- Right Hand Thumb Rule
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Flemings left Hand Rule for direction of current (for Motor)
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If the first 3 fingers of left hand are held mutually at right angle to each other. First finger indicates magnetic field middle finger indicates direction of current and thumb indicated force exerted.
Construction details of D.C. Machine:
Whether machine is D.C. generator or motor the construction basically remains the same.
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A cross section of typical D.C. machine
1) Yoke:
a) Functions
1. It serves the purpose of outermost cover of the D.C. machine. So that the insulating materials get protected from harmful atmospheric elements like moisture. Dust and various gases like
, acidic fumes etc.
2. It provides mechanical support to the poles.
3. It forms a part of the magnetic circuit.
It provides a path of low reluctance for magnetic flux. The low reluctance path is important to avoid wastage of power to provide same flux large current and hence the power is necessary if the path has high reluctance to produce the same flux.
4. Choice of material: - It is prepared by using cast iron, silicon steel is used which provides high permeability i.e. low reluctance and gives good mechanical strength.
2) Poles:
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Pole structure
Each Pole is divided into two parts namely
- Pole core
- Pole shoe
Functions of pole core and pole shoe: -
- Pole core basically carries a field winding which is necessary to produce the flux.
- It directs the flux produced through air gap to armature core to the next pole.
- Pole shoe enlarge the area of armature core to come across the flux, which is necessary to produce larger induced e.m.f. To achieve this, sports shoe has been given a particular shape.
Choice of material: -
It is made up of magnetic material like cast iron or cast steel.
As it requires a definite shape and size, laminated construction is used. The laminations of required size and shape are stamped together to get a pole which is then bolted to the yoke.
3) Field Winding (
:
The field winding is wound on the pole core with a definite direction.
A) Functions: -
To carry current due to which pole core on which the field winding is placed behaves as an electromagnet, producing necessary flux.
As it helps in producing the magnetic field i.e. exciting the poles as an electromagnet it is called Field winding or Exciting winding.
b) Choice of material: -
It has to carry current hence obviously made up of some conducting material.
So aluminium or copper is the choice. But field coils are required to take four types of shape and bent about pole core and copper has good pliability i.e. it can be bend easily. So copper is the proper choice. field winding is divided into various coils called field coils. These are connected in series with each other and wound in such direction around pole cores, such that alternate 'N' and 'S' poles are formed.
The total number of poles is denoted as P.
4) Armature:
The armature is further divided into two parts namely
- Armature core
- Armature winding
1. Armature core: - Armature core is cylindrical in shape mounted on the shaft. It consists of slots on its periphery and air ducts to permit the air flow through armature which serves cooling purpose.
a) Functions-
1) Armature core provides house for armature winding i.e. armature conductors.
2) To provide the path of low reluctance to the magnetic flux produced by the field winding.
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b) Choice of material: -
As it has to provide a low reluctance path to the flux, it is made up of magnetic material like cast iron or cast steel.
It is made up of laminated construction to keep Eddy current loss as low as possible. A single circular lamination used for the construction of armature core is shown in figure.
3. Armature winding
Armature winding is nothing but the interconnection of the armature conductors placed in the slots provided on the armature core periphery.
When the armature is rotated in case of generator magnetic flux gets cut by armature conductors and e.m.f gets induced in them.
a) Functions
1) Curvatures of e.m.f take place in the armature winding in case of generators.
2) To carry the current supplied in case of D.C. motors.
3) To do the useful work in the external circuit.
b) Choice of Material: -
As armature winding carries entire current which depends on external load, it has to be made up of conducting material which is copper.
5. Commutator:
The basic nature of e.m.f in the armature conductors is alternating. This needs verification in case of D.C. generator, which is possible by a device called commutator.
A) Functions:
1) To facilitate the collection of current from the armature conductors.
2) To convert internally developed alternating e.m.f to unidirectional (D.C.) e.m.f.
