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.     

瓦楞纸箱抗压强度的研究进展

目的综述国内外对瓦楞纸箱抗压强度的研究进展,探讨瓦楞纸箱的发展趋势。方法以查阅文献等形式,了解国内外瓦楞纸箱抗压强度的研究现状。论述对瓦楞纸箱力学性能的研究,讨论抗压强度经验公式的修订、抗压强度影响因素及提高方法。结论抗压强度的研究为瓦楞纸箱生产企业和包装设计者提供了必要的实验数据。轻量化、定量化、节约资源和降低成本等是瓦楞纸箱科学发展的要求,也为全球瓦楞纸箱的发展指明了方向。     

压痕形状对瓦楞纸箱抗压强度影响的试验

目的 在不同形状的压痕条件下,对瓦楞纸箱进行抗压试验,研究纸箱的变形情况和抗压能力。方法 首先设计无压痕纸箱、一字型压痕箱、八字型压痕箱以及菱形压痕箱;其次将各种压痕形状下的纸箱,利用纸箱抗压试验机进行空箱抗压实验,记录各自的最大压溃力;最后对实验数据进行分析,明确抗压强度与压痕形状的关系。结果 不同压痕形状对瓦楞纸箱的抗压强度有不同程度的影响,其中菱形影响最大。菱形压痕通过阻碍纸箱变形趋势可提高瓦楞纸箱的抗压强度。结论 在瓦楞纸箱侧板上通过施加阻碍纸箱工字型变形的压痕（如菱形压痕）,可以增加瓦楞纸箱的抗压强度,对瓦楞纸箱的生产设计具有参考意义。     

Effect of load history on the performance of corrugated fibreboard boxes

This paper investigates the effect of load histories (static and dynamic) on the compression strength and shock absorption properties of corrugated fibreboard boxes. Experiments were set up in the laboratory to simulate compressive forces and drops that occur during normal transportation of packaged products. The results show that static compression forces (not to failure) do not have significant influence on the compressive strength or shock absorption of corrugated boxes, and that dynamic compression forces do have a significant influence on these performance factors. This study was limited to one box size and style and suggests that more extensive research be undertaken to determine the effects of previous loading histories on a broad range of box configurations.     

Torsional and compression loading of paperboard packages: Experimental and FE analysis

The present study investigates torsional and compressive loading of a paperboard package. Finite element (FE) analyses simulating the tests were performed to improve understanding of the stresses and deformations in the paperboard during loading. A simple experimental characterization of the necessary material properties could be performed to represent the multi-ply paperboard as a single-ply structure. The results from the single-ply model were compared with a laminate model, and the differences between the models were small. Comparing experimental and FE simulations of box compression and torsion showed that the FE models could accurately predict the response curves. However, in the simulations, there was an overprediction of the maximum compressive force and maximum torque, which was expected since geometrical imperfections and the heterogeneous internal structure of the material were not accounted for in the material model or the FE model. Local yield lines formed at the onset of non-linearities in the package load–displacement curves. Therefore, the strength of the paperboard affects the maximum compressive strength and maximum torque, and the bending stiffness of the paperboard only had a minor effect. When a first local maximum was reached, the number of FE that reached the failure stress increased exponentially. The simulations also showed that box compression was not an effect of package height, but higher packages had a lower maximum torque.     

管式预粘合纸箱结构参数与抗压强度的相关关系

目的研究管式预粘合纸箱结构参数与抗压强度的相关关系,为优化纸箱结构设计以及提高其抗压强度提供依据。方法首先设计普通、四棱台、花形锁等3种代表性管式预粘合纸箱,进而确定3种纸箱影响抗压强度的关键结构参数。其次将各结构参数依次作为自变量,其余结构参数作为常量,利用纸箱抗压试验机进行空箱抗压试验,记录各自的最大压溃力。最后对实验数据进行分析,明确抗压强度与结构参数间的相关关系。结果 3种纸箱的抗压强度均随着周长的增大而增大,其抗压强度并非全部随高度的增大而降低。考虑周长因素时,普通箱的抗压强度最佳;考虑高度因素时,花形锁箱的抗压强度最佳;考虑箱型因素时,当普通箱长宽比接近1.0,四棱台箱下上底比在1.2~1.4范围内,花形锁箱的啮合点和花形锁圆心的连线与水平线所成夹角接近30°时,抗压强度最佳。因结构参数的影响,管式预粘合纸箱的抗压强度整体上显著优于标准开槽纸箱。结论预粘合纸箱的关键结构参数对其抗压强度有显著影响,在设计时应给予足够的重视。     

