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 Chief Delphi Physics Quiz 13
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#1
11-01-2017, 05:39 PM
 Ether systems engineer (retired) no team Join Date: Nov 2009 Rookie Year: 1969 Location: US Posts: 8,703
Physics Quiz 13

Imagine an ideal* brushed DC motor whose +/- coil wires are directly connected to an adjustable DC voltage power supply, and whose output shaft is connected to a dynamometer capable of maintaining a constant torque.

The power supply is adjusted to 12 volts applied to the motor, and the dynamometer is set to maintain a constant load of To ounce inches on the motor's output shaft, and as a result the motor spins at Wo RPM and the motor is drawing Io Amps. Assume this operating point is well within the motor's safe continuous-duty operating range.

Without changing anything else, the applied voltage is adjusted down to 10 volts. Assume the motor is still spinning at this lower voltage. Ignoring secondary effects such as windage and bearing friction etc in the motor, to a first approximation what happens to the motor speed and current due to the decrease in applied voltage?

a) speed decreases and current decreases

b) speed decreases and current stays roughly the same

c) speed decreases and current increases

d) speed increases and current decreases

e) speed increases and current stays roughly the same

f) speed increases and current increases

* assume free speed current is zero Amps

Last edited by Ether : 11-01-2017 at 06:15 PM.
#2
11-01-2017, 06:43 PM
 GeeTwo Technical Director AKA: Gus Michel II FRC #3946 (Tiger Robotics) Team Role: Mentor Join Date: Jan 2014 Rookie Year: 2013 Location: Slidell, LA Posts: 4,744
Re: Physics Quiz 13

Ether,
Thanks for the warm-up as I was planning to start working out a mental model for brushless motors!

Gus
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#3
11-01-2017, 07:45 PM
 Richard Wallace I live for the details. FRC #3620 (Average Joes) Team Role: Engineer Join Date: Jan 2003 Rookie Year: 1996 Location: Southwestern Michigan Posts: 4,035
Re: Physics Quiz 13

b).

Rep to the first concise, student-written response that explains why.
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I believe in intuition and inspiration. Imagination is more important than knowledge. For knowledge is limited, whereas imagination embraces the entire world, stimulating progress, giving birth to evolution. It is, strictly speaking, a real factor in scientific research.
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#4
11-01-2017, 08:14 PM
 noah.gleason Registered User FRC #0449 (The Blair Robot Project) Team Role: Programmer Join Date: Mar 2017 Rookie Year: 2016 Location: Bethesda, MD Posts: 69
Re: Physics Quiz 13

Quote:
 Originally Posted by Richard Wallace b). Rep to the first concise, student-written response that explains why.
Alright, here's my shot: The DC motor state equation is Voltage = k*speed + current over windings * R, which means that voltage is being split between back-EMF (the first term) and actually producing torque (second term). We can ignore k and R because this is asking about relative increase/decrease and both are positive constants. When voltage decreases, one of the two must decrease along with it. However, we're told that torque is constant, so I*R must remain constant. Therefore k*speed must decrease, so the motor gets slower.

EDIT: The instantaneous effect is that current drops, because velocity can't change instantly. This reduces the torque for a moment, slowing the motor down until the back-EMF compensates entirely for the change in voltage.
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Last edited by noah.gleason : 11-01-2017 at 08:39 PM.
#5
11-01-2017, 10:51 PM
 GeeTwo Technical Director AKA: Gus Michel II FRC #3946 (Tiger Robotics) Team Role: Mentor Join Date: Jan 2014 Rookie Year: 2013 Location: Slidell, LA Posts: 4,744
Re: Physics Quiz 13

Quote:
 Originally Posted by noah.gleason Alright, here's my shot:
Not quite as concise as I'd hoped, but I'll give reps. More reps to a better/simpler student explanation!
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Last edited by GeeTwo : 11-01-2017 at 10:55 PM.
#6
11-01-2017, 11:05 PM
 Brian M Design Lead FRC #1360 (Orbit Robotics) Team Role: CAD Join Date: Feb 2017 Rookie Year: 2012 Location: Ontario, Canada Posts: 149
Re: Physics Quiz 13

My turn!

B) because the same constant torque (To) is still applied to the shaft, thus speed decreases with the lower power input, but current stays the same.
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Last edited by Brian M : 11-01-2017 at 11:41 PM. Reason: ......same idea, reworded.
#7
11-02-2017, 01:18 PM
 GeeTwo Technical Director AKA: Gus Michel II FRC #3946 (Tiger Robotics) Team Role: Mentor Join Date: Jan 2014 Rookie Year: 2013 Location: Slidell, LA Posts: 4,744
Re: Physics Quiz 13

Quote:
 Originally Posted by Brian M My turn! B) because the same constant torque (To) is still applied to the shaft, thus speed decreases with the lower power input, but current stays the same.
OK, but why is the current the same?
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#8
11-02-2017, 02:02 PM
 Mark Wasserman Registered User FRC #2767 (Stryke Force) Team Role: Mentor Join Date: May 2017 Rookie Year: 2010 Location: kalamazoo Posts: 83
Re: Physics Quiz 13

