss.

(b) The efficiency of the machine is dependent on the quantum of losses and the cost of operation depends upon the efficiency of the machine.

(c) Break down and machine failure mostly depends upon the losses and least on mechanical factors.

At the time of designing the machine the operating temperature is fixed and the design finalized, if this is not done, then the losses would dominate and the temperature rise beyond the operating value damage the insulation which ultimately leads to break down of machine. The different types of losses are given in Figure.

1. Copper Losses : Copper losses are due to the resistance in the winding wire and the brush contact losses. The armature copper losses amounts to Ia2Ra which is normally 30 to 40% of full load losses. The field copper losses are

(a) Ish2Rsh ---------- For shunt field generator
(b) Ise2Rse ---------- For series filed generator

The field copper loss amounts to 20 to 30% of full load losses. The brush contact losses are usually included in the armature copper loss.

2. Magnetic Losses : These losses are also known as iron losses or core losses and are of two types :

(a) Hysteresis Loss (Wh) :

This is due to the reversal of magnetism in the armature core. The core undergoes one complete cycle of reversal after passing through a pair of poles. If P is the number of poles and N the armature speed in r.p.m. then the frequency of reversals is given by

f = PN/120

The loss is dependent upon the grade of iron, its volume, maximum flux density Bmax and the frequency of magnetic reversals and is given by

Wh = ηB1.6max f V watts

where η = Steinmetz hysteresis coefficient
V = Volume of the core in m3

The value of η for different material is given in Table.

 Material η(J/m3) Silicon Steel 191 Sheet Steel 502 Hard Cast Steel 7040 Cast Steel 750 - 3000 Cast Iron 2700 - 4000

(b) Eddy Current Losses :

When the armature core rotates, it also cuts the magnetic field due to which a small amount of e.m.f. is induced in the core. This sets up a large current in the body of the core and is called eddy current. If it is a solid core, the loss will be considerable and to reduce it, the core is built up of thin laminations which are stacked and riveted at If right angles to the path of eddy current. Each lamination from each other and hence the loss is considerably reduced, In short

(a) A solid core of large volume offers least resistance resulting, in large eddy current.

(b) A laminated core of much lesser core section offers large resistance reducing the eddy current to least.

Eddy current loss is given by

We = KB2max f2 t2 V2 watts

Where Bmax is maximum flux density
f is the frequency of magnetic reversal
t is the thickness of each lamination
V is the volume of armature core.

3. Mechanical Losses :

These losses are due to friction and are of two types

(a) air frictional losses which are also called windage loss of rotating armature.
(b) frictional loss at hearings and commutator.

The mechanical loss amounts to about 10 to 20% of full load losses. Magnetic and mechanical loss are collectively called stray losses. Since for a given machine stray losses and copper losses are constant, the total constant loss collectively amounts to the sum of stray losses and copper losses.

## Tuesday, 24 December 2019 ## Process of Commutation in DC Machine

Commutation: The current induced in the armature of a d.c. generator is alternating and a commutator is used to make the alternating current into unidirectional current by reversing the negative part of alternating current. The reversal of current takes place in the magnetic neutral axis. The brush short circuits the particular coil undergoing reversal. The method by which current in the short circuited coil is reversed as it crosses the magnetic neutral axis is referred to as commutation.

