Thermal welding success prediction tool for paper-based polylaminate beverage packages
Computational tools based on mathematical modelling are nowadays a well established and reliable instrument for the design, optimization and control of industrial artifacts and processes. Following the paradigm of virtual prototyping, numerical simulations can in fact be used to predict the performance of products or objects even before they are built, and guide the choice of optimal design configurations. In addition, numerical algorithms which provide fast response can be interfaced with mechanical machinery to improve the control of industrial processes. In the framework of such general industrial trends, this work [1] focuses on the development of a computational tool able to predict the quality and success of paper-based polylaminate package sealing in beverage packaging machinery. A successful sealing process is of course paramount to preserve the quality of the enclosed beverage and retain a sterile environment inside the package. In the specific process considered in [1], once the formed package has been filled with the beverage, its folding flaps (the grey regions in Figure 1) are first heated by means of a hot air jet, and finally pressed together for watertight welding of the plastic layers of the polylaminate material.
The paper sheet on the left of Figure 1 can be folded into the shaped package on the right of the figure just by rigidly rotating a set of planar quadrilateral and triangular surfaces along the folding lines indicated. In such a geometrical transformation, the topology and geometry of the faces as indicated in the left of the figure is not altered once they are deployed in their final configuration (on the right) nor is the length of each folding line.
As in our preliminary investigation in [1], we were not interested in the elastic, thermo-elastic or thermo-plastic deformation of the package, we considered only rigid displacement fields for each face. Hence, the geometry and the actual configuration of the package is fully described by the length of the folding lines of the original paper sheet, and by a set of angular parameters, α, β, γ and θ, as shown in the middle of Figure 1. In particular, the coordinates α and β describe the inclination with respect
to the horizontal line of the light-blue shaded rectangle and of the red shaded triangle, respectively. Similarly, the angular coordinates γ and θ describe the inclination of the respective rectangular faces highlighted in
gray in the figure. Notice that the four angular coordinates are not independent. Indeed, by enforcing kinematic compatibility conditions, it is possible to express β as a function of α and θ as a function of α and γ.
The experience of the technicians on the field suggests that good quality sealing is observed when the local temperatures in the polyethylene layer of the packaging material are in the correct window at the moment of
the final press. For such a reason, the main focus of the present investigation is on the accurate reproduction of the thermal field in all the package layers right before, and at the moment of the folding flaps sealing. To this end, we developed a tool for the simulation of the heat conduction in the package material, and of the heat exchanged with the surrounding air during the heating process. The heat equation, which governs the
heat conduction in isotropic materials is solved in each layer of the package by means of a Finite Element Method (FEM) discretization. Given the extremely small thickness of the package compared to its longitudinal extension, a plate FEM formulation was used. Plate Finite Elements are commonly found in structural mechanics to analyse the bending deformation of thin planar structures, and the resulting forces such as shear forces and moments. The main hypothesis of plate formulations is the Kirchoff–Love assumption, which assumes that a mid-surface plane can be used to represent a three dimensional plate in two dimensional form. The simulation tool developed is able to simulate the evolution of the thermal field in all the layers of the package [1], first under the action of the heating jet of air, and after that in the instants right before the
sealing occurs. Each simulation requires an execution time of roughly 10 minutes.
Figure 2 from [1] depicts the temperature distribution obtained at time (T_fin = 4.4s) for the experimental test case in which the heater air temperature was set to 350˚C and the power delivered to the heater rotor was set to 90% of the maximum value. The left plot refers to the temperature field computed on the internal surface of the polylaminate material, while the right plot represents the temperature computed on the external side. On the left image, the computational grid used for the longitudinal discretization is also displayed.
package machinery. In the image, the clearer colors indicate the hotter regions, and darker colors indicate colder regions. The image shows the top part of the package (purple) under the action of the hotter heating device (yellow). The superimposed rectangle on the folding flap of the package, indicates the area in which the temperature has been averaged and saved.
An experimental campaign was carried out to obtain measurements of the effective temperature on the external surface of the package which could be used to evaluate the accuracy of the predictions of the model developed. Figure 3 presents a thermal camera image of the package under the action of the heater. In the thermal image, clearer colors denote hotter regions, and darker colors indicate low temperature regions. In the image, the top part of the package (in purple) is under the hotter heater (in yellow). In the region of the package folding flap, a superimposition is applied to the image so as to indicate the reference folding flap area in which the local temperatures measured at each time instant have been averaged and saved so as to be compared with the simulation results.
Figure 4 from [1] shows a typical validation result obtained comparing the simulation results with experimental data. The plot shows the average temperature in the reference folding flap area as a function of time. The blue line in each plot represents the experimental value obtained through the thermal camera measurements on the external side of the package. The yellow lines refer to the numerical counterpart, obtained averaging the external side temperature in the reference folding flap area. Finally, the
green line in each plot indicates the numerical estimate of the average temperature in the reference folding flap area computed on the internal side of the package. The latter quantity, which is hardly measurable by
experimental means, is a very important indicator for the sealing process, which of course involves the internal side of the package.
The plot in Figure 4 suggests that the numerical results are generally in good agreement with the experimental measurements. In particular, it can be appreciated that the numerical solution is well reproducing the slope of the internal temperature curve during the package heating phase. In such time frame, the heater has completed its descent on top of the package, and a steady heating phase is occurring. Thus, by means of the specific correlations used to approximate the convection coefficient in the heater region, the model is able to capture the effective heat exchange between heater air and package.
Thus, the simulation tool developed predicts, in the span of few minutes, the temperature field in all the layers of the package polylaminate material during and after the heating phase, in which a hot air jet is investing the
package surface. The validation results suggest that the solver is able to reproduce with satisfactory accuracy the experimental temperature field
evolution in the region interested by the thermal welding. Given its accuracy and the velocity of each computation, the solver can be successfully employed both for new machinery design and for process calibration purposes. It can in fact consider different package dimensions, different material layers arrangements, as well as different heater temperatures and flow rates. To be able to fully interface the model with the machinery automated control system, we are currently developing a reduced order model based on the simulation tool described in the present article. Such a reduced solver is able to provide real time results and can then be used to provide real time feedback to the machinery control system.
