J. Pac .Sci. Tech.

Vol.24No.2（2015）

Original Paper～～～～～～～～～～～～～～～～～～～～～～～～～～～～

Method for Controlling Damage to Products
Subjected to Cumulative Fatigue Considering Damage Degree
at Each Layer in Stacked Packaging
Hiroaki KITAZAWA*,**, Katsuhiko SAITO*, and Yutaka ISHIKAWA**To devise a method for controlling the damage to products considering the degree of damage pershock (d) at each layer in stacked packaging, we laid board- or sheet-like cushioning materials between
each layer or outside the bottom of the boxes and studied the effects they had on the velocity change (Vc),the peak acceleration (PAcc), and d at each layer in the stacked packaging. The results of a drop test
indicated that the values of Vc and PAcc corresponding to the drop shock at each layer in the stacked
packaging can indeed be controlled by laying the board- or sheet-like cushioning materials between eachlayer or outside the bottom layer. Estimation results, obtained by a multiple regression analysis for the
calculation of a specific d, indicated that the layer having the maximum d (dMax) could be changed using
the cushioning materials, although the average d (dAv) throughout the packaging was not so changed.
These results will contribute to the development of a mixed packaging system for products with varying
fragility, damaged by cumulative fatigue.
Keywords: cumulative fatigue, multiple regression analysis, peak acceleration, repetitive shock, velocitychange1. Introduction
In a previous study, we demonstrated that the combination of the velocity change (Vc) and peakacceleration (PAcc) due to a dropping shock changed variously by the differences among the layers instacked packaging for strawberries damaged by cumulative fatigue1). Accordingly, the degree of damage
to the fruit per shock (d) varied according to the layer differences. These results indicated that thedifferences in the combinations of Vc and PAcc corresponding to different layers should be considered inorder to prevent products inside stacked packaging from being damaged because of cumulative fatigue
due to repetitive shock. The sensitivity of products inside stacked packaging to a single shock has beenthoroughly studied2,3). However, few reports consider methods for controlling the damage to products
inside stacked packaging due to cumulative fatigue caused by repetitive shock.
The aim of this study was to propose a method to control product damage, considering d at eachlayer in stacked packaging. When using packaging in actual transport, controlling measures are easily
applied. To control d at each layer, we laid board- or sheet-like cushioning materials between each layerof boxes and outside the bottom of the boxes.
*
Transport Packaging Laboratory, Kobe University, 5-1-1, Fukaeminami, Higashinada, Kobe 658-0022, Japan**

National Food Research Institute, National Agriculture and Food Research Organization, 2-1-12, Kannondai, Tsukuba,
Ibaraki 305-8642, Japan
Corresponding author: Hiroaki Kitazawa. Tel: 029-838-8037, Fax: 029-838-7996, E-mail: ktz@affrc.go.jp－ 69 －

Method for Controlling Damage to Products Subjected to Cumulative Fatigue
Considering Damage Degree at Each Layer in Stacked Packaging

2. Theory
2.1 Summary of experiment and analysis
First, we examined whether Vc and PAcc at each layer were changed by laying board- or sheet-likecushioning materials between each layer or outside the bottom layer. Next, we estimated the resulting
changes in the d values. The d values corresponding to the combination of Vc and PAcc were estimated bymultiple regression analysis.

2.2 Multiple regression analysis for estimation of d values corresponding to the
combination of Vc and PAcc
Assuming damage boundary curves (DBCs) corresponding to a specific d, each d value isdetermined according to two parameters: Vc and PAcc. Therefore, multiple regression analysis was
performed with Vc and PAcc as explanatory variables and d as the objective variable. We attempted tolead the equation of multiple regression to cross each DBC (Fig. 1) as follows:d = aVc + bPAcc + c,

(1)

Fig. 1 Estimation of d values corresponding to Vc and PAcc by multiple regression analysis.
where a, b, and c are constants. The data of Vc, PAcc, and d for the multiple regression analysis wereobtained from a previous report1), which considered a drop test for strawberries inside five-layered
stacked packaging (Table 1). To confirm the significance of the regression equation, an analysis ofvariance (ANOVA) was performed. Both analyses were performed using statistical software (Excel
Toukei 2012, Social Survey Research Information; Tokyo, Japan). We used multiple regression analysis
only for estimating the d values because the DBCs cannot be drawn from the analysis.

