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Garbowski T, Knitter-Piątkowska A, Grabski JK. Estimation of the Edge Crush Resistance of Corrugated Board Using Artificial Intelligence. MATERIALS (BASEL, SWITZERLAND) 2023; 16:1631. [PMID: 36837262 PMCID: PMC9961700 DOI: 10.3390/ma16041631] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Figures] [Subscribe] [Scholar Register] [Received: 01/15/2023] [Revised: 02/13/2023] [Accepted: 02/14/2023] [Indexed: 06/18/2023]
Abstract
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.
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Affiliation(s)
- Tomasz Garbowski
- Department of Biosystems Engineering, Poznan University of Life Sciences, Wojska Polskiego 50, 60-627 Poznań, Poland
| | - Anna Knitter-Piątkowska
- Institute of Structural Analysis, Poznan University of Technology, Piotrowo 5, 60-965 Poznań, Poland
| | - Jakub Krzysztof Grabski
- Institute of Applied Mechanics, Poznan University of Technology, Jana Pawła II 24, 60-965 Poznań, Poland
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Garbowski T, Knitter-Piątkowska A, Winiarski P. Simplified Modelling of the Edge Crush Resistance of Multi-Layered Corrugated Board: Experimental and Computational Study. MATERIALS (BASEL, SWITZERLAND) 2023; 16:458. [PMID: 36614797 PMCID: PMC9821909 DOI: 10.3390/ma16010458] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Figures] [Subscribe] [Scholar Register] [Received: 12/03/2022] [Revised: 12/28/2022] [Accepted: 12/30/2022] [Indexed: 06/17/2023]
Abstract
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.
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Affiliation(s)
- Tomasz Garbowski
- Department of Biosystems Engineering, Poznan University of Life Sciences, Wojska Polskiego 50, 60-627 Poznan, Poland
| | - Anna Knitter-Piątkowska
- Institute of Structural Analysis, Poznan University of Technology, Piotrowo 5, 60-965 Poznan, Poland
| | - Piotr Winiarski
- Schumacher Packaging Sp. z o.o., Wrocławska 66, 55-330 Krępice, Poland
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Garbowski T, Gajewski T, Knitter-Piątkowska A. Influence of Analog and Digital Crease Lines on Mechanical Parameters of Corrugated Board and Packaging. SENSORS 2022; 22:s22134800. [PMID: 35808303 PMCID: PMC9268991 DOI: 10.3390/s22134800] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Download PDF] [Figures] [Subscribe] [Scholar Register] [Received: 05/21/2022] [Revised: 06/09/2022] [Accepted: 06/23/2022] [Indexed: 02/06/2023]
Abstract
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.
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Affiliation(s)
- Tomasz Garbowski
- Department of Biosystems Engineering, Poznan University of Life Sciences, Wojska Polskiego 50, 60-627 Poznan, Poland
- Correspondence:
| | - Tomasz Gajewski
- Institute of Structural Analysis, Poznan University of Technology, Piotrowo 5, 60-965 Poznan, Poland; (T.G.); (A.K.-P.)
| | - Anna Knitter-Piątkowska
- Institute of Structural Analysis, Poznan University of Technology, Piotrowo 5, 60-965 Poznan, Poland; (T.G.); (A.K.-P.)
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Optimal Design of Double-Walled Corrugated Board Packaging. MATERIALS 2022; 15:ma15062149. [PMID: 35329601 PMCID: PMC8950760 DOI: 10.3390/ma15062149] [Citation(s) in RCA: 8] [Impact Index Per Article: 4.0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Subscribe] [Scholar Register] [Received: 02/28/2022] [Revised: 03/13/2022] [Accepted: 03/14/2022] [Indexed: 02/04/2023]
Abstract
Designing corrugated board packaging is a real challenge, especially when the packaging material comes from multiple recycling. Recycling itself is a pro-ecological and absolutely necessary process, but the mechanical properties of materials that are processed many times deteriorate with the number of cycles. Manufacturers are trying to use unprecedented design methods to preserve the load-bearing capacity of packaging, even when the material itself is of deteriorating quality. An additional obstacle in the process of designing the structure of paper packaging is the progressive systematic reduction of the grammage (the so-called lightweight process) of corrugated cardboard. Therefore, this research presents a critical look at the process of optimal selection of corrugated cardboard for packaging structures, depending on the paper used. The study utilizes analytical, simplified formulas to estimate the strength of cardboard itself as well as the strength of packaging, which are then analyzed to determine their sensitivity to changes in cardboard components, such as the types of paper of individual layers. In the performed sensitivity analysis, numerical homogenization was used, and the influence of initial imperfections on the packaging mechanics was determined. The paper presents a simple algorithm for the optimal selection of the composition of corrugated cardboard depending on the material used and the geometry of the packaging, which allows for a more conscious production of corrugated cardboard from materials derived, e.g., from multiple recycling.