3) To produce unidirectional torque in case of motors
b) Choice of Material: -
As it collects current from armature, it is also made up of copper segments.
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It is cylindrical in shape and is made up of wedge-shaped segments of hand drawn high conductivity copper. the segments are insulated from each other by thin layer of Mica.
Each commutator segment is connected to the armature conductor by means of copper lug or strip. This construction is shown in figure above.
6. Brushes and Brush Gear:
Brushes are stationary and resting on the surface of the commutator.
a) Function-
To collect current from the computer and make it is available to stationary external circuit.
b) Choice of Material: -
Brushes are normally made up of soft material like carbon.
To avoid wear and tear of commentator the brushes are made up of soft material like carbon.
7) Bearings:
Ball bearings are usually used as they are more reliable. For heavy duty machines roller bearing are preferred.
The rotating and stationary parts of an electrical machine can be called as rotor and stator respectively. The rotor or stator of electrical machines acts as a power-producing component and is called as an armature. The electromagnets or permanent magnets mounted on the stator or rotor are used to provide magnetic field of an electrical machine. The generator in which permanent magnet is used instead of coil to provide excitation field is termed as permanent magnet synchronous generator or also simply called as synchronous generator.
Construction of Synchronous Generator:
In general, synchronous generator consists of two parts rotor and stator. The rotor part consists of field poles and stator part consists of armature conductors. The rotation of field poles in the presence of armature conductors induces an alternating voltage which results in electrical power generation.
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Construction of Synchronous Generator
The speed of field poles is synchronous speed and is given by
Where, ‘f’ indicates alternating current frequency and ‘P’ indicates number of poles.
Synchronous Generator Working Principle:
The principle of operation of synchronous generator is electromagnetic induction. If there is a relative motion between the flux and conductors, then an emf is induced in the conductors. To understand the synchronous generator working principle, let us consider two opposite magnetic poles in between them a rectangular coil or turn is placed as shown in the below figure.
Now, if we consider a practical synchronous generator, then field magnets rotate between the stationary armature conductors. The synchronous generator rotor and shaft or turbine blades are mechanically coupled to each other and rotate at synchronous speed. Thus, the magnetic flux cutting produces an induced emf which causes the current flow in armature conductors. Thus, for each winding the current flows in one direction for the first half cycle and current flows in the other direction for the second half cycle with a time lag of 120 degrees (as they displaced by 120 degrees). Hence, the output power of synchronous generator can be shown as below figure.
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Construction details of D.C. Machine:
Whether machine is D.C. generator or motor the construction basically remains the same.
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A cross section of typical D.C. machine
1) Yoke
a) Functions
1. It serves the purpose of outermost cover of the D.C. machine. So that the insulating materials get protected from harmful atmospheric elements like moisture. Dust and various gases like
, acidic fumes etc.
2. It provides mechanical support to the poles.
3. It forms a part of the magnetic circuit.
It provides a path of low reluctance for magnetic flux. The low reluctance path is important to avoid wastage of power to provide same flux large current and hence the power is necessary if the path has high reluctance to produce the same flux.
4. Choice of material: - It is prepared by using cast iron, silicon steel is used which provides high permeability i.e. low reluctance and gives good mechanical strength.
2) Poles
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Pole structure
Each Pole is divided into two parts namely
4. Pole core
5. Pole shoe
Functions of pole core and pole shoe: -
- Pole core basically carries a field winding which is necessary to produce the flux.
- It directs the flux produced through air gap to armature core to the next pole.
- Pole shoe enlarge the area of armature core to come across the flux, which is necessary to produce larger induced e.m.f. To achieve this, sports shoe has been given a particular shape.
Choice of material: -
It is made up of magnetic material like cast iron or cast steel.
As it requires a definite shape and size, laminated construction is used. The laminations of required size and shape are stamped together to get a pole which is then bolted to the yoke.
3) Field Winding (
:
The field winding is wound on the pole core with a definite direction.
