scholarly journals Numerical Homogenization of Multi-Layered Corrugated Cardboard with Creasing or Perforation

Materials ◽  
2021 ◽  
Vol 14 (14) ◽  
pp. 3786
Author(s):  
Tomasz Garbowski ◽  
Anna Knitter-Piątkowska ◽  
Damian Mrówczyński
Keyword(s):  
Computational Models ◽  
Load Capacity ◽  
Torsional Stiffness ◽  
Numerical Homogenization ◽  
Corrugated Board ◽  
3D Geometry ◽  
Corrugated Cardboard ◽  
Numerical Tools ◽  
Packaging Industry ◽  
Theoretical Considerations

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.

scholarly journals Numerical Homogenization of Multi-Layered Corrugated Cardboard with Creasing or Perforation

2021 ◽  
Author(s):  
Tomasz Garbowski ◽  
Anna Knitter-Piątkowska ◽  
Damian Mrówczyński
Keyword(s):  
Computational Models ◽  
Load Capacity ◽  
Torsional Stiffness ◽  
Numerical Homogenization ◽  
Corrugated Board ◽  
3D Geometry ◽  
Corrugated Cardboard ◽  
Numerical Tools ◽  
Packaging Industry ◽  
Theoretical Considerations

The corrugated board packaging industry is increasingly using advanced numerical tools to design and estimate the load capacity of its products. That is why numerical analyzes are becoming a common standard in this branch of manufacturing. Such trend causes 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.

scholarly journals Crushing of Double-Walled Corrugated Board and Its Influence on the Load Capacity of Various Boxes

Energies ◽  
2021 ◽  
Vol 14 (14) ◽  
pp. 4321
Author(s):  
Tomasz Gajewski ◽  
Tomasz Garbowski ◽  
Natalia Staszak ◽  
Małgorzata Kuca
Keyword(s):  
Load Capacity ◽  
Analytical Techniques ◽  
Shear Stiffness ◽  
Mechanical Tests ◽  
Torsional Stiffness ◽  
Bending Test ◽  
Corrugated Board ◽  
Four Point Bending ◽  
Residual Thickness ◽  
Corrugated Cardboard

As long as non-contact digital printing remains an uncommon standard in the corrugated packaging industry, corrugated board crushing remains a real issue that affects the load capacity of boxes. Crushing mainly occurs during the converting of corrugated board (e.g., analog flexographic printing or laminating) and is a process that cannot be avoided. However, as this study shows, it can be controlled. In this work, extended laboratory tests were carried out on the crushing of double-walled corrugated board. The influence of fully controlled crushing (with a precision of ±10 μm) in the range from 10 to 70% on different laboratory measurements was checked. The typical mechanical tests—i.e., edge crush test, four-point bending test, shear stiffness test, torsional stiffness test, etc.—were performed on reference and crushed specimens. The residual thickness reduction of the crushed samples was also controlled. All empirical observations and performed measurements were the basis for building an analytical model of crushed corrugated board. The proven and verified model was then used to study the crushing effect of the selected corrugated board on the efficiency of simple packages with various dimensions. The proposed measurement technique was successfully used to precisely estimate and thus control the crushing of corrugated board, while the proposed numerical and analytical techniques was used to estimate the load capacity of corrugated board packaging. A good correlation between the measured reduced stiffness of the corrugated cardboard and the proposed analytical predictive models was obtained.

scholarly journals Analytical Determination of the Bending Stiffness of a Five-Layer Corrugated Cardboard with Imperfections

Materials ◽  
2022 ◽  
Vol 15 (2) ◽  
pp. 663
Author(s):  
Tomasz Garbowski ◽  
Anna Knitter-Piątkowska
Keyword(s):  
Load Capacity ◽  
Element Model ◽  
Critical Discussion ◽  
Bending Stiffness ◽  
Analytical Determination ◽  
Published Data ◽  
Corrugated Board ◽  
Correct Determination ◽  
Corrugated Cardboard

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.

