Power and Torque Calculation for a Motor

[mike3389]

Hi all,

Description of Problem:
I need to buy a motor to drive a custom-made spindle that I have made but I'm not completely sure what wattage the motor needs to be. Basically the spindle is just a hollow cylinder (closed on all sides) of stainless steel attached to the end of a shaft - the shaft will attach to the motor. The cylinder is 0.033m in radius and 0.1m long. The shaft is 0.05m long and has a radius of 0.0035m, so the total length of the spindle+shaft is 0.15m and the total weight of the spindle+shaft is 0.433kg. I need to be able to accelerate the spindle up to a max speed of 3200RPM (335 rad/s).

My Attempt:
I found online that Power (W) = Torque (Nm) x Angular Velocity (ω, rad/s), so this leads me to believe that once I know the torque required to turn the spindle then this equation should give me the power I need to accelerate my piece up to 335 rad/s. Am I right so far?

So to calculate the torque needed, I found an equation that says -
Torque (Nm) = Radius (m) x Force (N) x Sin(θ)

This is where I got a little confused. What value do I use as the radius? Do I take the full length of the shaft+spindle as the radius (0.15m) or do I take the radius of the hollow cylinder (0.033m)? Also is the Force just equal to the total weight of my shaft+spindle multiplied by gravity? (i.e. 0.433*9.8?)

Any help would be appreciated! If you need more info please ask.

[JAlberts]

The torque equation you show is for a drive type arrangement like a pulley drive assembly.

Since you do not include any external loads on your spindle in your description, for your application, to get the torque requirement of the spindle assembly you need to calculate the rotational torque required by each element of the spindle and sum these. The below link gives the equations you need to do this. This will give you the minimum motor torque required to accelerate your shaft to speed. Just make sure you include all of the elements of your spindle assembly including the motor shaft coupling, etc.

inertiaformulas.pdf

As to the horsepower requirement, I do not have the necessary knowledge to address this but since you have not indicated any external loads on your operating spindle then it seems that once your spindle is at your desired rpm then the motor horsepower required will only be that required to overcome the motor's internal bearings frictional loads (assuming you do not have any external bearings for your spindle).

I would recommend that, once you determine your spindle torque requirements, you discuss your requirements with a qualified motor supplier to determine the best motor selection for your application.