Optimal Design of Double-Walled Corrugated Board Packaging

New Models for Calculating the Maximum Compressive Force of Paper in Its Plane

The main objective of the presented research was to find a model that describes the maximum compressive force of paper in its plane. The research began with crushing tests of a number of packaging paper samples of various lengths. It was shown that due to the specific structure of the paper and the high heterogeneity of its structure, packaging paper is material where it is difficult to determine the maximum compressive stress. Next, three analytical models describing the load capacity of a flat paper web were investigated and an alternative empirical model was proposed. The results of the performed tests are directly applicable in the calculation of the mechanical properties of corrugated cardboard and the determination of the load capacity of cardboard packaging.

Evaluation of wave configurations in corrugated boards by experimental analysis (EA) and finite element modeling (FEM): the role of the micro-wave in packaging design

The aim of this paper is to study the mechanical behavior of corrugated board boxes, focusing attention on the strength that the boxes are able to offer in compression under stacking conditions. A preliminary design of the corrugated cardboard structures starting from the definition of each individual layer, namely the outer liners and the innermost flute, was carried out. For this purpose, three distinct types of corrugated board structures that include flutes with different characteristics, namely the high wave (C), the medium wave (B), and even the micro-wave (E), were comparatively evaluated. More specifically, the comparison is able to show the potential of the micro-wave which would eventually allow a significant saving of cellulose in the fabrication process of the boxes, thus reducing the manufacturing costs and causing a lower environmental footprint. First, experimental tests were carried out to determine the mechanical properties of the different layers of the corrugated board structures. Tensile tests were performed on samples extracted from the paper reels used as base material for the manufacturing of the liners and flutes. Instead, the edge crush test (ECT) and box compression test (BCT) were directly performed on the corrugated cardboard structures. Secondly, a parametric finite element (FE) model to allow, on a comparative basis, the study of the mechanical response of the three different types of corrugated cardboard structures was developed. Lastly, a comparison between the available experimental results and the outputs of the FE model was carried out, with the same model being also adapted to evaluate additional structures where the E micro-wave was usefully combined with the B or C wave in a double-wave configuration.

Estimation of the Edge Crush Resistance of Corrugated Board Using Artificial Intelligence

Recently, AI has been used in industry for very precise quality control of various products or in the automation of production processes through the use of trained artificial neural networks (ANNs) which allow us to completely replace a human in often tedious work or in hard-to-reach locations. Although the search for analytical formulas is often desirable and leads to accurate descriptions of various phenomena, when the problem is very complex or when it is impossible to obtain a complete set of data, methods based on artificial intelligence perfectly complement the engineering and scientific workshop. In this article, different AI algorithms were used to build a relationship between the mechanical parameters of papers used for the production of corrugated board, its geometry and the resistance of a cardboard sample to edge crushing. There are many analytical, empirical or advanced numerical models in the literature that are used to estimate the compression resistance of cardboard across the flute. The approach presented here is not only much less demanding in terms of implementation from other models, but is as accurate and precise. In addition, the methodology and example presented in this article show the great potential of using machine learning algorithms in such practical applications.

Influence of Imperfections on the Effective Stiffness of Multilayer Corrugated Board

There are many possible sources of potential geometrical inaccuracies in each layer of corrugated board during its manufacture. These include, among others, the processes of wetting the corrugated layers during profiling, the process of accelerated drying, the gluing process, and any mechanical impact of the pressure rollers on the cardboard. Work taking into account all the above effects in numerical modeling is not well described in the literature. Therefore, this article presents a simple and practical procedure that allows us to easily account for geometric imperfections in the calculation of the effective stiffness of corrugated board. As a main tool, the numerical homogenization based on the finite element method (FE) was used here. In the proposed procedure, a 3D model of a representative volumetric element (RVE) of a corrugated board is first built. The numerical model can include all kinds of geometrical imperfections and is used to calculate the equivalent tensile and bending stiffnesses. These imperfections were included in the 3D numerical model by appropriate modeling of individual layers, taking into account their distorted shape, which was obtained on the basis of a priori buckling analysis. This paper analyzes different types of buckling in order to find the most representative one. The proposed procedure is easy to implement and fully scalable.

Modified Compression Test of Corrugated Board Fruit Tray: Numerical Modeling and Global Sensitivity Analysis

This article presents a modified configuration of the box compression test (BCT), which reflects the actual behavior of the vegetable or fruit trays during transport and storage. In traditional load capacity tests, trays are treated as classic transport boxes, i.e., they are compressed between two rigid plates, which does not take into account the specific geometry of this type of packaging. Both the boundary conditions and the loads acting on the tray were modified. The paper presents the concept of a new test, as well as numerical models and a sensitivity analysis of the modified BCT to the basic geometrical dimensions of the tray. The conducted research clearly shows that the proposed configuration of the load-bearing capacity test of a tray is closer to the actual operation of the packaging. As a result, most of the parameters that are not active under the conditions of the classical BCT become more important in the new configuration, which corresponds to the observations on the real performance of the packaging.