Static and Dynamic Strength of Paperboard Containers Subjected to Variations in Climatic Conditions

The variability in climatic conditions during product distribution, especially across large distances, can be significant and is well known to affect the mechanical properties of many packaging materials. As the use of environmentally friendly materials, such as paperboard and bio‐cushions, increases, the challenge associated with overcoming the effects of extremes in temperature and relative humidity in the distribution chain becomes critical. To date, in the case of paperboard boxes, this is dealt with by accounting for the loss of static (compression) strength with increasing relative humidity. However, no method exists to address the dynamic loads induced by vehicle shocks and vibrations especially for configurations that involve stacked boxes and where the vibration intensity within the stack is influenced by the dynamic characteristic of the boxes themselves. In such scenarios, it is the variation in the stiffness of the box as a function of environmental conditions and dynamic load that needs to be established. This paper describes the evaluation of the fatigue resistance of paperboard boxes subjected to random excitation and compares the results with those obtained from quasi‐static compression tests under various environmental conditions. Results reveal a lack of correlation between the static and dynamic tests. This finding is attributed to changes in internal damping of the paperboard box samples which, when reduced, results in increased dynamic force. The paper concludes that static testing alone is insufficient to establish the fatigue resistance of stacked packaging subject to variations in climatic conditions. Copyright © 2017 John Wiley & Sons, Ltd.     

Localized Deformation in Compression and Folding of Paperboard

The localized deformation patterns developed during in‐plane compression and folding of paperboard have been studied in this work. X‐ray post‐mortem images reveal that cellulose fibres have been reoriented along localized bands in both the compression and folding tests. In folding, the paperboard typically fails on the side where the compressive stresses exists and wrinkles are formed. The in‐plane compression test is however difficult to perform because of the slender geometry of the paperboard. A common technique to determine the compression strength is to use the so‐called short‐span compression test (SCT). In the SCT, a paperboard with a free length of 0.7 mm is compressed. Another technique to measure the compression strength is the long edge test where the motion of the paperboard is constrained on the top and bottom to prevent buckling. A continuum model that previously has been proposed by the authors is further developed and utilized to predict the occurrence of the localized bands. It is shown that the in‐plane strength in compression for paperboard can be correlated to the mechanical behaviour in folding. By tuning the in‐plane yield parameters to the SCT response, it is shown that the global response in folding can be predicted. The simulations are able to predict the formation of wrinkles, and the deformation field is in agreement with the measured deformation pattern. The model predicts an unstable material response associated with localized deformation into bands in both the SCT and folding. Copyright © 2016 John Wiley & Sons, Ltd.     

冷冻食品包装用瓦楞纸箱结构设计研究

根据冷冻食品用瓦楞纸箱在冷库中易出现的塌箱现象,介绍了塌箱原因。从瓦楞纸箱结构设计的角度,研究了提高瓦楞纸箱抗压强度的方法。实验数据分析表明:按照纸板理论边压强度的1.25倍进行配纸,所得到的瓦楞纸板抗压强度可满足储运环境要求;此外,将常用02型箱型改为套合型箱型,也可明显提高纸箱的抗压强度。     

军用滑木箱的设计分析

介绍了按日本标准设计的横板式和国内竖板式军用滑木箱的结构设计参数，从木箱抗弯、抗静压及顶盖抗弯三方面对比了两种木箱的力学性能，分析了两种木箱的特点及适用范围。     

大长宽比对纸箱抗压能力影响的研究与分析

对获取纸箱抗压能力的3种主要技术手段:试验测试方法、经典公式计算方法和计算机仿真模拟方法的优缺点进行了对比分析。选择0201型BC楞瓦楞纸箱为对象,分别采取试验测试和经典公式计算,在纸板材料、纸箱高度、周长相同的条件下,对长宽比从1～3范围变化的纸箱抗压能力进行了计算和测试。结果表明:长宽比从1变化到3时,纸箱的抗压强度先升再降;当长宽比为1.6左右时,抗压强度达到最大值。试验结果和利用经典抗压能力计算结果的对比分析表明,计算结果均较大地偏离了试验结果。由于不能充分考虑到纸板加工质量、纸箱成型工艺、温湿度及其它因素的影响,经典抗压能力计算公式均是偏保守的。     

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.     