A) Functions: -
To carry current due to which pole core on which the field winding is placed behaves as an electromagnet, producing necessary flux.
As it helps in producing the magnetic field i.e. exciting the poles as an electromagnet it is called Field winding or Exciting winding.
b) Choice of material: -
It has to carry current hence obviously made up of some conducting material.
So aluminium or copper is the choice. But field coils are required to take four types of shape and bent about pole core and copper has good pliability i.e. it can be bend easily. So copper is the proper choice. field winding is divided into various coils called field coils. These are connected in series with each other and wound in such direction around pole cores, such that alternate 'N' and 'S' poles are formed.
The total number of poles is denoted as P.
4) Armature
The armature is further divided into two parts namely
- Armature core
- Armature winding
1. Armature core: - Armature core is cylindrical in shape mounted on the shaft. It consists of slots on its periphery and air ducts to permit the air flow through armature which serves cooling purpose.
a) Functions-
1) Armature core provides house for armature winding i.e. armature conductors.
2) To provide the path of low reluctance to the magnetic flux produced by the field winding.
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b) Choice of material: -
As it has to provide a low reluctance path to the flux, it is made up of magnetic material like cast iron or cast steel.
It is made up of laminated construction to keep Eddy current loss as low as possible. A single circular lamination used for the construction of armature core is shown in figure.
6. Armature winding
Armature winding is nothing but the interconnection of the armature conductors placed in the slots provided on the armature core periphery.
When the armature is rotated in case of generator magnetic flux gets cut by armature conductors and e.m.f gets induced in them.
a) Functions
1) Curvatures of e.m.f take place in the armature winding in case of generators.
2) To carry the current supplied in case of D.C. motors.
3) To do the useful work in the external circuit.
b) Choice of Material: -
As armature winding carries entire current which depends on external load, it has to be made up of conducting material which is copper.
5. Commutator
The basic nature of e.m.f in the armature conductors is alternating. This needs verification in case of D.C. generator, which is possible by a device called commutator.
A) Functions:
1) To facilitate the collection of current from the armature conductors.
2) To convert internally developed alternating e.m.f to unidirectional (D.C.) e.m.f.
3) To produce unidirectional torque in case of motors
b) Choice of Material: -
As it collects current from armature, it is also made up of copper segments.
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It is cylindrical in shape and is made up of wedge-shaped segments of hand drawn high conductivity copper. the segments are insulated from each other by thin layer of Mica.
Each commutator segment is connected to the armature conductor by means of copper lug or strip. This construction is shown in figure above.
6. Brushes and Brush Gear:
Brushes are stationary and resting on the surface of the commutator.
a) Function-
To collect current from computer and make it available to stationary external circuit.
b) Choice of Material: -
Brushes are normally made up of soft material like carbon.
To avoid wear and tear of commentator the brushes are made up of soft material like carbon.
7) Bearings:
Ball bearings are usually used as they are more reliable. For heavy duty machines roller bearing are preferred.
Types and Applications of DC motors:
Voltage and current relationship:
The voltage across armature and field winding is same equal to the supply voltage V.
The total current drawn from the supply is denoted as line current 
Now flux produced by the field winding is proportional to the current passing through it i.e. 
As long as supply voltage is constant which is generally so in practice, the flux produced is constant.
Hence D.C. shunt motor is called constant flux motor.
DC series motor:
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In this type of motor the series field winding is connected in series with armature and the supply as shown in figure. Let 
the resistance of all the series field winding then the value of 
is very small and it is made up of small number of turns having large cross section area.
Voltage and current relationship:
Let 
be the total current drawn from the supply
So
And,
Supply voltage has to overcome the drop across series field building in addition to 
drop across armature winding.
In series motor entire armature current is passing through the series field winding. So flux produced is proportional to the armature current.
For series motor
DC compound motor:
The compound motor consists of part of the field winding connected in series and part of the field winding connected in parallel with the armature. It is further classified as short shunt compound and long shunt compound motor.
