Deep Drawing of Paperboard Under Heat-Moisture Control

Deep drawing is a common process for shaping paperboard packages. To improve performance, the paperboard is kept in a room with high humidity before treatment. The surfaces of forming tools that come into contact with the paperboard are heated. A control problem for heating moist paperboard, with evaporation from the pore surface, is considered in this paper. Micro-CT images of three different paperboards are taken, segmented, and parameterized with respect to the specific pore surface in terms of the pore surface per pore volume, pore volume fraction, fiber thickness, average surface contact area between fibers, and unsupported fiber length. Simple averaging formulas are provided to compute the effective coefficients in the coupled water-diffusion and heat-transfer problem with a phase transition. The model is validated by experimental measurements and offers an opportunity for optimal heating control to simultaneously ensure compliance of the paperboard layer, leading to small delamination at its boundary, thereby avoiding folding.