Here
are some motor formulas that may be useful.
Calculating
Motor Speed:
A
squirrel cage induction motor is a constant speed device. It cannot operate for
any length of time at speeds below those shown on the nameplate without danger
of burning out.
To
Calculate the speed of a induction
motor,
apply this formula:
S_{rpm} = 120 x F
P
S_{rpm} = synchronous
revolutions per minute.
120 = constant
F = supply frequency (in
cycles/sec)
P = number of motor
winding poles
Example: What is the synchronous
of a motor having 4 poles connected to a 60 hz power supply?
S_{rpm} = 120 x F
P
S_{rpm} = 120 x 60
4
S_{rpm}_{ }= 7200
4
S_{rpm} =
1800 rpm
Calculating
Braking Torque:
Fullload
motor torque is calculated to determine the required braking torque of a motor.
To
Determine braking torque of a motor, apply this
formula:
T = 5252 x HP
rpm
T = fullload motor
torque (in lbft)
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 60 HP, 240V motor rotating at 1725 rpm?
T = 5252 x HP
rpm
T = 5252 x 60
1725
T = 315,120
1725
T = 182.7 lbft
Calculating
Work:
Work
is applying a force over a distance. Force is any cause that changes the
position, motion, direction, or shape of an object. Work is done when a force
overcomes a resistance. Resistance is any force that tends to hinder the
movement of an object. If an applied force does not cause motion the no work is
produced.
To
calculate the amount of work produced, apply this formula:
W = F x D
W = work (in lbft)
F = force (in lb)
D = distance (in ft)
Example: How much work is
required to carry a 25 lb bag of groceries vertically from street level to the
4th floor of a building 30' above street level?
W = F x D
W = 25 x 30
W = 750 lb
Calculating
Torque:
Torque
is the force that produces rotation. It causes an object to rotate. Torque
consist of a force acting on distance. Torque, like work, is measured is
poundfeet (lbft). However, torque, unlike work, may exist even though no
movement occurs.
To
calculate torque, apply this formula:
T = F x D
T = torque (in lbft)
F = force (in lb)
D = distance (in ft)
Example: What is the torque
produced by a 60 lb force pushing on a 3' lever arm?
T = F x D
T = 60 x 3
T = 180 lb ft
Calculating
Fullload Torque:
Fullload
torque is the torque to produce the rated power at full speed of the motor. The
amount of torque a motor produces at rated power and full speed can be found by
using a horsepowertotorque conversion chart. When using the conversion
chart,
place a straight edge along the two known quantities and read the unknown
quantity on the third line.
To
calculate motor fullload torque, apply this formula:
T = HP x 5252
rpm
T = torque (in lbft)
HP = horsepower
5252 = constant
rpm = revolutions per minute
Example: What is the FLT
(Fullload 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 lbft
Calculating
Horsepower:
Electrical
power is rated in horsepower or watts. A horsepower is a unit of power equal to
746 watts or 33,0000 lbft per minute (550 lbft 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 and efficiency, and voltage
are known, apply this formula:
HP = V x I x Eff
746
HP = horsepower
V = voltage
I = curent (amps)
Eff. = efficiency
Example: What is the horsepower
of a 230v motor pulling 4 amps and having 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
Horsepower
Formulas

To
Find

Use
Formula

Example

Given

Find

Solution

HP

HP = I
X E X Eff.
746

240V,
20A, 85% Eff.

HP

HP = 240V
x 20A x 85%
746
HP=5.5

I

I = HP
x 746
E X Eff x PF

10HP,
240V,
90% Eff., 88% PF

I

I = 10HP x 746
240V x 90% x 88%
I = 39 A

To
calculate the horsepower of a motor when the speed and torque are known, apply
this formula:
HP = rpm x T(torque)
5252(constant)
Example:
What is the horsepower of a 1725 rpm motor with a FLT 3.1 lbft?
HP = rpm x T
5252
HP = 1725 x 3.1
5252
HP = 5347.5
5252
HP = 1 hp
Calculating
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. Motor 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, apply this formula:
rpmsyn = 120 x f
Np
rpmsyn = synchronous speed (in
rpm)
f = supply frequency in
(cycles/sec)
Np = number of motor poles
Example: What is the synchronous
speed of a four pole motor operating at 50 hz.?
rpmsyn = 120 x f
Np
rpmsyn = 120 x 50
4
rpmsyn = 6000
4
rpmsyn = 1500 rpm