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Mechanics of Corrugated and Composite Materials. MATERIALS 2022; 15:ma15051837. [PMID: 35269068 PMCID: PMC8911994 DOI: 10.3390/ma15051837] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Track Full Text] [Download PDF] [Subscribe] [Scholar Register] [Received: 02/21/2022] [Accepted: 02/26/2022] [Indexed: 02/05/2023]
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Modeling Warp in Corrugated Cardboard Based on Homogenization Techniques for In-Process Measurement Applications. APPLIED SCIENCES-BASEL 2022. [DOI: 10.3390/app12031684] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 02/04/2023]
Abstract
A model for describing warp—characterized as a systematic, large-scale deviation from the intended flat shape—in corrugated board based on Kirchhoff plate theory is proposed. It is based on established homogenization techniques and only a minimum of model assumptions. This yields general results applicable to any kind of corrugated cardboard. Since the model is intended to be used with industrial data, basic material properties which are usually not measured in practice are summarized to a few parameters. Those parameters can easily be fitted to the measurement data, allowing the user to systematically identify ways to reduce warp in a given situation in practice. In particular, the model can be used both as a filter to separate the warp from other surface effects such as washboarding, and to interpolate between discrete sample points scattered across the surface of a corrugated board sheet. Applying the model only requires height measurements of the corrugated board at several known (not necessarily exactly predetermined) locations across the corrugated board and acts as an interpolation or regression method between those points. These data can be acquired during production in a cost-efficient way and do not require any destructive testing of the board. The principle of an algorithm for fitting measured data to the model is presented and illustrated with examples taken from ongoing measurements. Additionally, the case of warp-free board is analyzed in more detail to deduce additional theoretical conditions necessary to reach this state.
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Non-Local Sensitivity Analysis and Numerical Homogenization in Optimal Design of Single-Wall Corrugated Board Packaging. MATERIALS 2022; 15:ma15030720. [PMID: 35160666 PMCID: PMC8836536 DOI: 10.3390/ma15030720] [Citation(s) in RCA: 4] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Subscribe] [Scholar Register] [Received: 12/20/2021] [Revised: 01/14/2022] [Accepted: 01/17/2022] [Indexed: 11/16/2022]
Abstract
The optimal selection of the composition of corrugated cardboard dedicated to specific packaging structures is not an easy task. The use of lighter boards saves material, but at the same time increases the risk of not meeting the guaranteed load capacity. Therefore, the answer to the question “in which layer the basis weight of the paper should be increased?” is not simple or obvious. The method proposed here makes it easy to understand which components and to what extent they affect the load-bearing capacity of packages of various dimensions. The use of numerical homogenization allows for a quick transformation of a cardboard sample, i.e., a representative volume element (RVE) into a flat plate structure with effective parameters describing the membrane and bending stiffness. On the other hand, the use of non-local sensitivity analysis makes it possible to find the relationship between the parameters of the paper and the load capacity of the packaging. The analytical procedures presented in our previous studies were used here to determine (1) the edge crush resistance, (2) critical load, and (3) the load capacity of corrugated cardboard packaging. The method proposed here allows for obtaining a comprehensive and hierarchical list of the parameters that play the most important role in the process of optimal packaging design.
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Analytical Determination of the Bending Stiffness of a Five-Layer Corrugated Cardboard with Imperfections. MATERIALS 2022; 15:ma15020663. [PMID: 35057380 PMCID: PMC8777652 DOI: 10.3390/ma15020663] [Citation(s) in RCA: 7] [Impact Index Per Article: 3.5] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Subscribe] [Scholar Register] [Received: 12/29/2021] [Revised: 01/12/2022] [Accepted: 01/14/2022] [Indexed: 02/01/2023]
Abstract
Bending stiffness (BS) is one of the two most important mechanical parameters of corrugated board. The second is edge crush resistance (ECT). Both are used in many analytical formulas to assess the load capacity of corrugated cardboard packaging. Therefore, the correct determination of bending stiffness is crucial in the design of corrugated board structures. This paper focuses on the analytical determination of BS based on the known parameters of the constituent papers and the geometry of the corrugated layers. The work analyzes in detail the dependence of the bending stiffness of an asymmetric, five-layer corrugated cardboard on the sample arrangement. A specimen bent so that the layers on the lower wave side are compressed has approximately 10% higher stiffness value. This is due to imperfections, which are particularly important in the case of compression of very thin liners. The study showed that imperfection at the level of a few microns causes noticeable drops in bending stiffness. The method has also been validated by means of experimental data from the literature and simple numerical finite element model (FEM). The obtained compliance of the computational model with the experimental model is very satisfactory. The work also included a critical discussion of the already published data and observations of other scientists in the field.
