2012 Project Lead The Way Inc Principles of Engineering Speed Depends on Load Torque When a motor is loaded with no torque it spins at noload speed w 0 w 0 noload speed ID: 750945
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Slide1
Maximizing Motor Power at Constant Voltage
© 2012 Project Lead The Way, Inc.
Principles of EngineeringSlide2
Speed Depends on Load TorqueWhen a motor is loaded with no torque, it spins at no-load speed, w0 . w0 = no-load speed
When a motor is loaded with the stall torque
tstall or more, the motor will stop. tstall = stall torqueSlide3
Speed vs. Torque is LinearTorque t
Speed w
tstallw0
Half speed
Stall
No-load speed
Slide4
Optional slide for the genius:Speed vs. Torque Depends on VoltageTorque tSpeed w
7 V
5
V
3 V
motor speed 120
motor speed 90
m
otor speed 60Slide5
Power Power = Torque x Angular Speed
P = t • wSlide6
Power = Torque x SpeedTorque t
Speed w
tstallw0
No power. Why?
No power. Why?Slide7
Maximum Power at Half Stall TorqueTorque
tSpeed w
tstallw0
Maximum power. Why?
t
stall
Slide8
Why half stall torque?
Multiply both sides by torque, product on left is power.
Linear equation from last slide.
Down-facing parabola.Slide9
Torque tPower P
Maximum power
Stall
No load
Maximum Power at
Half
Stall Torque
t
stall
Slide10
VEX® Application: Pick a Gear RatioStep 1. This motor is stalled. What is the stall torque?
Step 2. At what torque will the motor deliver maximum power?
d = 3 in.F = 1.4 lb
VEX motor
t
stall
= d x F
┴
= (3 in.)(1.4
lb
)
= 4.2
lb
·
in
.
t
maxPower
= ½
t
stall
= ½
(
4.2
lb
·in.) = 2.1 lb·
in
.Slide11
VEX Application: Pick a Gear RatioStep 3. The same motor as in the last slide is being used to power a winch with a drum of radius 2 in. lifting 0.2 lb. What torque is the motor applying?tout = d x F┴ = (2 in.)(0.2 lb) = 0.4 lb·in.
d = 2 in.
F = 0.2 lbsSlide12
VEX Application: Pick a Gear RatioStep 4. Instead of direct drive, what gear ratio would make the motor deliver maximum power?
GR =
d = 2 in.
F = 0.2
lbsSlide13
VEX Application: Pick a Gear RatioNow the winch is geared so that the motor is delivering half its stall torque, for maximum power.
GR
=
GR =Slide14
Human Application: Bicycle “gears”Can you explain why changing “gears” on a bike helps a person win a race that goes up and down hills?Slide15
ReferencesMicromo (n.d.). DC Motors Tutorials. Retrieved from http://www.micromo.com/dc-motor-tutorials.aspxMIT Center for Innovation in Product Development (1999). Designing with DC Motors. Retrieved from http://lancet.mit.edu/motors/index.htmlWikipedia
(2009). Derailleur Bicycle Drivetrain. Retrieved from http://en.wikipedia.org/wiki/File:Derailleur_Bicycle_Drivetrain.svg