Machine Design

# Introduction to Electric Motors

## MOTORS

Electric motors, both ac and dc types, come in many shapes and sizes. Some are standardized versions for general-purpose applications. Others are intended for specific tasks. In any case, motors should be selected to satisfy the dynamic requirements of the machines on which they are applied without exceeding rated motor temperature. Thus, the first and most important step in motor selection is determining load characteristics -- torque and speed versus time. Selection is also based on mission goals, power available, and cost.

Starting and running torque are the first parameters to consider when sizing a motor. Starting torque requirements can vary from a small percentage of full load to a value several times full-load torque. Starting torque varies because of a change in load conditions or the mechanical nature of the machine. The latter could be caused by the lubricant, wear of moving parts, or other reasons.

Motor torque supplied to the driven machine must be more than that required from start to full speed. The greater the reserve torque, the more rapid the acceleration.

Drive systems that use gear reducers have parts that rotate at different speeds. To calculate acceleration torque required for these systems, rotating components must be reduced to a common base. The part inertias are usually converted to their equivalent value at the drive shaft. Equivalent inertia W2K22 of the load only is found from:

W2K22 =(W1K12)(N1/N2)2

where W1K21 = load inertia in lb-ft2, N1 = load speed in rpm, and N2 = motor speed in rpm.

Bodies having straight-line motion are often connected to rotating driving units by rack-and-pinion, cable, or cam mechanisms. For these parts, the equivalent WK2 is found from:

WK2 = W(S/2ΠN)2

where W = load weight, S = translation speed in fpm, Π is pi, and N = rotational speed in rpm.

Acceleration time:
Acceleration time of a motor-driven machine is directly proportional to total inertia and inversely proportional to the torque. For motors with constant acceleration torque, acceleration time is:

where WK2 = rotational inertia in lb-ft2, (N2 - N1) = the speed difference, and Tx = acceleration torque in lb-ft. For translating bodies, acceleration time is:

where W = weight of the load in lb, (S2 - S1) = the translation speed difference, and Fx = translation force in lb.

An approximation method is necessary to find acceleration time if acceleration torque is not linear during speed increase. The quickest method is to break up the speed versus torque curves of the driving unit and the driven machine into segments and calculate acceleration time for each segment. Accurate acceleration times usually result.

Power rating:
The horsepower required to drive a machine is typically referred to as motor load. The most common equation for power based on torque and rotational speed is: hp = (torque X rpm)/5,250.

If load is not constant and follows a definite cycle, a horsepower versus time curve for the driven machine is helpful. From this curve both peak and rms horsepower can be determined. Rms load horsepower indicates the necessary continuous motor rating. Peak load horsepower is not necessarily an indication of the required motor rating. However, when a peak load is maintained for a period of time, the motor rating usually should not be less than peak load horsepower.

Duty cycle:
Continuous steady-running loads over long periods are demonstrated by fans and blowers. On the other hand, machines with flywheels may have wide variations in running loads. Often, the flywheel supplies the energy to do the work, and the motor does nothing but restore lost energy to the flywheel. Therefore, choosing the proper motor also depends on whether the load is steady, varies, follows a repetitive cycle of variation, or has pulsating torque or shocks.

For example, motors that run continuously in fans and blowers for hours or days may be selected on the basis of continuous load. But devices like automatically controlled compressors and pumps start a number of times per hour. And motors in some machine tools start and stop many times per minute.

Duty cycle is a fixed repetitive load pattern over a given period of time which is expressed as the ratio of on-time to cycle period. When operating cycle is such that the motor operates at idle or a reduced load for more than 25% of the time, duty cycle becomes a factor in sizing the motor. Also, energy required to start a motor (that is, accelerating the inertia of the motor as well as the driven load) is much higher than for steady-state operation, so frequent starting could overheat the motor.

For most motors (except squirrel-cage motors during acceleration and plugging) current is almost directly proportional to developed torque. At constant speed, torque is proportional to horsepower. For accelerating loads and overloads on motors that have considerable droop, equivalent horsepower is used as the load factor. The next step in sizing the motor is to examine motor performance curves to see if the motor has enough starting torque to overcome machine static friction, to accelerate the load to full running speed, and to handle maximum overload.

Service factors:
A change in NEMA standards for service factors and temperature rise has been brought about because of better insulation. For instance, a 1.15 service factor -- once standard for all open motors -- is no longer standard above 200 hp.

Temperature rises are measured by the resistance method in the temperature rise table. Motor nameplate temperature rise is always expressed for the maximum allowable load. That is, if the motor has a service factor greater than unity, the nameplate temperature rise is expressed for the overload. Two Class-B insulated motors having 1.15 and 1.25 service factors will, therefore, each be rated for a 90°C rise. But the second motor will have to be larger than the first in order to dissipate the additional heat it generates at 125% load.

Service factor indicates how much over the nameplate rating a motor can be driven without overheating. NEMA Standard MGI-143 defines service factor of an ac motor as "...a multiplier which, when applied to the rated horsepower, indicates a permissible horsepower loading which may be carried under the conditions specified for the service factor..." In other words, multiplying nameplate horsepower by the service factor tells how much the motor can be overloaded without overheating. Generally, service factors:
• Handle a known overload, which is occasional.
• Provide a factor of safety where the environment or service condition is not well defined, especially for general-purpose motors.
• Obtain cooler-than-normal motor operation at rated load, thus lengthening insulation life.
Motor efficiency:
Small universal motors have an efficiency of about 30%, while 95% efficiencies are common for three-phase machines. In less-efficient motors, the amount of power wasted can be reduced by more careful application and improved motor design.

Motor efficiency also depends on actual motor load versus rated load, being greatest near rated load and falling off rapidly for under and overload conditions.