The visual and mechanical quality of paperboard packaging components formed by deep drawing closely corresponds to the wrinkle distribution within the material wall section. Assessing this quality of paperboard packaging components currently relies on very slow or even subjective methods. Therefore, counting the number of wrinkles and measuring the mean distance between wrinkles proved to be a sensitive strategy for the evaluation of quality levels in deep drawing formed paperboard containers like cups or trays. A method introduced by Hauptmann proposes the measurement of the distances between 10 wrinkles in machine direction and 10 wrinkles in cross direction for each sample. However, this method is unsatisfactory because it can only observe a small part of each sample and is subject to deviation through the individual judgement of the person carrying out the survey. Further methods, as well as their respective application range, are listed in Table . Hence, it is desirable to automate the wrinkle survey to be carried out without operator influences to the measurement. This paper introduces such an automated measuring method. The given method relies on recording the sample surface topography through laser‐distance measurement. An evaluation algorithm, which enables the detection of wrinkles in the topographic data, is proposed. Furthermore, it is shown that the method yields feasible results and is capable of generating reliable quality information in considerably reduced time frames.

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The application of the wrinkle measuring method described in Müller et al. (2017) and the subsequent evaluation algorithm of a range of deepdrawn samples were used to determine the influences and interdependencies of blankholder force, tool temperatures, and drawing height on the formation of wrinkles in paperboard. The main influences were identified and quantitatively evaluated. For the given experimental space, a regression function was derived and validated in further experiments. It was shown that a quadratic regression was superior to the previously used linear regression. The findings were discussed and compared with the results of similar experiments from past publications. Special attention was given to the wrinkles formed and the resulting quality of the formed paperboard cups. The restrictions of the data acquisition from the measuring method that was used and limitations of the model were presented to demonstrate the reliability of the results.

We estimate the orientation of wood fibers in porous networks like paper, paperboard or fiberboard by computing digital thermal conductivity experiments on micro-computed tomography (μCT) images with artificial isotropic thermal conductivity parameters. The accuracy of mechanical and thermal constitutive models for porous wood fiber based materials crucially depends on knowing the wood fiber orientation. Unfortunately, due to the high porosity, the micro-heterogeneity of wood fibers, the high carbon content of organic materials and the unknown additives present in industrial paper, μCT-scans often exhibit low contrast and strong artifacts. Conventional image processing approaches encounter difficulties, as they rely upon convex fiber cross sections. We propose a solution by circumventing the segmentation of single wood fibers in μCT images, by performing thermal conductivity simulations on binarized wood fiber structures, where an artificial isotropic thermal conductivity is associated to the fibers and the pore space is considered as isolating. The local and global temperature fluxes are assembled into a fiber orientation tensor. This method overcomes the limitations of the mentioned local image processing approaches, as individual fibers need not be resolved and convergence for increasing resolution is a consequence of abstract mathematical theory. We use our novel method to analyze large three-dimensional μCT-scans and a synchrotron scan of a paperboard sample, serving as the starting point of an accurate micromechanical modeling of the effective anisotropic mechanical behavior of paper and paperboard. These results are crucial for calculating the mechanical strength of deep-drawn paperboard, which will be accomplished in a subsequent article

To evaluate the influence of different normal pressures and the fiber orientation on the in-plane compression behavior of paperboard during the deep drawing process, a new method was developed. In addition, the influence of the wrinkle formation on the dynamic coefficient of friction and the bending resistance was examined. To evaluate the eligibility of the in-plane compression testing method, a validation strategy was developed to compare the results from the new alternative tests with the punch force profiles from the deep drawing process within an empirical model.

Deep drawing of paperboard with rigid tools and immediate compression has only a small presence in the market for secondary packaging solutions due to a lack of understanding of the physical relations that occur during the forming process. As with other processes that deal with interactions between two solids in contact, the control of the factors that affect friction is important due to friction’s impact on runnability and process reliability. A new friction measurement device was developed to evaluate the factors influencing the friction behavior of paperboard such as under the specific conditions of the deep drawing process, which differ from the standard friction testing methods. The tribocharging of the contacting surfaces, generated during sliding friction, was determined to be a major influence on the dynamic coefficient of friction between paperboard and metal. The same effect could be examined during the deep drawing process. With increased contact temperature due to the heating of the tools, the coefficient of friction decreased significantly, but it remained constant after reaching a certain charging state after several repetitions. Consequently, to avoid ruptures of the wall during the forming process, tools that are in contact with the paperboard should be heated.

To evaluate the influence of different normal forces and contact temperatures on the frictional behavior of paperboard during the deep drawing process, a new measurement punch was developed to measure the normal force, which induced the friction within the gap between the forming cavity and punch. The resulting dynamic coefficient of friction was calculated and reproduced via a new developed substitute test for the friction measurement device, which was first introduced in Lenske et al. (2017). The normal force within the forming gap during the deep drawing process was influenced by the blankholder force profile, the contact temperature, and the fiber direction. The friction measurements with the substitute test showed a strong dependency between the applied normal force and the dynamic coefficient of friction. Furthermore the frictional behavior was influenced by the contact temperature and the wrinkle formation.

Noticeable improvements were achieved in the method for quality evaluation of formed paperboard containers. The method now allows for in situ evaluation of unavoidable wrinkle structures along the sealing rim of formed containers. An image of the sealing rim was provided. In this image, the contour of the sample was detected. The contour line was then offset to the inside of the sample, so that the new line was on the sealing rim, regardless of the original contour geometry. Along this offset contour line, the wrinkle structure was evaluated by using a previously described cross-correlation-based method. The repeatability and accuracy of the method were validated by comparing the detection results with the results from thorough human examiners. Furthermore, an approach to find the optimum settings for the wrinkle detection program is described and an outlook on implications for industrial adaptation of this method is given.