Long shunt compound motor
In this type the shunt field winding is connected across the combination of armature and the series field winding as shown in figure
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Voltage and current relationship:
Let 
be the resistance of series field and 
resistance of shunt field winding.
The total current drawn from supply is 
So, 
But,
And,
V=
But as
Short shunt compound motor:
In this type the shunt field is connected properly in parallel with armature and the series field is connected in series with the combination as shown in figure.
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The entire line current is passing through the series field winding
Now the drop across the shunt field winding is to be calculated from the voltage equation
But, 
Drop across shunt field winding=V-
A long shunt compound motor can be of cumulative or differential type. Similarly, short shunt compound motor can be cumulative order differential type.
Torque and speed equations:
Before analysing the various characteristics of motors, latest device the torque and speed equations as applied to various types of motors
For the torque equation
This is because 
to a constant for a given motor.
Now 
is the flux produced by the field winding and is proportional to the current passing through the field winding.
For a D.C. shunt motor. 
Is constant as long as supply voltage is constant. Hence flux is also constant.
For shunt motors
For DC series motor 
same as 
. Hence flux is proportional to the armature current 
For series motor similarly as 
We can write the speed equation as 
Neglecting brush drop
So for shunt motor the flux is constant
While for series motor flux is proportional to 
These relations play an important role in understanding the various characteristics of different type of motors.
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Back EMF in DC motor:
- It is seen in the generating action that when a conductor cuts the line of flux EMF gets induced in the conductor. In a DC motor after a motoring action a major start rotating and armature conductor cut the main flux so is there a generating action existing in a motor after Mona following actions
- There is induced EMF in the rotating armature conductors according to Faraday’s law of electromagnetic induction this induced EMF in the armature always act in the opposite direction to the supply voltage.
- This is according to the Lenz’s law which states that the direction of the induced EMF is always so as to oppose the cause producing it.
- In a DC motor electrical input that is the supply voltage is the cause for the armature current and the motoring action and hence this induced EMF oppose the supply voltage this EMF tries to set up a current through the our nature which is in the opposite direction to that which supply voltage is force in through the conductor
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As this EMF always opposes the supply voltage it is called back EMF and denoted as 
.Though it is denoted as 
basically it gets generated by the generating action which we have seen earlier in case of generators. So its magnitude can be determined by the EMF equation which is derived earlier.
Where all symbols carry the same meaning as seen earlier in case of generators
This EMF issued systematically in figure a so if v is supply voltage in volts &
is the value of the armature resistance the equivalent electric circuit can be shown in figure b
Voltage equation of DC motor:
From the equivalent circuit the voltage equation for a DC motor can be obtained as
The brush drop is practically neglected.
Hence the armature current 
is expressed as
Significance of back EMF:
Due to the presence of back EMF the DC motor becomes a regulating machine that is motor adjust itself to draw the armature current just enough to satisfy the load demand.
His basic principle of this fact is that the back EMF is proportional to speed 
When load is suddenly put on the motor. Motor tries to slow down. So speed of the motor reduces due to which back EMF also decreases. So the net voltage across the armature
Increases and motor draws more armature current.
Due to the increased armature current force experienced by the conductors and hence the torque on the armature increases. The increase in the torque is just sufficient to satisfy increase load demand.
When load on the motor is decreased the speed of the motor tries to increase. Hence back EMF increases. This 
to reduce which eventually reduces the current drawn by the armature. The motor speed stops increasing when the armature current is just enough to produce the less torque required by the new load.
So back EMF regulate the flow of armature current and it automatically alters the armature current to meet the load requirement. This is the practical significance of the back EMF.
Head start the speed N of the motor is zero hence the back EMF is also zero.
1) A 220-volt DC motor has an armature resistance of 0.75 ohm. It is drawing and armature current of 30 A, driving a certain load. Calculate the induced EMF in the motor under this condition.
