Induction Motor Formulas with Calculations

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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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