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WO2017067799A1 - Corps élastique comprenant une surface ondulée - Google Patents

Corps élastique comprenant une surface ondulée Download PDF

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Publication number
WO2017067799A1
WO2017067799A1 PCT/EP2016/074077 EP2016074077W WO2017067799A1 WO 2017067799 A1 WO2017067799 A1 WO 2017067799A1 EP 2016074077 W EP2016074077 W EP 2016074077W WO 2017067799 A1 WO2017067799 A1 WO 2017067799A1
Authority
WO
WIPO (PCT)
Prior art keywords
resilient body
body according
undulations
notional
undulating
Prior art date
Legal status (The legal status is an assumption and is not a legal conclusion. Google has not performed a legal analysis and makes no representation as to the accuracy of the status listed.)
Ceased
Application number
PCT/EP2016/074077
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English (en)
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WO2017067799A8 (fr
Inventor
Robert Stanley Farr
Current Assignee (The listed assignees may be inaccurate. Google has not performed a legal analysis and makes no representation or warranty as to the accuracy of the list.)
Unilever NV
Conopco Inc
Original Assignee
Unilever NV
Conopco Inc
Priority date (The priority date is an assumption and is not a legal conclusion. Google has not performed a legal analysis and makes no representation as to the accuracy of the date listed.)
Filing date
Publication date
Application filed by Unilever NV, Conopco Inc filed Critical Unilever NV
Publication of WO2017067799A1 publication Critical patent/WO2017067799A1/fr
Publication of WO2017067799A8 publication Critical patent/WO2017067799A8/fr
Anticipated expiration legal-status Critical
Ceased legal-status Critical Current

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Classifications

    • B—PERFORMING OPERATIONS; TRANSPORTING
    • B65—CONVEYING; PACKING; STORING; HANDLING THIN OR FILAMENTARY MATERIAL
    • B65D—CONTAINERS FOR STORAGE OR TRANSPORT OF ARTICLES OR MATERIALS, e.g. BAGS, BARRELS, BOTTLES, BOXES, CANS, CARTONS, CRATES, DRUMS, JARS, TANKS, HOPPERS, FORWARDING CONTAINERS; ACCESSORIES, CLOSURES, OR FITTINGS THEREFOR; PACKAGING ELEMENTS; PACKAGES
    • B65D81/00—Containers, packaging elements, or packages, for contents presenting particular transport or storage problems, or adapted to be used for non-packaging purposes after removal of contents
    • B65D81/02—Containers, packaging elements, or packages, for contents presenting particular transport or storage problems, or adapted to be used for non-packaging purposes after removal of contents specially adapted to protect contents from mechanical damage
    • B65D81/05—Containers, packaging elements, or packages, for contents presenting particular transport or storage problems, or adapted to be used for non-packaging purposes after removal of contents specially adapted to protect contents from mechanical damage maintaining contents at spaced relation from package walls, or from other contents
    • B65D81/107—Containers, packaging elements, or packages, for contents presenting particular transport or storage problems, or adapted to be used for non-packaging purposes after removal of contents specially adapted to protect contents from mechanical damage maintaining contents at spaced relation from package walls, or from other contents using blocks of shock-absorbing material