Process of Commutation in DC Machine

If the reversal of current is gradual, then it is called smooth commutation. Smooth commutation means no spark at the brush and the surface between brush and the segment is unaffected. Consider a portion of the segments with armature coil between them touching a brush at any instant of rotation of armature coil as shown in Fig. In the figure, the coils have been labeled as A, B, C, D, E and corresponding segments have been numbered as 20 to 25. In Fig (a), the brush is in contact with segment no. 21 to which coils A and B feed the current of magnitude lc. The direction of current in the coil A is clockwise while in coil b is anticlockwise. As the armature moves in the direction of rotation the brush slides and makes contact with commutator segments 21 and 22 as shown in Fig. (b). At this position, the coil B is getting short circuited thereby current in coil B decreases. Note that as the brush slides and touches the commutator segment No. 22 which is in contact with segment No. 21, the current in coil B which was an it clockwise drops down. If i1 is the current which enters the brush from coil C through segment No. 22 (Ic — i1) is the current which enters brush from coil B through segment No. 21. The area of the copper carbon contact decides the distribution of current. As the area of copper carbon contact in segments 21 and 22 become equal, i1 would have become Ic. Then the current in coil B becomes zero as shown in Fig. (c). Process of Commutation in DC Machine
After another brief period, the area of contact of brush in segment No. 22 will be more than in segment No. 21. If at this position the current entering the brush from coil A through segment No. 21 is i2 the remaining current (lc - i2) will try to pass through B and segment No. 22 to reach the brush. In this process the current in coil B rises from zero to a value i, in the reverse direction to that shown in Fig. 2.59 (a). As the brush slides further the value of i2 increases and when the brush is in contact with segment No. 22, the current i2 would have risen to a value equal to lc. From the above, it can be seen that for every shift of position of brush from one segment (say 21) to its adjacent segment, say (22).

a. The current in the coil connected in between segment Nos. 21 and 22 decreases, becomes zero and increases in the reverse direction.

b. Due to reversal of the current in the coil in question, a static e.m.f. is induced in the coil, which opposes the flow of current, the least is the time for reversal, higher is the magnitude of induced e.m.f. The time required for the coil current to change by + Ic to - Ic is called the commutation period time and is given by

Tc = Brush width /Commutator peripheral speed

CAUSES FOR SPARKING AT COMMUTATOR

The nature of current flowing in the local circuit of the coil being commuted depends on the following factors.

a. Resistance between the surfaces of brush material and segment material.
b. Resistance of the coil under commutation.
c. E.m.fs induced in the short circuited coil due to

i. Self inductance
ii. Mutual inductance with other coils undergoing commutation simultaneously. This is possible only when brush is more than one commutator segment width as in the case of duplex winding.

d. E.m.f. induced in the coil due to its rotation in the armature cross magnetising flux.

1. Sparking at Commutator :

The armature coil possesses an appreciable amount of reluctance because it is embedded in the armature core which has high magnetic permeability. Due to the current reversal in commutation, self induced e.m.f. is produced in the coil. The quicker is the time of reversal, higher is the magnitude of self induced e.m.f. This voltage although of little magnitude, makes a large current through the coil whose resistance is low due to short circuit. When the coil undergoes short circuit in the magnetic neutral axis, no e.m.f. is induced due to rotation of the armature and the self induced e.m.f. which is present during this time causes severe sparking at brushes. Higher is the rate of rotation of armature, higher is the rate of reversal of current in the short circuited coil and higher is the magnitude of self induced emf resulting in large spark at brush-contact.

2. Effect of Sparking

Sparking at the brush contacts has the following effects :

a. The surface of the commutator segments gets carbonised. Consequently it short circuits all the coils of the armature.

b. Sparking can damage commutator surface decreasing the contact surface. Due to this the brush jumps resulting in more sparking.

c. Sparking can result in excess heating of the commutator segments raising its temperature which can unsolder the armature coil leads.

3. Reactance Voltage :

Let Tc = be the time of commutation
= (brush width - width of mica) /Peripheral velocity

Wb = Width of brush in metres
Wm = Width of mica in metres

v = Peripheral velocity of commutator segment in cm/sec

Then T = [Wb — Wm]/V seconds

If I is the current through the armature conductor, then the total change in commutation current is equal to

I - (- I) = 2I Amperes

Reactance Voltage = L (2I /Tc), for linear commutation
Reactance Voltage = 1.11 x L (2I /Tc) for sinusoidal commutation

Note: If the current varies at a uniform rate, it is called linear commutation.

