How to calculate motor torque and power

[deadstar33]

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.

 

[russ_watters]

What does this spindle do? Is it attached to anything or does it just spin freely by itself? If it spins freely by itself, it is such a small load that I'd just find a small motor rated for the speed you want and try it (and you can even use a potentiometer to regulate it). If it's wrong, you can just try another.

As you've found out, without a torque it is impossible to find power and you have nothing producing torque except air resistance, near as I can tell.

 

[deadstar33]

Oh okay, I though the weight of the spindle itself would act as a load on the motor seeing as it weighs nearly half a kilogram? And the spindle will just be submerged in water and rotating at different speeds between 0-3200RPM, so there's no additional load other than the viscous resistance of the water. Is there a way for me to calculate the power I need or do I not need to? I haven't worked with motors before so I don't know a lot about this.

Thanks.

 

[deadstar33]

My apologies, you already said that the load is so small that it shouldn't be very significant. That's okay then. So can I just ignore the power of the motor and look at the speed rating?

 

[russ_watters]

Oh okay, I though the weight of the spindle itself would act as a load on the motor seeing as it weighs nearly half a kilogram?

A torque is applied tangential to the axis of rotation, at a distance from the axis. If your object is balanced, there is no torque around the axis.

However, the support system for the object (bearings) will encounter resistance based on internal friction, which depends on the weight they support. But that is a tiny fraction of the weight.

And the spindle will just be submerged in water and rotating at different speeds between 0-3200RPM, so there's no additional load other than the viscous resistance of the water. Is there a way for me to calculate the power I need or do I not need to? I haven't worked with motors before so I don't know a lot about this.

Is the spindle smooth or does it have a shape that makes the water move with it? Like paddles? Viscous friction in water is pretty difficult to calculate. And while it is a lot more in water than in air, if the spindle is smooth, I'd start with the assumption that it is still pretty small.

 

[deadstar33]

Yeah it's a smooth cylinder and the water is initially at rest so it will move with the cylinder as it rotates. The viscous friction should be a tiny load.

Cheers, that was very helpful.