EXPERIMENTAL OPTIMIZATION OF PERFORATIONS FOR CORRUGATED BOARD BOXES

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1 The 4 th edition of the Interdisciplinarity in Engineering International Conference Petru Maior University of Tîrgu Mureş, Romania, 2009 EXPERIMETAL OPTIMIZATIO OF PERFORATIOS FOR CORRUGATED BOARD BOXES adina EIDOI #1, Vasile BOLOŞ *2, M.I. BUZDUGA #3 # Rondocarton Ltd Cluj-apoca Apahida/Cluj,Street. Aviatorillor r. 2a, Sânnicoară, RO ,Cluj County,Romania 1 nadina.neidoni@rondo-ganahl.co * Petru Maior University oftîrgu-mureş Tîrgu Mureş, icolae Iorga street, no. 1, , Mureş County,Romania 2 vasile.volos@ing.upm.ro # Technical University of Cluj-apoca Cluj-apoca,Street.Memorandumului r. 28, RO , Cluj County, Romania 3 mircea.buzdugan@insta.utcluj.ro ABSTRACT The paper presents a practical method of optimizing type, dimensions and position of perforations for shelf ready packaging. The optimization criterion is the box compression test, in accordance with the ISO 12048:1994(E) international standard, which assesses the performance of a package in terms of its strength or the protection it offers to its contents when it is subjected to compressive forces. The exemplification is performed on a shelf ready box on corrugated board, material type 211.5E, using the box compression tester MESSPHYSIK ALPHA 50. Keywords: packaging, optimization, corrugated board, box, compression test 1. Introduction owadays, the complete supply chain, from the producer to the final consumer imposes to corrugated board boxes to be suitable for storing, shipping and displaying in the sale points [1]. In order to correspond to this versatility, corrugated board packages have to be provided with perforations which allow the rapid metamorphosis from a storing and/or shipping packaging, into a display (figure 1. a. and b.), the so called shelf ready packaging [2]. On the other hand, perforations weaken compression strength of the corrugated board, with a value depending on their type, dimensions and position. Fig. 1 - Shelf ready packaging Therefore, performing box compression tests in order to get the optimum shape and dimensions of the boxes becomes mandatory. In accordance with the ISO 12048:1994(E) international standard [3], the test is used to assess the performance of a package in terms of its strength or the protection it offers to its contents when it is subjected to compressive forces. A test may be performed either to as a single test to investigate the effects (deformation, collapse or failure) of compression or stacking, or as part of a sequence of tests designed to measure the ability of a 287

2 package to withstand a distribution system that includes a compression or stacking hazard. The test may also be used as a stacking test to investigate performance under particular conditions of loading, as, for example, when the bottom package in a stack rests on an open-decked pallet [4]. 2. Principle, apparatus, procedure and theory of the compression test The test package is placed between the platens of a compression tester and either: a) in the case of a compression test, a load is applied until failure occurs or predetermined values for load or displacement are reached; or b) in the case of a stacking test, a predetermined load is applied for a predetermined time or until failure occurs. The compression tester, motor-driven, platentype,is capable of applying load through uniform movement of one or both platens at a relative speed of 10mm/min 3mm/min., dimensioned so as to extend over the whole area of that side of the test package or interposed devices with which it is in contact. Wherever possible the test shall be carried out in the same atmospheric conditions as used for conditioning (23 g Celsius and 50% humidity) [5]. The load is applied by the relative movement of the platens at the appropriate speed, in such a way that peaks in excess of the predetermined load do not occur, until predetermined value is reached or until collapse occurs, whichever is first. If collapse occurs first, one must record the value of the load reached. In real operating conditions, compressive strength of boxes is reduced due to the following reasons: - the box content exercises forces that determine the wall deformation to outside - compressive forces are acting on the boxes for long periods (weeks-months) - during manipulation and shipping the boxes are exposed to vibrations, shocks or different strokes, also air parameters are variable, so that moisture equilibrium of the box changes relatively frequent - during storage, compression forces are not uniformly distributed on the surface of the box throughout the perimeter of the box. When load increases, a first critical point is reached (point "a", Figure 2.). At this point the walls of the box are elastically deformed to the outside, while the corners remain unaffected [5, 6]. Compressive forces are concentrated towards the corners of the box, which will be more affected than its sides and when the second critical point "b" is exceeded, the corners begin to crush. When reaching maximum load, the point "c" of the stress-strain diagram, sides are folded and edges are crushed [7]. Consequently, the resistance of a box is given both by the corrugated board stiffness and edgewise compressive strength. The values of compressive strength of boxes can be determined by calculation, if we know [8, 9]: - the Edgewise Compression Strength, obtained after tests ECT [k/m] - the corrugated board stiffness S b, on machine direction SbMD and on crossmachine direction S bcd [m] - the perimeter of the box, Z [m] These parameters compose the McKee's wellknown equation which has the general form: b b BCT k ECT Sb Z b For the particular case of corrugated board boxes, McKee's formula becomes: BCT k ECT Sb Z where: 1 Sb Sb Sb m MD CD A simplified practical form of McKee's formula, applicable to corrugated paperboard is: BCT k ECT T Z 2 Fig.2 - Theoretical stress-strain diagram 3. Experimental results Tests were carried out using the MESSPHYSIK ALPHA 50 BCT tester, presented in figure 3. Test parameters are: B 0...Batch number F max...maximum load "M...Strain at compressive strength FB...Breaking load t...test duration sf max...stroke at F max sb...stroke at break The test reports give several statistic results [10-12]. The mean value is in this case the arithmetic mean, which for a data set represents the sum of the observations divided by number of observations. In probability theory and statistics, the median is described as the number separating the higher half of a population from the lower half. If there is an even 288

