Motors and Mechanical

NEW!!! NEW!!! NEW!!! COMPUTATIONS FOR MOTORS

This page offers formulas for finding useful information about electrical motors. It is dedicated to sharing information, formulas and other documentation to aide in finding the given electrical, force or power values. The formulae below are commonly known and used universally. I use them here in examples to demonstrate the application of conversion formulae. I have done my best to be accurate but I cannot guarantee that all of the following information is correct or appropriate for your purposes.

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Finding Motor Speed
Finding Braking Torque
Finding Torque
Finding Full-load Torque
Finding Horsepower
Finding Synchronous Speed
General Approximations

Finding Motor Speed

A squirrel cage induction motor is a constant speed motor. It must operate at the speed specified on the nameplate or it will burn out.

To Calculate the speed of an induction motor:

Srpm = 120 x F
P

Srpm = synchronous revolutions per minute.
120   = constant
F       = power supply frequency (in cycles/sec)
P       = number of motor winding poles

• Example: What is the synchronous of a motor having 2 poles connected to a 60 hz power supply?

Srpm = 120 x F
            P
Srpm = 120 x 60
            2
Srpm = 7200
             2
Srpm = 3600 rpm

Finding Braking Torque

Full-load motor torque is needed to determine the required braking torque of a motor.

To calculate the braking torque of a motor:

T = 5252 x HP
rpm

T = full-load motor torque (in lb-ft)
5252 = constant (33,000 divided by 3.14 x 2 = 5252)
HP = motor horsepower
rpm = speed of motor shaft

• Example: What is the braking torque of a 40 HP, 240V motor rotating at 1725 rpm?

T = 5252 x HP
    rpm
T = 5252 x 40
     1725
T = 210,080
     1725
T = 121.8 lb-ft

Finding Torque

Torque is the force that causes an object to rotate. Torque consist of a force acting on distance and is measured is pound-feet (lb-ft). Torque may exist even though no movement occurs.

To calculate torque:

T = F x D

T = torque (in lb-ft)
F = force (in lb)
D = distance (in ft)

• Example: What is the torque produced by a 70 lb force pushing on a 3' lever arm?

T = F x D
T = 70 x 3
T = 210 lb ft

Finding Full-load Torque

Full-load torque is the force needed to produce the rated power at maximum RPM of a motor. The amount of torque a motor produces at rated power and full speed can be found by using a horsepower-to-torque conversion chart.

To calculate motor full-load torque:

T = HP x 5252
rpm

T = torque (in lb-ft)
HP = horsepower
5252 = constant
rpm = revolutions per minute

• Example: What is the Full-load torque of a 30HP motor operating at 1725 rpm?

T = HP x 5252
    rpm
T = 30 x 5252
     1725
T = 157,560
     1725
T = 91.34 lb-ft

Finding Horsepower

Electrical power is rated in horsepower or watts. A horsepower is a unit of power equal to 746 watts or 33,0000 lb-ft per minute (550 lb-ft per second). A watt is a unit of measure equal to the power produced by a current of 1 amp across the potential difference of 1 volt. It is 1/746 of 1 horsepower. The watt is the base unit of electrical power. Motor power is rated in horsepower and watts.

Horsepower is used to measure the energy produced by an electric motor while doing work.

To calculate the horsepower of a motor when current, efficiency, and voltage are known:

HP = V x I x Eff
746

HP = horsepower
V = voltage
I = current (amps)
Eff = efficiency

• Example: What is the horsepower of a 230v motor drawing 4 amps with 82% efficiency?

HP = V x I x Eff
        746
HP = 230 x 4 x .82
        746
HP = 754.4
        746
HP = 1 Hp

Eff = efficiency / HP = horsepower / V = volts / A = amps / PF = power factor

To calculate the horsepower of a motor when speed and torque are known:

HP = rpm x T(torque)
5252(constant)

• Example: What is the horsepower of a 1725 rpm motor with a FLT 3.1 lb-ft?

HP = rpm x T
         5252
HP = 1725 x 3.1
         5252
HP = 5347.5
         5252
HP = 1 hp

Finding Synchronous Speed

AC motors are considered constant speed motors. This is because the synchronous speed of an induction motor is based on the supply frequency and the number of poles in the motor winding. Motors that are designed for 60 hz use have synchronous speeds of 3600, 1800, 1200, 900, 720, 600, 514, and 450 rpm.

To calculate synchronous speed of an induction motor:

Srpm₌ 120 x f
Np

Srpm = synchronous revolutions per minute.
f = supply frequency in (Hertz)
Np = number of motor poles

• Example: What is the synchronous speed of a four pole motor operating at 50 hz.?

Srpm₌ 120 x f
                 Np
Srpm₌ 120 x 50
             4
Srpm₌ 6000
            4
Srpm₌1500 rpm

Adapted from Electrical motor Controls by Rockis & Mazur

General Approximations - RULES OF THUMB

Use these in the field for fast approximations:

At 3600 rpm, a motor develops a 1.5 lb-ft of torque per HP at rated HP output
At 1800 rpm, a motor develops a 3 lb-ft of torque per HP at rated HP output
At 1200 rpm, a motor develops a 4.5 lb-ft of torque per HP at rated HP output
At 900 rpm, a motor develops a 6 lb-ft of torque per HP at rated HP output

At 575 volts, a 3-phase motor draws 1 AMP per HP at rated HP output
At 460 volts, a 3-phase motor draws 1.25 AMP per HP at rated HP output
At 230 volts a 3-phase motor draws 2.5 AMP per HP at rated HP output

At 230 volts, a single-phase motor draws 5 AMP per HP at rated HP output
At 115 volts, a single-phase motor draws 10 AMP per HP at rated HP output