AU2015202905B2 - A method and apparatus - Google Patents
A method and apparatus Download PDFInfo
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- AU2015202905B2 AU2015202905B2 AU2015202905A AU2015202905A AU2015202905B2 AU 2015202905 B2 AU2015202905 B2 AU 2015202905B2 AU 2015202905 A AU2015202905 A AU 2015202905A AU 2015202905 A AU2015202905 A AU 2015202905A AU 2015202905 B2 AU2015202905 B2 AU 2015202905B2
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Abstract
The present invention relates to a method and apparatus for determining material properties of a paper sheet, namely any one or a combination of shear modulus, 5 bending stiffness and shear strength. 6516573_1 (GHMatters) P98597.AU.1 BYRON 28/05/15
Description
A METHOD AND APPARATUS
FIELD OF THE PRESENT INVENTION
The present invention relates to a method and apparatus for determining material properties of a paper sheet that can be used in the manufacture of any suitable product, including but by no means limited to corrugated board. The material properties that may be determined include any one or a combination of shear modulus, bending stiffness and shear strength. Material properties such as these can then be used to predict the performance characteristics of a product made from the paper sheet, such as corrugated board and cartons.
BACKGROUND OF THE PRESENT INVENTION
One of the objectives of the pulp and paper industry is to manufacture a product having known specified properties at the lowest possible costs. Measuring the properties of 15 the paper that are used to manufacture the product can be an indication and in some instances, an important indication, of the final performance of the product.
Tests for measuring the properties of paper sheets presently used include tensile strength tests, water Cobb tests, tear strength, concora medium tests, and so forth.
0 TraditionaIly many of these tests have been performed manually. Over recent years, changes in technology have involved a degree of automation of the test methods, thereby reducing the potential for human error and increasing the speed and consistency at which the test methods are performed.
5 Corrugated board is a high strength product used in the manufacture of cartons that are used for a range of purposes, including storing fresh food items under moist conditions such as high humidity environments and cold storage. The cartons are also expected to perform over a various time frames from relative short periods such as a few days, to extended periods such as a few months or even years. The ability for a product to resist deterioration or degradation under various environments, particularly moist and cycling humidity environments, as the products ability to resist “creep”, which can be an important characteristic depending on the circumstances.
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Moreover, the performance of the corrugated board is dependent on a vast number of different variables including, but by no means limited to: quality of the fibre material feed, for instance virgin fibre versus recycled fibre; grammage ofthe corrugated medium and the liner boards; the flute spacing of the corrugated medium; adhesion of 5 the corrugated medium to the liner boards; moisture resistance of the liner boards and corrugated medium, the humidity of the environment in which the product is being used, the expected life time of the carton and so forth. In view of these variables, fully assembled corrugated board is often tested after manufacture to validate this performance. However, a difficulty with this practice is that the performance of the corrugated board may not satisfy predetermined performance criteria.
The invention may provide an alternative test method that can be used, for example, on paper sheets, prior to the paper sheets being manufactured into a corrugated board.
SUMMARY OF THE PRESENT INVENTION
In one form of the invention, there is a method for determining material properties of a paper sheet, the method including:
0 a) supporting the paper sheet on a pair of supports that are separated by a first spacing, and applying a first force to the paper sheet intermediate of the supports to cause the paper sheet to deflect between the supports by a first deflection;
b) measuring the first deflection of the paper sheet between the pair of supports that is attributable to the first force and measuring the first force applied, wherein the deflection of the paper sheet during step a) can be expressed as the sum of the bending deflection ratio (¾) and the shear deflection ratio (<5S) according to equation 1:
PL3 μΡΙ S = S,,+es = 48bD + 4Gbl (equation 1) wherein:
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P is the first force, b is the width of the paper sheet, t is the thickness of the paper sheet, D is the bending stiffness of the paper sheet, 5 μ is the shape factor of the paper sheet,
L is the first spacing between the supports, G is the shear modulus of the paper sheet;
c) holding the paper sheet so as to provide a fixed end and a free section, and 10 applying a second force to the paper sheet at the free section of the paper sheet that is located at a second spacing from the fixed end, so as to cause the paper sheet to deflect by a second deflection;
d) measuring the second deflection of the paper sheet that is attributable to the second force and measuring the second force applied, wherein the deflection of the paper sheet during step c) can be expressed as the sum of the bending deflection ratio (¾) and the shear deflection ratio (<5S) according to equation 2:
0 5 = 5b + 5s = — + — (equation 2) ΰ 5 3bD Gbt \ Ί / wherein:
P is the second force, b is the width of the paper sheet,
5 t is the thickness of the paper sheet,
D is the bending stiffness of the paper sheet, μ is the shape factor of the paper sheet, L is the spacing between the fixed cantilever support and the point of applied load, and
G is the shear modulus of the paper sheet;
e) using the first deflection, the first force, and the first spacing in equation 1, and using the second deflection, the second force, and the second spacing
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-42015202905 18 May 2020 in equation 2, and solving equations 1 and 2 to determine the bending stiffness (D) and shear modulus (G) of the paper sheet.
