Torque required to drive shaft

[deadstar33]

Hi,

I'm trying to choose the right motor for a test rig I've built. I have a shaft attached to a cylinder that weighs 6kg, and I need to know how much torque would the motor I'm getting need to be able to produce in order to rotate the cylinder at 100RPM.

My attempt:
Torque = Force x r
where r = radius of the cylinder = 0.08m

Force = mass x acceleration
where mass = 6kg

accel = velocity/time
velocity = r x ω (rotational speed)
where ω at 100RPM = 6.28 rad/sec
So v = 0.08 x 6.28 = 0.5 m/s
Therefore accel = 0.5/t

Therefore T = 6 x 0.5/t x 0.08
= 0.24/t Nm

Is it as simple as this or is there more to it? And how do I know what t should be to work out the acceleration if all I know is what velocity I want it to rotate at? Would every motor have the acceleration spec listed with it or something?

Thanks in advance.

 

[paisiello2]

There is more to it than that:

1) Is the shaft the same diameter as the cylinder?

2) ω = 100RPM = (100 *2∏rad/revolution)/(60s/min.) = 10 rad/s approx.

3) There must be some friction or external force acting on the cylinder (other than your shaft) else once you start rotating it will continue to spin in perpetuity.

 

[deadstar33]

1. The diameter of the shaft is 0.017m (17mm) and the diameter of the cylinder is 0.16m.

2. Sorry you're right, it's 6.28 rad/s at 60RPM and ~10rad/s at 100RPM.

3. Do you mean like air resistance? Or friction due to having imperfect bearings on the shaft? I don't have much experience with motors so I'm just trying to understand as much as I can about the problem and how to select the right motor.

Thanks.

 

[paisiello2]

I mean anything that provides resistance that requires a torque to keep the 100rpm going.

Or maybe you meant your question was how much torque is required to accelerate the cylinder from 0 to 100rpm?

 

[deadstar33]

Yeah that's what I meant. I'm guessing the torque will then depend upon how fast I'm accelerating it from 0 to 100RPM? i.e. if I want to be able to accelerate it from 0 to 100 in 1 second it would require more torque than the same increase over 10 seconds. If that's the case, it presumably depends upon the motor in question...

 

[paisiello2]

Yes, it will depend on how fast you want to accelerate it but also depend on the mass moments of inertia of the cylinder and shaft.

 

[deadstar33]

I see. Is there an equation that relates the mass moment of inertia to the torque in some way then? I calculated the mass moment of inertia of the cylinder and shaft together to be 0.033kgm^2.

 

[paisiello2]

Yes, there most certainly is:

∑T = I_CM$\alpha$

where

∑T = summation of all the torques acting on the object about the axis
I_CM = the mass moment of inertia of the object about the axis passing through the center of mass
$\alpha$ = the angular acceleration of the object about the axis

 

[deadstar33]

Thanks