CD tension profile of the web will change proportional to variations in a roller or roll CD diameter profile. Surface speed is the product of RPMs and circumference (and circumference is the product of Pi, 3.1415, and diameter). Changes in web speed change web strain and web tension (as a function of the web’s spring constant = thickness x modulus). The above-average diameter lanes of a roller or roll will steal tension from the below-average diameter lanes.
Uniformly distributed tensioning of cylindrical rollers is usually preferred.
Non-uniform CD profiles can be beneficial or detrimental.
Gauge bands at winding or CD wear patterns of rubber rollers can create wrinkles of thin webs. Large CD diameter changes can promote high strains of web deformation or breakage, zero tension of buckling web lanes, or shear wrinkles of rapid CD tension changes.
However, one of the most useful tricks of web handling is creating the CD tension profile by creating concave roller with tape collars under each web edge, encouraging the web to spread and prevent wrinkling.
Solutions
Cylindrical rollers are the first choice for web handling.
Transport rollers should be cylindrical to less than one half of the web strain from tension. For polyester and paper products running at 0.1%, the roller should be cylindrical with a profile error less than 0.5 mm/m (0.5mil per inch) of radius. (e.g., 100mm or 4-inch diameter idler should be less than +/- 25microns or +/- 1 mil). Rubber covered roller should be machined to less than twice this specification. Precision process rollers may need to be 25X better than transport rollers.
Cores and winding rolls rarely meet the CD diameter profile specification of rollers.
Cores, especially paper cores, will have more diameter errors than machined roller shells. Cores may be warped by the engagement method of core chucks or shafts.
The greatest CD diameter problem of rolls is the cumulative CD profile of the web on top of the core. Webs intended to be flat will have imperfections in their CD thickness profile, often worse at the edges of flat web-making processes, such as paper mills, film extrusion/tenters, and foil mills. Some products have an intentional CD thickness profile from printing, coating, die-cutting, laminating, and folded patterns.
Fortunately, web thickness profile does not correlate 1:1 to roll diameter profile. The compressibility of the web (including its roughness, laminate layers, and coating) reduces the diameter created by the thickest web lanes.