Measuring Torque of a Stepper Motor Using a Suspended Weight Method

[roam]

1. The problem statement, all variables and given/known data

I am trying to experimentally measure the torque of a stepper motor at various velocities. I'm not quite sure how this should be done. Here is a diagram of my proposed method so far:

Basically a weight is to be suspended from the motor by a string, and I will measure by how much the string has moved up after one full revolution. Then I believe the torque must be: $\tau = m \times g \times \Delta L$. Is this a correct method?

Homework Equations

Torque = Force x Distance

The Attempt at a Solution

I would greatly appreciate it if someone could confirm whether this is a correct method to get a roughly correct measurement of torque (within perhaps ~80% of the manufacturer quotedvalue at a given velocity)?

Do I need to take the shaft diameter into account (or perhaps some other factors)? What is the simplest way of doing this?

 

[Simon Bridge]

Torque = Force x Distance

... sort of: the "distance" in question cannot be any old distance - it has to be the length of the moment arm. In your equation $mg\Delta L$ is the work, $W=Fd$, not the torque.

The equivalent relation for rotation is $W=\tau\theta$ ... where the angle is in radians.

 

[CWatters]

Another way to measure the torque is to mount the motor on a pivot so the case can rotate (within limits), attach an arm to it with some sort of spring scale on the end.

 

[Windadct]

Also in your diagram the Moment Arm - is the radius of the shaft ( from the center to where the string contacts it- so pretty small) -- so you can decrease the needed weight but adding a wheel/spool to the shaft to increase the radius. By choosing a good radius it will make the calculations easier ( e.g. if you want In*Lbs as units- use a 1" radius wheel)

 

[roam]

Thank you Simon, CWatters, Windadct for your responses. I'm still a bit confused.

So, basically, I must measure the radius and use $\tau= mg \times r$, OR find the angle and use $\tau = (mg \Delta L)/\theta$?

When the motor turns the string will be wound around the stepper motor shaft, and I must measure the shaft radius with string around it (the amount of string is supposed to change by a minuscule amount whenever I change the speed). I think this would be a very difficult and inaccurate way of measuring $\tau$...

In the diagram below I have indicated $\theta$:

Is this the right idea? This angle can be measured with a protractor. Even if the string is wound several times and we get the same θ, ΔL would be different. Therefore we get different torques each time. So is this a correct method?

P.S. Unfortunately I do not have access to an appropriate spool, or a spring scale at the moment. I have to work with only a ruler and a protractor.

 

[Simon Bridge]

Neglecting energy that goes to turn the motor components: $$\tau_{ave} = \frac{mg\Delta L}{2N\pi}$$ would be a reasonable approximation.
Notice that's an average for N entire turns. Picking a big value for N will probably be best.

$\vec \tau = \vec F_g\times \vec r \implies \tau=mgr$ ...where r is the radius of the shaft, would be the torque exerted by gravity.
Since the stepper motor accelerates around one turn, it must be providing more torque than that.

 

[roam]

Thank you for the explanation Simon. It's all clear now. :)