## Web Lines | When Do Small Rollers and Cores Cause Defects?

Are you exerting excessive strain on your web?

When does a small roller or small core size cause web defects?

• Curl in thick films
• Compression cracking in paperboard

What is the stress or strain that damages your material? I think the easiest way is to figure out the strain limits of your web.

What elongation percent will break or otherwise damage the web? What compressive strain will damage the web? Typical values might be 2% or 5%, but it depends highly on your material. Once we have a number, we can figure out what we do that could exert this excessive strain on the web.

With no tension, the strain change from inside surface to outside surface is thickness/radius. The outside will be at +t/2r, the inside surface at -t/2r. If you do the bending under tension, add the average strain to these two values. Outside strain is e+t/2r, inside strain is e-t/2r, where strain from tension is e = F/(twE) from (F)orce, (t)hickness, (w)idth, and E(Young's modulus of elasticity).

For example, if the paperboard web is 0.1 in. (2.5 mm) thick and bends over a 2-in. (50-mm) radius (4-in. diameter), the strain change from inside to outside surface will be t/r = 0.1 / 2 = 0.05 = 5%. The center of the web will have no strain change, the outside surface will tension +2.5%, and the inside surface will compress –2.5%. If the web is under strain from tension as it wraps the roller, say 0.2%, then the bending will change inside strain to –2.3%, and the outside surface strain will be 2.7%.

The baseline tensile strain of 0.2% would represent the average strain, but this will vary across the web if there are roller diameter variations or roller misalignment. Misalignment in the plane of the web, causing bending, is the strong effect; whereas misalignment perpendicular to the span, causing twisting, is a very weak effect.

Stress can be found by multiplying strain by modulus to get tensile stress in psi.

Another strong variable is the material mechanical properties vs. environmental conditions and time. I don't understand paper properties in great detail, but different papers will have different mechanical properties, and they will be a strong function of moisture content. Film mechanical properties will dramatically change at elevated temperatures.

You may calculate this strain from curvature and tension of winding on a small core and find it doesn't seem to exceed your material’s yield strain, but you get curl anyway. This is likely due to the difference in yield as a function of time or strain rate. Bending over a roller for a few milli-seconds is different than bending over a core for a week. Polymers flow viscoelastically in long time scales.

Thick webs with low yield strains will need bigger roller diameters.

Reducing core-set curl is just one argument for winding on bigger cores.

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.

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