# 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.

I welcome any comments or corrections. Thanks to all who have notified me of inaccuracies. This type of participation makes this site more valuable. Please click here for a link to email your comment, correction, suggestion or question.

## Choose Your Topic Below

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

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