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3. Experiment
3.1 Condition for Vc and PAcc measurements in drop test with each material
The dummy sample used to measure Vc and PAcc was a five-layered stack of corrugated fibreboard
boxes (external dimensions: 355 mm × 254 mm × 75 mm) each containing four 300–320-g clay-packed
polyethylene terephthalate resin-made trays (external dimensions: 166 mm × 117 mm × 40 mm). A
20-mm-thick layer of foamed urethane sheets was placed on each tray to stop its rebound. Each box was
fastened by two plastic bands, and then the boxes were stacked. The bottom and top boxes were definedas the 1st and 5th layers, respectively. The total weight of the stacked packaging was ~6.5 kg.
The board- or sheet-like cushioning material used to control Vc and PAcc should be easily
obtainable and not change the total weight of the packaging. In addition, it should be sufficiently hard to－ 71 －

Method for Controlling Damage to Products Subjected to Cumulative Fatigue
Considering Damage Degree at Each Layer in Stacked Packaging

avoid the collapse of the cargo. Thus, we used a foamed plastic board (FPB), a corrugated plastic board(CPB), and a foamed rubber sheet (FRS). The thickness of each material was 5 mm. The specifications ofeach material are given in Table 2. Each material was laid between the layers or outside the bottom layer(Fig. 2). The condition wherein the material was laid outside the bottom layer was labelled “0-1.”
Similarly, when the material was laid between the 1st and 2nd, 2nd and 3rd, 3rd and 4th, and 4th and 5th layers,
the conditions were labelled “1-2,” “2-3,” “3-4,” and “4-5,” respectively.

Fig. 2 Cushioning material for controlling Vc and PAcc; laying the corrugated plastic boardndrd

between the 2 and 3 layers (CPB-2-3).
The Vc and PAcc measurements for each material were performed with the same conditions as inprevious reports1,4). That is, a three-dimensional accelerometer (2366 W; Showasokki, Tokyo Japan; size:
8.0 mm × 7.0 mm × 5.5 mm; weight: 1.2 g) was attached to the internal centre of one of the tray bottoms
using double-sided tape and kept in place by the weight of the clay. The dummy sample, i.e., thefive-layered stack of boxes, was dropped perpendicularly by hand. Then, the Vc and PAcc were measured.
In our previous study on strawberry fruit, we found that a drop height of around 0.2 m was enoughto damage the fruit during transport5). Thus, the drop height was set to 0.1 m. In the “0-1” condition,－ 72 －

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the distance between each layer of material and the counterface surface was adjusted to 0.1 m. The
counterface surface was a 10-mm-thick silicone rubber sheet (density: 0.27 g/cm3, compression stress at
25% distortion: 126.1 kPa) on an iron board to reduce the PAcc. The measurement conditions were as
follows: sampling interval, 500 μs; data, 2000 points; filer mode, automatic; trigger level, 0.4%; andpre-trigger, 5%. These conditions were set using a shock measurement and analysis system (SMH-12,
Shinyei Technology, Kobe, Japan), connected to the accelerometer and shock vibration analysis software(SMS-500M, Shinyei Technology).
The Vc and PAcc data without any materials were obtained from the previous report1) and shown in
Table 1 and were used for the control condition.

3.2 Estimation of d at each layer
The values of Vc and PAcc obtained from the measurement results of 3.1 were substituted into
Equation (1). Thus, the d values obtained from dropping were estimated for each material. The averageand maximum d values of the all 5 layers were also calculated: dAv and dMax, respectively.

4. Results and Discussion
4.1 Multiple regression analysis for estimation of d values corresponding to the
combination of Vc and PAcc
From the result of the multiple regression analysis of the data shown in Table 1, we obtained thefollowing equation with a high coefficient of correlation:d = 1.51E-02Vc + 7.85E-05PAcc − 1.32E-02 (r = 0.9848).

