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.