Uniform web width is desirable, but that is only possible with perfect tension control on your machines. Flat roll edges are desirable, but that is not allowed by physics unless you wind at zero tension, a practical impossibility. Some web materials, such as metals, are easy in this regard. Some webs, such as some nonwoven structures and some elastomers, make this darn near impossible. What is going on here to connect these observations? It is the material property called Poisson ratio, which is given the Greek symbol Nu.

Projecting tension control

Poisson ratio is simply the reduction in width divided by the increase in length due to a tension increase. The common word for this behavior is “necking,” though unfortunately that word also is used to describe a reduction in web width at slot-die coaters due to surface energy. The Poisson ratio for most materials is around 0.3. We can use that to calculate the required tension control precisions. An example for a stiff material, such as paper or polyester, might go like this:

Web tension = 3 lb/in. for a 0.003-in.-thick web (1,000 psi)

Web MD strain = 0.1% (for E = 1,000,000 psi)

Web CD strain = -0.03% (for nu = 0.3)

Desired width tolerance = 0.030 in. on a 30-in. wide web (0.1%)

Even +/- 100% tension changes would not exceed the width tolerance.

Thus, if you have a stiff material, even extremely poor tension control coupled with very tight tolerances would seldom matter. However, what about a stretchy nonwoven? Nonwovens can have a Poisson ratio of 3, 10 times that of most materials. Repeating this for a lively (low modulus) nonwoven, you might get:

Web tension = 1 lb/in. for a 0.010-in.-thick web (100 psi)

Web MD strain = 1% (for E = 10,000 psi)

Web CD strain = -3% (for nu = 3)

Desired width tolerance = 0.2 in. on a 10-in.-wide web (2%)

In this case, a +/- 30% tension error would ruin width tolerances, a common enough situation. Thus, width tolerances of nonwovens commonly are at risk even though the tolerances are 20 times looser than what is typical of stiff materials. Also note that we shouldn’t use our entire width budget on one error source.

More roll = more problems

The problems are more severe for all materials in wound rolls, whose shape is required by physics to be something like that in Figure 1. The width variations tend to be notably larger in the roll than in the web, making flat or even close-to-flat roll edges practically impossible. Worse yet, about half of the roll-width changes may be permanent due to creep.

There is much more I would like to say about this subject because width changes are far more complicated than the above indicates. For example, the Poisson ratio inside a wound roll can be less than zero for paper and netting materials. The width changes in a web are worse on the ends than in the middle due to biaxial stress. Finally, width changes depend on span length, time, temperature, moisture, chemistry and several higher-order behaviors such as slitter band wobble. Thus, while the complications of web length would make a good conference paper, the complications of width could be chapter-length. 

David R. Roisum, Ph.D.
920-312-8466; drroisum@aol.com
ARC Member, ARC TV Presenter,
R2R Presenter, Converting School Educator