scholarly journals Crushing of Double-Walled Corrugated Board and Its Influence on the Load Capacity of Various Boxes

2021 ◽  
Author(s):  
Tomasz Gajewski ◽  
Tomasz Garbowski ◽  
Natalia Staszak ◽  
Małgorzata Kuca
Keyword(s):  
Load Capacity ◽  
Shear Stiffness ◽  
Mechanical Tests ◽  
Torsional Stiffness ◽  
Bending Test ◽  
Corrugated Board ◽  
Four Point Bending ◽  
Residual Thickness ◽  
Flexographic Printing ◽  
Four Point Bending Test

As long as the non-contact digital printing is not a common standard in the corrugated packaging industry, corrugated board crushing is a real issue that affects the load capacity of the boxes. Crushing mainly occurs during the converting of corrugated board (e.g. analog flexographic printing or laminating) and is a process that cannot be avoided. However, as show in this study, it can be controlled. In this work, extended laboratory tests were carried out on the crushing of double-walled corrugated board. The influence of fully controlled crushing (with a precision: ±10 μm) in the range from 10 to 70 % on different laboratory measurements was checked. Most of the typical mechanical tests were performed e.g. edge crush test, four-point bending test, shear stiffness test, torsional stiffness test, etc. on reference and crushed specimens. The residual thickness reduction of the crushed samples was also controlled. All empirical observations and performed measurements were the basis for building an analytical model of crushed corrugated board. The proven and verified model was then used to study the crushing effect of the selected corrugated board on the efficiency of simple packages with various dimensions.

scholarly journals Estimation of the Compressive Strength of Corrugated Board Boxes with Shifted Creases on the Flaps

2021 ◽  
Author(s):  
Damian Mrówczyński ◽  
Tomasz Garbowski ◽  
Anna Knitter-Piątkowska
Keyword(s):  
Static Load ◽  
General Trend ◽  
Load Capacity ◽  
Numerical Approach ◽  
Modern World ◽  
Load Bearing Capacity ◽  
Corrugated Board ◽  
New Ideas ◽  
Packaging Industry ◽  
The Aesthetic

In the modern world, all manufacturers strive for the optimal design of their products. This general trend is recently also observed in the corrugated board packaging industry. Colorful prints on displays, perforations in shelf-ready-packaging and various types of ventilation holes in trays, although extremely important for ergonomic or functional reasons, weaken the strength of the box. To meet the requirements of customers and recipients, packaging manufacturers outdo each other in new ideas for the construction of their products. Often the aesthetic qualities of the product become more important than the attention to maintaining the standards of the load capacity of the packaging (which, apart from their attention-grabbing functions, are also intended to protect transported products). The particular flaps design (both top and bottom) and their influence on the strength of the box is investigated in this study. The updated analytical-numerical approach is used here to predict the strength of the packaging with various flap’s offsets. Experimental results indicated a significant decrease in the static load-bearing capacity of packaging in the case of shifted flap creases. The simulation model proposed in our previous work has been modified and updated to take into account also this effect. The results obtained by the model presented in the paper are in satisfactory agreement with the experimental data.

scholarly journals Estimation of the Compressive Strength of Corrugated Board Boxes with Shifted Creases on the Flaps

Materials ◽  
2021 ◽  
Vol 14 (18) ◽  
pp. 5181
Author(s):  
Damian Mrówczyński ◽  
Tomasz Garbowski ◽  
Anna Knitter-Piątkowska
Keyword(s):  
Static Load ◽  
General Trend ◽  
Load Capacity ◽  
Numerical Approach ◽  
Modern World ◽  
Load Bearing Capacity ◽  
Corrugated Board ◽  
New Ideas ◽  
Packaging Industry ◽  
The Aesthetic

