Download 1.2.6.A.FT MaximizingMotorPower

Activity 1.2.6 Maximizing Motor Power –
fischertechnik
Introduction
An engineer often must design a system to get
the most out of limited resources. When
designing a laptop or mobile phone, for example,
an engineering team works to make the battery
last as long as possible, for example. A vibrating
cell phone uses a motor with an off-center load,
and it needs to be designed with a gear train that
delivers the most power or the highest efficiency.
These design decisions can be made by making
only four measurements of a motor. These four
measurements describe the most important
properties of a particular motor at a given voltage.
In this activity you will learn how to make those
four measurements. You will also learn how to
choose a gear ratio to make a motor deliver
maximum power or maximum efficiency for a
given task.
Equipment
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Fischertechnik 2 V micromotor
Fischertechnik hubs and pulley
DC power supply or one AA battery and holder
Multimeter
Timing device for timing to 0.01 s precision
Vernier force sensor or other device able to
measure ~200 mN
Alligator jumper cables
Thread
Clamp
© 2012 Project Lead The Way, Inc.
Principles Of Engineering Activity 1.2.6 Maximum Motor Power FT – Page 1
Procedure
1. Set the DC power supply to deliver constant voltage. This is accomplished
by turning the current knob all the way clockwise. Then use the voltage
knob to set the voltage to 1.0 V. Alternatively, provide power with one AA
battery (one, not two as shown here.)
1.0 V
2. Connect the power source to the motor using alligator jumper cables.
3. Measure the no-load speed of the motor by counting the motor’s
revolutions using a thread.
a. Mount the motor to the
table top using a clamp
and fischertechnik parts.
b. Attach a hub to the motor axle
when the power is removed,
and use the hub to anchor the
end of a thread that is
approximately 5 ft long. Hold
the motor in a stalled position
with the thread wrapped one to
three times around the motor
shaft
© 2012 Project Lead The Way, Inc.
Principles Of Engineering Activity 1.2.6 Maximum Motor Power FT – Page 2
c. Start the timer as you release the thread. You will minimize tangles
if you keep the thread relatively straight. It does not matter if the
thread winds with slack in it; you are only counting revolutions.
Since you want to know the motor’s speed with no load, do not slow
the motor down by hanging onto the thread more than necessary.
Stop the timer when the end of the thread reaches the motor.
Unwind the thread, counting revolutions as you go.
n = number of rotations = _______
Time for n rotations = _________
4. Calculate the no-load speed = rotations/time. Using the fact that 2
radians = 1 rotation, convert the no-load speed to radians per second.
This is the fastest that the motor will spin at this voltage.
no-load = No-load speed = _________ rotations/second
 = _________ radians/second
5. Record the no-load current. The power supply displays current, but a
multimeter should be used for accuracy.
If current greater than the range setting of an ammeter passes through
the meter, it blows the fuse of the meter and can damage the meter.
Always start with ammeter range settings greater than the current can
possibly be. The power supply gives a rough indication of the current, so
you can go right to the correct range setting on the ammeter.
Ino-load= No-load current = _________ A
6. Measure the stall torque of the motor. Accomplish this by
affixing something to the shaft of the motor so that a force
can be applied at a precise distance from the axis of
rotation. You will actually calculate the torque by measuring
a force and an off-axis distance.
Use a caliper to measure the diameter of the shaft; the
off-axis distance d is half of this diameter.
d = distance from axis of rotation to point where force is applied =
_______ m
© 2012 Project Lead The Way, Inc.
Principles Of Engineering Activity 1.2.6 Maximum Motor Power FT – Page 3
F┴ = force to stall the motor = ______ N
stall = stall torque = d × F┴ = ______ N·m
7. Record the stall current of the motor.
If a current greater than the range setting of an ammeter passes through
the meter, it blows the fuse of the meter and can damage the meter.
Always start with ammeter range settings larger than the current could be.
Istall = Stall current = _________ A
8. Congratualations! You have measured everything you need to measure to
characterize your motor. You have all of the most important design
parameters that describe the motor’s performance for operation at 3 V.
Let’s put them in one place, creating a specification sheet, or spec sheet
as it is commonly called.
Specification Sheet
Motor model: ________
For operation at 3 V:
No-load current:
________
Stall current:
________
No-load speed:
________
Stall torque:
________
9. Engineers make many design decisions by calculating important results
from these specs. For example, what is the torque at which the motor
delivers maximum power? Refer to the presentation Maximizing Motor
Power if needed.
=Motor torque for maximum power = ½ stall torque = ________ N·m
© 2012 Project Lead The Way, Inc.
Principles Of Engineering Activity 1.2.6 Maximum Motor Power FT – Page 4
10. Engineers often want to select a component based on something they
calculate from the specs. Suppose you are selecting a cell phone vibration
motor and want at least 200 mW of power. Will this motor do the trick?
Calculate the maximum output power of this motor. Note that the speed of
the motor at half the stall torque is half the no-load speed.
 = Motor speed at maximum power = ½ no-load speed = ________ rad/s
Pout = Motor output power at maximum power =  × = ________ W
11. It is common for motor output power to be reported in horsepower.
Convert the output power to hp. Show your work.
Pout = ________ W × __________________ = _________ hp
12. Use the Internet to look up the power output of a power tool or air
compressor on the market. Describe what you found out. Compare to your
motor.
13. Because you characterized your motor, you can make a lot of design
decisions. Suppose you want to use your motor to drive a robot that
requires 0.05 N·m of torque on the drive axle. A gear train will transfer
power from the motor to the drive axle. That 0.05 Nm will be the output
torque from the gears. The motor will deliver the input torque to the gears.
What gear ratio would you need to use to make this motor deliver
maximum power to the drive shaft?
𝐺𝑅 =
𝜏𝑜𝑢𝑡
=
𝜏𝑖𝑛
14. Because you measured the specs of your motor, you can predict how
much electrical power it will consume. Let’s do that calculation for when
the motor is exerting half of its stall torque – when it is working at
maximum output power. How much electrical power is flowing into the
motor?
© 2012 Project Lead The Way, Inc.
Principles Of Engineering Activity 1.2.6 Maximum Motor Power FT – Page 5
Voltage = V = 1.0 V
Current = I = halfway between stall current and no-load current
= _______ A
Electrical Power = Pin = I · V = __________________ = ___________ W
15. Sometimes engineers will design a device to be as efficient as possible
instead of designing it to be as powerful as possible. How efficient is your
motor? Calculate the efficiency of the motor when it is operating at
maximum power.
𝜂=
𝑃𝑜𝑢𝑡
𝑃𝑖𝑛
=
16. It was easy to calculate the torque at which the motor would deliver
maximum power. (Review: How did you calculate that torque? Look back
at step 9.) It is not so easy to calculate the torque at which the motor will
deliver power at maximum efficiency. But there is an algorithm for it. An
algorithm is a procedure to follow. Steps 10, 14, and 15 walked you
through the algorithm for calculating the efficiency for a given torque.
What are the steps of the algorithm?
17. You could find the maximum efficiency by calculating the efficiency at
many different torques and picking the highest efficiency. That would
require many iterations of the algorithm! Computers are very good at
automating that work. Open the spreadsheet 1.2.6 Motor Power at
Constant Voltage and enter the specifications of your motor.
© 2012 Project Lead The Way, Inc.
Principles Of Engineering Activity 1.2.6 Maximum Motor Power FT – Page 6
This spreadsheet is automated to calculate efficiencies for 100 torques
between 0 N·m and the stall torque you enter. It automatically updates the
two graphs to specify how four design parameters for your motor are
dependent on the torque delivered by the motor. The first graph shows
efficiency (in blue) and motor output power (in red). Discuss the graphs
created by your spreadsheet with your lab partner.
a. Paste images of your graphs here.
b. What are the x- and y-axes for each curve? Notice two y-axes on each
graph!
Color:
y-variable
vs.
blue:
_____________ vs. ______________
red:
motor power
green:
_____________ vs. ______________
purple:
_____________ vs. ______________
vs.
x-variable
motor torque .
© 2012 Project Lead The Way, Inc.
Principles Of Engineering Activity 1.2.6 Maximum Motor Power FT – Page 7
18. Find the point on the efficiency graph that is the maximum efficiency.
Indicate this spot on the graph that you pasted into this document in
step 17a above. You can indicate the spot on the graph by inserting a
circle into this Word document using the following steps:
a. Select: Insert > Shapes > select oval.
b. Right click the oval.
c. Change fill to “no fill.”
d. Change the outline color to a setting that will effectively draw
attention to a precise location on the graph.
e. Change the line weight to be large enough to be obvious but small
enough to be precise.
19. Based on your graphs, what is the maximum efficiency?

