Motor Quiz
 

What voltage would be required to operate a CIM at 60 oz-in at 3700 rpm?

Re: Motor Quiz
 

9 volts

Re: Motor Quiz
 

Wild guess?

Re: Motor Quiz
 

10.1 V

Re: Motor Quiz
 

yep :) never did like quizes, multiple guess tests are better.

Re: Motor Quiz
 

At 10.1 volts the free speed is (10.1/12)*5310 = 4469 rpm

The stall torque is (10.1/12)*343.4 = 289 oz-in.

So at 3700 rpm the torque would be 49.7 oz-in, not 60 oz-in.

Re: Motor Quiz
 

I see, so stall torque also scales in the same way. A convenient way to can all this then would be with giving the speed vs. torque curve as speed/free speed + torque/stall torque = voltage/spec voltage.

For another shot then:

10.43V

Re: Motor Quiz
 

10.5 Volts, give or take.

I arrived at my answer by a very different (and probably incorrect) method from the poster above. I figured motor constants for RPM/Volt and Oz-In/Amp, found how much current it would take to hold 60 oz-in at stall, considered the resistance of the motor's windings, then figured out how many volts it would need to hold 60 oz-in at stall, then I figured how many volts it would need to spin 3700 RPM at no load, then added those two voltages to arrive at my answer. I did have some rounding error, but perhaps my method is entirely flawed and just happened to be close by coincidence? I am on holiday here....

EDIT: Revising my answer with less rounding, I get 10.458 Volts by the above method.

I'm confused by the above poster's method of adding ratios of speed and torque. Why does that work?

Re: Motor Quiz
 

My work:

CIM Motor Constants
442.5 RPM/Volt
2.581954 oz-in / A
Resistance of motor windings is 0.0902255639 Ohms by Ohm's Law

Thus:
60 oz-in requires 23.238214 A to stall, from a 2.09668 V source

Also, it takes 8.3615819 V to spin 3700 RPM under no load

Add the voltages to arrive at 10.458 V needed to spin 60 oz-in load at 3700 RPM

Check: At this voltage:

Free speed is 4627.65 RPM
Stall Torque is 299.2731 oz-in

Operating parameters are at:
20.0486% of stall
79.9514% of free speed = 3699.87 RPM

Less than 0.4% Calculation error.

Can someone tell me if this is the proper way to do this, or if my hairbrained idea just happened upon a lucky coincidence?

Re: Motor Quiz
 

Come on engineers, significant figures.
2 digits of data yielding 8 digits of precision?
Use 10.5 or 11 volts and call it a day.:D

Re: Motor Quiz
 

See attached speed vs torque drawing.

E is the desired operating point with speed C and torque D

Line AB is the 12V speed vs torque curve (given)

If we can find G, then the "mystery" voltage is 12*(G/A).

Proceed as follows:

From similar triangles, (G-C)/D = A/B

Multiply both sides by D/A to get (G-C)/A = D/B

Expand the left side to get G/A - C/A = D/B

Move C/A to the other side to get G/A = C/A + D/B

So V = 12*(G/A) = 12*(C/A + D/B) which is what Aren did.


Of course, this ignores the 2.7 amp free current. What role should that play in this analysis?

Re: Motor Quiz
 

The whole concept using "significant figures" this way, although still taught in high schools, is deeply flawed.

Re: Motor Quiz
 

The above method is arithmetically identical to what Aren did:

current to hold "D" oz-in at stall = (D/B)*Istall

volts to hold "D" oz-in at stall = (D/B)*Istall*R = (D/B)*Istall*(12/Istall) = 12*(D/B)

volts to free-spin at "C" rpm = 12*(C/A)

adding these 2 gives:

"mystery volts" = 12*(C/A+D/B)

Re: Motor Quiz
 

It's also at least touched on at the college level. I'm curious why you say it's flawed--besides the fact it confused me every time I tried to use it! (I typically hold about a 2-3 decimal digit precision in the final answer, but I'll often go to 4-5 decimal digits or more during calculations.)

Re: Motor Quiz
 

Yes, I know my significant figures and decimal places are a complete mess. I was rushing. I too would like to hear Ether's explanation of the flaws in the significant figure method taught in schools.

The 2.7A free-running current I believe plays a role in determining the motor's torque constant. Rather than being 343.4 Oz-In / 133A it would be 343.4 oz-in / (133-2.7 A)

I'm actually rather surprised I did this correctly, albeit in a somewhat roundabout method. This was fun.

