I’m working with an artist to create an interactive spinning painting and am looking to source a suitable DC motor that is appropriate for our application.

I have experience with digital electronics (Arduino, RasPi, etc), but am not 100% confident in my analog skills or estimating motor requirements based on physical properties for my application. Looking to learn!

The painting will be done on a 2x2’ x 1/2" square plywood board weighing approximately 5 pounds (roughly 80oz, or 2.27kg). We’re looking to spin it at a relatively low rate - only in the neighborhood of 60-120 RPM.

What I don’t know much about is how to use this information to choose a particular motor based on its rated torque specification. For example, this beauty has a rated maximum torque of 300 oz-in - is that enough to safely spin this painting?

We are also think about using a simple tensioned belt and pulley mechanism in order to minimize unwanted movements and strain on the rotor. Perhaps we could use different sized pulleys while we’re at it to gain an additional torque or speed advantage if needed.

Any help in thinking through this situation and using appropriate formulas to make an educated decision of motor is appreciated!

That sounds like it might work. The main force to check is to make sure that the gearmotor would be able to supply enough torque to overcome the moment of inertia of your canvas. Generally you want to keep the torque to about 20% to 30% of the stall torque. Using a belt and pulley system is probably a good idea because it would remove the radial and axial forces from the output shaft of the gearmotor.

I’m not very familiar with moment of inertia calculations (more of an electronics engineer than mechanical). I see that it is measured in slightly different units than torque - how do I figure out the required torque for my gearmotor based on moment of inertia?

Here is what the moment of inertia calculation is giving me with my known parameters (2.26kg weight and 4in diameter pulley): I = mr^2 I = 2.26kg * (.0508m ^ 2) I = .00583kg * m^2 I = 0.583kg * cm^2 (?)

The motor I’m looking at is rated for 21kg*cm. How do I compare this to the moment of inertia to figure out whether it will be strong enough to start spinning and continue spinning (ideally at the RPMs needed)?

To get the torque, you need to multiply the moment of inertia by the angular acceleration. By the way, it looks like you used the mass of the canvas and the radius of your pulley. The moment of inertia should be calculated using the mass and shape of the canvas. You might find this Wikipedia page with a list of moments of inertia helpful.

I have no requirements for how fast it needs to get up to speed, so let’s assume that the angular acceleration is 1 radians/s^2. This value is a bit hard to visualize though - would this be insanely slow? It’s OK if it takes a few seconds to “rev up”, but not if it takes 30 minutes.

Using the appropriate formula from that Wikipedia page (rectangular plate spinning about it’s center), I get: I = m/12 * (h^2 + w^2) I = (2.26kg / 12) * (.6096m^2 + .6096m^2) I = 0.1883kg * .7432m^2 I = 0.1399kg * m^2

To calculate required motor torque, I am using this calculation: t = I * a

If a is 1, then my torque ends up being equal to my moment of inertia, only with N*m units.

When I pop my 0.1399 N*m value into online torque conversion calculators, I’m getting: 0.1399 N*m = 1.427 kg*cm = 19.812 oz*in

Since the motor I’ve specced can deliver 21 kgcm (or 300 ozin) of torque, my motor seems to be way overpowered for my application - which I would much prefer over it being underpowered

Your calculations look okay, as long as you are doing something to limit the acceleration of the motor to the value you are using in your calculations, like ramping up the speed. You should avoid instantly applying full power to the motors as that will apply the full torque of the motor instantly, which can be much higher than your calculated value and could damage the motor or gearbox.

Ultimately, for something like this where presumably you are spinning about the center of mass and any weight-related torques balance out, the torque of the motor really only matters if you need to reach a particular angular acceleration when first getting the painting spinning or if there is friction in the system you need to overcome to maintain the rotation.

The motor should get here pretty soon, and I’ve also ordered a motor driver Arduino shield to go with it. I’ll go ahead and whip a sketch and make sure it has a nice long ramp up profile, then tweak it later if needed.