Sag in commercial thermoforming



Our previous analytical solution gives sag advancing implicitly as inline image, or for inline image, sag advances with the cube root of time for a thin wide rectangular Newtonian isothermal sheet. This previous analytical work applies to sheets that are pinned along just two edges, and not all the way around. Corresponding sagometer experimental results confirmed this cube root relation. This work compares the inline image prediction with measured commercial thermoforming behavior on rectangular sheets that are, of course, pinned all the way around. Then sag parallel superposition is used to extend inline image for a sheet pinned all the way around. We evaluate sag parallel superposition using a finite element method (FEM) employing ANSYS Polyflow. The equation inline image assumes sagging sheet cylindricity, and from our FEM we find that this assumption is reliable when inline image. We compare sag measured in commercial thermoforming, using high-impact polystyrene (HIPS) sheets that are pinned all the way around, by extending inline image with parallel superposition. It is found that the time evolution of the commercial sag follows nearly exactly the same shape as the isothermal prediction. We measure sag runaway, and although the isothermal analysis inline image, predicts the sag runaway time accurately, our isothermal theory overpredicts the amount of sag in the nonisothermal commercial operation by as much as a factor of 14. It is also shown how to use sheet sag measurements from commercial thermoforming to deduce the Newtonian viscosity of a thermoforming resin at a temperature that is above its softening point. © 2013 American Institute of Chemical Engineers AIChE J, 60: 1529–1535, 2014