# Torque vs Current of a DC motor

1. Aug 5, 2011

### Jazz House

Hello all,

I hope you can fill a couple of holes in my understanding. As part of a school assignment I have investigated the relationship between torque and current in a DC motor. I have used linear regression and the linear fit is pretty good. I have done research on the relationship between voltage and speed, and current and torque. Both relationships, according to my sources, are linear. In addition to this, a quick google image search on DC current/torque curves yields many line graphs.

Can anyone point me to why this relationship exists? I realize that looking at all the relevant formulas like V=IR, torque=BAINcostheta, F=BILsintheta.... there are no powers and the angles aren't really considered a variable. This points to a linear relationship between torque and current.

But what I really want to know is like the principles behind this. Is there something in the motor principle I might not have spotted??

Also, I have grounded my regression line to the origin of the graph using excel. I don't think this accounts for no-load torque. I guess what I am asking here is whether there is still torque at a negligible current.

If this is in the wrong section I am sorry. I don't really think this is homework (it's more of a major assessment item) and I merely seek advice. I know what it's like to have newcomers post in wrong forums (I normally hang around the saxophone forum!) :)

Thanks a lot for any help!

JH

2. Aug 5, 2011

### xts

Torque/current is simpler. Take it first then.
DC motor you use relies on a force between fixed magnet and rotating coil. As the magnetic field generated by coil is proportional to the current flowing in it, then force between magnet and coil is also proportional to the current, then torque is further proportional to the current. Of course, other factors (like friction, resistance, etc) disturb the rule, but it works as the first approximation and you found it true.

Voltage/speed is a bit more complicated. Let's try this way: as the motor rotates, your coil is repeatedly swapped: voltage is applied in opposite direction every 1/2 rotation. After every such swap the current starts to flow from 0 and then rises linearily with time (as the coil has some inductivity). Average current is then proportional to the voltage and to the duration of the half-cycle. Or is proportional to the voltage and reverse proportional to the speed. Thus, in order to keep the average current constant (which means - the motor provides constant torque), the voltage must be proportional to the speed.

I guess what I am asking here is whether there is still torque at a negligible current.
Theoretically yes, but you may not forget about friction - you need some torque to overcome it.

3. Aug 5, 2011

### Jazz House

That's fantastic help for me!!

As for the torque at negligible current, should this have an effect on the linear regression I have applied. Does this mean I should ground the line to the origin still, or shall I remove that grounding??

It makes a big difference to the coefficient of determination when I ground the line to the origin. It goes from .95 to .897. The value of .95 (no grounding) accounts for torque at negligible current.

Thanks again.

4. Aug 5, 2011

### xts

Of course, you should remove the grounding.

So - little excercise for you: plot both fits together with data andlook at them. And compute what is a quality of fit ($\chi^2$) for both cases? You see the difference... So grounding your data occurs to be something non-physical.

5. Aug 5, 2011