# Induction motor working principle and its equations

The induction motor can simply classify as single phase induction motor and three phase induction motor. The main induction motor working principle behind these motor are same. Induction motor working principle is also similar to the electromagnetic induction principle and induction motor is also known as the rotating transformer.

## Synchronous Speed of Induction Motor (Ns)

The rotational speed of the rotating magnetic field produced by the stator is called synchronous speed. This depends on the frequency of the three phase supply and the number of pole pairs for which the stator three phase winding has been made.

The contact of electrical machines angle in air gap space can be measured in two units of angles.

1. Electrical Angles: Electrical angle are measured only flux distribution in the air gap
1. Mechanical Angles: This angle is measured only two of the air gap.

General Electrical Angle – θe

General Mechanical Angle – θm

Number of Poles – p

The synchronous speed of induction motor can also say as the rotating field of the electromagnetic field.

θe = p.θm

## Slip of Induction Motor

The rotor of the three-phase induction motor is always running at the speed which is slightly below the synchronous speed of the induction motor.

This is the main requirement for the induction motor to produce torque. The per unit difference between the synchronous speed (Ns) and rotor speed (Nr) is known as the slip of the induction motor.

S =Ns- NrNs x 100%

Per unit Slip – S

Synchronous Speed – Ns

Rotor Speed – Nr

For the motor which continually running which must be a torque generate on the rotor. To produce the torque there must be a current in the rotor side.

The meaning of this is being induced voltage in the rotor winding. To have an induced voltage on the rotor winding must see a rotational speed of the air gap and magnetic flux. The relative speed of three phase induction motor should always positive (Ns- Nr>0)

## The frequency of Rotor in induced emf.

The frequency of the rotor induced emf depends on the slip of the motor and the frequency of the stator supply voltage. Following is the equation for the frequency of the rotor induced emf of the motor.

Fr = S. Fs

Fs- Frequency of the stator supply voltage

Fr – Frequency of rotor induced electromagnetic force

S – Per unit slip of the motor.

## Relationship of poles to Synchronous speed

Synchronous speed of the induction motor is directly proportional to frequency and indirectly proportional to a number of pole pairs.So the equation can derive as following.

Ns=60fp

Ns – Synchronous Speed

F – Frequency

P – Numbers of Pole Pairs.

When the poles are calculated directly (not Pole pairs) the equation can also write as