## Thursday, 19 December 2019 ## Armature Reaction in DC Generator

When the generator is under operation, the current in the armature due to the e.m.f. generated produces a flux in the armature. The effect of the armature flux produced by the armature current distorts and weakens the main flux produced by the field poles due to which sparking at brush and low voltage at terminals may result. The study of the effect on the redistribution of flux under the main pole is done under armature reaction topic.

Whenever a brush contacts two or more commutator segments, the coils connected to these segments are short circuited for a brief period. After the period of short circuiting the current in these coils change their direction. The changes that may takes place in the coil after the period of short circuiting commutation. If the change is gradual it is called commutation and if it is sudden it is called rough commutation. Rough commutation leads to sparking at the brush contacts.

To study the armature reaction the following terms are to be understood clearly.

a) Geometrical neutral axis (GNAT):

lt is an axis midway between the opposite and adjacent poles. Geometrical neutral axis for two pole and four pole generator (without flux) is shown in Figure.

b) Magnetic Neutral Axis:

The magnetic neutral axis is perpendicular to the lines of force between two adjacent opposite poles.

(a) magnetic neutral axis due to field flux alone.
(b) the magnetic neutral axis due to armature flux alone.

When the armature rotates, the end of the pole through which the conductors enters the magnetic region is called the Leading Pole Tip (LPT).

d) Trailing Pole lip (TPT):

It is also sometimes called Lagging Pole tip. It is the tip of the pole through which the conductor leaves the magnetic region. H. the direction of rotation is changed the leading and trailing tips also change. Refer to Fig.

To study the effect of armature flux on the field flux, it is necessary to consider separately the distribution of magnetomotive force of the main field and armature. For the purpose of the convenience a bipolar generator is taken to illustrate the effect of armature reaction.

1. Distribution of Main Field E.m.f:

Consider a bipolar generator with armature at the centre kept stationary and the main field excited. Since there is no rate of change of flux linkage in the armature, the e.m.f. induced in the armature conductor is zero. Hence, the distribution of flux'due to main pole is only shown. In this condition the distribution of flux in the air gap is uniform and the magnetic neutral axis (MNA) and geometrical neutral axis (GNA) coincide. This condition can also occur where a generator is on no load.

2. Distribution of Armature E.m.f.

Consider the flux produced due to armature current alone. In this case; the distribution of flux is as shown in Fig. The direction of armature current would be the same as it would actually be when the generator is on load. Using the Flemings right hand rule the direction of induced e.m.f. is found.
The downward current is represented by a cross and upward current is represented by a dot. The net effect of the magnetic flux around individual conductors is to send the flux downwards through the armature. This can be found out by using cork screw rule. The magnitude of armature e.m.f. depends upon the magnitude of armature current. In this case also the Geometrical Neutral Axis (GNA) and Magnetic Neutral Axis (MNA) coincide.

3. Distribution of Resultant E.m.f. :

The distribution of flux due to main pole is to-wards south pole. In Fig (a) under north pole Φp represents the direction of magnetic flux in the north pole, Φa represents the direction of magnetic flux in the north pole due to the armature current. The resultant of Φp and Φa is ΦR whose direction is towards the trailing pole tip (TPT). Therefore, the flux inside the north pole- would bend towards TPT which causes crowding of flux at TPT and wearing of flux at leading end of north pole.
In Fig. (a) in the armature, the direction of flux of the mainpole (Φp) is again towards south pole but the direction of flux due to armature current (Φa) is downward towards the geometrical neutral axis. The resultant direction of (Φp), and (Φa) is (ΦR) which takes a shift from the axis of the pole. The angle of shift is θ°. The direction of flux due to the main pole Φp, in south pole coincides with pole axis and is shown in Fig. (a) and the direction of flux (Φa) due to armature current in the south pole is upwards towards the geometrical neutral axis. The result of Φp and Φa is ΦR: The flux bends again and resumes its normal pole axis. Thus, there is a shift in the direction of flux from the normal pole axis to an axis with a shift of θ°. The complete resultant flux pattern due to the effect of armature flux on the main pole flux is shown in Fig (b).

