## The Pressure of Winding Rolls

Web Lines

Too much pressure inside a roll means more wound roll problems: Adhesive layers ooze, nonwoven and other crush-sensitive products don’t bounce back, photographic coatings fog, and tacky films block. Add core impressions, starring, spoking, crushed cores, and cores stuck on shafts. Worst of all, more yielding and permanent deformation increases, causing bagginess or loose edges.

Too little pressure inside a roll has its own negative side effects, including sagging rolls, cinching, telescoping, and scratching.

Potentially worse than internal roll pressure that’s too high or low is to have both occurring in one roll at the same time. High-pressure, tightly wound layers near the core with looser, lower pressure layers in the roll’s outer layers is great, but the reverse is trouble. High and low pressures across the roll, a.k.a. hard and soft bands, are more trouble, usually creating the most deformed sheet.

What determines the pressure buildup inside a roll? When a tensioned web is wrapped around a cylinder, the radial pressure pushing downward is equal to the T in PLI divided by the radius in inches (P=T/R). If a second layer is placed on top of it, it seems the pressure under the first layer should double.

Imagine the pressure of one layer, two layers, one hundred layers, one thousand layers. The number of layers in a roll is equal to the radial buildup divided by web thickness. A radial buildup of 5 in. of 1-mil film is 5,000 layers. Does this mean the pressure is 5,000x the pressure of one layer?

The answer is no. Wrapping 5,000 layers in a roll is different than stacking 5,000 bricks. With bricks, gravity creates the pressure and continues to apply that pressure independent of any compression or slight shifting in the layers under the stack’s weight. But in a wound roll, the pressure is created by the tension created by the elastic web’s strain. If anything happens to reduce the web strain, the pressure contribution of that layer will decrease.

Compression within a wound roll, unlike compression in a stack of bricks, reduces pressure at the bottom of the stack. Any compression of the structure below a given layer in a roll reduces that layer’s strain, its tangential tension, and its contribution to internal roll pressure.

Many things contribute to internal compression in a wound roll: cores compress or shrink, air bleeds out of the roll, coated layers compress or ooze, and papers or nonwovens get permanently thinner.

How loose a roll gets depends on the ratio of how much strain the initial tension created compared to how much a roll layer compresses. If the radial compression equals the initial strain, the layer will have zero tangential tension, thus, zero contribution to radial pressure.

A winding roll is a mechanical structure. A roll’s radial compressibility or modulus plays a dominant role in how high internal roll pressures will climb. More important is the ratio of radial modulus to the tension or Young’s modulus. When a roll’s radial compression is small relative to the tensioning strain, roll pressure builds and builds with more layers. Rolls with relatively high radial compressibility don’t see a strong tourniquet effect and wind to larger buildup ratios without problems.

If you could look up the mechanical properties of your roll, you could model this pressure buildup process. But there’s one big hitch in this plan—a roll’s radial modulus is non-linear as a function of pressure. One of the key variables that controls roll pressure is a function of pressure. More roll pressure creates a stiffer radial stack.

Maybe that explains why winders don’t come with a preset recipe to wind a perfect roll. That’s why finding the perfect wind may seem more like cooking than engineering, maybe pressure cooking.