On-line model for gauge control of calendering processes

For a calendered polymer sheet, it is desirable that all types of shape defects, especially nonuniform gauge and improper layflatness, can be avoided. In general, shape defects arise mostly from inappropriate control of the bending behavior of the calendering rolls. To assist in control of the roll bending behavior, an analytical on-line model that simulates the face contour of the bent roll with or without roll bending systems has been developed. The roll bending system adjusts the roll profile by applying an external bending moment to both ends of the roll. The roll deflection is calculated using a modified beam theory for the bending and shear components as well as the Poisson effect. The polymeric flow pressure developed in the bite region is estimated based on the classical lubrication approximation utilizing the power law constitutive relationship. Analytical solutions are obtained to speed up the computation. The analytical model, therefore, is compact enough to be implemented on a personal- or micro-computer and also fast enough for on-line simulation or control. Good agreement has been found when the present solution is compared with other published results and on-line measurements.