Before considering this reaction the magnetic neutral axis was in line with the geometrical neutral axis. The magnetic neutral axis (MNA) shifts by an angle θ perpendicular to the resultant mmf due to which the brush takes a forward lead through an angle θo to lie in its new position of MNA. Due to this shift the armature current gets redistributed and some armature conductors which were earlier under the influence of north pole come under the influence of south pole and vice versa. The angle θ° of shift of magnetic neutral axis (MNA) increases with the increase in armature current due to increase in load. If the brushes arc not shifted to this MNA sparking may occur brush contact points. .

4. Effect of Armature Reaction :

The following are the effects of armature current on the machine

a. It distorts uniformity of the main flux and hence has cross magnetising effect.
b. It produces a demagnetising effect on the main pole.
c. It reduces the e.m.f. induced in the armature.
d. if brushes are not shifted to MNA sparking at brush contacts occur.
e. In self excited generator, short circuit creates heavy armature reaction resulting in demagnetisation of pole cores. The result is that the residual magnetism is completely lost.
f. The efficiency of the generator decreases.

5. Demagnetising and Cross Magnetising Conductors:

Due to the armature current, there is a shift of magnetic neutral axis (MNA) by an angle θo which is dependent on the load on the generator. Before the shift of MNA the magnetic neutral axis and geometrical neutral axis were same. The conductors which were adjacent to the geometrical neutral axis upto an angle of θo were outside the influence of the pole and no e.m.f. were induced in that conductor. Before the shift of MNA, the effect of these conductors, is to distort the main field. Now consider the effect of these conductors which are still adjacent to geometrical neutral axis even after the shift of MNA. The conductors lying upto an angle θo on both sides of geometrical neutral axis at top and bottom are subjected to a flow of current due to the induced e.m.f. in the rest of the armature conductors in such a direction as to set up magnetic flux around it in the armature. The direction of magnetic field of these conductors is opposite to the direction of the magnetic field set up by the conductors adjacent to the GNA at top and bottom upto an angle of θo is to demagnetise the main flux.

Now consider the conductors on both sides of the MNA and under the pole influence. It sets up a current in such a direction that the magnetic flux produced by it in the armature will distort the main flux giving an effect of cross magnetisation. These conductors are known as cross magnetising conductors. Both these demagnetising and cross magnetising conductors play an important role in the armature reaction.

## Tuesday, 17 December 2019 ## Characteristics of DC Shunt Generator

1. No load Characteristics of DC Shunt Generator

The no load characteristics of shunt generator is the same as that of a separately excited generator. This is due to the fact that a very low percentage of about 1% to 3% of armature current flows through the shunt field winding which has negligible effect on the characteristics.

2. Load Characteristics of DC Shunt Generator :

As in the case of no load characteristic the load characteristics also does not differ much from that of separately excited generator. The only difference is the armature current. In the case of separately excited generator the armature current is equal to load current whereas in the case of shunt generator the armature current is the sum of load current and shunt field current which is again a low percentage value of armature current. The connection diagram and the characteristics of shunt generator is given in Figure a and b.

3. External and Internal Characteristics of DC Shunt Generator :

The shunt generator is connected as shown in above Figure a and is run at rated speed and the field current is adjusted for rated terminal voltage at no load. Now the switch S is closed and the load is gradually increased by decreasing its resistance in steps. The reading of the field current, load current and terminal voltage is noted for each step. The graph for terminal voltage against load current is drawn with the present value of field current and speed as shown in Figure b. The curve gives the external characteristics. It is seen that the terminal voltage drops as load increases. This is due to

a. drop in the armature IaRa
b. reduction in the main flux due to armature reaction
c. reduction in field current due to fall in terminal voltage