Quote:
 Originally Posted by GeeTwo OK, but why is the current the same?
Let me see if I get this right:

Because torque and current go hand in hand. If the torque is constant then current must follow.
#9
11-02-2017, 02:36 PM
 Bob Steele FIRST Senior Mentor - Washington AKA: Bob Steele FRC #1983 (Skunk Works Robotics) Join Date: Jan 2003 Rookie Year: 2002 Location: Seattle, Washington Posts: 1,585
Re: Physics Quiz 13

In a DC motor, the output torque is directly proportional to the current through the windings

not sure what hand in hand means but I think this is what you mean....
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#10
11-02-2017, 03:02 PM
 Cyberphil That Guy AKA: Phil FRC #0103 (Cybersonics) Team Role: Engineer Join Date: Feb 2008 Rookie Year: 2007 Location: Doylestown, PA Posts: 856
Re: Physics Quiz 13

Quote:
 Originally Posted by Mark Wasserman .... then current must follow.
Someone has been reading too much DUNE.
#11
11-02-2017, 03:55 PM
 Richard Wallace I live for the details. FRC #3620 (Average Joes) Team Role: Engineer Join Date: Jan 2003 Rookie Year: 1996 Location: Southwestern Michigan Posts: 4,035
Re: Physics Quiz 13

Quote:
 Originally Posted by Cyberphil Someone has been reading too much DUNE.
You are thinking of Spice. Torque is not proportional to Spice.

But the Spice must flow...
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Richard Wallace

Mentor since 2011 for FRC 3620 Average Joes (St. Joseph, Michigan)
Mentor 2002-10 for FRC 931 Perpetual Chaos (St. Louis, Missouri)
since 2003

I believe in intuition and inspiration. Imagination is more important than knowledge. For knowledge is limited, whereas imagination embraces the entire world, stimulating progress, giving birth to evolution. It is, strictly speaking, a real factor in scientific research.
(Cosmic Religion : With Other Opinions and Aphorisms (1931) by Albert Einstein, p. 97)
#12
11-02-2017, 04:09 PM
 Mark Wasserman Registered User FRC #2767 (Stryke Force) Team Role: Mentor Join Date: May 2017 Rookie Year: 2010 Location: kalamazoo Posts: 83
Re: Physics Quiz 13

Quote:
 Originally Posted by Bob Steele In a DC motor, the output torque is directly proportional to the current through the windings not sure what hand in hand means but I think this is what you mean....
So now we know torque and current are directly proportional, can someone list at least 2 scenarios in FRC land where we could put this new found knowledge to use and how you might implement it?
#13
11-02-2017, 04:29 PM
 Brian M Design Lead FRC #1360 (Orbit Robotics) Team Role: CAD Join Date: Feb 2017 Rookie Year: 2012 Location: Ontario, Canada Posts: 149
Re: Physics Quiz 13

Quote:
 Originally Posted by GeeTwo OK, but why is the current the same?
Because the % stall is the same?
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#14
11-02-2017, 04:32 PM
 Brian M Design Lead FRC #1360 (Orbit Robotics) Team Role: CAD Join Date: Feb 2017 Rookie Year: 2012 Location: Ontario, Canada Posts: 149
Re: Physics Quiz 13

Quote:
 Originally Posted by Mark Wasserman So now we know torque and current are directly proportional, can someone list at least 2 scenarios in FRC land where we could put this new found knowledge to use and how you might implement it?
Well you wouldnt because we use 12 and 5v, and then only pwm to control speed. Maybe to compensate for battery undervoltage but even then wouldnt encoders and sensors solve that?
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#15
11-02-2017, 07:03 PM
 noah.gleason Registered User FRC #0449 (The Blair Robot Project) Team Role: Programmer Join Date: Mar 2017 Rookie Year: 2016 Location: Bethesda, MD Posts: 69
Re: Physics Quiz 13

Quote:
 Originally Posted by Mark Wasserman So now we know torque and current are directly proportional, can someone list at least 2 scenarios in FRC land where we could put this new found knowledge to use and how you might implement it?
I've got one but it's important: modeling your motors for open-loop control or for feed-forward in closed-loop. By driving the robot at a bunch of steady voltages, you can find the velocity vs. voltage curve (it's actually a line). The y-intercept of that line will give you the minimum amount of torque/current you need to overcome friction. The slope of that line gives K in the motor state equation I discussed above.

Once you have that equation, accelerate the robot any way you want (driving around works) and measure the voltage, velocity, and acceleration (use the derivative of velocity, not an accelerometer, they're too noisy). By subtracting out the voltage that the motor "should" draw according to the line you got above, you can find how much voltage is going towards "productive" (i.e. not fighting friction) torque. Plotting that voltage against acceleration gives you R, the resistance of the windings. With these measurements, you can upgrade your open-loop/feedforward from voltage=12*(velocity sp/max speed) to voltage = k*velocity sp + intercept + r*(acceleration), which almost fully characterizes the motor. The only things missing are inductance and capacitance, both of which are negligible for a drive motor and probably negligible for any mechanism slower than a can grabber.
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