Re: Motor Quiz
 

Are you saying that there's more than 4 significant digits in the 'best' answer?
Me too, because I'm not sure in which way you find flaw.

The statement I use is "Just because your calculator shows 8 digits doesn't mean they are all important".

On the other hand, it is very important to know just how many digits you really have to work with, and a good idea of physical reality to check for reasonableness.

Re: Motor Quiz
 

In real life, there are no multiple choice questions.

Usually....

Re: Motor Quiz
 

Several parallel thoughts come to mind:

1) for a detailed (and humorous) treatment, see this link.

2) rounding the answer to 11 volts as suggested here gives a profoundly wrong answer*. At 11 volts, the torque at 3700 rpm is 75.5 oz-in

3) with modern computers and calculators, there is no reason to drop any digits of precision during intermediate calculations. carry all the precision through, then round the final answer. the number of digits to keep is not a simple matter of looking number of digits in the datum with the least digits. in the specific case of this problem, tenths of a volt is a reasonable (and necessary) precision to get a reasonably correct answer:

61 oz-in @ 3710 rpm requires 10.52 volts

59 oz-in @ 3690 rpm requires 10.40 volts

... so if you want to round to 10.5 volts that would be reasonable, but not 11 volts*


*we are talking about correct answers to the problem as stated. I know that manufacturing tolerances of the motor could cause wide variation.

Re: Motor Quiz
 

No. But I am saying using only 2 digits (11 volts), as suggested, is not a correct answer.

More detail posted here.

Agreed. But a student should learn how to use the calculator in such a way that all those digits get used through the intermediate calculations.

I agree completely.

Re: Motor Quiz
 

I agree that the whole "sig figs" deal is flawed. I had a science teacher in high school who extolled it, and perhaps it was his inability to do basic algebra that led me to skepticism of that as well. My beef with it is that it is so dependent on the base in which you are representing the numbers. If you're going to worry about such things, actually do the stats with how the initial standard deviations or uncertainties propagate through the calculations. If you don't care that much, just round your final answer at the end to something that's not way than you care about, but still gives detail relevant to the problem and its context. My answer 10.43 was perhaps too many digits: 10.4V would perhaps have been more appropriate given how much control we actually have over (and how much we actually about) the voltages in question. But it doesn't really matter that much. And as Ether has pointed out, 11V is just plain wrong. And one should never round in the intermediate steps. The best way to go about these calculations is to solve for the answer symbolically and then just plug in your parameters, since the general solution in infinitely more useful and this avoids any intermediate rounding errors. I do a lot of calculations in excel and keep all the digits (the first 30 some anyway) around. However, when reporting these intermediate values, I will often round to keep it uncluttered.

Also (to sanddrag mostly), my method of solving was based on the fact that stall torque and free speed scaled with voltage, so I whipped a quick mathematical model that did just that. Your (sanddrag's) approach went through the physics of it from the start, which is equally valid (in fact, that's where we get the linear dependence of stall torque and free speed on voltage, as well the linear performance curve between them).

Re: Motor Quiz
 

To use the phrase "deeply flawed" suggests that you have difficulty with the meanings of the ideas behind precision and accuracy.
Suggesting that because it is "still taught in high schools" and thus maybe has little relevance, is possibly offensive.

Just try a small exercise:
Imagine that the motor may rotate 3701 revolutions in a single minute. Not an unreasonable possibility. Or even that the 60 oz-in is actually 60.01 oz-in. Recalculate your answers.
Every digit that you include beyond four becomes irrelevant, it is just calculator detritus.

IMHO, sometimes people use excessive digits in their calculations of answers like curse words, to emphasize their supposed superiority where it is not necessary.

The precision of the measurement determines the accuracy of the result.

Re: Motor Quiz
 

Those are desired values, not measured values, and should not be considered when doing significant figures. It's assumed that Ether wants those values as close as possible.

Where significant figures should be applied is on the input values (In Aren's calculations the Free speed, Stall torque, and Spec voltage). All were given to at least 3 significant figures (It should be safe to assume that Spec Voltage wasn't 12v +/- 0.5, but rather +/-0.05 or even better).

Re: Motor Quiz
 

And as the motor heats up near the end of a match?
Ohm's law breaks down, and nature takes her tax.