= ___________ %
max
20. At what torque does the maximum efficiency occur?

max efficiency = ___________ N·m
21. Using the torque from step 20 as the x-coordinate on the second graph,
find the current used by your motor when it is operating at maximum
efficiency. Circle this point on your second graph following the method
listed in step 18.

max efficiency = ___________ A
© 2012 Project Lead The Way, Inc.
Principles Of Engineering Activity 1.2.6 Maximum Motor Power FT – Page 8
22. How much electrical power does the motor use when it is operating at
maximum efficiency?
Pelec = I · V = ______________ = ________ W
23. The efficiency tells you what percent of the electrical energy is
transformed to mechanical energy. The rest of the energy becomes heat
energy, increasing the temperature of the motor. Power is the rate at
which energy is transformed. At what rate is heat energy deposited into
the motor when it is operating most efficiently?
Pheat = ( 1 - 
) Pelec =
max
© 2012 Project Lead The Way, Inc.
Principles Of Engineering Activity 1.2.6 Maximum Motor Power FT – Page 9
Conclusion
1. Explain what it means to “characterize” a component to be used in a
system.
2. In this activity you used math and science to calculate how to use a motor
in a design, instead of using trial and error. What are the advantages of
using math and science in engineering design? What are the advantages
of trial and error?
3. Explain how efficiency is related to electrical energy, mechanical energy,
and heat energy.
4. The motor in the design shown at left has the specifications shown at
right. What gear ratio should be used for maximum power?
For operation at:
9V
No-load current: 100 mA
Stall current:
3A
No-load speed:
20 rad/s
Stall torque:
60 N·m
© 2012 Project Lead The Way, Inc.
Principles Of Engineering Activity 1.2.6 Maximum Motor Power FT – Page 10