# Three Easy Steps to Sizing Motors

Mar 15, 2012

Drive and Motor Sizing Made Easy
Size your drive and motor in three easy steps:

• Determine the application requirements
• Size the motor to meet the application
• Size the drive to meet the motor and the application

Determine the Application Requirements
What are the torque requirements?

• Motor torque (not power) is usually the decisive factor
• Torque requirement establishes current requirement
• Continuous torque requirements
• Variable torque vs. constant torque
• Intermittent (peak) torque requirements
• Starting torque
• Acceleration torque
What is the speed requirement?
• Maximum speed
• Minimum speed

Torque, what is it?
A measure of the effect of a force applied at a distance to an axis.

• Torque is a force that tends to rotate or turn things
• Torque(lb-ft) = Force (lb) x Radius (ft)

Variable Torque
Variable torque changes as the operating speed changes.

• Fans
• Centrifugal pumps
• Centrifugal blowers
• Mixers (material dependent)

Constant Torque
Constant torque remains the same as the speed changes.

• Conveyers
• Positive displacement pumps
• Extruders
• Crushers
• Mixers (material dependent)
• Rotary kilns
• Hoists
• Elevators

Constant vs. Variable Torque
Why should I care? Isn’t all torque the same?

Yes. But ….

• Motor current is proportional to torque
• Motor heating is proportional to current
• In the case of a TEFC motor, cooling is proportional to speed

Result — a TEFC motor's ability to thermally handle torque varies with speed

A constant torque load often requires a larger TEFC motor than that required for an equivalent variable torque load.

• Alternative is a separately driven fan, TEBC motor

Intermittent Torque
Intermittent torque is torque that is required for a relatively short period of time. Examples:

• Torque to breakaway the load and start motion
• Friction
• Torque to accelerate the load
• Inertia

Speed
With direct mechanical drive, motor speed is determined by mechanical speed and physical dimensions.

Speed (RPM) = v (ft/min) / (r (ft) x 2 x pi)

Speed Example
Speed (RPM) = v(ft/min) / (r(ft) x 2 x pi)

Speed (RPM) = 750(ft/min) / (1 (ft) x 2 x pi) = 119 (RPM)

Power
Power is the product of torque times speed.

• Power (HP) = Torque (lb-ft) x Speed (RPM) / 5252
• For our example:
• Torque = 100 lb-ft
• Speed = 119 RPM
• Power = 100 (lb-ft) x 119 (RPM) / 5252 = 2.3 HP
 HP Base Speed Rated Torque 3 1790 9 5 1790 15 7.5 1790 22 10 1790 29 15 1790 44 30 1790 88 40 1790 117

Motor Sizing
In our example:

• Torque = 100 lb-ft
• Speed = 119 RPM
• Power = 100 x 119 / 5252 = 2.3 HP
What size motor do we pick?
• 3 HP @ 1790 RPM?
• 40 HP @ 1790 RPM?

A motor only develops its nameplate power at its nameplate speed. At a reduced speed it develops a proportionately reduced power.

Motor Sizing
What if we add a gear box?

• Torque at motor = torque / gear ratio
• Speed at motor = speed x gear ratio

Now what motor do we pick?

Intermittent Torque
Torque for Acceleration

• Torque = Inertia x Acceleration rate
• If you know:
• Inertia (WK2) in lb-ft2
• Acceleration time in sec.
• Change in motor speed in RPM
• Then:
• Torque = WK2 (lb-ft2) x Speed(RPM) / (Accel time(sec.) x 307.6)

Intermittent Torque
Torque for Acceleration

• Assume for our example:
• Total WK2 = 1.2 lb-ft2
• Includes 100 lb load, drum, 15:1 gear box and motor
• Change in speed is 1790 RPM
• If accel time is 10 seconds
• Accel Torque = 1.2(lb-ft2) x 1790(RPM) / (10(sec.) x 307.6)
• Accel Torque = 0.7(lb-ft)
• Total torque = 6.7 + 0.7 = 7.4 lb-ft; less than rated motor torque
• If accel time = 1 second
• Accel Torque = 1.2(lb-ft2) x 1790(RPM) / (1(sec.) x 307.6)
• Accel Torque = 7.0 (lb-ft)
• Total torque = 6.7 + 7.0 = 13.7 lb-ft, 150% of rated motor torque

Pick A Drive

• Assume for our example:
• Motor is 3 HP, 1790 rpm, 4.2 FLA, 9 lb-ft
• Torque to lift load and accel in 10 s is 7.4 lb-ft
• Max current is less than 4.2 amps
• Use 3 HP normal duty drive, 4.9 amps, with 110%
O.L. (5.4 amps peak)
• Torque to lift load and accel in 1 s is 13.7 lb-ft
• Max current is about 6.4 amps
• Use 3 HP heavy duty drive, 5.6 amps, with 150%
O.L. (8.4 amps peak)

Special Cases
Intermittent torque is required for a relatively long time.

• Large inertias
• Results in long accel time, several minutes
• Drive and motor sized for acceleration torque
• Examples
• Centrifuges
• Kilns
• Long periods of breakaway torqu
• Mixer starting with product

Watch the limits

• Limits that can come in to play
• Torque
• AC Motors have max torque limits, about 200% (Drive limits motor to about 70% of motor’s rated breakdown torque)
• Speed
• Limited by maximum safe mechanical speed
• Limited by maximum drive frequency
• Limited by reduced maximum torque above base speed
(Constant HP operation)
• Current
• Limited by inverter
• Full speed motor current rises when line voltage is low
• Regenerative (braking) torque
• If less than 10% flux braking may be good enough
• If more than 10% but intermittent, such has stopping only, use brake chopper and resistor
• If more than 10% and continuous, consider a regenerative drive