Investigation of the effect of column stacked corrugated boxes on load bridging using partial four‐way stringer class wooden pallets

Pallets are the foundation of the global packaging supply chain. They provide a way to store and transport products in an efficient manner. The load capacity of pallets greatly depends on the type of packages carried by the pallet; however, current pallet design methods do not consider the effect of packages on the load carrying capacity of the pallet. This results in excessive use of materials which reduces the sustainability of unit loads, drives costs up, and creates potential safety issues. The objective of this study was to investigate the effect of corrugated box size and headspace on pallet deflection and stress distribution on the top of the pallet as a function of pallet stiffness across multiple pallet support conditions. Data analysis identified that box size had a significant effect on the deflection of the pallet. This effect was only significant for warehouse racking across the width and length support conditions. As much as a 53% reduction in pallet deflection was observed for high stiffness pallets supporting corrugated boxes with 25.4‐mm headspace when the size was increased from small to large. The redistribution of vertical compression stresses towards the supports as a function of the increasing box size was observed. The increased concentration of compression stresses on top of the supports and the resulting lower pallet deflection could significantly increase the actual load carrying capacity of some pallet designs. The effect of box headspace was significant in some scenarios but inconsistent; thus, more investigation with a larger sample size is recommended.     

Investigation into the load bridging effect for block class pallets as a function of package size and pallet stiffness

Pallets and corrugated boxes are ubiquitous in the global supply chain. However, the interactions that exist between the boxes and pallets are ignored during the pallet design process resulting in the over designing of pallets and the waste of raw materials. The goal of this research is to understand how pallet performance is affected by headspace, box size, and base design across multiple support conditions using block class wooden pallets. Headspace and base design had no effect on pallet deflection for the experimental weights used throughout testing. However, the effect of box size was significant on pallet deflection across multiple support conditions. The effect was greatest for lower stiffness pallets and low‐stiffness support conditions (racking across the width; RAW) with up to a 50% reduction in pallet deflection observed by switching from small to large boxes on a very low‐stiffness pallet. Evaluation of pressure mat data showed an increase in the redistribution of pressure away from the center of the pallet and toward the supports as box size increased. The redistribution of pressure toward the supports is known as load bridging and validates the observed reduction in pallet deflection as a function of box size. The results indicate that incorporating this effect of packages into current pallet design practices could result in more effective and cheaper pallet designs.     

The effect of pallet top deck stiffness on the compression strength of asymmetrically supported corrugated boxes

During unitized shipment, the components of unit loads are interacting with each other. During floor stacking of unit loads, the load on the top of the pallet causes the top deck of the pallet to bend, which creates an uneven top deck surface resulting in uneven or asymmetrical support of the corrugated boxes. This asymmetrical support could significantly affect the strength of the corrugated boxes, and it depends on the top deck stiffness of the pallet. This study is aimed at investigating how the variations of pallet top deck stiffness and the resulting asymmetric support affect corrugated box compression strength. The study used a scaled-down unit load compression test on quarter-scale pallet designs with different deckboard thicknesses using four different corrugated box designs. Pallet top deck stiffness was determined to have a significant effect on box compression strength. There was a 27%–37% increase in box compression strength for boxes supported by high-stiffness pallets in comparison with low-stiffness pallets. The fact that boxes were weaker on low-stiffness pallets could be explained by the uneven pressure distribution between the pallet deck and bottom layer of boxes. Pressure data showed that a higher percentage of total pressure was located under the box sidewalls that were supported on the outside stringers of low-stiffness pallets in comparison with high-stiffness pallets. This was disproportionately loading one side of the box. Utilizing the effects of pallet top deck stiffness on box compression performance, a unit load cost analysis is presented showing that a stiffer pallet can be used to carry boxes with less board material; hence, it can reduce the total unit load packaging cost.     

