Maximizing Motor Power at Constant Voltage 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 ID: 770963
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Maximizing Motor Power at Constant Voltage © 2012 Project Lead The Way, Inc. Principles of Engineering
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 torque
Speed vs. Torque is LinearTorque t Speed w tstallw0 Half speed Stall No-load speed
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 60
Power Power = Torque x Angular Speed P = t • w
Power = Torque x SpeedTorque t Speed w tstallw0 No power. Why? No power. Why?
Maximum Power at Half Stall TorqueTorque tSpeed w tstallw0 Maximum power. Why? t stall
Why half stall torque? Multiply both sides by torque, product on left is power. Linear equation from last slide. Down-facing parabola.
Torque tPower P Maximum power Stall No load Maximum Power at Half Stall Torque t stall
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 .
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 lbs
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 lbs
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 =
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?
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