Torque needed to rotate a cylinder

[JohnS-I]

Hello,

I'm designing a machine as a final assignment for my internship. It's a machine that wraps SS tubing around a cylinder, making coils.
While trying to figure out how much torque I'd need to rotate the cylinder I found that I'm really in the dark on the subject (the teacher I had didn't pay nearly enough attention to calculations like this).

I live in the Netherlands so I use the metric system. I hope that won't be too much of a problem.

Here's what I do know:

T = I x a

T = Torque
I = Moment of Inertia (mass x radius^2)
a = angular acceleration

The cylinder weighs in at 12.53 Kg and it's radius is 143.75 mm.

I don't know if I need to convert these numbers which is what's stopping me from calculating the MoI.

As for the angular acceleration, I believe that it's got something to do with difference in rotating speed and time, I just don't know what to do with those numbers either.

Max. RPM: 5
Acc. time: 5 sec.

All help/explanations are very much appreciated!

Note: I have checked out some of the existing (older) threads on the subject but that didn't make me understand things enough to base my own calculations on.

 

[jack action]

The equation you are looking for is:
$$T_{in} = \sum{T_{out}} + I\alpha$$
Where:

$T_{in}$ is the input torque;
$\sum{T_{out}}$ is the sum of all output torques (or resistances);
$I\alpha$ is the moment of inertia and angular acceleration.

When there will be no acceleration (i.e. constant rpm), the $I\alpha$ part is zero.

The summation of all resistances is probably more important to identify and will be present at all rpms. It consists of the friction (Ex.: the bearings) and probably the pulling force that the tubing will create while making the coil. That last one may be the main resistance to overcome during the operation.

The math part is easy. It is properly evaluating the different resistances that is difficult.

 

[anorlunda]

Isn't the most important parameter the force needed to bend the tube? You gave no info about the tube.

 

[Dr.D]

Be aware that, as the material wrapped on the cylinder comes to rest relative to the mandrel, the effective MMOI is going to be continually increasing. This is a common situation in a steel or aluminum sheet mill.

 

[JohnS-I]

Thank you for your replies.

@anorlunda I forgot to put that in the post, the force needed to bend the tube is 220 Nm although to be absolutely save the number I'm going to be using in the equation is 315 Nm. Is that the resistance you meant @jack action?

So in order to create a coil, what I need to overcome are the 315 Nm it takes to bend the tube + the Nm it takes to rotate the cylinder. The latter is the one I am not sure how to figure out.

 

[Baluncore]

The cylinder rotates slowly and is not very heavy. I believe the 315 Nm torque required to accelerate and maintain cylinder rotation will be very small compared with the torque needed to coil the tube. Use worst case values to estimate the torques.

First the 12.53 kg cylinder with radius 144 mm must be accelerated to 5 RPM in 5 seconds.

Then it must continue to rotate at 5RPM while overcoming the friction of the bearings that support the cylinder. The force on those bearings will be the weight of the cylinder plus the reaction to the tube bending force. You need to know what type of bearings are specified to support the cylinder so as to identify an appropriate friction coefficient.