Investigation of pallet stacking pattern on unit load bridging

Considering the effect of packages during pallet design will reduce costs and improve the sustainability of supply chains. Currently, many mechanical interactions between the pallet and the package product are not being considered during the pallet design process. This study investigates the effect of the magnitude and type of interlocking between layers of packaged products. The bending of the pallet supporting a unit load of corrugated boxes was measured under four common support conditions, warehouse rack storage spanning the pallet width and length, fork tine support across the pallet width, and floor stacking. Five different pallet stacking patterns were analyzed from column stacking to fully interlocked stacking. It was determined that interlocking packages reduces pallet deflection up to 53%. This is more significant for lower stiffness pallets and when the payload carried by the pallet is greater than the rated load capacity of the pallet. Increasing the magnitude of the interlocking reduces the deflection of the pallet by 11.6%. These results provide a guideline on improving pallet design and help further the understanding of the interaction between pallets and the orientation of packaged products placed on the pallet.     

Effect of Pallet Deckboard Stiffness on Corrugated Box Compression Strength

The packaging industry has long considered pallets to be rigid structures. However, in a unit load, the weight of the product produces compressive forces that are distributed across the pallet causing the top deckboards to deflect. Corrugated paperboard boxes are highly susceptible to changing support conditions; therefore, the deckboard deflection directly impacts the vertical compression strength of the box. Therefore, the objective of this study is to evaluate the effect of pallet deckboard stiffness on the vertical compression strength and deflection of corrugated paperboard boxes. Additional treatments included gaps between the deckboards and location of the box relative to the pallet stringers. Copyright © 2016 John Wiley & Sons, Ltd.     

Application of beam on elastic foundation to the interaction between a corrugated box and pallet deckboard

Corrugated boxes are ubiquitous in shipping and warehousing logistics. In physical distribution, corrugated boxes are often shipped in a unit load form where the interaction between the components determines the effectiveness and safety of the overall system. When lower stiffness pallets are used to support the corrugated boxes, the compression strength of boxes is reduced due to the uneven support conditions caused by the deforming top deckboards of the pallet. In this study, a modification of the principle of beam on elastic foundation was used to predict the effect of pallet deck stiffness on the performance of a corrugated box. In the model, the corrugated box acts as the elastic foundation, and the deckboard is represented as the beam. Pallet deck stiffness, pallet connection stiffness, and package stiffness are required model inputs. The resulting model was capable of predicting the normalized distribution of forces along the boxes' length sidewall but was not capable of predicting the compression strength of the box at failure.     

Flexural stiffness of selected corrugated structures

Top‐to‐bottom compression strength of a corrugated fibreboard box is partly dependent on the load‐carrying ability of central panel areas of the box. The ability of these central panel areas to resist a bending force from loading may increase the stacking strength of the box. The difference in the compression strengths of boxes that have identical dimensions and were fabricated with identical components but different flute types, is primarily caused by flexural stiffness of the box panels. Top‐to‐bottom compression strength of boxes can be accurately predicted by flexural stiffness measurements and edge crush test (ECT) of the combined boards. This study was carried out to analyse the flexural stiffness, to measure bending force and bending deflection by a four‐point bending test for various corrugated fibreboards, and to provide the major constructional factors which play a role in improving the compression strength of the box. Copyright © 2004 John Wiley & Sons, Ltd.     

瓦楞纸箱尺寸的优化设计

以产品为类直方体、外包装容器为瓦楞纸箱的托盘包装系统为研究对象,提出了能同时降低包装用料成本和仓储成本的瓦楞纸箱尺寸优化设计方法。介绍了优化设计方案,分别建立了瓦楞纸箱省料模型和托盘装载优化模型,从瓦楞纸箱设计、托盘装载、仓储空间各个环节进行优化,以提高托盘表面利用率和仓储空间利用率,降低包装成本,并给出了纸箱尺寸优化流程。     

瓦楞纸箱结构优化CAD系统

研究用计算机辅助优化设计瓦楞纸箱结构尺寸,使对于纸箱内每个单元内包装货物所花费的纸箱包装和流通运输整体费用最少。所开发的计算机软件,可以进行内包装件在瓦楞纸箱中的装箱方式和瓦楞纸箱货物在集装箱内的集装方式的最优选择,给出所需瓦楞纸板的配料图、瓦楞纸箱的制造尺寸图、瓦楞纸箱装箱排列图和集装箱集装排列图及有关数据。     

