Uncovering the Mystery of Non-Linear Torque in Muscle-Powered Energy Conversion

[Heros]

Hi, i didnt know where to put this question cos its kind of multitopic, here is why...
I am working on a better way to take mechanical energy from muscles, i made a teste bench for pedalling in very different ways, including traditional(circular) pedalling, the thing is. I am measuring the power of the athletes with a big dc motor(working as dynamo) attached with a lot of possible connections of incandescent car bulbs, and so, i tested diferents speeds and number/setup of light bulbs to produce different "brake" powers.
The thing is that after a lot of experiments to determine the torque vs speed function for every light bulbs setup and i discovered nothing surprising, the torque function is like this Torque=k*speed+RestingFriction being k of course the constant i was looking for.

I made a curve fit and got a very good precision(r^2=1 on excel) for every experiment, and found that of course, the more bulbs connected in parallel the higher K but not in a linear fashion, but that's not the problem...
The mistery begun when my girlfriend(she helps me a lot in my research) asked me why i didnt shortcircuited the motor and then we tried, at first the results were a K a little bit bigger than 8 bulbs in parallel( of course because that's a very low resistance arrangement) and when speeds got faster, the data begun to increase in a non linear fashion, so non linear, that with a linear fit i got a r^2=0.9456, then tried parabolic and got a beautifull r^2=1...?

So...why is bulb resistance linear and short ciruit not? I suspected about filament temperature, but it would just make it a negative concavity curve, i think...

Excuse my english...thanks a lot :)

 

[berkeman]

Hi, i didnt know where to put this question cos its kind of multitopic, here is why...
I am working on a better way to take mechanical energy from muscles, i made a teste bench for pedalling in very different ways, including traditional(circular) pedalling, the thing is. I am measuring the power of the athletes with a big dc motor(working as dynamo) attached with a lot of possible connections of incandescent car bulbs, and so, i tested diferents speeds and number/setup of light bulbs to produce different "brake" powers.
The thing is that after a lot of experiments to determine the torque vs speed function for every light bulbs setup and i discovered nothing surprising, the torque function is like this Torque=k*speed+RestingFriction being k of course the constant i was looking for.

I made a curve fit and got a very good precision(r^2=1 on excel) for every experiment, and found that of course, the more bulbs connected in parallel the higher K but not in a linear fashion, but that's not the problem...
The mistery begun when my girlfriend(she helps me a lot in my research) asked me why i didnt shortcircuited the motor and then we tried, at first the results were a K a little bit bigger than 8 bulbs in parallel( of course because that's a very low resistance arrangement) and when speeds got faster, the data begun to increase in a non linear fashion, so non linear, that with a linear fit i got a r^2=0.9456, then tried parabolic and got a beautifull r^2=1...?

So...why is bulb resistance linear and short ciruit not? I suspected about filament temperature, but it would just make it a negative concavity curve, i think...

Excuse my english...thanks a lot :)

Welcome to the PF.

It sounds like you may be saturating the motor/generator. Above a certain output current, the magnetics can start to saturate and lose their effectiveness. Do you have specs on the motor/generator? Can you measure that short-circuit current?

 

[Heros]

Hi berkeman, thanks for your reply.
Its a 750 watts 48 volts chinese motor, i measured last week a 28 amp top.
But i don't think that's the reason, because at near zero speed the curve at short circuit had a very similar K than 8 bulbs in parallel.( 0.006235 and 0.006153 respectively).

 

[nasu]

How do you relate all this to Ohm's law not being linear?

 

[Heros]

How do you relate all this to Ohm's law not being linear?

Sorry, i jumped off what i though that was obvious, but nothing is obvious...
When a permanent magnet motor moves, creates an electromagnetic force over the electrons in the copper windings, that can be assumed as a kind of voltage, called "lenz force", that "voltage" creates a current across the conductor, and that current, creates an electromagnetic field that interacts with the permanent magnetic field of the motor, trying to "brake" its movement...
Thats how i relate them...

 

[zoki85]

Its a 750 watts 48 volts chinese motor, i measured last week a 28 amp top.

You've said very little about your generator with that.
Output voltage vs load current of DC generators can have qualitatively different characteristics.
Besides, it looks like you change more things at same time in these tests. And yes, incadescent light bulbs have nonlinear resistance

 

[nasu]

Sorry, i jumped off what i though that was obvious, but nothing is obvious...
When a permanent magnet motor moves, creates an electromagnetic force over the electrons in the copper windings, that can be assumed as a kind of voltage, called "lenz force", that "voltage" creates a current across the conductor, and that current, creates an electromagnetic field that interacts with the permanent magnetic field of the motor, trying to "brake" its movement...
Thats how i relate them...

So where is Ohm'a law in all this? And what would mean that is not linear?
You mean that the conductors in the motor do not follow Ohm's law?

Maybe is just that the title is not appropriate.

 

[Heros]

You've said very little about your generator with that.
Output voltage vs load current of DC generators can have qualitatively different characteristics.
Besides, it looks like you change more things at same time in these tests. And yes, incadescent light bulbs have nonlinear resistance

All dc motors/generator use the same force font, current, and it flows through copper en all the cases, i don't see why that much interest in the motor itself.
I can guess light bulbs have non-linear behavior, but that's exactly the opposite that i got, a perfect straight line, and when connected in short circuit got the cuadratic fashion torque curve...

 

[Heros]

Hi berkeman, thanks for your reply.
Its a 750 watts 48 volts chinese motor, i measured last week a 28 amp top.
But i don't think that's the reason, because at near zero speed the curve at short circuit had a very similar K than 8 bulbs in parallel.( 0.006235 and 0.006153 respectively).

And if magnetics would get saturated, the curve would loose slope as speed increases, not getting more slope as it does.

 

[Nugatory]

The thing is that after a lot of experiments to determine the torque vs speed function for every light bulbs setup and i discovered nothing surprising, the torque function is like this Torque=k*speed+RestingFriction being k of course the constant i was looking for.

If I'm understanding you properly, you mean you generated a number of (torque, speed) pairs and fit them to a line of slope k. How did you measure the torque and speed?

 

[256bits]

Exactly.

 

[CWatters]

Is the motor/wire getting hot?

 

[zoki85]

All dc motors/generator use the same force font, current, and it flows through copper en all the cases, i don't see why that much interest in the motor itself.

And most people look alike, except that they behave different in extreme case situations

 

[Heros]

If I'm understanding you properly, you mean you generated a number of (torque, speed) pairs and fit them to a line of slope k. How did you measure the torque and speed?

Yes that's it, data pairs.
I measured them by putting the motor on a very high place, the motor has a pulley of a known diameter, and i winded many different known wheights... I left the motor accelerate until a terminal speed, when wheighttorque+braketorque=0, then i just measured the speed.

 

[Heros]

Is the motor/wire getting hot?

Not that much, i can touch it after a 15 minutes elite cyclist test.