Tapered Tension

This is not exactly a PLC question, but I see here many experts in the winding / rewinding applications. We have a rewinder machine (central shaft winder) which is capable to support tapered tension on the rewind shaft. Tension is tapered as function of the rewind roll diameter. This function comes in three flavors: linear, hyperbolic, and parabolic. I have experience only with linear tapered tension. I understand math formulas behind hyperbolic or parabolic tapered tension, and I am wondered what type of material would require such “exotic” function. Maybe someone has an experience in using such parabolic or hyperbolic tapering tension. Please, share this information.

Thank you.

PaulB.

linear means its going to put the material evenly on the roll...ie the wind will be a nice little circle, at the Christmas paper plant we unwound, printed and rewound very large rolls (36, 42, and 48 inch diameter).

Parabola is "cone shaped", I worked in a plant where we wound twine on cone shaped rolls after twisting.

Hyperbola means there will be more material mass at the ends than the middle, again this is something you may see around twine or thread where a roll may feed from both ends...kind of like having 2 parabola's meeting at their point.

Maybe others can offer a better explanation.

I am not sure about other fields but thread, string, twine, rope, yarn...cloth industries use all of them.

Thank you, Ron. Do you know about any source where I could read more on this subject.

PaulB

Paul,

I think linear taper is where you want to control tension throughout the roll buildup. Hyperbolic taper is where you want to control torque throughout the roll buildup. I would expect that material properties/geometry will dictate which makes sense to use.

Marc

Marc,

Thanks for the reply. This machine is speed loop rewinder with the PID tension trim. Tension reference is tapered as a function of the diameter of the roll, which builds up during rewinding. This function may be selected as linear, hyperbolic, or parabolic.
My experience mostly in paper where linear tapering is used. I would like to know where other types of tapering will be usefull. Our company bought design of this machine. People,who design this machine, provided this multifunctional tapering option either just in "case" or they are not telling us what is it for. I want to educate myself to be able to explain this option to our customer. From Ron's post it seems you would use such tapering if you need not cylindrical shape roll, but cone shape. Do you think it is also matter what type of material is used?
This machine is for rewinding printing web materials. Our company usially deals with the papers, foils, films and is using linear tapered tension. Nobody knows where to use other types of tapering.

Good lord.

Linear taper is a direct tension modification (reduction OR increase) with diameter as a roll builds up (or down).

Hyperbolic and Parabolic taper curves provide for a geometric tension modification as a roll builds up (or down).

The different curves are used to affect the actual packing (hardness, 'density', etc) of the roll as it builds up.

Generally, a linear curve is sufficient, and on a winder usually starts with a value, and then decreases slightly as the diameter increases in a linear fashion. This primarily prevents spalling or core crushing from too hard a roll.

Generally the 'more esoteric' curves are used where it is a requirement to pack very tightly at core, but loosely at some point over (core_diam * 2), or where it is important NOT to pack tightly at the core, but increase pack density as rolls build up.

These are used often on materials with either very high slip characteristics (to prevent blowout at core), or sometimes on pressure sensitive materials that require very gentle handling.

Paul,

I did not phrase my initial response well at all.

What I meant to say was that linear taper gives a linear relationship between tension and diameter.



Hyperbolic taper gives a linear relationship between torque and diameter.


The net effect is what rdrast said - linear is fine for most applications that actually need taper, and hyperbolic is used when you need a faster tension response at the core and less response at larger diameters.

I can not comment on parabolic taper because I have never used it, and couldn't find a "standard" formula to calculate the tension output from a parabolic taper.


In addition to rdrast's comments about when and where different taper philosopies are used, this link might be of use. In it (about half-way down) they talk (too briefly) about why certain taper philosophies are used for different types of webs.


Hope that helps somewhat,

Marc

Thank you, Marc. The link which you provied helped. Now I undertstand better where would you use different tension tapering.

PaulB

Tension Taper Algorithms

Does anyone have some algorithms they would like to share? Linear, hyperbolic, Hybrid, and etc. A spreadsheet attachment would be ideal.

+1 to Tim1234567890's suggestion