## Tracking Wrinkles: Part II

The easiest way to explain roller diameter variation tracking is to walk you through the chain of events.

Diameter variations create web strain variations. The tensioned web will attempt to form to the roller's shape. The average web strain will not change, but the web will stretch more in large-diameter lanes and relax in small-diameter lanes.

Strain variations create web tension variations. Elastic materials have a direct relationship between stress and strain. Multiply the strain change by the material's elastic modulus to get the induced tensile stress change.

Roller-induced tension variations exert a torque on the web span. A torque is a force at a distance. As tension varies across the web width, the difference in the centerline of web tension upstream versus downstream applies a bending moment to the web.

Torque will bend or curve a web. If you apply a torque to the end of a pencil, you will see it change from straight to curved. Torque applied to the web does the same thing, though the curvature may be too small to see.

A curved web will violate the parallel entry rule. Without lateral tracking, the induced web curvature has an entry angle that is not parallel to the downstream roller. If there is poor traction, the slipping web need not obey the parallel entry rule. Result: The web will track to the small-diameter lane.

With good traction, the web curvature will displace laterally to the large-diameter side. To satisfy the parallel entry rule, the downstream head of the bent web will shift relative to the upstream tail. Result: The web will track to the large-diameter lane.

Yikes. Rube Goldberg designed less complicated chains of events.

Looking at the details of this chain of events, you can find some important tidbits to help you understand how diameter variations create or don't create tracking wrinkles.

Diameter variations should be viewed as percent change, not absolute. A 20-mil change is significant on a 4-in.-dia roller, but less so on a 20-in.-dia roller. For predictable web behavior, think about diameter variations that are on the same order of magnitude as the web's strain. If the diameter change is too dramatic, say 5%, it is more than the web can conform to, and you are guaranteeing a slip condition.

Bending a web isn't free, it requires force. The web often is limited by a roller's available friction force. This is one reason why rollers with small wrap angles and friction rarely wrinkle: The roller can't exert enough force on the web to create or hold it in a wrinkled shape.

The last tracking wrinkle source is web bagginess or length variations.

The wrinkle mechanism is similar to tracking wrinkles from pre-roller width expansion. Baggy or nonuniform webs have subtle curvature. Though small, the subtle curvature is enough to violate the parallel entry rule.

As the baggy or curved web moves onto the roller, the contact point will shift toward the long lanes or outside curvature, moving the web's position on the roller laterally. For a baggy edge, this will shift the web toward the loose side. For a baggy center, this will shift both sides toward the roller's center, creating a wrinkle.

For all tracking wrinkle causes, shorter spans will prevent wrinkles. Since web bending mechanically is the same as beam bending, the force required to shift the web will go up with span length cubed. As spans get shorter, there may not be enough traction to drive the web to buckling and wrinkling.

Eliminate tracking wrinkles by understanding and stopping them at the source. If you can't stop the source, prevent the wrinkle by reducing traction or decreasing span length. If this is difficult, consider using a special anti-wrinkle or spreader roller.