Maximizing Motor Power at Constant Voltage Principles Of Engineering 2012 Project Lead The Way, Inc. Speed Depends on Load Torque When 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 Linear Speed w No-load speed w0 Half speed Stall = + tstall Torque t
Speed w Optional slide for the genius: Speed vs. Torque Depends on Voltage 7 5 3 V V V m ot
m ot or or s sp ee d m 12 pe ot
0 ed or sp 90 ee d 60 Torque t Power Power = Torque x Angular Speed P=t
w Power = Torque x Speed Speed w No power. Why? w0 No power. Why? tstall Torque t
Speed w Maximum Power at Stall Torque w0 Maximum power. Why? tstall = + Torque t tstall
Why half stall torque? = + Linear equation from last slide. Multiply both = + () sides by torque, [
] = + product on left is power. Down-facing parabola. Maximum Power at 1/2 Stall Torque Power P
= + No load Maximum power tstall Torque t Stall VEX Application: Pick a Gear Ratio
Step 1. This motor is stalled. What is the stall torque? = (3 in.)(1.4 lb) = 4.2 lbin. VEX motor F = 1.4 lb tstall = d x F d = 3 in. Step 2. At what torque will the motor deliver maximum power? tmaxPower = tstall = (4.2 lbin.) = 2.1 lbin.
VEX Application: Pick a Gear Ratio Step 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? d= tout = d x F n. F = 0.2 lbs 2i
= (2 in.)(0.2 lb) = 0.4 lbin. VEX Application: Pick a Gear Ratio Step 4. Instead of direct drive, what gear ratio would make the motor deliver maximum power? d= GR = n. F = 0.2 lbs
2i VEX Application: Pick a Gear Ratio Now 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? References
MIT Center for Innovation in Product Development (1999). Designing with DC Motors. Retrieved from http://lancet.mit.edu/motors/index.html Micromo (n.d.). DC Motors Tutorials. Retrieved from http:// www.micromo.com/dc-motor-tutorials.aspx Wikipedia (2009). Derailleur Bicycle Drivetrain. Retrieved from http:// en.wikipedia.org/wiki/File:Derailleur_Bicycle_Drivetrain.s vg
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