# Increasing the output torque of a DC motor with gears

• I

## Main Question or Discussion Point

Hello everyone,

I see videos showing the output torque can be increased by using gears and this is usually demonstrated with DC motors (simple DC motors can be removed from toys). I understand the general logic:

* The DC rotates in a high speed.
* The gear system reduces the output speed.
* If we neglect the friction losses the power must be the same for the DC rotor shaft and the final gear.
* As the power is torque times angular velocity, and as the final gear rotates with a lower speed the output torque is higher. Therefore a rope connected to the final gear can pull heavy objects.

My question is why the gears are necessary. If the rope is directly connected to the DC motor shaft it cannot pull the same object. If it could rotate slowly with the same power it could generate the required torque. When I try to obstruct the rotation of a DC motor with my finger I can make it rotate slower but is there a limit for how slow it can rotate?

I see a very similar thing in car engines. If you want to move the car you need to use a lower gear with a higher gear ratio (preferably 1st gear), however if the same power is generated with even the highest gear the same torque must be obtained on the wheels. However as far as I know the car engines do not work efficiently in low RPMs and they do not work at all below some limit, therefore the same power cannot be generated with the higher gears. In my opinion if we had an ideal engine which work efficiently at all RPMs we would not need transmissions. Is the case with DC motors similar?

Related Classical Physics News on Phys.org
A.T.
In my opinion if we had an ideal engine which work efficiently at all RPMs we would not need transmissions.
Correct.

Is the case with DC motors similar?
It is different and transmissions can be avoided sometimes:
https://www.greenoptimistic.com/electric-cars-gears/

jbriggs444
Homework Helper
2019 Award
If you want to move the car you need to use a lower gear with a higher gear ratio (preferably 1st gear), however if the same power is generated with even the highest gear the same torque must be obtained on the wheels. However as far as I know the car engines do not work efficiently in low RPMs and they do not work at all below some limit, therefore the same power cannot be generated with the higher gears. In my opinion if we had an ideal engine which work efficiently at all RPMs we would not need transmissions. Is the case with DC motors similar?
Most internal combustion engines are, at some level of approximation, constant torque devices. That is, over some range of speeds, the output torque is roughly constant. At the high end and low ends, the torque will drop off, of course. For constant torque, more RPM means more power. The power curve is what you get when you multiply torque by RPM. The power curve will peak somewhere to the right of the flat spot on the torque curve.

You use a transmission so that you can keep the engine RPM in a range that has near-peak power. Or near-peak efficiency -- or whatever metric you are after.

Thanks a lot for your replies. Could you please also explain me why I need gears to pull heavy objects with a simple DC motor, the ones can be found in very simple toys? The below part of my question;

My question is why the gears are necessary. If the rope is directly connected to the DC motor shaft it cannot pull the same object. If it could rotate slowly with the same power it could generate the required torque. When I try to obstruct the rotation of a DC motor with my finger I can make it rotate slower but is there a limit for how slow it can rotate?
How do these motors work? Do they also have a curve? I read the article in the link posted by @A.T. but I believe the motors I mentioned are different from the ones explained in the article.

jbriggs444
Homework Helper
2019 Award
How do these motors work? Do they also have a curve?
I believe that the torque curve for a typical DC motor is normally a straight line that starts with maximum torque at zero RPM and declines to zero torque at max RPM. A quick trip to Google confirms.

If you multiply torque by RPM, that means that you have a power curve like:

One could also derive an efficiency curve.

A.T.
Could you please also explain me why I need gears to pull heavy objects with a simple DC motor,
The motor doesn't pull, it creates a torque. In order to pull something you need at least one gear/spool/pulley, which is a form of transmission, where the gearing is determined by the radius.

The motor doesn't pull, it creates a torque. In order to pull something you need at least one gear/spool/pulley, which is a form of transmission, where the gearing is determined by the radius.
Then maybe my question must have been why I needed more than one gear to pull a heavy object. Again my logic is the same, if the DC motor was an ideal motor which could have the same power output at all the RPMs only one gear must have been enough to create the required torque output.