V=200V 
Are the given values
For a motor,
V=
220=
+30*0.75
=197.5 V
This is the induced EMF called a back EMF in a motor
2) Find the useful flux per pole on no load of a 250V 6 pole shunt motor having two circuit connected armature winding with 225 conductors. At normal working temperature the overall armature resistance including brushes is 0.2 ohm. The armature current is 13.3A at the no load speed of 908 RPM.
Solution
V=250 P=6 Z=220 A=2
As two circuit armature
N=908 r.m.s
For a DC shunt motor
250=
+13.3*0.2 i.e. 
Back emf
is given by
Power equation of a DC motor
The voltage equation of a DC motor is given by
V= 
Multiplying both sides of the above equation by 
V
= 
This equation is called as power equation of a DC motor
V
=net electric power input to the armature measured in watts
Power loss due to the resistance of the armature called armature copper loss.
So difference between V
and 
is input losses gives the o/p of the armature.
So 
is called electric equivalent of gross mechanical power developed by the armature.
This is denoted as 
Therefore I/P to the armature-armature copper loss = gross mechanical power developed in the armature
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DC shunt motor
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In this type the field winding is connected across the supply as shown in figure
Let 
be the resistance of shunt field winding and 
be the resistance of armature winding.
The value of 
very small while 
is quite large. Hence shunt field winding has more number of turns with less cross sectional area.
Find no load vtg E2
Remove the load and measure the reading of V2 meter ew will get n load vtg E2
E2 = V2 when load is absent
Now connect load and measure V2 this is now the load voltage
For each reading E2 will be same but V2 will change acc. To load
- Form Results Plot graph for efficiency and regulation against I2 and O/P power W
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Efficiency: it is the ratio output power to input power of transformer
= 
Output power = input power – total loss
Input power = O/P + losses
O/P power = KVA 
Cos Ø2 
1000
Or = V2 
I2 Cos Ø2
Losses = Pi + PCU (F.L)
= iron + copper loss
Full load = 
Half load (H.L) or 50% or 0.5 = 
= 
Maximum efficiency – for numerical:
The efficiency of T/F is Maximum when copper loss equates iron loss this is the condition for max efficiency
i.e. Pi = PCU
= 
PCU = Pi at max n
Where K
VA at max n given = Full load KVA 
Torque equation of DC Motor gives the amount and nature of electrical torque Te developed whenever it is taken into service. Basically the performance of DC machine centres around two equations. One is EMF equation and another is Torque Equation. Therefore, understanding of torque equation is a must for performance analysis. These equations equally apply for both i.e. generator and motor operation mode of DC machine. In generator mode of operation, this torque opposes the prime mover torque to convert the mechanical energy into electrical energy. But, in motor operation mode, electrical torque is utilized to drive the load coupled to motor shaft.
Torque in DC Motor depends upon the constructional as well as operational parameters. Constructional parameters include number of poles P, number of conductors Z and number of parallel paths ‘a’ in armature. Operational parameters include armature current Ia and field excitation.
Torque produced in a DC Motor is given as
Te = KaØIa …….(1)
Where Ø = Total flux per pole
Ian = Armature current, and
Ka = (PZ/2πa).
Since Ka depends upon the constructional design of DC Motor or generator, it is known as armature constant. Here P is number of poles, Z is total number of armature conductor and ‘a’ is the number of parallel paths in armature.
Equation (1) is the torque equation for DC machine. This equation is applicable for both DC Motor and Generator.
Derivation of Torque Equation of DC Motor:
As we know that, a current carrying conductor experiences a force when kept in external magnetic field. This force is given as
F = iLB …….. (2)
Where i is the current flowing in the conductor, L is length of conductor and B is the density. We will apply this concept to derive the torque equation of DC machine. But before we go to derive, there are some important points which must be known:
- In DC machine, rotor carries the armature winding and field winding is mounted on stator. Thus rotor conductors are in the magnetic field produced by stator field winding.