Definitions

  • the present invention relates to a resilient body comprising a gradually undulating surface.
  • Packaging for consumer products is widely seen as a waste by-product of modern society.
  • packaging is disposed of by an end user and the packaging needs to be subsequently handled in some way, e.g. by going to landfill or by being recycled.
  • packaging One requirement of packaging is to provide structural integrity, so that the product can be handled through the supply chain and in use by the consumer. Therefore, if it were possible to modify packaging to improve its structural properties, it becomes possible to use less material to achieve the same structural effect, and thus reduce the amount of disposed packaging.
  • WO02/016122 discloses flat panels which contain positive and negative deviations in the surface. There is no disclosure of improving structural properties such as bending and stretching.
  • US 5,965,235 discloses a flat sheet onto which has been introduced deformations on one side only in order to provide separation between multiple stacked sheets. The surface contains sudden changes in the profile of the sheet.
  • WO99/07273 discloses a wipe article having a random series of peaks and valleys thereon.
  • JP3141022 discloses a bottle which comprises a region of decoration which resembles a cluster of ice cubes.
  • WO02/13916 discloses a golf ball with randomly spaced dimples on an otherwise flat land between, e.g. in a Voronoi tessellation.
  • the invention in a first aspect, relates to a resilient body comprising a gradually undulating surface, the undulating surface defined by a notional two-dimensional surface having a plurality of positive and negative undulations normal to the notional two-dimensional surface and randomly distributed thereon, such that in any and all profiles of the undulating surface, the mean undulation is statistically zero.
  • the present invention utilises an optimised geometry to provide improved linear mechanical properties such as stretching and bending. Improvements in crushing resistance have also been found. This increases the resistance to elastic buckling and crumpling under applied loads.
  • the present invention provides a method for applying random, statistically isotropic corrugations to a (possibly curved) panel, such as the wall of a packaging container, which increase the bending stiffness.
  • the panel may initially be flat, but the method is applicable to panels that have any shape or topology - for example including holes or handles - with a radius of curvature larger than that of the corrugations.
  • the method ensures that locally, the properties of the corrugated panel are statistically isotropic and on average are the same across the curved panel, with no seams or discontinuities, no matter what geometry or topology the initially curved panel may have.
  • the topology of the final surface should be the same as that of the initial surface:
  • corrugations are applied to a panel, but this initial panel may itself optionally be foamed or topologically complex or a laminate or a sandwich composite.
  • the random corrugated sheet may also be used as a layer in a sandwich composite.
  • grade undulating is meant that the surface profile is smooth and contains no sudden changes of direction.
  • profile of the surface is therefore mathematically differentiate to first order. For example, a sudden change in direction would imply an infinite rate of change of direction and the surface would therefore not be differentiate.
  • profiles of the undulating surface is meant a portion of the surface, such as a slice through the surface or an extended region of the surface. Because the surface is undulating the profile must extend over a representative distance of the surface in order for the mean undulation in the profile to be statistically zero.
  • a profile can thus be a perpendicular slice through the surface giving a trace in one dimension or could be an area of the surface giving a two dimensional sample of the surface. Indeed the profile could even be the entire surface.
  • statically zero is meant that the measurement of the mean undulation in any profile will not necessarily be exactly zero but will be zero as testable by statistical methods. For example taking a number of profiles of the surface, no matter their extent, will together provide a mean undulation that approaches zero the more samples of the profile are taken. As an example, if the head side of a coin is represented by +1 and the tails side of a coin are represented by -1 , then the average of a number of coin tosses is also statistically zero, even if the actual value measured for a limited number of coin tosses might be non-zero.
  • resilient is meant that the body returns or is able to recoil or spring back into shape after being bent, compressed or stretched in any direction up to an elastic limit.
  • statically isotropic is meant that the surface has the same linear material properties regardless of the direction they are measured in, to a high level of statistical confidence.
  • mean undulation is meant the average height of the surface.
  • the surface has statistically isotropic material properties. This means that the material properties are independent of the alignment of the surface.
  • a significant advantage of the present invention is that the undulations can be applied to complex geometries without breaking or disturbing the pattern in any way.
  • the notional surface is curved, and more preferably undulating surface forms a three-dimensional shape.