瓦楞纸箱的有限元建模及屈曲分析

建立了瓦楞纸箱的有限元模型并进行了屈曲分析,计算了该瓦楞纸箱的临界载荷和屈曲模态.将临界载荷与利用凯利卡特公式计算的抗压强度进行了对比.分析结果表明,利用有限元的方法计算的瓦楞纸箱临界屈曲载荷与凯利卡特公式计算抗压强度非常接近.因此利用屈曲分析计算瓦楞纸箱的抗压强度是一种可行的方法.     

Prediction of bending strength of long corrugated boxes

Long corrugated boxes were supported at both ends and bent by a concentrated force applied at the middle. Boxes with different lengths, cross‐sectional shapes, flute directions and board strengths were tested, using a standard compression tester with a fixed platen in accordance with ASTM D‐642. An equation was developed to relate compression strength to the various properties of the box. The correlation coefficient R² for the fit to actual data was about 0.4. Boxes having the flutes run around the box had a 20% higher compression strength than with horizontal flutes. The most significant factor was found to be the board edge crush strength. The results suggest that failure of boxes in bending is due to localized crushing at the point of application of the load, rather than whole‐box collapse. Copyright © 2001 John Wiley & Sons, Ltd.     

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.     

瓦楞纸箱自锁底结构的设计与分析

目的以奶品瓦楞纸箱的自锁底结构为研究对象,研究不同自锁底结构的力学特性。方法以奶品礼箱为对象,设计6种不同自锁底结构、3种不同尺寸的18种瓦楞纸箱,根据国家标准,分别进行空箱抗压实验与95 cm的跌落实验。结果空箱抗压实验结果显示,18种自锁底箱体能够承受的最大压力在1133~1437 N之间,其中2片粘合翼均在侧面板上的X2-0结构能够承受的最大压力最大,达到了1437N;X2-5结构能够承受的最大压力接近X2-0结构,达到1421 N。6种不同自锁底结构的底面跌落数据显示,底面跌落时最大加速度均在51~59 m/s2之间,其中X2-0结构纸箱的薄弱角缩进尺寸最小,为11mm。结论对比了不同缩进量的6种自锁底结构的抗压和跌落试验结果,X2-5型具有较大的抗压性能和耐冲击性能。     

截面结构对纸箱抗压强度的影响及定量表征

目的研究截面结构的改变对多边形瓦楞纸箱抗压强度的影响规律。方法改变垂直侧板数量、边长、相邻侧板围成角度进行抗压试验,分析多边形纸箱变形失效过程及抗压强度的变化规律,建立以独立的垂直侧板边长代替周长的计算模型。结果当其他影响纸箱抗压强度的条件一定时,侧板数量的增多会使抗压强度值增大。八边形瓦楞纸箱的侧板边长越接近正多边形、围成角度越接近135°时,抗压强度越大。结论瓦楞纸箱变形失效本质是由侧板结构受压后整体失稳造成的,所提出的计算模型能较真实地反映纸箱受压的力学特性,且能有效表征多边形瓦楞纸箱抗压强度。     

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.     

瓦楞纸箱抗压强度计算方法

在对Mckee计算纸箱抗压强度的简化公式进行研究的基础上,本文给出了一种利用微计算机计算瓦楞纸箱(顶到底)抗压强度的方法。与Mckee简化公式相比较,本文给出的方法还可以考虑纸箱的长宽比和高度比等因素对纸箱抗压强度的影响。     

蜂窝纸板箱的静态压缩特性研究

建立了蜂窝纸板箱的基本方程,并对蜂窝纸板箱进行了有限元模拟,利用ANSYS对其压缩特性进行了计算;得到了中面受均布载荷时无衬垫和带有蜂窝纸板衬垫两种情况下蜂窝纸板箱的应力图和变形图;同时分析了箱体的应力和变形特点.结果表明:在蜂窝纸板箱底部的中央位置应力和变形均为最大值,这将影响其抗压性能;蜂窝纸板衬垫可以有效地降低最大应力值.此结论为蜂窝纸板箱的优化设计提供了参考依据.