Machine Design

Motor sizing made simple

The proper sizing of three-phase induction motors saves energy and reduces downtime.

Walt Dryburg
Rockwell Automation
Washington, Pa.

A motor driving a load is an energy balancing act. On one side is the mechanical demand of the turning load. On the other is waste heat the motor generates turning that load. A small-sized motor that can't dissipate waste heat fast enough rapidly burns out. Motors sized too large stay cool but waste energy and money in inefficient operation. Selecting the optimal size is as easy as following a few guidelines.

Loads fall into three categories. Those that need constant torque, those where torque changes gradually, and those where torque changes abruptly.

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Motors are rated by the output power they can produce over a given time period without overheating. These ratings are on the motor nameplate. Manufacturers build motors with different duty cycles to match the three load categories. Duty cycle is the ratio of time the motor produces rated power divided by the total elapsed time. Motors with less than 100% duty cycle must turn off for an amount of time specified by the duty cycle to cool-down after operating. A motor with a 50% duty cycle must stay off for the same amount of time it has been on. Motors with less than 100% duty cycle also have a maximum run-time limit such as 30 min. A 50% duty cycle motor with a 30 min run time means the motor can operate at its rated output for 30 min. Then it must stay off at least 30 min — for 60 min total time — before running again.

Constant torque applications: Machines such as centrifugal compressors and extruders have relatively steady torque requirements. After they start, accelerate, and reach running speed, the torque demand varies no more than a few percent. To size a motor for this kind of application, match the motor output rating to the load's torque converted to horsepower:

where T = torque in lb-ft.

Don't forget the duty cycle! These machines run constantly, so choose a continuous-duty motor for this type of application.

Variable-torque applications, such as centrifugal pumps and fans, have a load that varies slowly, often over a range of 20 to 100%. A motor for these conditions gets sized for the highest continuous load, which is typically at the highest speed. It is important to know not only the peak value but also its duration as well. Peak load is the point that will challenge the motor's ability to turn the load. The motor must be big enough to manage the peak load and have a duty cycle that outlasts its duration.

Shock load torque can vary wildly and abruptly in equipment such as saws, compactors, and punch presses. As the load skyrockets the motor slows slightly producing more torque. If the change is extreme, the load may exceed the motor's break-down torque causing it to stall. The most critical parameter for these applications is the breakdown figure rather than fullload torque to keep the machine from stalling. So choose a motor with high breakdown torque.

Constant load: This is the simplest case. Determine the load from the nameplate on the driven unit, or, if this is impractical, measure the torque required to turn the load. Choose a motor for which the load is 75 to 100% of the motor's rated capacity. When the load is steady with a long duty cycle it is safe to load the motor close to its fullload capacity, in the area of 95%. This will optimize efficiency and keep the motor cost to a minimum.

Variable load: To size a motor for these applications, you must know the entire load range over which it will operate. Pay particular attention to the peak load and how long the application stays at peak. A pump load, for instance, may range from 20 to 100% over its operating cycle. Use peak load to calculate the motor size because the motor must be able to drive through the peak demands without overheating.

Motor service factors are safety factors. They indicate how much the motor capacity can be exceeded for short periods without overheating. For instance, a standard design B motor with a service factor of 1.15 can operate at 15% greater than its rated output without overheating. This is important for motors where loads vary and may peak slightly above the rated torque. However, since service factors are safety margins, they are to be used sparingly. A motor that operates continuously above its rated output will have a short life.

For variable loads calculate the RMS horsepower requirement and size the motor so the load falls within 75 to 100% of the motor capacity.

Starting torque, also known as locked-rotor torque, is produced when power is applied to the motor and the rotor is not yet turning. Starting torque must exceed load torque for the motor to accelerate the load.

Pull-up torque is the torque available as the load accelerates and motor rpm increases. The motor will stall if the load exceeds this value. Note this value is less than the starting torque.

Breakdown torque is the maximum torque that a motor can produce at full speed.

Full-load torque is the maximum torque that the motor can sustain at operating speed without overheating.

Inertia is a load that must be overcome. The motor must be able to start the load from dead still, accelerate it to operating speed, and then continue applying enough torque to maintain speed. During this startup phase current is five to seven times that needed at full load.

The process of overcoming high inertia-loads at startup generates extreme heat. The National Electrical Manufacturers Association, or NEMA, has designated four motor design types identified by the letters A, B, C, and D. Design types specify various parameters of a motor's startup and operating qualities, helping to identify which type of load a motor can handle. Design type A motors work well with more constant torque applications and low inertia. Type A motors have medium to high starting currents that create rapid heat buildup. The high starting torque of Design D motors handles the very high-inertia loads with lower starting current, minimizing heat buildup in the motor during start. But the lower starting current means type D motors slip more than type A. Type D motors slip 5 to 13% compared to the less than 5% slippage for types A through C. Industry standard is the type B motor with its normal starting torque and low starting current. As the industry standard it is usually the best economic choice.

Continuous duty is the simplest case. It begins with start-up, followed by long periods of steady operation where the heat generation and dissipation stabilize, and then ends with shutdown. Motors in these applications can operate at or near their rated capacities because the temperature rise is controlled.

Intermittent duty is a more complex problem. Again, heat is the principle villain. Analogous to commercial airplane landings, the life of a motor is closely related to the number of starts it makes because it must survive the heat generated at startup. For this reason, motors are limited to the number of starts and stops they can make in an hour.

Selecting a motor for intermittent duty involves an educated guess. A rule of thumb is that for every 10°C cooler that a motor operates, its life doubles. So for maximum life you want a motor to run at less than maximum temperature. A motor sized for peak load alone may burn out rapidly in intermittent duty. However, choosing the next larger size motor (say 10 instead of 7.5 hp), brings greater capacity for coping with frequent starts,

Starting qualities for the four basic motor designs. Design B is the general-purpose unit, and is usually less expensive. Because starting torque is low, it may not be able to start a high-inertia load. Choose another design that has adequate low-speed torque.

Motors operating at altitudes substantially above sea level cannot operate at their full service factor because the air is less dense at high altitudes and does not cool as well. Derate the motor on a sliding scale to stay within safe limits of temperature rise. Typically, the service factor is 1.15 at an altitude of 3,300 ft or below. At 9,000 ft it is derated to 1.00. So when choosing your next motor, calculate the horsepower load demands, determine whether conditions call for continuous or intermittent duty cycle, and pick the best design type A through D for the type of load the motor will be driving.


National Electrical Manufacturers Association, (703) 841-3200,
Rockwell Automation, (414) 212-5200,

Maximum number of starts for selected motors
HP TWO POLE (3,600 rpm) FOUR POLE (1,800 rpm)
  A B C A B C
5 8.1 5.7 83 16.3 27 43
10 6.2 11 92 12.5 51 46
20 4.8 21 110 9.6 99 55
50 3.4 39 145 6.8 232 72
100 2.6 92 110 5.2 441 110
A = Maximum number of starts per hour
B = Maximum product of starts per hour
C = Minimum rest time between starts, in seconds
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