  • the body may be a container or a mould for an object such as a container, preferably for containing a consumer product. Additionally the body may be secondary or tertiary packaging such as a box or pallet.
  • the undulating surface provides improvements in material strength and can result in less packaging material being used, it is preferable that the body is made up of at least 50wt% of the undulating surface, more preferably at least 75 wt%, most preferably at least 85% wt%.
  • the undulating surface does not contain any sudden changes of direction, as these can introduce a source of structural weakness, especially to crushing.
  • the radius of curvature at any point on the undulating surface is not less than 0.1 times the mean magnitude of the amplitudes of undulation, preferably is not less than 0.2 times, more preferably not less than 0.5 times. In a preferred embodiment it is about 1.0 times the mean magnitude of the amplitudes of undulation.
  • no part of the undulating surface exhibits a slope relative to the notional surface of greater than 60 degrees, preferably greater than 50 degrees.
  • the present invention can in principle apply to materials of any thickness, preferably the undulating surface has a material thickness of from 0.1 to 3mm, more preferably less than 2mm, most preferably less than 1 mm.
  • the undulating surface may be made from a variety of materials; however a plastic, cardboard or metal material is preferred.
  • the benefits of the invention are more significant when the magnitude of the undulations is greater than the thickness of the surface.
  • the ratio of the mean amplitude of the undulations to the thickness of the surface is greater than 2:1 , preferably greater than 5:1 , more preferably greater than 10:1 .
  • the undulations preferably all have the same or similar magnitudes of amplitude, so that they project the same or similar distance from the notional surface.
  • the magnitude of the amplitude of the undulations for a plurality of positive and negative undulations extending across the undulating surface is essentially the same across the surface.
  • all of the undulations have the same magnitude of amplitude.
  • the length scale of the undulations is consistent throughout the surface. As such, preferably the distance, parallel to the notional surface, between the "peak" of a positive undulation and its nearest neighbouring "peak” of a positive undulation is substantially the same for all such "peaks" on the undulating surface.
  • the distance, parallel to the notional surface, between the "peak” of a positive undulation and its nearest “trough” of a negative undulation is substantially the same for all such "peaks” on the undulating surface. It is also preferred that the size and spacings of the positive undulations are essentially the same as the negative undulations. Thus, preferably the mean distance, parallel to the notional surface, between the "peaks” of the positive undulations are essentially equal to the mean of the distance between the "troughs" of the negative undulations. It has also been found that a continuously undulating surface is preferable to one which has only a few scattered undulations separated by intervening flat surface. Thus preferably one peak flows into a trough and vice versa throughout the surface.
  • the ratio of (1 ) the mean distance, parallel to the notional surface, between the "peak” of a positive undulation and its nearest “trough” of a negative undulation, to (2) the mean amplitude of the undulations is from 10:1 to 1 :3, preferably 5:1 to 1 :1 , more preferably from 3:1 to 1.5:1.
  • the undulations are preferably smooth and contain no sudden changes of direction.
  • the profile of the undulating surface between a "peak" and its neighbouring "trough” is S-shaped.
  • the surface comprises at least 10 positive undulations and at least 10 negative undulations.
  • the ratio of (1 ) the minimum lateral dimension of the surface, to (2) the mean distance, parallel to the notional surface, between the "peak" of a positive undulation and its nearest "trough” of a negative undulation is greater than 5:1 , preferably greater than 10:1 , more preferably greater than 20:1 .
  • minimum lateral dimension of the surface is meant the closest separation of two parallel planes between which the surface will fit without touching either plane.
  • the starting surface may be an undulating surface as produced according to the present invention.
  • a second set of undulations can be superimposed onto such an undulating surface, e.g. to produce a hierarchical structure. If the second set of undulations is smaller than the first set then such a hierarchical structure is provided. Therefore preferably the ratio of the magnitude of (1 ) the amplitude of the undulations on the notional two-dimensional surface, to (2) the amplitude of the positive and negative undulations normal to the undulating surface is greater than 3:1 .
  • the invention in a second aspect, relates to a process for the generation of a body as described herein, the process involving (1 ) generating a mathematical three- dimensional scalar field, (2) mathematically placing the notional two-dimensional surface into the three-dimensional scalar field, (3) recording the value of the scalar field over the two-dimensional surface, (4) creating a mathematical representation the undulating surface by applying undulations normal to the two-dimensional surface in proportion to the value of the scalar field at that point on the surface, (5) generating the body from the representation so obtained in step (4).
  • the shape of the surface can be generated as a mathematical object in steps (1 ) to (4) and step (5) is the production of the object according to the mathematical description so obtained.