From the curve, it is seen that for a given field current on load the voltage drop due to armature resistance is equal to CD, the voltage drop due to reduction in field current is equal to DF and the voltage drop due to armature reaction is equal to FG. Thus the total voltage drop CG amounts to the sum of the voltage drops due to armature resistance, reduction in field current and armature reaction. The terminal voltage is the difference between OA and CG. Further increase in load current drops the terminal voltage upto a point B is reached and any further decrease in load resistance momentarily increases the load current producing more armature reaction. This increases the armature drop laRa reducing the terminal voltage. The rapid reduction in terminal voltage results in decreased load current. The cumulative effect is a short circuit of armature resulting in the terminal voltage falling to zero at point H. OH is the load current due to the voltage generated by the residual flux. The point B is called breakdown point. It is evident that any further effort to decrease load resistance beyond the breakdown point B will decrease the load current due to rapid decrease in terminal voltage. Over the normal operating range the internal characteristics is obtained by adding armature drop (CD) to the external characteristics.

## Monday, 16 December 2019 ## Voltage build up in a Self Excited Generator

VOLTAGE BUILD UP IN A DC SHUNT GENERATOR:

The following are the essential conditions for building up of voltage in self excited generator.

a. There must be residual magnetism in the poles.

b. The field must be connected in such a way as to strength the residual magnetism, when the current due to induced e.m.f. flows through them.

c. If excited on open circuit its shunt field resistance should be less than the critical resistance value.

d. If excited on load, then the shunt field resistance should be more than a certain minimum value of resistance as given by internal characteristics.

e. In the case of a series generator there must be some load on the generator for building up of e.m.f.

Assuming that some residual magnetism is present in the poles, the shaft is rotated to rated speed. Due to this residual magnetism initially some amount of e.m.f. is produced which circulates small current in the field coil. It results in increase in flux which in turn increases the induced e.m.f. and this process continues till full rated e.m.f. is generated.
The generated e.m.f. has to overcome ohmic drop in the field winding (If Rsh). So long as the generated e.m.f. is in excess, this energy would continue to be stored in the pole fields. In Figure, the emf generated corresponding to field current OA is OB out of which AC corresponds to ohmic drop in the field. While whole of the e.m.f. generated to corresponding field current OF is utilised towards ohmic drop leaving nothing for L.di/dt. Hence no energy is stored in the poles. Consequently no further increase in the flux and generated e.m.f. is there. If OP line represents the shunt field resistance, the maximum e.m.f. generated is OE. If this resistance is decreased building up of voltage will be higher. If a tangential line is drawn to the linear portion of the OCC curve, it gives the value of resistance of the field winding for generation of e.m.f. This resistance is called critical resistance. The generator would fail to generate e.m.f. if the shunt field resistance is greater than critical value.
In case the generator fails to build up e.m.f. the following may be the causes

a. Improper direction of rotation
b. Shaft speed is too low
c. Improper brush contacts
d. Short circuit or open circuit armature or field
e. Improper connections of field
f. Lack of residual magnetism

CAUSES AND REMEDIES FOR NON BUILDING UP OF E.M.F

Some of the causes and remedies for non building up of e.m.f. in the D.C. generator is given in Table.

