## Web Lines: Is Wound Roll Pressure Greater Than Tire Pressure?

I'll bet you that your wound roll has more internal pressure than a car tire. To win this bet, I have to prove that internal roll pressure is above 30 psi (just over 2 bar or 200 kPa).

Measuring car tire pressure is easy. Measuring pressure inside a wound roll is certainly not so easy. How would you measure it, and what is the least expensive way?

A tire pressure gauge measures the difference between the atmospheric pressure outside the car tire and the internal tire pressure. If you are on earth, which most of us are, you are under pressure all the time.

If your tire pressure is 29 psi (or 2 bar or 200 kPa), the actually pressure in the tire is 43.5 psi (or 3 bar or 300 kPa) since atmospheric pressure adds 14.5 psi (or about 1 bar) to every reading. This differential reading is called the gauge pressure.

Pressure in wound rolls comes from web tension. When you stretch a rubber band around something, it creates tension proportional to how much the band is elongated beyond its untensioned length (a.k.a. strain). The pressure under a rubber band on a cylinder or a tensioned web wrapped around a core is the tension in force per width divided by the cylinder radius.

If the tension is 1 lb/in. of width (175 N/m) over a 2-in. radius (0.050 m), the pressure under the single wrap will be 1 PLI/2 in. or 0.5 psi (175 N/m/0.05 m = 3.5 kPa.

This single wrap is much lower (60x) than car tire pressure. However, if we add nine more layers, the combined pressure could increase to 5 psi (35 kPa), and 99 more layers could get us to 50 psi (350 kPa). At this point, it seems that our wound roll, with only 100 layers, could be above car tire pressure.

This is as small as 0.1 in. (2.5 mm) of buildup if the 100 layers are a 0.001-in. (0.025-mm) thick product. Imagine how much higher the pressure could get with 1 in. (25 mm) or 10 in. (0.25 m) of buildup on a core. Yes, 1,000 psi (7 MPa) or 35x atmospheric pressure is not out of the question.

These additive calculations assume that each layer maintains its pressure-created tension and strain. In many materials, this isn't true. Radial compression lowers tension in the roll, and pressures do not build up to ocean depth levels.

Stretchy films, like polyethylene (PE) or polypropylene (PP) can get up to 1,000 psi in a roll. Stiffer films, like polyethylene terephthalate (PET), can be all over the map, depending on their thickness, surface roughness, and winding tensions/methods, but 50-500 psi might be expected at the loose and tight extremes of winding.

Uncoated papers and foils tend to wind with low internal roll pressure, less than 100 psi. Pressure under a thick gauge band can have pressure 5-50x average internal roll pressures.

A frictional sandwich is an easy and inexpensive way to measure roll pressure. Make a frictional sandwich by inserting an unlubricated strip of steel feeler gauge (0.002 in.) in a folded piece of brass shim stock (0.001 in.), like a hot dog in a bun. Wind this brass-steel-brass sandwich into a roll with part of the sandwich sticking out the side of the roll (or both sides for narrow rolls).

After winding, pull on the steel feeler gauge and measure the force to get it to break away from the brass and slide just a bit. This force is the frictional force created by the pressure in the roll over the area of contact on the steel. With a little math, you can convert this frictional force into local internal roll pressure.

Friction Force (F) = COF (brass to steel, about 0.25) × Internal Roll Pressure (P) × Area of Contact (A). The area of contact is the steel strip width times the length of steel in the roll times 2 (since friction develops on both sides of the steel). Therefore: P = F/(COF × A).

• Example | Steel strip is 0.5 in. wide and 4 in. are in the roll, A = 2 in.2. If measured force is 20 lb, P = (20 lb)/(0.25 × 2) = 40 psi.

In this case, 40 psi is greater than 30 psi, and I win my bet. Send your money to me at [address withheld by PFFC lawyers].

Web handling expert Tim Walker, president of TJWalker+Assoc., has 25 years of experience in web processes, education, development, and production problem solving. Contact him at 651-686-5400; This email address is being protected from spambots. You need JavaScript enabled to view it.; www.webhandling.com.