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- Unidirectional torque is produced in DC machine. This is because, as we go from one pole to another pole, the direction of conductor current reverses. What does this exactly mean? This means when the direction of magnetic field changes (as we move from North to South Pole) the current direction also changes resulting in unidirectional torque.
Let us now move forward to derive the torque equation using (2). Since Ø is the total flux per pole and P is the total number of poles, therefore total air gap flux (Øt) will be
Øt = PØ
If D and L are the rotor diameter and the length of the machine in meters, then
Cross Sectional area of machine = πDL
Therefore,
Magnetic Flux Density B = Total Flux / Area
= (PØ / πDL) Wb/m2
Again, total armature current is Ia and number of parallel path is ‘a’, therefore current in each conductor = (Ia / a)
Now, from equation (2),
Force on each conductor, F = (Ia / a) (PØ / πDL) (L)
= (IaPØ / πaD)
This force F is causes the rotor to rotate around its axis. The perpendicular distance of this force F from the rotor axis is (D/2). Therefore, the torque produced by this force for a single conductor is given as below.
Torque on single conductor = FD/2
= (IaPØ / 2πa)
As there are total Z conductors, the total torque is the sum of torques acting on all the Z conductors.
Total Torque Te = Zx (IaPØ / 2πa)
= (ZP / 2πa) Ø Ia
Assuming Ka = (ZP / 2πa) = constant for a given machine
Torque equation of DC Motor, Te = KaØIa
⇒Te α ØIa
Torque of a given DC Motor depends on the armature current and magnetic flux.
Voltage and current relationship:
The voltage across armature and field winding is same equal to the supply voltage V.
The total current drawn from the supply is denoted as line current 
Now flux produced by the field winding is proportional to the current passing through it i.e. 
As long as supply voltage is constant which is generally so in practice, the flux produced is constant.
Hence D.C. shunt motor is called constant flux motor.
DC series motor:
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In this type of motor the series field winding is connected in series with armature and the supply as shown in figure. Let 
the resistance of all the series field winding then the value of 
is very small and it is made up of small number of turns having large cross section area.
Voltage and current relationship:
Let 
be the total current drawn from the supply
So
And,
Supply voltage has to overcome the drop across series field building in addition to 
drop across armature winding.
In series motor entire armature current is passing through the series field winding. So flux produced is proportional to the armature current.
Series motor
DC compound motor:
The compound motor consists of part of the field winding connected in series and part of the field winding connected in parallel with the armature.it is further classified as short shunt compound and long shunt compound motor.
Long shunt compound motor
In this type the shunt field winding is connected across the combination of armature and the series field winding as shown in figure
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Voltage and current relationship:
Let 
be the resistance of series field and 
resistance of shunt field winding.
The total current drawn from supply is 
So, 
But,
And,
V=
But as
Short shunt compound motor:
In this type the shunt field is connected properly in parallel with armature and the series field is connected in series with the combination as shown in figure.
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The entire line current is passing through the series field winding
Now the drop across the shunt field winding is to be calculated from the voltage equation
But, 
Drop across shunt field winding=V-
A long shunt compound motor can be of cumulative or differential type. Similarly, short shunt compound motor can be cumulative order differential type.
Torque and speed equations:
Before analysing the various characteristics of motors, latest device the torque and speed equations as applied to various types of motors
for the torque equation
This is because 
to a constant for a given motor.
Now 
is the flux produced by the field winding and is proportional to the current passing through the field winding.
For a D.C. shunt motor. 
Is constant as long as supply voltage is constant. Hence flux is also constant.
for shunt motors
For DC series motor 
same as 
. Hence flux is proportional to the armature current 
For series motor lly as 
We can write the speed equation as 
neglecting brush drop
So for shunt motor the flux is constant
While for series motor flux is proportional to 
These relations play an important role in understanding the various characteristics of different type of motors.
