ABSTRACT
The fundamental objective of online shape measurement and closed-loop control is to provide a rolled product whose resulting atness adheres to the speci ed geometric tolerances when relaxed (off-line, nontensioned, and at ambient temperature).* Flatness is a descriptive indication characterizing the nature and extent of the strip’s manifest geometric departure from a reference plane. These manifest departures are the direct result of the relaxed strip nding an equilibrium condition of its rolled-in, internal stress patterns, by de ecting out of plane, in localized regions whose transverse differential strain-induced compressive stresses exceed the material’s buckling threshold. Latent (hidden) stresses may be present in relaxed, “still water at” strip, but their couplings to adjacent components of the parent strip constrain, distribute, and diffuse these stress patterns to amplitudes that
do not induce visually apparent buckles or other geometric/ atness distortions. However, these stored latent stress patterns may become exposed and form manifest distortions if the parent strip is later slit, punched, sheared, cut, etc., allowing a decoupling of the internal stress patterns from their former diffusing, adjacent constraints.