基于屈曲准则的瓦楞纸板强度仿真分析

分别建立了典型的A、C、B楞型单瓦楞纸板的有限元模型,计算了3种瓦楞纸板的临界屈曲载荷。以临界屈曲载荷为纸板抗压能力的判定准则,定量分析了3种瓦楞纸板的抗压能力,同时研究了材料与结构对瓦楞纸板抗压能力的影响及每种瓦楞纸板的材料抗压效率。分析结果表明,大瓦楞有更好的抗压能力,其抗压能力的提高主要是依靠其结构实现的,约束条件能够极大地改变瓦楞纸板的抗压效率。     

塑料托盘的有限元分析及实验验证

目的基于Workbench设计和分析塑料托盘结构的可靠性和可行性。方法通过建立塑料托盘的有限元模型,对其施加相应载荷,模拟塑料托盘试验时的受力情况,分别计算托盘在均载堆码、叉举、底铺板、弯曲下的挠度值,并与实验结果进行比较。结果塑料托盘4个挠度值的实验结果和模拟结果相对误差在10%以内。结论采用Workbench对托盘进行受力分析具有可靠性和可行性。     

加筋平托盘面板复杂载荷下最大挠度算法研究

根据板的小变形理论,结合加筋平托盘的简化模型以及变厚度板的挠度方程,推导出在地面承载、叉举和上架等3种不同工况下加筋平托盘受到复杂载荷时的最大挠度方程。由于载荷函数和弯曲刚度函数都是关于x,y的函数,其求解相当复杂,因此对其作离散化处理,离散化的最大挠度方程易于编程,且为研究平托盘面板结构对最大变形的影响提供了便利的途径。研究表明,离散化的最大近似挠度方程能够保证精度要求,其相对误差小于0.4%。最后展示了该算法的软件应用实例。     

Experimental investigation on bending fatigue failure of corrugated paperboard

A series of 3‐point bending fatigue tests were conducted to investigate the bending fatigue behaviour of flute type B and C corrugated paperboard samples under cyclic loading. The S‐N curve was obtained. The fatigue failure of corrugated paperboard may be described by both Basquin‐type and exponential‐type S‐N curves; however, the exponential‐type S‐N curve is more appropriate. The stiffness is gradually degraded with almost same energy dissipation in most stress cycles, but it decreases abruptly with the enlarged energy dissipation when the testing cycle is very close to the ultimate cycles of fatigue failure. The corrugated board deforms constantly under the action of cyclic loading, and no visible crack appears. The fatigue failure modes and mechanisms are same for the corrugated boards with B‐flute and C‐flute; however, the S‐N curve of corrugated board is closely related to the flute structure. The results obtained in this paper may be applied to the dynamic design and accelerated vibration test of stacked corrugated boxes.     

How Small Is a Point Load? A Preliminary Study of the Deformation and Failure of Cartons Subjected to Non‐Uniform Loads

Consumer packaging made from carton board is subjected to a variety of loads as it moves through the value chain. Packaging designers need tools for predicting the strength of packages under these loading conditions. For evenly distributed loads, there are methods for measuring and estimating compression resistance that can provide useful guidance. For loads concentrated to a small area, little work has been published. The aim of this preliminary study is to aid the development of a future test method for point loads by investigating how the size of the load application site influences the mechanical behaviour of the package. Rigid spheres of a range of sizes were used to compress packages. Small spheres gave rise primary damage in the form of a vertical yield line and secondary damage in the form of a parabolic yield line. Larger spheres produced a series of parabolic yield lines of increasing size. No vertical yield line appeared for the larger spheres. The larger spheres showed a stiffness transition at a displacement that could be estimated by considering the geometry of the test. Copyright © 2017 John Wiley & Sons, Ltd.     

Some experimental aspects of the compression behaviour of boxes made up of G‐flute corrugated boards

The load‐bearing capacity of boxes made up of thin‐walled G‐flute corrugated boards was investigated by performing monotonic and cyclic compression tests on boxes of various geometries. Results provided a large experimental database on the influence of the box dimensions and compression velocities on buckling parameters such as critical load and the corresponding critical axial deformation. Cyclic loading tests permitted the detection of the onset of an irreversible strain state, which could be related to damage initiation and propagation in the microstructure of the panels of boxes. Moreover, main differences, which could be observed between G‐flute corrugated boards and folding boards, were emphasized. Finally, the ability of some usual modelling approaches to predict the critical load of boxes was discussed. Copyright © 2009 John Wiley & Sons, Ltd.     

