# Is no-load to stall amp draw linear with DC motors?

I have two DC motors with no-load current draw of 200mA. The datasheet goes on include a stall-current draw of 2.2A.

The torque is given for both extremes. Considering you know the torque that is being exerted (and presumably that is the force required to be exerted to stop the motor from turning) is this relationship linear?

I am concerned because I will obviously load the motors when using them but am not sure how to calculate the estimated current draw under arbitrary load. Do you simply throw the contraption together and measure the current being drawn by the motors and when you see that value approaching the stall current then its obvious you are overloading your motor?

Actually, it is linear. I found this online just now. But I am still concerned with the second part of my question regarding calculating loaded current draw. From the graph below its obvious you can determine current by a given torque load - but how do you calculate that? Or what other methods are known?

• You can't 'calculate' load from the motor characteristic -- load is the characteristic of the load. Do you know your load characteristic? Can you calculate it? Can you measure it? Or what do you mean? – david Aug 12 '13 at 1:32

## 2 Answers

In the steady-state case, it's a simple linear interpolation:

$I_S$ is the stall current.

$\omega_{nl}$ is the no-load speed.

$I_{nl}$ is the no-load current.

For a motor loaded such that it spins with a speed $\omega_L$, the current draw is:

$$I_L = (I_S- I_{nl}) (1-\frac{\omega_L}{\omega_{nl}}) + I_{nl}$$

For example, you have a motor with a 2.2A stall current, 0.2A no-load current, and let's assume the no-load speed is 1000 rpm. Technically $\omega$ usually refers to rads/s, but here the units cancel out; the only important factor is what the relative speed of the motor compared to the no-load speed is.

At a 250 rpm load speed, the current draw is:

$$I_L = (2.2A - 0.2A) (1-\frac{250}{1000}) + 0.2A = 1.7A$$

Keep in mind that even though the steady-state current of the motor is 1.7A, the peak current could be much more. Starting up the motor would draw close to the stall current of 2.2A, decreasing until the motor reaches steady state. Depending on how quickly the motor is able to get to steady state, this may be significant or not.

• I did not consider using the rpm to approach this problem. Although, determining the rpm of the motor would be an issue in itself. Perhaps the use of a hall sensor/magnet switch would work with a microcontroller - but what other options are there? – sherrellbc Aug 12 '13 at 0:53
• There are many options for measuring rotational speed: rotary encoders, hall effect sensors, LED/photodiode combo, etc. If all you want to check for is stall, measuring rotational motion directly is the best. Any other method will be susceptible tolerances and drift of various parameters. If you want to be careful about motor current draw, you should measure current directly (for the same reason as above). – helloworld922 Aug 12 '13 at 2:06

Ratio of motor speed to no-load speed is a pretty good clue to the percentage of stall torque you are loading the motor with. If you have lost 25% of the unloaded speed, that is 25% of stall torque (assuming a well regulated supply).