  • the scalar field is generated by mathematical analogy with Cahn-Hilliard theory of incomplete polymer phase separation. Detailed description of the invention
  • Figure 1 is a schematic representation of a model surface illustrating how various parameters are defined.
  • Figure 2a is a periodic image of a simulation of incomplete Cahn-Hilliard phase separation.
  • Figure 2b is the simulation shown in figure 2a but with a corner of the illustrated cube missing to illustrate that the pattern does not vary according to orientation.
  • Figure 3a is an image of a mathematical representation of a cylinder which has been treated to the application of undulations according to the present invention.
  • Figure 3b is an image of a mathematical representation of the cylinder shown in figure 3a which has been further treated to the application of smaller undulations to create a hierarchical structure.
  • Figure 4 shows images of mathematical descriptions of various patterns applied to a planar square surface (a) 'flat', (b) 'ribs', (c) 'ribs rotated 90°', (d) 'Cahn-Hilliard', (e) 'cubes', (f) 'cubes rotated 90°', (g) 'p31 m' and (h) 'p31 m rotated 90°.
  • Figure 5a is a chart showing the finite element results for stretching stiffness, S, divided by the stretching stiffness of a flat sheet, for the surfaces shown in figure 4.
  • Figure 5b is a chart showing the finite element results for bending stiffness, B, divided by the bending stiffness of a flat sheet, for the surfaces shown in figure 4.
  • Figure 6 is images of a variety of 3D printed test cylinders made from acrylonitrile butadiene styrene (ABS), the corrugation patterns are: (a) " p31 m', (b) " cubes' (p3m1 symmetry), (c) " helix' (a ribbed geometry, but rotated by 30° away from alignment with the cylinder axis, (d) " ribs', (e) “ flat' and (f) " ribs rotated 90°'.
  • ABS acrylonitrile butadiene styrene
  • Figure 7 is a chart showing part of the same chart as figure 5b, with the results from mechanical tests also included as filled diamond symbols.
  • Figure 8 is an image of the mechanical testing arrangement showing a cylinder under test and a Stable Micro Systems Texture Analyser'.
  • Figure 9 is an image of a solid object resembling the shape of a consumer product for containing liquid detergent made from ABS and printed by a 3D-printer.
  • Figure 10 is an image of a solid object based on the object shown in figure 9 but wherein part of the surface has been treated to the mathematical addition of undulations to the surface before being printed. A portion of the surface has not been treated and left flat for the application of a label.
  • the plate thickness itself is defined as the volume of material per unit projected area of the plate. Therefore introducing a corrugation pattern by these definitions does not change the amount of material used in the plate or packaging.
  • a corrugation design which is defined statistically was also generated.
  • the route chosen is to base the design on the Cahn-Hilliard theory of polymer phase separation. This pattern is statistically isotropic, defined in three dimensions and has a single length scale.
  • the value of the amplitude is more easily defined: it is difference in " height' (normal to the notional surface bearing the corrugations) between the highest and lowest points on one side of the surface.
  • a 0
  • the value is specified by the code which generates the geometry.
  • the ridge-type geometries are likely to be highly anisotropic, with bending stiffness across the ridges being much higher than when the deformation is aligned with the ridges, and similarly for stretching. These are included because some of the scaling properties of these structures can be calculated, and because they make useful test cases.
  • the irregular, random corrugation pattern can be designed to be statistically isotropic, and also have other favourable properties (in a statistical sense).
  • the above method is used to assign a value of to every point of the surface of interest, and then translate these points by an amount proportional to the assigned value, and in a direction normal to the original surface.
  • FIG. 3a An example is shown for a cylinder in figure 3a. It is also possible to use the random corrugated surface generated as a new starting surface and superimpose a further level of corrugation. Such a design is shown in Figure 3b.
  • the Calculix FE solver was used for the finite element simulations.
  • the unit system is Newtons and millimetres.
  • a 20mm by 25mm plate is used, cantilevered along one of the long edges (see figure 4a), comprising 140 by 175 quadratic hexahedral elements with full integration (element type C3D20 in Calculix or Abaqus), which is considered to give reasonably accurate answers for a plate simulation, and not be particularly prone to locking, soft modes or anomalously high stiffness in certain deformation modes.
  • Figure 4 shows square portions 20mm by 20mm of the patterns used in the finite element simulations. The actual geometries are rectangular, with one side 20% longer than shown (20mm by 25mm).
  • the geometries are (a) to (h): “ flat', " ribs', “ ribs rotated 90°', " Cahn-Hilliard', " cubes', “ cubes rotated 90°', " p31 m' and “ p31 m rotated 90°'.
