MCEN 4037
Updated 2/10/11
Electric Motor Comparison: Theory
Introduction
The performance of electric motors can be characterized by several measures: efficiency,
maximum output power and torque, speed regulation and power factor. Measurement of
efficiency requires measurement of the power input to and output from the motor. Input
power is easily determined for electric motors from the supplied voltage and current. Output
power and torque are usually measured by dynamometers, which are also the most widely used
devices for power and torque measurements on internal-combustion engines, steam turbines,
etc. Speed regulation is a measure of how constant the speed of the motor is when subjected
to increased loads. Power factor refers to the phase relationship of voltage and current drawn
by the motor. If too low, the power factor can result in additional electric utility charges.
Note: Remember to report the uncertainty of all measurements and calculations.
Theory and Analysis
The experimental setup consists of two interchangeable AC-motors (1/2 and 3/4 horsepower)
whose performance is measured by a one horsepower dynamometer/generator. The
dynamometer, or “dyno” as it is called in the automotive industry, is basically a DC generator
coupled to a force-measuring device, such as a weight scale or load cell that is used to measure
the torque produced by the AC-motor. The electrical output of the dynamometer/generator is
connected to power-dissipating resistors that create a load that the AC-motor must overcome.
DC generators operate by applying moving a conductor through a magnetic field. In a
dynamometer, the magnetic field can be varied, resulting in a variable load. By adjusting the socalled excitation current, one can apply a varying load to the AC-motor being tested.
The torque is measured by measuring the force exerted through a moment arm attached to the
outer casing of the dynamometer. In our case both a mechanical scale and load cell are
available to measure the force. The power generated by the AC-motor is obtained from the
dynamometer according to the following equation:
Pg 
2RLN
33000
(1)
where,
Pg - output power, hp,
R - lever arm (0.500 ft.),
L - indicated load, lbf,
N - rotational speed, rev/min.
The 33,000 is a unit conversion factor that ensures that the power is in units of horsepower
(what would the conversion factor be if the desired units were watts?).
The tachometer of the dynamometer shaft has an optical transistor that switches between 0V
and 5V depending on whether one of the 20 teeth of the rotating gear is blocking the path of
the light sensor. The tachometer measures the number of 0-5V pulses within a given amount of
time to determine the speed of the rotating shaft. An important motor characteristic is speed
regulation, which is defined as how well the motor maintains its speed when subjected to
different loads.
1) Calculate the average speed for each load condition and estimate the speed uncertainty.
2) Compute the speed of each motor at each load condition as a percentage of the rated
speed of the motor. The rated speeds and rated powers are listed on the metal name plate
of the motor.
3) On the same graph, plot the percent of rated speed versus output power (in hp) for all load
conditions for each motor. Similarly, plot the percent of rated speed versus percent of
rated power for both motors for all loads on the same plot. Analyze and discuss these two
plots.
The maximum possible power that can be delivered to the motor is known as the apparent
power. The actual power consumed by the motor is referred to as the average power
(discussed later). The apparent power delivered to the motor may be calculated using the rootmean-square values of the current and voltage supplied to the motor as shown in the equation
below:
Papparent  I rmsVrms
where Papparent is in watts, Irms is in amps, and Vrms is in volts.
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(2)
4) Calculate the apparent power (in hp) for each motor for all output power settings (in hp).
The average power consumed by the motor can be found by taking the dot product between
the current and voltage, Equation 3. Average power can also be found by averaging the
instantaneous power consumed by the motor. The instantaneous power of the motor is simply
the instantaneous voltage multiplied by the instantaneous current, v(t)i(t).
If the current and voltage are in phase, the average power equals the apparent power. If the
voltage and current delivered to the motor are not in phase, the disparity between the average
power and the apparent power provides a measure of the power factor, Equation 4. The
power factor is related to the phase angle, , between the sinusoidal waveforms of the current
and the voltage and is defined as the ratio of the average power to the apparent power.
Pave  I  V  I rmsVrms cos 
Power Factor  cos  
Pave
Papparent
(3)
(4)
I = the current in amps,
V = the voltage in volts,
 = phase angle between current and voltage
The angle  in Equations 3 and 4 is known as the power factor angle and is the phase angle of
the load impedance. The phase angle, , can vary between +90 and -90; therefore, the power
factor can vary between 0 and 1 [4].
Estimating uncertainty in average power must be done differently than previous uncertainty
calculations because average power is a sine wave. One way to estimate the uncertainty is to
(1) calculate the average power for 10-15 individual cycles, and then (2) calculate the standard
deviation in these 10-15 Pave values.
5) Calculate the average power (in hp) delivered to the motors for all output power settings (in
hp).
6) Calculate the power factor for the motors at the different output power settings. Construct
a plot of the power factor versus output power (in hp). Discuss the relationship.
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The efficiency of the motor is defined as
e
OutputPower
InputPower
(5)
7) Calculate the efficiency of each motor for all output power levels. Plot the efficiency versus
the output power for both motors in a single figure. Discuss the characteristics of the
curves and what variable was used as the “input power.”
Remember that these questions are designed to help you in preparing your report. Your report
should not be merely a restatement of the questions with the answers.
References
1. J.P. Holman, Experimental Methods for Engineers, 5th Ed., McGraw-Hill, New York,
1989, p. 397.
2. T.R. Beckwith and R.D. Marangoni, Mechanical Measurements, 4th Ed., AddisonWesley, Reading, MA, 1990, p. 489.
3. E.O. Doeblin, Measurement Systems, Application and Design, 4th Ed., McGraw-Hill,
New York, 1990, p. 425.
4. J.D. Irwin and D.V. Kerns, Jr., Introduction to Electrical Engineering, Prentice Hall,
Englewood Cliffs, New Jersey, 1995, pp.179-180.
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