Calculation for Motor Selection

Question

I need help with the selection of a motor and a motor driver

I need to spin a 700g (65mm radius) round ball at 35,000 RPM. I need to bring it up to speed slowly, so I also need a motor driver/speed controller and something that tells me what the current rpm is. I have attached an image for reference.

How should I know what torque or power the motor should have?

Answer 1

The text in your image could be improved by making it lighter than the background, but that's not important to the solution.

By using "torque required for rotating mass" as the search terms, I found many resources to assist your goal. Unfortunately, most of them use Imperial measurements and it appears that you're using the metric system. Not to worry, Torque for Dummies (paraphrased) has the calculations in metric.

The solution from the linked page is aimed to calculate torque for a spinning disk, not a sphere, but I suspect the mass portion of the calculation and the diameter/radius are the critical inputs.

Say that a DVD has a mass of 30 grams and a diameter of 12 centimeters. It starts at 700 revolutions per second when you first hit play and winds down to about 200 revolutions per second at the end of the DVD 50 minutes later. What’s the average torque needed to create this acceleration? You start with the torque equation:

A DVD is a disk shape rotating around its center, which means that its moment of inertia is

Thanks to NMech for the correction for the rotational inertial of a sphere, maintaining the original link information above.

$$\frac{2}{5} m r^2$$

The diameter of the DVD is 12 centimeters, so the radius is 6.0 centimeters. Putting in the numbers gives you the moment of inertia:

How about the angular acceleration,

Here’s the angular equivalent of the equation for linear acceleration:

But because the angular velocity always stays along the same axis, you can consider just the components of the angular velocity and angular acceleration along this axis. They are then related by

First, you need to express angular velocity in radians per second, not revolutions per second. You know that the initial angular velocity is 700 revolutions per second, so in terms of radians per second, you get

Similarly, you can get the final angular velocity this way:

Now you can plug the angular velocities and time into the angular acceleration formula:

The angular acceleration is negative because the angular velocity of the disk decreased. The negative acceleration then leads to a reduction in this angular velocity.

You’ve found the moment of inertia and the angular acceleration, so now you can plug those values into the torque equation:

Obviously, you'll have to replace the example values with your own. This is left as an exercise to the reader.

Note: all quoted text and formulae images directly imported from linked site.

Answer 2

I would take a different approach to fred_dot_u.

You said you want to bring the sphere up to speed slowly, so lets assume that the acceleration doesn't matter (within reason).

I think there are 2 limiting factors you will have to take into account when choosing your motor.

1. The friction/drag the sphere experiences at 35000 RPM.

2. The top speed of the motor, or more specifically, the torque of the motor at 35000 RPM. This will have to be greater than the drag.

Figuring out #1 is fairly difficult. It will depend heavily on the bearings, balance, and alignment of the sphere. Realistically you will need to test it. You'll have to adapt to what you have on hand for testing but here's an example:

• Mount the device on it's side or use pulleys so that you can spin the sphere using a dangling weight. Use a tachometer and stop watch to determine the angular acceleration due to the known force the weight applies. Use that to calculate the moment of inertia. Alternately estimate using math and the mass and position of the parts.

• Use an airgun or some other method to spin the sphere up to 35000 RPM. Shut off the airgun, and use a stopwatch and tachometer to determine the rate of deceleration. Use this and the moment of inertia to calculate the deceleration torque.

• Find a motor that can apply at least this much torque at 35000 RPMS

• Note that as long as the sphere inertia is consistent throughout the procedure, it doesn't matter. For example if there's a sample that goes inside, running with or without it won't change the resulting drag value.

An alternate approach would be to simply guess, test, and iterate. A large, high KV drone motor for example might work. You'd hook that up, and test the result. If it doesn't work, you can use the motor torque/RPM chart and the speed you DID get to to make a decent guess about what motor would work. It should only take a few iterations if you take your testing data into account each time.

Also, don't forget that if you're only building one, it is often most cost and time efficient to simply choose a much more powerful motor than you think you will need. It may be more expensive, but almost certainly cheaper and faster than multiple iterations using smaller motors.