When things in life are linear, they make sense. Driving two hours usually gets you twice as far as driving one hour. Adding two doughnuts a day to your diet likely will lead to gaining twice as much weight as one doughnut a day. These are linear relationships — they “add up.”

In converting, some things are linear. If you pull on 1-mil polyester with 1 PLI, it will stretch 0.2%. If you double the tension, it will stretch twice as much (this should be far from the yield point).

If you double the air pressure on a nipped roller, you will double the air cylinder's contribution to the nip load (don't forget gravity and tension).

In winding, few things are linear. You may see pressure and friction within your winding roll go up 10x or even 50x if you do the following:

• Double the winding tension.
• Double the winding nip load.
• Double your product thickness variations.
• Double the length or diameter of the roll.

Why are all these winding effects non-linear? There are two different strong effects in winding that can change faster than linear. Both involve the softness or compressibility of a roll in the radial direction — what you could consider (thanks to Mr. Whipple of Charmin fame) a roll's squeeze-able softness (or lack thereof).

Technically, this is referred to as the radial modulus of elasticity or stack modulus when the property is measured in a stack of sheets representing the layer in a wound roll. If you measure the compressibility — what percent the layers will compress for a given increase in pressure — you will find a strongly non-linear relationship, nearly exponential.

Radial modulus is one of the strongest variables in how tight a roll will be for a given winder setting and roll size. This makes winding non-linear because as you shift toward the stiff end of the continuum from spongy to fully compressed layers, a roll gets little or no relief of adding tensioned layers from compression and circumferential relaxation.

More tension, more nipping, less roughness, and higher speed all can increase radial modulus, leading to a dramatic increase in roll tightness. Increasing thickness variations has the same effect because the thick, larger diameter lanes will see above-average tension and nip load, creating an increased tightness in those winding bands.

The thick gauge bands will gain much more in tightness than the non-thick bands lose, creating an overall tighter roll. If you ever wondered why some rolls telescope and others don't, it may be the non-telescoping rolls have worse gauge variations locking them up with high pressure and friction.

The other big non-linear effect in winding is air entrainment. You folks with a porous web, such as tissue and nonwoven, won't see this, but everyone else will. Large diameter, higher speed, lower tensions, and lower nip loads all will allow more air into a roll.

This will loosen a roll in two ways. Air will fluff up a roll, making its radial modulus lower, and it may bleed out over time, allowing the pressure and friction creating tensions to relax away.

Besides porosity, higher surface roughness provides a space for entrained air to stay with the roll, reducing air effects. More roughness or texture to a product likely will lower a product's natural stack modulus also, so it may have two effects leading looser rolls.

These non-linear effects make winding difficult to predict. If you change too many of these factors, be prepared to be surprised when you wind a roll. The roll might just explode or form a black hole. Proceed with caution.

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.