On the thermal welding of paper-based polylaminate packages: modelling, numerical implementation and sensitivity analysis

This work presents a numerical model for the simulation of package sealing in industrial machines for beverage packaging. The simulations are aimed at the prediction of the temperature field in all the layers of the polylaminate material composing the package. The package sealing is in fact carried out by means of thermal welding. Thus, accurate predictions of the temperatures following the package heating via hot air jet and right before the folding flaps are pressed together is paramount to in turn predict sealing success. The heat equation is solved in the package volume by means of a plate FEM formulation in which arbitrary order Lagrangian shape function are used for both the longitudinal and the normal discretization. The resulting semi-discretized equations are time advanced by means of an Implicit Euler scheme with constant time step. The solution of the system is complemented by forward sensitivity computation to obtain, at each time step, quantitative assessment of the effect of process parameters variations on the temperature output. The numerical results are compared to experimental measurements so as to validate the developed simulation tool. The results obtained suggest that the solver is able to reproduce with satisfactory accuracy the experimental temperature field evolution in the portion of the package interested by the thermal welding.