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Working Principle of a Single Phase Induction Motor

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. Both the theories are similar and explain the
reason for the production of torque when the rotor is rotating
Induction Motor Synchronous Speed
An induction motor cannot run at synchronous speed under normal operating
conditions because it relies on a difference between the stator’s rotating magnetic field
speed and the rotor’s speed to generate torque. If an induction motor were to run at
synchronous speed, the rotor would not experience any torque due to the absence of a
relative motion between the stator’s magnetic field and the rotor, leading to a stoppage
of the motor.
 A DC series motor should always be started with load because at no load it will rotate
with dangerously high speed Important: When the motor is connected across the
supply mains without load, it draws small current from the supply mains This current
will flow through the series field and armature, the speed tends to increase so that
back emf may approach the applied voltage in magnitude The increase in back emf
weakens the armature current and hence the field current This cause again increases
the speed so the back emf Thus, the field continues to weaken and speed continues
to increase until the armature produced such centrifugal force that it is coming out
from its shaft and gets damaged.

DC series motors have a higher starting torque than DC shunt motors of the same
rating due to several factors:
In a DC series motor, the field winding is connected in series with the armature
winding, meaning the field current is the same as the armature current. This
results in a stronger magnetic field at the start, leading to a higher starting
torque.
The torque in a DC series motor is directly proportional to the square of the
armature current before magnetic saturation, which means a small increase in
armature current can result in a significant increase in torque.
The field winding in a DC series motor uses fewer turns of thicker wire, which
allows it to handle higher currents without overheating, contributing to the
higher starting torque.
DC series motors are designed to have a high starting torque, making them
suitable for applications that require a significant initial force, such as electric
locomotives, hoists, and cranes.
In contrast, a DC shunt motor has a field winding connected in parallel with the
armature winding, leading to a lower starting torque because the field current is
not equal to the armature current, and the torque is directly proportional to the
armature current.
The rotor design of a DC series motor is optimized for high starting torque,
whereas the rotor of a DC shunt motor is designed for constant speeds, which
limits its starting torque.
DC shunt motors have a field winding with high resistance, which draws a small
current, resulting in a lower starting torque compared to the DC series motor.
The starting torque of a DC shunt motor is lower and more constant, making it
less suitable for applications requiring a high initial torque.
DC series motors can provide a higher starting torque due to their construction,
which allows for a stronger magnetic field at the start, enhancing the initial force
generated.
 CHAT

Commutation in DC Machines
Commutation in a DC machine is the process of converting the alternating current
generated in the armature winding into direct current using a commutator and
stationary brushes. This process is essential for the operation of DC generators and
motors, ensuring that the current flowing through the armature coil reverses
direction every half turn, which helps in maintaining a steady torque in one
direction. Ideal commutation occurs when the current reversal is completed within
the commutation period, avoiding sparking and potential damage to the machine.
3 Phase IM Equivalent Circuit
To derive the exact equivalent circuit of a 3-phase induction motor (IM) on a per-
phase basis, follow these steps:
1. Identify the Components:
Stator Resistance (R1): Represents the resistance of the stator windings.
Stator Leakage Reactance (X1): Represents the reactance due to the leakage
flux in the stator windings.
Rotor Resistance (R2): Represents the resistance of the rotor windings.
Rotor Leakage Reactance (X2): Represents the reactance due to the leakage
flux in the rotor windings.
Magnetizing Reactance (XM): Represents the reactance due to the
magnetizing flux.
Core Loss Resistance (Rc): Represents the core losses.
2. Per-Phase Equivalent Circuit:
The per-phase equivalent circuit is derived by considering the motor as three
single-phase circuits connected in a star or delta configuration.
Each phase of the 3-phase induction motor can be represented by a single-
phase equivalent circuit.
3. Transfer Rotor Parameters to Stator Side:
The rotor parameters are referred to the stator side using the turns ratio (K).
The referred rotor resistance is R2′=K2R2​and the referred rotor reactance is
X2′=K2X2​.
4. Combine Components:
Combine the stator and referred rotor components to form the equivalent
circuit.
The equivalent circuit includes the stator resistance (R1), stator leakage
reactance (X1), referred rotor resistance (R2′), referred rotor reactance (X2′),
magnetizing reactance (XM), and core loss resistance (Rc).
5. Final Per-Phase Equivalent Circuit:
The final per-phase equivalent circuit can be represented as: [ \text{Stator
Voltage} = \text{Stator Resistance} + \text{Stator Leakage Reactance} +
\text{Referred Rotor Resistance} + \text{Referred Rotor Reactance} +
\text{Magnetizing Reactance} + \text{Core Loss Resistance} ]
Mathematically, this can be expressed as: [ V_{ph} = R1 + jX1 + \frac{R2}{K^2} +
j\frac{X2}{K^2} + jXM + Rc ]
6. Simplify for Steady-State Analysis:
For steady-state analysis, the magnetizing branch (XM and Rc) can often be
neglected if the core losses and magnetizing current are small compared to
the load current.
The simplified per-phase equivalent circuit is: [ V_{ph} = R1 + jX1 + \frac{R2}
{K^2} + j\frac{X2}{K^2} ]
This exact equivalent circuit allows for the evaluation of the motor’s performance
characteristics under steady-state conditions, including torque, efficiency, and
power transfer
What is a Three-Point Starter?
An electrical device known as a three-point starter is used to start and
maintain the speed of a DC shunt motor. The connection of resistance in
this circuit is in series which decreases the initial high current and
protects the equipment against any electrical failures. Here, the event of
back e.m.f plays an essential part in operating the motor. This EMF
extends when the motor's armature begins to rotate in the magnetic
field by acting against the voltage supply.
WHAT IS SLIP ? DEDUCE A RELATIONSHIP BETWEEN MOTOR COOLENT FREQUENCY AND SUPPLY
FREQUENCY IN TERMS OF SLIP OF AN IM
Slip Frequency Relationship
Slip in an induction motor is the difference between the synchronous speed of the
rotating magnetic field and the actual rotor speed. It is a measure of how much the
rotor lags behind the rotating magnetic field. The slip is expressed as a fraction or
percentage of the synchronous speed.