(2)

The results of the ANOVA showed that the P value, indicating the significance, was 3.68E-15; this value
is sufficient to explain the significance of Equation (2). Therefore, this equation is reliable for estimatingd according to the combination of Vc and PAcc.

4.2 Effects of each material and its position on the Vc and PAcc at each layer
The data of Vc and PAcc in each layer for each material are shown in Tables 3 and 4, respectively.
Each Vc value tended to be large in the upper layer compared with the lower layer, which supports theprevious report1). The combination of Vc and PAcc changed variously with each material (Fig. 3). Thus,
it was suggested that the hardness of the whole packaging and/or each layer was changed by using eachmaterial when it was assumed as a spring. It was also reported that the transmissibility of the acceleration
at the upper layer was larger than that at the lower layer when a half-sine shock pulse was applied to thestacked packaging2). Thus, in the current study, it was suggested that the transmissibility of theacceleration at each layer was changed by using each material laid at a different position. Moreover, in
this study, the material of the counterface surface for the drop test was an elastic silicone rubber sheet; itselastic properties might affect the combination of Vc and PAcc at each layer. To clarify this issue, further
studies are needed.

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Method for Controlling Damage to Products Subjected to Cumulative Fatigue
Considering Damage Degree at Each Layer in Stacked Packaging

thFig. 3 Shock pulses at the 5 layer under the following conditions: no material (Control; A),
FPB-0-1 (B), CPB-2-3 (C), and FRS-1-2 (D).
1)

The data for “no material” were obtained from the previous report .
The Vcs for A, B, C, and D are 2.46, 2.51, 2.21, and 2.40 m/s, respectively.
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4.3 Estimation of d at each layer
The d values calculated according to the results in Tables 3 and 4, along with Equation (2), areindicated in Table 5. For each material, the d values at the 1st and 4th layers tended to be larger than thoseof the control because the Vc and/or PAcc values in those layers tended to be large compared with thecontrol. Therefore, in most cases, it was estimated that the dMax values at each layer were larger than thecontrol. On the other hand, a decrease in the d values compared with the control was observed at the 2nd
and 3rd layers in several conditions, corresponding to a decrease in the Vc and/or PAcc values comparedwith the control. Thus, it was estimated that the dAv values were not changed by using the material, except
in the FPB-3-4 and 4-5 conditions.
The trends in the d values at each layer in the FPB-0-1, CPB-2-3, and FRS-1-2 conditions areshown in Fig. 4. For the FPB-0-1 condition, the dAv value was the same as that of the control. However,the dMax value was smaller than that of the control because the d value at the 1st layer decreased comparedwith the control. For the CPB-2-3 and FRS-1-2 conditions, each dMax value was larger than that of thecontrol because the d values at the 1st layer increased compared with the control. However, in bothconditions, the d values decreased compared with the control in the layers above the 2nd layer. Therefore,
the dAv values were the same as those of the control.

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Method for Controlling Damage to Products Subjected to Cumulative Fatigue
Considering Damage Degree at Each Layer in Stacked Packaging

Fig. 4 Varying d by laying board- or sheet-like cushioning materials at each layer.

5. Conclusion
Our results indicate that the values of Vc and PAcc due to drop shock at each layer in stacked
packaging can be controlled by laying board- or sheet-like cushioning materials between each layer oroutside the bottom layer. Moreover, our results suggest that the layer with the maximum d (dMax) could bechanged variously using these materials, although the average d (dAv) throughout the packaging was not
so changed.

6. Future Prospects
We suggest applying the current results to strawberries damaged by cumulative fatigue. For
strawberries, the difference in the firmness caused by the differences in the cultivar6) or harvested period7)
links directly to the sensitivity to shock during transport. Thus, a non-destructive method to distinguish
the firmness of strawberries has been developed8). The application of the aforementioned non-destructive
method has been limited to arranging the fruit depending on the destination9) because there was no mixed
packaging system for fruits with different firmness.
On the other hand, our results will contribute to the development of a mixed packaging system for
fruits with different fragilities, wherein the fruits can be placed at different layers depending on theirfirmness (Fig. 5). The control range of d can be widened by using board- or sheet-like cushioning－ 76 －

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Vol.24No.2（2015）

materials, although it seems that the mixed packaging might be sufficient without these materials (Table
5). Our future research will focus on applying the present results in designing cushioning packaging for
products that are damaged by cumulative fatigue.