I think what @jbriggs444 has shared explains it as it shows there is a torque limit a DC motor can create (in my ideal motor scenario the torque would go to the infinity while the RPM goes to zero.)

jbriggs444
Homework Helper
2019 Award
If the DC motor was an ideal motor which could have the same power output at all the RPMs only one gear must have been enough to create the required torque output.
Yes. That is what transmissions are for -- to take non-ideal motors and make them [more nearly] ideal. A DC motor is not ideal. It does not produce the same power output at all rotation rates.

The gearing produces a trade-off between higher spin speed with lesser torque, and lower spin speed with greater torque -- please think of a fast motor gear-driving a slow winch -- you could maybe stop the motor by pinching the shaft with heavy gloves on your fingers, but you couldn't stop the slow towing cable that way.

russ_watters
Mentor
Then maybe my question must have been why I needed more than one gear to pull a heavy object. Again my logic is the same, if the DC motor was an ideal motor which could have the same power output at all the RPMs only one gear must have been enough to create the required torque output.
I don't know what definition of "ideal" you are using, but that doesn't follow, to me. "Infinite torque" sounds like a divide-by-zero error to me. "Ideal" usually means 100% efficiency/no losses, not constant power. I see no reason why constant power should be expected.

Also, to clarify we're talking about "full throttle" operation here: The lines on the graphs @jbriggs444 provided are maximums and the motor(s) can operate anywhere under them. For a DC motor, the "throttle" is Voltage.

Then maybe my question must have been why I needed more than one gear to pull a heavy object. Again my logic is the same, if the DC motor was an ideal motor which could have the same power output at all the RPMs only one gear must have been enough to create the required torque output.

I think what @jbriggs444 has shared explains it as it shows there is a torque limit a DC motor can create (in my ideal motor scenario the torque would go to the infinity while the RPM goes to zero.)

The torque doesn't go to infinity, and if the motor RPM speed goes to zero, so does the torque. I suggest that you take 2 same-size coins and place them flat on a table, 1 edge-on to the other -- you'll notice that if you revolve 1 around the other, it will rotate on its central axis exactly twice on 1 revolution. For same size coins pinned with axles at their centers, the rotation of 1 of them being transferred to rotation of the other, the RPMs and torque for the 2 same-sized coins are approximately equal. But if you start with a fast dime, transfer to a medium-speed quarter, and from there to a slower half-dollar, you'll get a slower, higher-torque half-dollar, from a higher-speed lower-torque dime.

russ_watters
Mentor
The torque doesn't go to infinity, and if the motor RPM goes to zero, so does the torque.
This isn't necessarily true for a DC motor; it is capable of producing torque at zero RPM.

This isn't necessarily true for a DC motor; it is capable of producing torque at zero RPM.
That's true. I was trying to correct a misimpression, and in doing so, I neglected something myself. Thanks for catching that error.

Merlin3189
Homework Helper
Gold Member
One point you need to bear in mind is current. If you look at JBriggs graphs for the DC motor, the current isn't shown. It is essentially proportional to the torque.
So if your load is not too great, then the motor certainly can support a bigger load at a lower RPM. But the current rises proportionally to torque. Then you get more heating in the resistance of the windings and that is proportional to the square of current. Pretty soon your motor is getting much too hot.

That's a lesson I learn't very young. I had a motor boat powered by clockwork. If you took it out of the water while it was still running, you stopped it to save the energy left in the spring. When I later got a battery powered boat, I did the same, stopping the propeller with my finger until I could unfasten the top and switch it off. I must have been a bit slow and maybe had new batteries (big D cells). When I opened it up, the motor was smoking! I don't know who put me right, but it impressed itself on my memory. I was a bit fascinated by it, because it seemed so counterintuitive to me. The best way to save the batteries until I could get to the switch, was to let it run free, the opposite of saving spring power.

I know how the torque and speed are transmitted from a gear to another gear. My question was mainly on why the DC motors/engines cannot generate enough torque by rotating slower and I have the answer now.

The ideal motor/engine with the meaning of constant power motor/engine was only a definition by me for this case specific mainly to be able to explain my question better and I think it worked for me.

As I have got my answer from this forum as it has been always I appreciate all and thank you again.

A.T.