  • Figure 5a shows finite element results for the stretching and Figure 5b for bending of corrugated plates, scaled by the theoretical results for a flat plate, and plotted as a function of plate thickness divided by lateral scale of the corrugation. All results are on a log-log scale. It can be seen that in general, introducing corrugations reduces the stretching stiffness (except for the case where the corrugations are ribs parallel to the stretching direction) and increases bending stiffness (except for the case where the corrugations are ribs parallel to the cantilevered edge).
  • the Cahn-Hilliard random corrugation pattern is amongst the highest in stiffness for both bending and stretching. It should also be noted that its mechanical behaviour will be statistically isotropic (independent of orientation). Mechanical Testing
  • Corrugated cylindrical geometries were generated by computer. These were then used to 3D print the shapes using a commercial 3D printer, out of ABS (acrylonitrile butadiene styrene). This is a glassy polymer at room temperature (Tg3 ⁇ 4 105°C), with a quoted density in the range 1060 to 1080kgnr 3 and Young's modulus in the range 1 .4 to 3.1 GPa.
  • ABS acrylonitrile butadiene styrene
  • the printed pieces were floated in salt solution, and found the concentration needed to ensure neutral buoyancy.
  • the density measured in this way was found to be in the range 1060 to 1070kgnr 3
  • the scale of the printing was adjusted to ensure the shapes all fit within the available sample volume, so we do not know in advance how large each of the pieces will be.
  • the radii (inner and outer) and heights were therefore measured for each of the pieces, and the thickness of the plates (in terms of mass per unit normal projected area) were then determined by measuring the mass, converting to volume by the density of ABS, and dividing by the area of a cylinder with the measured average (mean of inner and outer) radius. See table 1 for results where the heights and radii were measured triplicate with vernier callipers.
  • the cylinder height L, circumference C, lateral scale ⁇ and corrugation amplitude a are designed to be in the ratio L : C : ⁇ : a :: 9 ⁇ /3 :42 : 1 : 0.5, and corrugations are produced by moving points outwards from the basic uncorrugated cylinder, so the heights based on mean radius, ⁇ and C might not match the prediction exactly.
  • Corrugations offer the prospect of increasing the bending stiffness dramatically, at the expense of stretching stiffness; and therefore where bending stiffness is the limiting design constraint, such as in large panels with little or no curvature, this is a worthwhile compromise.
  • Simple ridge-type patterns however lead to very anisotropic mechanical properties, and the advantage of some of the other patterns studied here (such as " p31 m' and " Cahn-Hilliard') is that it is possible to increase the bending stiffness more or less equally for any orientation of the bending stress.
  • the elastic buckling of cylindrical shells is very sensitive to imperfections, for example deviations from a perfect circular cross-section. Therefore even though the buckling forces of perfect shells can be very high, this level of strength is never observed in practice.
  • the strength of imperfect cylinders under axial loads with imperfection amplitudes on the order of the wall thickness can be several times lower than for the case of perfect cylinders. This represents a severe example of sensitivity, since in real applications, cylindrical shells are likely to be thin-walled, so that imperfections of this magnitude are unavoidable.
  • corrugated shells are designed to have the effective thickness (from an elastic point of view; not the actual volume of material per unit projected area) is greatly increased. Therefore, even if the product Vsl? remains largely unchanged, we expect structures made from corrugated walls with isotropic elastic behaviour to be significantly less sensitive to imperfections than the corresponding non-corrugated structures.
  • the most interesting pattern studied is based on the Cahn-Hilliard theory of incomplete polymer phase separation, which gives good results for bending stiffness compared to most other patterns, and has a similar value for the quantity VSZ? (where S is the effective stretching stiffness and B the bending stiffness of the corrugated plate) to that of a flat plate.
  • the quantity Vsl? is the key parameter setting the linear buckling force of thin-walled hollow cylinders under axial compressive loads.
  • the enhanced and isotropic bending stiffness can be an advantage on its own if packaging contains large flat regions, such as the front and back of a liquid detergent bottle.
  • the similarity of the quantity Vsz? to the uncorrugated plate suggests that there will be no advantage to isotropic corrugations in the case of axial
  • the Cahn-Hilliard corrugation pattern investigated has other useful properties: it gives statistically isotropic behaviour for bending and stretching stiffness, and it can be applied to any surface, whether curved or flat or of complex topology. When applied to such a surface, the pattern does not need to be locally scaled, nor do " seams' need to be introduced between incompatible regions of the pattern: instead, the pattern is statistically the same everywhere over the surface. Furthermore, this process of applying the pattern to an arbitrary surface can be iterated, using a similar pattern at a smaller length scale, to create hierarchical corrugations.
  • figure 9 shows a 3D printed object made of ABS in the form of a liquid detergent container.
  • Figure 10 is the same container with the surface altered according to the method described herein to apply the random undulations.
  • the nature of the patterning means that the application of the undulations is not affected and no seams exist despite the irregular shape of the object.