Causes and Remedies for Failure of E.M.F. in Generator

 No Causes Remedies 1 The direction of rotation must have been reversed in which case residual magnetism will he opposed. Change the direction of rotation 2 Speed too low Generator should be rotated at the constant speed 3 Brushes not resting on the commutator or in the wrong position Brushes to be set or shifted to the correction position of MNA 4 Residual magnetism is completely lost A generator should give a reading upto 5% of its full voltage when it run without excitation. If it does not fulfil the above condition, then run the generator as d.c. motor for few seconds. If d.c. supply is not available, a battery of e.m.f. 10% of the generator voltage must be used for sending current to re-establish the residual magnetism. This is called flushing of the field 5 Short circuit in the armature Remove the short circuit which may lie in the generator itself, the switch hoard or external circuit lf the short circuit is in the external circuit, the generator will excite when it is disconnected from the load 6 Short circuit in the field circuit Test and remove short circuit which may be on the terminals or within the coil. Faulty coil will show much less resistance than the perfect coil 7 Open circuit in the armature Test and repair for open circuit if possible 8 Open circuit in the field winding Test for open circuit. If the break is in the field coil, remove it or rewind it if required 9 High resistance in the field winding High resistance in the field circuit will not allow the generator to build up its normal voltage, so cut it out from the field circuit 10 Wrong connection of the field winding Reverse its connection 11 Load on the machine In case of series generator there must be some load on it, while in other case no load or small load is required on the generator 12 Series field opposes shunt field flux in compound machine Reverse the connection of the series field winding

## Sunday, 15 December 2019 ## Equation for Currents and Voltages in DC Generator

Relation between Currents and Voltages:

Let, IL be the load current in amperes
Ise be the series field current in amperes
Ish be the shunt field current in amperes
Ia be the armature current in amperes
Ra be the armature resistance in ohms
Rsh be the shunt field resistance in ohms
Rse be the series field resistance in ohms
Eg be the generator e.m.f. in volts
V be the terminal voltage in volts

Then the equation for currents and voltages are given in the succeeding paragraphs.

1. Equation for D.C. Shunt Generator :

In a D.C. shunt generator the load resistance is connected across the armature brushes. So also the field coils. The current from the generator brushes is split into two components, one for the shunt field coil and the other for the load. The armature resistance is shown inside the brushes for the sake of calculation and there would be a definite voltage drop across the armature resistance.

As seen from Figure,

Ia = IL + Ish

The load voltage will be less than the generated voltage.
This is because of the voltage drop in the armature circuit.

Eg = VL + IaRa DC Shunt Generator on Load
2. Equation for D.C. Series Generator :

In a D.C. series generator, the field coils are connected in series to the armature. Hence, the field resistance (Rse) will act in series to armature resistance (Ra). The load is connected across the armature and series field. The current in the series field and load are same i.e.,
Ia = Ise = IL

But the voltage equal is as under

Eg - laRse - IaRa = V
or Eg - la (Rse + Ra) = V
or Eg - IL (Rse + Ra) = V DC Series Generator
3. D.C. Compound Generator :

A D.C. compound generator is a combination of shunt and series generators. If the shunt field is connected across the armature, it is called short shunt compound generator and when the shunt field is connected across the armature and field, i.e., across the load, it is called long shunt compound generator. The equation for compound generator is as follows :

Equation for Short shunt compound generator :

Ia = Ish + IL
and V + ILRse = Vsh
Vsh + IaRa = Eg
or Eg = V + Ise Rse + IRa

## Thursday, 12 December 2019 ## DC Armature Winding

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The complete process of armature winding involves number of operations like insulating the core, inserting the coils into the slots connecting the leads to the commutator, baking and varnishing etc. Without the perfect knowledge of the winding diagram, it would be impossible to wind the armature to that perfection to match the designed requirements. The slots of the armature are either open or semi closed type.
DC Windings are generally classified as under,

Definition of Terms involved in DC Armature Winding:

Certain terms used in connection with the armature winding is defined below:

Pole Pitch:

It is defined as the peripheral slot distance between two adjacent poles. If ‘n’ is the number of slot in the armature and ‘P’ is the number of field poles, then

Pole pitch = No: of slots in armature/ No: of poles in field = n/p
For example if the number of slots in the armature is 24  and the number of poles in the field is 4, then the pitch is 24/4 = 6. If the windings are made for lesser than the pole pitch, the winding is said to be chorded or short pitched. The electrical angle between pole to pole is 180o electrical because it generates half a cycle of emf and the electrical angle between slot to slot is called pitch angle. It is given by

Slot pitch angle = 180oe/No: of slots between poles = 180oe/Pole pitch

Coil Span or Coil Pitch (Ys) :

It Is defined as the distance in terms of armature slots between two sides of a coil. In other words, it is the periphery of the armature spanned by the two sides of the coil. if the coil span is equal to the pole pitch, it is said to be full pitched coil and if the coil span is lesser than the pole pitch or fractional pitched coil, it is then said to be short pitched coil.