3 number of observations, the median is not unique, so one often takes the mean of the two middle values. In our case, the median is the geometric mean of the two middle values. The median is less sensitive to extreme scores than the mean and this makes it a better measure than the mean value income, especially for highly skewed distributions. The range is the length of the smallest interval which contains all the data. It is calculated by subtracting the smallest observation from the greatest and provides an indication of statistical dispersion. standard deviation indicates that the data points tend to be very close to the mean, whereas high standard deviation indicates that the data are spread out over a large range of values. Standard deviation is commonly used to measure confidence in statistical conclusions. The standard deviation is calculated as: 1 i i1 x x 2 We take the example of the box presented in Figure 1. The developed diagram of the box is presented in Figure 4. The results of the tests performed on the different boxes without perforations (dotted lines on figure 3) are presented in table 1 and in the graphs depicted in Figure 5. It can be seen from the graphs that the shape of the practical curves is quite different from the theoretical one in the sense that the critical points are not easily discernible. Fig. 3 - The BCT machine The standard deviation is a measure of the variability or dispersion of a population. A low Fig. 4 - The developed diagram box 289

4 Table 1. Compression test report of the box without perforations Fig. 5 - Box compression tests graphs 290

5 In order to optimize the compressive strength of the box we performed BCT tests repeated for ten different boxes and for several types, dimensions and positions of the perforation. 4. Conclusions The statistical results of the tests give rise to a range of interesting conclusions in terms of optimizing perforations. The most resilient box has been demonstrated to be the one without perforations, but such a box is not really a shelf ready packaging box. On the other hand, from the range of the perforating boxes, the best behavior has been registered to the box having 2x2 mm perforations in position B (i.e. 45 mm from the bottom edge of the box). From the point of view of the maximum load, the median diminishes only with 0,101 k comparative with the box without perforations and the mean value, that takes account of the extreme scores, only with 0,082 k. In both cases the standard deviation has been almost the same. The other test parameters: strain at compressive strength, breaking load, stroke at F max and stroke at break have been superior in this case either. In conclusion, it can be said that BCT in the design stage represents a very important issue in optimizing performances for a corrugated board packaging. References [1] Yam, K., Encyclopedia of Packaging Technology, John Willey &Sons Inc., [2] Mark J. Kirwan, Paper and Paperboard Packaging Technology, Blackwell Publishing Ltd., 2005 [3] *** ISO 12048:1994 (E) Standard; Packaging Complete, filled transport packages Compression and stacking tests using a compression tester [4] Thakkar, B.K., et al., Experimental and numerical investigation of creasing in corrugated paperboard, Philosophical Magazine, Taylor & Francis Group, Vol. 88, os , 1 11 October 2008, [5] Modzelewska, I., Climatic conditions vs. hygrostability and strength properties of corrugated board, Folia Forestalia Polonica, Wyd. AR Poznan, 37, 2006, pp [6] Isaksson, P., Hagglund, R., A mechanical model of damage and delamination in corrugated board during folding, Engineering Fracture Mechanics, 72, 2005, pp [7] Harrysson, A., Ristinmaa, M., Large strain elastoplastic model of paper and corrugated board International Journal of Solids and Structures, 45, 2008, pp [8] Luo, S., et al., The Bending Stiffness of Corrugated Board, AMD-Vol. 145/MD-Vol. 36, Mechanics of Cellulosic Materials 1992, pp [9] Gavrilescu, D., Toth, S., Cartonul ondulat (Corrugated Board), Editura T3, Romania, [10] Barlow, R., Statistics, John Willey &Sons Ltd., [11] Ryan, T., Modern Engineering Statistics, John Willey &Sons Inc., [12] Antoniou, A., Wu-Seng, L., Practical optimization, Springer Science+Business Media,