Three Easy Steps to Sizing Motors

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

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