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  • Engineering & Computer Science (AREA)
  • Mechanical Engineering (AREA)
  • Springs (AREA)
  • Treatments Of Macromolecular Shaped Articles (AREA)
  • Diaphragms And Bellows (AREA)
  • Containers Having Bodies Formed In One Piece (AREA)
  • Laminated Bodies (AREA)

Abstract

L'invention concerne un corps élastique comprenant une surface ondulant progressivement, la surface ondulée définie par une surface bidimensionnelle imaginaire comprenant une pluralité d'ondulations présentant chacune une amplitude positive ou négative normale à la surface bidimensionnelle imaginaire et réparties de manière aléatoire sur celle-ci, de sorte que dans chacun des profils sur la surface ondulée, l'amplitude moyenne soit statistiquement de zéro.
PCT/EP2016/074077 2015-10-23 2016-10-07 Corps élastique comprenant une surface ondulée Ceased WO2017067799A1 (fr)

Applications Claiming Priority (2)

Application Number Priority Date Filing Date Title
EP15191199.7 2015-10-23
EP15191199 2015-10-23

Publications (2)

Publication Number Publication Date
WO2017067799A1 true WO2017067799A1 (fr) 2017-04-27
WO2017067799A8 WO2017067799A8 (fr) 2017-05-26

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PCT/EP2016/074077 Ceased WO2017067799A1 (fr) 2015-10-23 2016-10-07 Corps élastique comprenant une surface ondulée

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AR (1) AR106434A1 (fr)
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Citations (6)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
WO1999007273A1 (fr) 1997-08-12 1999-02-18 The Procter & Gamble Company Article d'essuyage muni d'une couche de gaze et d'une surface d'essuyage en trois dimensions
US5965235A (en) 1996-11-08 1999-10-12 The Procter & Gamble Co. Three-dimensional, amorphous-patterned, nesting-resistant sheet materials and method and apparatus for making same
JP3141022B2 (ja) 1999-11-26 2001-03-05 三菱電機株式会社 燃焼器具の制御装置
WO2002013916A2 (fr) 2000-08-15 2002-02-21 The Procter & Gamble Company Balle de golf presentant des alveoles de forme non circulaire
WO2002016122A1 (fr) 2000-08-25 2002-02-28 Massachusetts Institute Of Technology Panneau a courbure bidimensionnelle
US20100156147A1 (en) * 2008-12-23 2010-06-24 Honda Motor Co., Ltd. Headliner packaging system with hinged clamp

Patent Citations (6)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
US5965235A (en) 1996-11-08 1999-10-12 The Procter & Gamble Co. Three-dimensional, amorphous-patterned, nesting-resistant sheet materials and method and apparatus for making same
WO1999007273A1 (fr) 1997-08-12 1999-02-18 The Procter & Gamble Company Article d'essuyage muni d'une couche de gaze et d'une surface d'essuyage en trois dimensions
JP3141022B2 (ja) 1999-11-26 2001-03-05 三菱電機株式会社 燃焼器具の制御装置
WO2002013916A2 (fr) 2000-08-15 2002-02-21 The Procter & Gamble Company Balle de golf presentant des alveoles de forme non circulaire
WO2002016122A1 (fr) 2000-08-25 2002-02-28 Massachusetts Institute Of Technology Panneau a courbure bidimensionnelle
US20100156147A1 (en) * 2008-12-23 2010-06-24 Honda Motor Co., Ltd. Headliner packaging system with hinged clamp

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Publication number Publication date
AR106434A1 (es) 2018-01-17
WO2017067799A8 (fr) 2017-05-26

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