# Torque required to drive shaft

1. Apr 11, 2014

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?

2. Apr 11, 2014

### paisiello2

There is more to it than that:

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

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.

3. Apr 14, 2014

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.

4. Apr 14, 2014

### 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?

5. Apr 14, 2014

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...

6. Apr 14, 2014

### 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.

7. Apr 15, 2014

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.

8. Apr 15, 2014

### paisiello2

Yes, there most certainly is:

∑T = ICM$\alpha$

where

∑T = summation of all the torques acting on the object about the axis
ICM = 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

9. Apr 15, 2014