Fig. 5 Concept of mixed packaging style for products having different sensitivities to repetitive shock.
ndrdHere, a corrugated plastic board is laid between the 2 and 3 layers of boxes (CPB-2-3; case C in Fig. 4).

Acknowledgements
A part of this study was supported by the Scheme to Revitalize Agriculture and Fisheries inDisaster Area through Deploying Highly Advanced Technology of the Ministry of Agriculture, Forestry
and Fisheries of Japan. We thank Akira Michishita, an assistant manager at Shimadzu Corporation, forsupporting the density evaluation of each material and Naoko Hasegawa of the technical staff at the
National Food Research Institute for supporting the drop test.

References
1) Kitazawa, H. and Saito, K.: J. Pack. Sci. Tech., 23(4), 277–285. (2014).
2) Nakajima, T., Saito, K., Kubo, M. and Teragishi, Y.: J. Pack. Sci. Tech., 8(3), 123–134. (1999).
3) Nakajima, T., Saito, K., Kubo, M. and Teragishi, Y.: J. Pack. Sci. Tech., 9(1), 33–46. (2000).
4) Kitazawa, H., Saito, K. and Ishikawa, Y.: Pack. Tech. Sci. 27(3), 221–230. (2014).
5) Kitazawa, H., Ishikawa, Y., Lu, F., Hu, Y., Nakamura, N. and Shiina, T.: Hort. Res. (Japan), 9(2),
221–227. (2010).
6) Salentijn, E. M. J., Aharoni, A., Schaart, J. G. Boone, M. J. and Krens, F. A.: Physiol. Plant., 118(4),571–578. (2003).
7) Kitazawa, H., Sato, T., Ishikawa, Y., Nakamura, N. and Shiina, T.: Food Preserv. Sci., 36(6), 265–269.
(2010).
8) Kashiwazaki, M., Nagasuge, T., Soutome, H., Nakajima, M. and Omori, S.: J. Jpn. Soc. Agric. Mach.,71(6), 90–97. (2009).
9) Kashiwazaki, M., Nagasuge, T., Soutome, H., Nakajima, M. and Omori, S.: J. Jpn. Soc. Agric. Mach.,69(6), 49–56. (2007).
(Received 15 October 2014)(Accepted 6 February 2015)－ 77 －

Method for Controlling Damage to Products Subjected to Cumulative Fatigue
Considering Damage Degree at Each Layer in Stacked Packaging

多段積み包装における段ごとの損傷度を考慮した蓄積疲労により損傷する物品の損傷制御方法の提案
北澤

裕明*,**、斎藤勝彦*、石川豊**

多段積みされた包装において、段ごとの衝撃 1 回あたりの損傷度（d）を考慮することによって、物品の損傷を制御するための方法を提案するために、本研究では多段積み包装における各包
装容器と包装容器の間もしくは包装全体の最底面への板またはシート状の緩衝材の配置が、段ごとの速度変化（Vc）、ピーク加速度（PAcc）および d に及ぼす影響を評価した。落下試験の結果
より、板またはシート状の緩衝材を用いることにより、各段における Vc と PAcc を様々に変化させることができることが明らかとなった。また、これらの変化に伴い、各段における d がどのように変化するのかを重回帰分析を用いて推定したところ、包装全体における d の平均値（dAV）
は、殆ど変化しないものの、d が最大（dMax）となる段が様々に変化する可能性が示唆された。
これらの結果は、異なる易損性を持つ、蓄積疲労により損傷する物品を混載することを可能とする包装設計の実現に貢献するものと期待された。

キーワード: 蓄積疲労、重回帰分析、ピーク加速度、繰り返し衝撃、速度変化－ 78 －