Velocity of pulley when spooling line?

[Wallys]

Hi.
I have a scenario where I am spooling line onto a hollow housing of given minor and major diameters. The velocity of the line being fed into the housing is determined by a feed-pulley of known diameter and r.p.m. I need to calculate the r.p.m. of that the housing needs to be turned in order to accommodate even spooling. Can someone help.

 

[sophiecentaur]

Do you want the housing (drum?) to have a peripheral speed equal to the line velocity however much line is wound inside the drum? (Is that what you mean by "even spooling"?)
To relate rotation speed to line velocity you can just use
line speed = 2π r f
where f is the rotation rate in turns per second and r is the coil radius.
I guess the best way to ensure this is to calculate the speed needed for the empty drum to fill at the right speed and to operate the drum at this speed. You could use a slipping mechanism to allow the drum to slow down as it fills up. Some sort of fluid drive could achieve this. Otherwise you would need a servo control to match the speeds - using the above formula. Not a trivial problem, though.

 

[Wallys]

Thank you for the reply.
The answer to your first question is, yes. The drum will be servo controlled through a PLC. The drum also has a give width. I therefore need the formula to program the controller.

 

[sophiecentaur]

I have been thinking some more about this. If you are going to have to use a servo then why not use a servo system which actually looks at the position of a 'bailer arm' with respect to the last coil and adjusts the speed / rotation of the drum to get even spooling. This would be a more 'complete' feedback loop than one which makes assumptions about where the line should end up. I appreciate that it may be more difficult to sense position than speed / revolutions but it may be worth considering if the conditions in the drum aren't too 'hostile'.
It would detect 'riding turns' whereas you system would go on regardless.

 

[alphy]

Hello,

To determine the velocity of the pulley when spooling line, we can use the formula v = ωr, where v is the linear velocity, ω is the angular velocity in radians per second, and r is the radius of the pulley.

First, we need to calculate the linear velocity of the line being fed into the housing. This can be done by multiplying the circumference of the feed-pulley (2πr) by its rotational speed in revolutions per minute (rpm). This will give us the linear velocity of the line in inches per minute.

Next, we need to calculate the angular velocity of the pulley. This can be done by dividing the linear velocity by the radius of the pulley. This will give us the angular velocity in radians per minute.

Finally, to determine the rpm of the housing, we can divide the angular velocity of the pulley by the circumference of the housing (2πR), where R is the radius of the housing. This will give us the rpm that the housing needs to be turned in order to accommodate even spooling.

I hope this helps. Let me know if you need any further clarification.