托盘装载优化系统的研究与开发

以外包装为瓦楞纸箱的类直方体产品的托盘包装为对象,以提高托盘包装空间利用率为目的,研究托盘装载优化系统的设计,并给出了优化数学模型,利用Vc++6.0开发工具结合OpenGL技术,开发出符合我国联运托盘标准和运输仓储条件的托盘装载优化系统的应用程序。     

JG3军用合成制动液运输包装跌落仿真分析

目的研究JG3军用合成制动液在不同厚度瓦楞纸箱运输包装情况下,角跌落过程对包装箱内部制动液吹塑桶小包装应力、应变的影响。方法利用ANSYS/LS-DYNA软件,对不同厚度瓦楞纸箱运输包装的JG3军用合成制动液进行角跌落仿真实验,获取内部制动液吹塑桶小包装的有效应力及塑性应变数据,分析不同运输包装条件下制动液吹塑桶小包装的应力、应变特点。结果随着瓦楞纸箱运输包装厚度的增大,相同角跌落条件下,包装箱内的制动液吹塑桶小包装总体应力、塑性应变变小;在最厚的瓦楞纸箱包装条件下,部分制动液吹塑桶小包装存在应力、塑性应变集中区域。结论瓦楞纸箱运输包装对内装物的保护作用并非瓦楞厚度越大越好。     

瓦楞楞型对瓦楞纸箱蠕变性能的影响

采用四元件模型对不同楞型的瓦楞纸箱的压缩蠕变特性进行了研究。研究结果表明:四元件模型可以用于模拟不同楞型的瓦楞纸箱的短期蠕变行为;在3种楞型中,B型瓦楞纸箱的瞬时弹性变形系数数值最小;A型瓦楞纸箱在Kelvin模型中的延时弹性变形系数和粘性系数最小;Maxwell模型中的粘滞系数与应力水平关系明显,随着应力水平的上升,下降比较明显,其中A型瓦楞纸板不可恢复永久变形最大;随着应力水平的上升,各种楞型的瓦楞纸箱的松弛时间均呈明显下降趋势,其中A型瓦楞纸箱下降程度最为明显。     

The effect of pallet connection stiffness,deck stiffness and static load level on the resonant response of pallet decks to vibration frequencies occurring in the distribution environment

This paper summarizes the results of a preliminary study of the relationship between pallet design and the resonant response of pallet decks to sinusoidal vibration. Sine sweep frequency vibration tests between 3 Hz and 50 Hz were conducted to determine the effect of pallet deckboard stiffness, joint stiffness and the static load level on the resonant response of pallet decks. As the stiffness of the pallet joints and deckboards increases, the resonant frequency of the unit load increases and transmissibility decreases. As the static load on the pallet increases the resonant frequency of the unit load decreases and the transmissibility increases. The survivability of a unitized product, sensitive to vibration, during shipping and distribution is affected by the pallet design. Pallets designed using rigid connections and stiffer decks will reduce damage to vibration‐sensitive products. Copyright © 1999 John Wiley & Sons, Ltd.     

Modelling load retrievals in puzzle-based storage systems

Puzzle-based storage systems are a new type of automated storage systems that allow storage of unit loads (e.g. cars, pallets, boxes) in a rack on a very small footprint with individual accessibility of all loads. They resemble the famous 15-sliding tile puzzle. Current models for such systems study retrieving loads one at a time. However, much time can be saved by considering multiple retrieval loads simultaneously. We develop an optimal method to do this for two loads and heuristics for three or more loads. Optimal retrieval paths are constructed for multiple load retrieval, which consists of moving multiple loads first to an intermediary ‘joining location’. We find that, compared to individual retrieval, optimal dual load retrieval saves on average 17% move time, and savings from the heuristic is almost the same. For three loads, savings are 23% on average. A limitation of our method is that it is valid only for systems with a very high space utilisation, i.e. only one empty location is available. Future research should investigate retrieving multiple loads for systems with multiple empty slots.