Consider- 3Фslip ring I.M
Cut section diagram: -
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The induction motor has following important parts: -
- Stator: - it is the stationary part of induction motor and it is one of important part in induction motor.
- Rotor: - the rotor is the rotating part of induction motor which consists of rotor wdg.
- Stator winding: - this wdg. Is mounted on devastator and it generates the RMF i.e. rotating magnetic field.
- Rotor winding: - rotor winding is used to rotate the shaft of motor. This wdg is provided on rotor
- Frame: - it provides the mechanical support to the motor. It is the outer covering of motor. It protects the internal parts of motor from damage.
- Shaft: - shaft is used to connect to the load and four rotations.
- Slip rings and brushes: - slip rings are mounted on the shaft which is connected with brushes from which connection is given to the external resistant or rheostat
- Cooling fan: - this is provided for cooling purpose of motor and its internal parts.
Principle of operation of induction motor:
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- When the 3ФA.C supply is connected across the stator of induction motor, the current starts flowing through the stator wdg. I.e. the stator condition.
- Due to this current of flux (Ф) is established in the stator wdg. This flux (Ф) is alternating (changing) in nature. Thus this flux links with the rotor also, and a Rotating Magnetic Field (RMF) is produced.
- This flux (Ф) induces in the rotor also. The RMF is produced in the air gap between stator and rotor.
- The rotor is rotating part which is till stationary, show the rotating magnetic field is cut by stationary rotor and an EMF is induced in the rotor winding. According to faraday's law of EMI the rotor EMF gives the rise to rotor current which opposes the main cause producing it according Lenz's law.
Types of induction motor:
Two main types depending upon the rotor
- Squirrel cage induction motor (squirrel cage rotor)
- Slip ring induction motor (slip ring or wound rotor)
Induction motor is also available in 1Фsupply i.e.
1. Resistance split phase induction motor
2. Capacitor start induction motor
3. 1Фinduction motor i.e. A.C series motors
4. Shaded pole induction motor
Torque equation of induction motor: -
Torque produced in induction motor depends upon the following factors
1. The rotor power factors (Cos) under running condition
2. The rotor current under running condition
3. The part of RMF which induces EMF in rotor wdg i.e. flux (Ф)
We can mathematically say that,
, As per DC (M) equation
But in case of induction motor
Suffix 1 -> used for stator/stator parts (qty)
Suffix 2-> used for rotor/rotor parts (qty)
Therefore, 
---- (1)
= flux that induces the EMF in rotor
= rotor current under running condition
= P.F of rotor
But, 
stator vtg 
also i.e
---- (2)
Transformation ratio i.e. given by 
Therefore,
And hence
also
at slip ’S’ is given by 
And also 
at slip ‘S’ is 
=S.
Hence 
in equation can be replaced by 
i.e. 
U
=
---- (3) ---- (
)
4
=
------ (4)
Subtract (3) and (4) into (1) equation we get,
At starting condition slip S=1 So,
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A DC generator or direct current generator is one kind of electrical machine, and the main function of this machine is to convert mechanical energy into DC (direct current) electricity. The energy alteration process uses the principle of energetically induced electromotive force.
The DC generator working principle is based on Faraday’s laws of electromagnetic induction.
When a conductor is located in an unstable magnetic field, an electromotive force gets induced within the conductor. The induced e.m.f magnitude can be measured from the equation of the electromotive force of a generator.
If the conductor is present with a closed lane, the current which is induced will flow in the lane.
In this generator, field coils will generate an electromagnetic field as well as the armature conductors are turned into the field. Therefore, an electromagnetically induced electromotive force (e.m.f) will be generated within the armature conductors. The path of induced current will be provided by Fleming’s right-hand rule.
Torque slip region for stable regimen
S= small
Unstable: -
Types of Torque:
Total Torque
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A Single- Phase Induction Motor consists of a single- phase winding which is mounted on the stator of the motor and a cage winding placed on the rotor. A pulsating magnetic field is produced, when the stator winding of the single-phase induction motor shown below is energised by a single- phase supply.