Back Pitch and Front Pitch :

Back pitch is defined as the distance in conductors by which a coil advances and is denoted by the letter Yb. Front pitch is defined as the distance in conductors from the end of the first coil to the beginning of the second coil and is denoted by Yf. The resultant pitch is defined as the distance in conductors from the beginning of the first coil to the beginning of the second coil.

Overhang :

The conductor is inserted into the slot and taken back from another slot to form a coil. The ends of the coil are connected to commutator segments. The inductor portion of the coil is the conductor inside the slot responsible for production of emf and the rest of the coil is the overhand as shown in Figure.

Commutator Pitch:

Commutator pitch is defined as the segmental difference between winding connections of any two consecutive oils. It is the distance at commutator between the beginning of first coil and the beginning of second coil.

Single Layer and Double Layer Winding :

In a single layer winding, only one conductor or one coil side is placed in each slot as shown in Fig (a) whereas in the double layer winding, there are two conductors or coil sides arranged in each slot in two layers as shown in Fig (b). In the double layer winding, one side of the coil lies in the upper half of one slot and the other side of the coil lies in the lower half of some other slot at a distance of approximately one pitch away. Double layer windings are most commonly used for all medium sized machines.

Lap and Wave Winding:

There are mainly two types of windings and are known as Lap winding and have winding. The difference between the two is simply due to the dissimilar arrangements of the end connection at the front of commutator end of armature. Each winding can be arranged progressively or retrogressively. However, for both the windings the rules of winding are common. In Fig. shows lap and wave winding for single coil. Note the position of connections at commutator and the distance of the resultant pitch.

The common rules that apply for both the type of windings are

a. For the full pitched winding, the front pitch and the hack pitch shall be approximately equal to pole pitch in which case increased e.m.f. would result. Fractional pitched windings are also used in special cases.

b. Both pitches should be odd, otherwise placing of coils in the armature would be difficult. if front pitch and hack pitch are even, then both the coil sides would occupy either in the upper half or lower half in which case it would be difficult to wind.

c. The number of commutator segments should be equal to the number of slots or coils as the front end of the conductors are joined in pairs.

d. Upon completing winding. the windings should close by itself after traversing the slots.

e. The number of commutator segments shall be equal to the number of slots.

If two similar windings on the same armature connecting the even numbered commutator bars to one winding and odd numbered commutator bar to second winding, it is termed as duplex winding, and similarly if three windings each connected to one third of the commutator bars are connected, then it is termed as triplex winding.

Armature Winding Diagrams:

In any dc armature winding, a coil is a loop of number of wires in series consisting of two inductor portions and two end turns or overlaps. The inductor portion of the coil is inserted into the slot of the armature. Pitch of the coil means span of the coil i.e the slot distance between two inductor portion of the coil. Back pitch is the distance between the two conductors which forms the loop and front pitch is the distance between the conductor of one loop and the first conductor of the next loop. Both the lap and wave winding pitch distance is explained above.

One side of the armature conductor is fixed to the commutator segments. The end coils have to be connected to these segments. The segmental distance between the two coil ends is called commutator pitch and is denoted b Yc which is given by,

Yc = {Total no. of segment + 1} / P2

In the case of single layer winding the slot contains only one layer of coil whereas in the case of double layer winding the slot contains two layers. The first layer is at the bottom of the slot which is well insulated from the core as well as from the second layer. The second layer is wound on top of the slot over the insulated first layer.