In the modern world, all manufacturers strive for the optimal design of their products. This general trend is recently also observed in the corrugated board packaging industry. Colorful prints on displays, perforations in shelf-ready-packaging and various types of ventilation holes in trays, although extremely important for ergonomic or functional reasons, weaken the strength of the box. To meet the requirements of customers and recipients, packaging manufacturers outdo each other with new ideas for the construction of their products. Often the aesthetic qualities of the product become more important than the attention to maintaining the standards of the load capacity of the packaging (which, apart from their attention-grabbing functions, are also intended to protect transported products). A particular flaps design (both top and bottom) and its influence on the strength of the box are investigated in this study. An updated analytical–numerical approach is used here to predict the strength of packaging with various flap offsets. Experimental results indicated a significant decrease in the static load-bearing capacity of packaging in the case of shifted flap creases. The simulation model proposed in our previous work has been modified and updated to take into account this effect. The results obtained by the model presented in this paper are in satisfactory agreement with the experimental data.

scholarly journals Characterization of packaging grade papers from recycled raw materials through the study of fibre morphology and composition

2013 ◽  
Vol 9 (1) ◽  
pp. 20-28
Keyword(s):  
Raw Materials ◽  
Technical Problem ◽  
Fibre Length ◽  
Recycled Paper ◽  
Corrugated Board ◽  
Fibre Composition ◽  
Fibre Width ◽  
Packaging Industry ◽  
Fibre Morphology

The restrictions in availability of forest-based raw materials along with favourable environmental policies towards alternative sources of raw materials have forced corrugated packaging industry to shift towards recycled paper and other fibre sources such as non-wood and agro-residues. The variability in raw pulp materials with increasing percentages of recycled fibres is a very common technical problem for the corrugated packaging industry worldwide. Corrugating packaging production is facing the challenge to ensure a satisfactory strength of packages despite the increase of recycled paper as the main fibrous component. Sustainable manufacturing of papers of consistent and acceptable quality requests comprehensive characterization of the fibrous components, which are becoming more heterogeneous. Understanding the influence that heterogeneous recycled raw materials have on packaging grade paper properties offers great potential value to the corrugated board and packaging industry. 57 linerboards and corrugating medium were selected to represent all the variety of paper grades available on the market at the moment for the production of corrugated board in Spain. The papers were analyzed for their fibre morphology (fibre length, fibre width, lumen diameter, cell wall width and flexibility) and fibre composition (softwood to hardwood and nonwood fibre count and weight) and their strength (compression, bursting and crushing resistance) was evaluated. All the determinations were in accordance with the relevant TAPPI Test Methods. The significant differences found in most of the anatomical characteristics, fibre composition and strength properties among the paper grades reflected the diverse raw materials used for their production as well as their qualitative differences. By means of simple correlation the influence of fibre characteristics and composition on the strength of the papers was determined under two different conditions, at 23 oC and 50% RH and at 20 oC and 90% RH. The results demonstrate that besides the physical-mechanical characterization of packaging grade papers, fibre anatomy and composition can be used successfully as a complementary practical test to predict the performance of papers. The application of the predicting correlations is proposed for the evaluation of the fibre supplies for the packaging industry. An enormous potential for cost reduction can be created by the selection of the most appropriate and inexpensive combination of grade papers for a specific packaging use.

Analytical Solution of Hydrostatic Pocket Tilting

2016 ◽  
Vol 821 ◽  
pp. 113-119 ◽  
Author(s):  
Eduard Stach ◽  
Jiří Falta ◽  
Matěj Sulitka
Keyword(s):  
Computational Models ◽  
Load Capacity ◽  
Navier Stokes ◽  
Navier Stokes Equation ◽  
Detailed Model ◽  
Limit Values ◽  
Inertia Effects ◽  
Proposed Model ◽  
Machine Tool Structure

Tilting (parallelism error) of guiding surfaces may cause reduction of load capacity of hydrostatic (HS) guideways and bearings in machine tools (MT). Using coupled finite element (FE) computational models of MT structures, it is nowadays possible to determine the extent of guiding surfaces deformation caused by thermal effects, gravitational force, cutting forces and inertia effects. Assessment of maximum allowable tilt has so far been based merely on experience. The paper presents a detailed model developed for description of the effect of HS bearing tilt on the load capacity characteristics of HS guideways. The model allows an evaluation of the tilt influence on the change of the characteristics as well as determination of the limit values of allowable tilt in interaction with compliant machine tool structure. The proposed model is based on the model of flow over the land of the HS pocket under extended Navier-Stokes equation. The model is verified using an experimental test rig.