Compression Strength Estimation of Corrugated Board Boxes for a Reduction in Sidewall Surface Cutouts-Experimental and Numerical Approaches

Corrugated cardboard boxes are generally used in modern supply chains for the handling, storage, and distribution of numerous goods. These packages require suitable strength to maintain adequate protection within the package; however, the presence and configuration of any cutouts on the sidewalls significantly influence the packaging costs and secondary paperboard waste. This study aims to evaluate the performance of CCBs by considering the influence of different cutout configurations of sidewalls. The compression strength of various B-flute CCB dimensions (200 mm, 300 mm, 400 mm, 500 m, and 600 mm in length, with the same width and height of 300 mm), each for five cutout areas (0%, 4%, 16%, 36%, and 64%) were experimentally observed, and the results were compared with the McKee formula for estimation. The boxes with cutout areas of 0%, 4%, 16%, 36%, and 64% showed a linear decreasing tendency in compression force. A linear relationship was found between compression strength and an increase in cutout sizes. Packages with 0% and 4% cutouts did not show significant differences in compression strength (p < 0.05). Furthermore, this study shows a possible way to modify the McKee estimation for such boxes after obtaining empirical test data since the McKee formula works with a relatively high error rate on corrugated cardboard boxes with sidewall cutouts. Utilizing the numerical and experimental results, a favorable estimation map can be drawn up for packaging engineers to better manage material use and waste. The results of the study showed that the McKee formula does not appropriately estimate the box compression strength for various cutout sizes in itself.

Simplified Modelling of the Edge Crush Resistance of Multi-Layered Corrugated Board: Experimental and Computational Study

The edge crush test is the most popular laboratory test in the corrugated packaging industry. It measures the edge crush resistance of a sample in the cross-fiber direction (CD), also known as the ECT index. This parameter is widely used for the specification of the board by its producers. It is also utilized in most analytical formulas describing the load capacity of the packaging. On the other hand, the ECT value can be estimated from both analytical and numerical models based on the basic parameters of each constituent paper. Knowing the compressive strength in CD (commonly known as SCT) and the elastic properties of the individual layers, the sample geometry (i.e., the period and height of the corrugated layer), as well as the boundary conditions, the ECT value can be calculated. This is very useful as new boards can be virtually analyzed before being manufactured. In this work, both detailed numerical models based on finite elements (FE) methods and very simple analytical (engineering) models were used for the ECT calculations. All presented models were validated with experimental data. The surprising consistency and high precision of the results obtained with the simplest approach was additionally analyzed in the study.

Sensitivity Analysis of Open-Top Cartons in Terms of Compressive Strength Capacity

Trays in which fruit and vegetables are transported over vast distances are not only stored in extreme climatic conditions but are also subjected to long-term loads. Therefore, it is very important to design them correctly and select the optimal raw material for their production. Geometric parameters that define the shape of the packaging may also be optimized in the design process. In this work, in order to select the most important parameters that affect the load capacity of a tray, sensitivity analysis was used. A sensitivity analysis is often the first step in the process of building artificial-intelligence-based surrogates. In the present work, using the example of a specific tray's geometry, the selection of starting parameters was carried out in the first step, based on the Latin hypercube sampling method. In the next step, local sensitivity analyses were performed at twenty selected starting points of the seventeen-dimensional space of the selected parameters. Based on the obtained results, it was possible to select the parameters that have a significant impact on the load capacity of the tray in the box compression test and whose influence is negligible or insignificant.

Influence of Analog and Digital Crease Lines on Mechanical Parameters of Corrugated Board and Packaging

When producing packaging from corrugated board, material weakening often occurs both during the die-cutting process and during printing. While the analog lamination and/or printing processes that degrade material can be easily replaced with a digital approach, the die-cutting process remains overwhelmingly analog. Recently, new innovative technologies have emerged that have begun to replace or at least supplement old techniques. This paper presents the results of laboratory tests on corrugated board and packaging made using both analog and digital technologies. Cardboard samples with digital and analog creases are subject to various mechanical tests, which allows for an assessment of the impact of creases on the mechanical properties of the cardboard itself, as well as on the behavior of the packaging. It is proven that digital technology is not only more repeatable, but also weakens the structure of corrugated board to a much lesser extent than analog. An updated numerical model of boxes in compression tests is also discussed. The effect of the crushing of the material in the vicinity of the crease lines in the packaging arising during the analog and digital finishing processes is taken into account. The obtained enhanced computer simulation results closely reflect the experimental observations, which prove that the correct numerical analysis of corrugated cardboard packaging should be performed with the model taking into account the crushing.