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Influence of Impregnation with Modified Starch of a Paper Core on Bending of Wood-Based Honeycomb Panels in Changing Climatic Conditions. MATERIALS 2022; 15:ma15010395. [PMID: 35009541 PMCID: PMC8746181 DOI: 10.3390/ma15010395] [Citation(s) in RCA: 4] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Subscribe] [Scholar Register] [Received: 11/28/2021] [Revised: 12/18/2021] [Accepted: 12/30/2021] [Indexed: 01/27/2023]
Abstract
The main objective of the study was to determine the effect of impregnation of the paper core with acetylated starch on the mechanical properties and absorbed energy in the three-point bending test of wood-based honeycomb panels under varying temperatures and relative air humidity conditions. Nearly six hundred beams in various combinations, three types of facings, three core cells geometries, and two paper thicknesses were tested. The experiment results and their statistical analysis prove a significant relationship between the impregnation of paper with modified starch and mechanical properties. The most effective in absorbing energy, the honeycomb panels, consisted of a core with a wall thickness of 0.25 mm and a particleboard facing.
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Garbowski T, Knitter-Piątkowska A, Marek A. New Edge Crush Test Configuration Enhanced with Full-Field Strain Measurements. MATERIALS 2021; 14:ma14195768. [PMID: 34640164 PMCID: PMC8510352 DOI: 10.3390/ma14195768] [Citation(s) in RCA: 8] [Impact Index Per Article: 2.7] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Subscribe] [Scholar Register] [Received: 08/31/2021] [Revised: 09/25/2021] [Accepted: 09/29/2021] [Indexed: 11/16/2022]
Abstract
The standard edge crush test (ECT) allows the determination of the crushing strength of the corrugated cardboard. Unfortunately, this test cannot be used to estimate the compressive stiffness, which is an equally important parameter. This is because any attempt to determine this parameter using current lab equipment quickly ends in a fiasco. The biggest obstacle is obtaining a reliable measurement of displacements and strains in the corrugated cardboard sample. In this paper, we present a method that not only allows for the reliable identification of the stiffness in the loaded direction of orthotropy in the corrugated board sample, but also the full orthotropic material stiffness matrix. The proposed method uses two samples: (a) traditional, cut crosswise to the wave direction of the corrugated core, and (b) cut at an angle of 45°. Additionally, in both cases, an optical system with digital image correlation (DIC) was used to measure the displacements and strains on the outer surfaces of samples. The use of a non-contact measuring system allowed us to avoid using the measurement of displacements from the crosshead, which is burdened with a large error. Apart from the new experimental configuration, the article also proposes a simple algorithm to quickly characterize all sought stiffness parameters. The obtained results are finally compared with the results obtained in the homogenization procedure of the cross-section of the corrugated board. The results were consistent in both cases.
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Affiliation(s)
- Tomasz Garbowski
- Department of Biosystems Engineering, Poznan University of Life Sciences, Wojska Polskiego 50, 60-627 Poznań, Poland;
| | - Anna Knitter-Piątkowska
- Institute of Structural Analysis, Poznan University of Technology, Piotrowo 5, 60-965 Poznań, Poland
- Correspondence:
| | - Aleksander Marek
- Faculty of Engineering and Physical Sciences, University of Southampton, Highfield SO17 1BJ, UK;
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Garbowski T, Knitter-Piątkowska A, Mrówczyński D. Numerical Homogenization of Multi-Layered Corrugated Cardboard with Creasing or Perforation. MATERIALS 2021; 14:ma14143786. [PMID: 34300705 PMCID: PMC8304969 DOI: 10.3390/ma14143786] [Citation(s) in RCA: 14] [Impact Index Per Article: 4.7] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Subscribe] [Scholar Register] [Received: 05/31/2021] [Revised: 07/02/2021] [Accepted: 07/05/2021] [Indexed: 11/16/2022]
Abstract
The corrugated board packaging industry is increasingly using advanced numerical tools to design and estimate the load capacity of its products. This is why numerical analyses are becoming a common standard in this branch of manufacturing. Such trends cause either the use of advanced computational models that take into account the full 3D geometry of the flat and wavy layers of corrugated board, or the use of homogenization techniques to simplify the numerical model. The article presents theoretical considerations that extend the numerical homogenization technique already presented in our previous work. The proposed here homogenization procedure also takes into account the creasing and/or perforation of corrugated board (i.e., processes that undoubtedly weaken the stiffness and strength of the corrugated board locally). However, it is not always easy to estimate how exactly these processes affect the bending or torsional stiffness. What is known for sure is that the degradation of stiffness depends, among other things, on the type of cut, its shape, the depth of creasing as well as their position or direction in relation to the corrugation direction. The method proposed here can be successfully applied to model smeared degradation in a finite element or to define degraded interface stiffnesses on a crease line or a perforation line.
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Affiliation(s)
- Tomasz Garbowski
- Department of Biosystems Engineering, Poznan University of Life Sciences, Wojska Polskiego 50, 60-627 Poznań, Poland;
| | - Anna Knitter-Piątkowska
- Institute of Structural Analysis, Poznan University of Technology, Piotrowo 5, 60-965 Poznań, Poland
- Correspondence:
| | - Damian Mrówczyński
- Research and Development Department, Femat Sp. z o. o., Romana Maya 1, 61-371 Poznań, Poland;
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