Electrical motors are the machines which convert the electrical input to the mechanical energy. All motors are made up of a stator (the stationary part) and the rotor (the rotating part). As motor runs on electricity, there are various properties which are associated with its working. Such properties include a number of poles, speed, frequency, slip, starting current and rated horsepower. Previously we shared the book on AC Motors which explains all these properties briefly, this post is focused on the induction motor formulas and calculation examples.

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Contents

### Synchronous speed, frequency, and poles

Synchronous speed, frequency, and poles of the induction motor are related by the formula:

η_{sync} = (120 * f_{e}) / P

η_{sync }= Synchronous speed

f_{e }= Frequency of the system

P = Number of poles installed in the machine

Calculation: Find the synchronous speed of 4 pole induction motor which operates at 60 Hz.

Solution: η_{sync} = 120 * 60 / 4 = 1800 r/min

### Motor Slip

Slip of a motor can be found from the formula:

s = (η_{sync}-η_{m})/ η_{sync }* 100

η_{sync }= Speed of magnetic field

η_{m }= Mechanical shaft speed

Calculation: The rotor speed of a 4 pole induction motor at 50 Hz is 1200 r/min. Calculate its slip.

Solution: Rotor speed = η_{m} = 1200 r/min

Where η_{sync} = 120 * 50 / 4 = 1500 r/min

s = (1500 – 1200) / 1500 * 100 = 20

### Torque, Power, and Speed

τ_{ind} = P / ω_{m}

τ_{ind} = Induced torque in Nm

P = power in kW

ω_{m} = Speed in r/min

Calculation: Find the shaft torque of the 10 hp induction motor whose rotor speed is 1500 r/min.

Solution: τ_{ind} = (10 hp * 746 kW/hp) / (1500 r/min * 2 π rad/r * 1 min/60 s) = 47.49 Nm

### Starting Current calculator

I_{L} = S_{start} / (√3 * V_{T}),

where S_{start} = Rated HP of the motor * Code factor

(Code factor is a number which is reserved for class) For example, all motors of class A have a fixed code factor which should be multiplied with rated HP in the above equation.)

V_{T} = Rated voltage

Calculation: Find the starting current of 10 hp, three phase 220 V A class motor.

Solution: The maximum kVA/hp for A class motor is 3.15 (code factor).

S_{start} = 10 hp * 3.15 = 31.5 kVA

I_{L} = 31.5 kVA / (√3 * 220) = 82.66 A

You might want to learn: How to calculate Current from HP