scholarly journals Nonlinear Finite Element Analysis of the Fluted Corrugated Sheet in the Corrugated Cardboard

2014 ◽  
Vol 2014 ◽  
pp. 1-8 ◽  
Author(s):  
Zhiguo Zhang ◽  
Tao Qiu ◽  
Riheng Song ◽  
Yaoyu Sun
Keyword(s):  
Finite Element Analysis ◽  
Maximum Stress ◽  
Static Pressure ◽  
Nonlinear Finite Element ◽  
Drop Test ◽  
Maximum Displacement ◽  
Element Analysis ◽  
Corrugated Board ◽  
Pressure Test ◽  
Corrugated Cardboard

The choice of corrugated medium, flute size, combining adhesive, and linerboards can be varied to design a corrugated board with specific properties. In this paper, the nonlinear finite element analysis of the fluted corrugated sheet in the corrugated cardboard based on software SolidWorks2008 was investigated. The model of corrugated board with three or more flutes is reliable for stress and displacement measurement to eliminate the influence of the number of flutes in models. According to the static pressure test, with the increase of flute heightHor arc radius of flute, the maximum stress in the models decreased and the maximum displacement increased. However the maximum stress and maximum displacement in the models increase nonlinearly in the static pressure test with the increase of the flute angleθ. According to the drop test, with the increase of flute heightH, the maximum stress of goods on the upper board in the drop test decreased. The maximum stress of the model in the drop test decreases firstly and then increases with the increase of flute angle, and the optimal flute angleθcould be 60° for corrugated board. All the conclusions are consistent with experimental data or product standards.

Corrugated Board Flute-Shaped Finite Element Analysis and Optimization

2013 ◽  
Vol 477-478 ◽  
pp. 1205-1209 ◽  
Author(s):  
Wei Yuan ◽  
Gai Mei Zhang ◽  
Da Zhi Liao ◽  
Jing Liu
Keyword(s):  
Finite Element Analysis ◽  
Finite Element ◽  
Compressive Strength ◽  
Gradual Transition ◽  
Radius Of Curvature ◽  
Element Analysis ◽  
Corrugated Board ◽  
Key Points ◽  
Corrugated Cardboard ◽  
Corrugated Structure

UV-shaped corrugated cardboard Fusion V-shaped and U-shaped structure the advantages made, to make up for the lack of V-type and two U-shaped corrugated cardboard, the higher the compressive strength, good elasticity, is widely used UV type corrugated manufacturing corrugated board. But no strict standards for UV-shaped concrete structure of corrugated board size parameter corresponding corrugating roll no uniform size of the corrugated shape, in order to achieve the best elasticity and compressive strength. First, by mathematical methods, the corrugated structure is analyzed, and analysis to facilitate research, to select the 1/4 cycle corrugated. Create multiple vertical auxiliary line level is divided into 10 equal parts, to identify key points in shape between the V-shaped and U-shaped curve, connecting into multiple segments curve. Studied the actual thickness of the corrugated board of 3.8mm, a smaller thickness and therefore a straight line can be connected to each group of the resultant key points simplify the corrugated curve, model 1/4 of a cycle of UV-shaped corrugated first determined, using the symmetry of the model to establish a cycle, 300mm side length of the square created by one cycle of replication, about 38 of the corrugated board corrugated cycle. Use of finite element analysis in ANSYS corrugated structure, including a gradual transition to a simplified model of the 11 U-shaped flute-shaped corrugated cardboard from the V-shaped set of material properties, loads are cloth pressure, research corrugated cardboard stress and strain, i.e., the smaller the radius of curvature of the curve can be obtained along corrugated, the closer the U-shaped, corrugated board having a larger strain, i.e. has good flexibility, consistent with the empirical data to prove the feasibility of this analysis method.

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