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The word Pulsating means that the field builds up in one direction falls to zero and then builds up in the opposite direction. Under these conditions, the rotor of an induction motor does not rotate. Hence, a single -phase induction motor is not self-starting. It requires some special starting means.
If the 1 phase stator winding is excited and the rotor of the motor is rotated by an auxiliary means and the starting device is then removed, the motor continues to rotate in the direction in which it is started.
The performance of the single- phase induction motor is analysed by the two theories. One is known as the Double Revolving Field Theory, and the other is Cross Field Theory.
The double revolving field theory of single- phase induction motor states that a pulsating magnetic field is resolved into two rotating magnetic fields. They are equal in magnitude but opposite in directions. The induction motor responds to each of the magnetic fields separately. The net torque in the motor is equal to the sum of the torque due to each of the two magnetic fields.
The equation for an alternating magnetic field is given as
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Where βmax is the maximum value of the Sinusoidally distributed air gap flux density produced by a properly distributed stator winding carrying an alternating current of the frequency ω, and α is the space displacement angle measured from the axis of the stator winding.
So, the equation (1) can be written as
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The first term of the right-hand side of the equation (2) represents the revolving field moving in the positive α direction. It is known as a Forward Rotating field. Similarly, the second term shows the revolving field moving in the negative α direction and is known as the Backward Rotating field.
The direction in which the single- phase motor is started initially is known as the positive direction. Both the revolving field rotates at the synchronous speed.
ωs = 2πf in the opposite direction.
Thus, the pulsating magnetic field is resolved into two rotating magnetic fields. Both are equal in magnitude and opposite in direction but at the same frequency.
At the standstill condition, the induced voltages are equal and opposite as a result; the two torques are also equal and opposite. Thus, the net torque is zero and, therefore, a single- phase induction motor has no starting torque.
Methods for Making Single Phase Induction as Self- Starting Motor:
The single-phase induction motors are not self-starting because the produced stator flux is alternating in nature and at the starting, the two components of this flux cancel each other and hence there is no net torque. The solution to this problem is that if we make the stator flux rotating type, rather than alternating type, which rotates in one particular direction, then the induction motor will become self-starting.
Now for producing this rotating magnetic field, we require two alternating flux, having some phase difference angle between them. When these two fluxes interact with each other, they will produce a resultant flux. This resultant flux is rotating in nature and rotates in space in one particular direction only.
Once the motor starts running, we can remove the additional flux. The motor will continue to run under the influence of the main flux only. Depending upon the methods for making asynchronous motor as Self-Starting Motor, there are mainly four types of single -phase induction motor namely,
- Split phase induction motor,
- Capacitor start inductor motor,
- Capacitor start capacitor run induction motor,
- Shaded pole induction motor.
- Permanent split capacitor motor or single value capacitor motor.
Applications:
These are used in low power applications and widely used in domestic applications as well as industrial. And some of those are mentioned below:
- Pumps
- Compressors
- Small fans
- Mixers
- Toys
- High speed vacuum cleaners
- Electric shavers
- Drilling machines
References:
1. V. Del Toro “ Principles of Electrical Engineering”, Prentice Hall
2. I.J. Nagrath “ Basic Electrical Engineering”, Tata McGraw Hill
3. D.F. Fitzgerald, A. Grabel Higginbotham “ Basic Electrical Engineering”, McGraw Hill
4. Mittal & Mittal “ Basic Electrical Engineering”, Tata McGraw Hill
5. B.L. Theraja and A.K. Theraja“A Text Book of Electrical Technology”, Volume - I & II
6. J. Millman & Halkias “ Electronic Devices & Circuits”, Tata McGraw Hill
7. Herbert Taub “ Digital Circuits & Microprocessors”, McGraw Hill