In another form of the invention, there is an apparatus for determining material properties of a paper sheet, the apparatus including:
a pair of supports that supports the paper sheet over a span between the supports;
a cantilever assembly that locates a fixed end of the paper sheet and from which a free end of the paper sheet extends;
at least one load cell that is operable to:
(i) measure a first force that is applied to the paper sheet intermediate of the supports to cause the paper sheet to deflect between the supports, wherein a first deflection of the paper sheet is expressed as the sum of the bending deflection ratio (δΒ) and the shear deflection ratio (5S) according to equation 1:
PL3 pPL S = SB+es = 48bD + 4Gbl (equation 1) wherein:
P is the first force, b is the width of the paper sheet,
5 t is the thickness of the paper sheet,
D is the bending stiffness of the paper sheet, μ is the shape factor of the paper sheet, L is the first spacing between the supports, and G is the shear modulus of the paper sheet;
(ii) measure a second force that is applied to the free end of the paper sheet held by the cantilever assembly, wherein a second deflection of the paper
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| sheet is expressed as the sum of the bending deflection ratio (¾) and the shear deflection ratio (<5S) according to equation 2: | |
| 5 | 5 = 5b + 5s = — + — (equation 2) ΰ 5 3bD Gbt \ Ί / wherein: P is the second force, b is the width of the paper sheet, |
| 10 | t is the thickness of the paper sheet, D is the bending stiffness of the paper sheet, μ is the shape factor of the paper sheet, L is the spacing between the fixed cantilever support and the point of applied load, and |
| 15 | G is the shear modulus of the paper sheet; at least one displacement sensor that is operable to (i) measure the first deflection of the paper sheet between the pair of supports that is attributable to the first force, and (ii) measure the second deflection of the |
| 20 | paper sheet at the free end of the paper sheet that is subject to the second force; and a processor that receives data on the first force and the second force, on the first deflection and the second deflection, and the processor is arranged |
| 25 | to use the data to solve equations 1 and 2, to provide the bending stiffness (D) and shear modulus (G) of the paper sheet. In another form of the invention, there is a method for determining material properties of a paper sheet, wherein the method includes the steps of: |
| 30 | a) supporting the paper sheet on a pair of supports that are separated by a spacing, applying a force to the paper sheet intermediate of the supports to cause the paper sheet to deflect between the supports; |
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b) recording the deflection of the paper sheet between the pair of supports that is attributable to the force and recording the force applied, wherein the deflection varies according to equation 1 in which the deflection is a function of the force applied to the paper sheet, the spacing between the supports, and bending stiffness (D) and shear modulus (G) of the paper sheet to be determined as unknowns, wherein the deflection of the paper sheet during step a) is expressed as the sum of the bending deflection ratio (¾) and the shear deflection ratio (<5S) according to equation 1:
PL3 μΡΤ S = SB+es = 48bD + 4Gbl (equation 1) wherein:
P is the force b is the width of the paper sheet, t is the thickness of the paper sheet,
D is the bending stiffness of the paper sheet, μ is the shape factor of the paper sheet, L is the first spacing between the supports, and G is the shear modulus of the paper sheet;
wherein step a) is carried out at least twice, in which the spacing between the supports is different when recording the force applied and deflection according to step b), thereby providing two sets of input data, including deflection for the respective force and spacing between the supports;
c) using the input data and equation 1 to create two equations in which the bending stiffness (D) and shear modulus (G) are unknowns, and solving the equations to determine the bending stiffness (D) and shear modulus (G) of the paper sheet.
In another form of the invention, there is a method for determining material properties of a paper sheet, wherein the method includes the steps of:
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a) supporting the paper sheet on pairs of supports, the pairs of supports being separated at two different spacings, and applying a force to the paper sheet intermediate of the supports to cause deflection of the paper sheet between the supports;
b) recording the force applied to the paper sheet between pairs of supports that is attributable to the deflection, and thereby provide two sets of data including data on the force and deflection for respective spacings between the pairs of supports;
c) using the data obtained from step b) in equation 1 defining the deflection (δ) as a function of:
a shear deflection that is proportional to a ratio of the spacing between the supports (L) to shear modulus of the paper sheet (G), namely the shear deflection ratio (<5S), plus a bending deflection that is proportional to a ratio of the spacing between the supports cubed (L3) to bending stiffness of the paper
0 sheet (D), namely the bending deflection ratio (<5S):
PL3 gPL ί = ίΒ+,5ι = 48ΪΟ + 44Μ (equation 1) wherein: P is the force,
5 b is the width of the paper sheet, t is the thickness of the paper sheet, D is the bending stiffness of the paper sheet, μ is the shape factor of the paper sheet, L is the first spacing between the supports, and
G is the shear modulus of the paper sheet;
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-βίο form two equations in which the bending stiffness (D) and shear modulus (G) are unknowns and solving the two equations to determine the bending stiffness (D) and shear modulus (G).
One embodiment of the present invention is based on the realisation that a set of material properties of paper sheets can be tested or measured prior to the paper sheets being manufactured into a product. The set of material properties of the paper sheets can, for example, be derived by carrying out one type of test method that is performed on repeated occasions. The material properties of the paper sheets measured or tested can be used for a range of purposes, including and without limitation, to predict the performance of a corrugated board made from the paper sheets.
In another embodiment, the present invention relates to a new method of measuring 15 the shear strength of paper.
Throughout this specification the term “paper sheet”, or variations thereof such as a “sheet of paper” embraces any planar structure including single ply sheets and multiple ply sheets. The term “paper sheet” therefore embraces any non-corrugated sheet
0 including liner board, corrugating medium prior to being corrugated, namely a flat planar sheet, and paper layers laminated to non-paper materials such as polymeric film, metallic foil, coatings of wax and so forth.
In an embodiment the method for determining material properties of a paper sheet that 2 5 can be used in, but by no means limited to, the manufacture of corrugated board, wherein the method including:
a) supporting the paper sheet on a pair of supports that are separated by a first spacing, and applying a first force to the paper sheet intermediate of the supports to cause the paper to deflect between the supports by a first deflection, (this being the so- called three point test);
b) recording the first deflection of the paper sheet between the pair of supports that is attributable to the first force and recording the force applied;
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c) holding the paper sheet provide a fixed end of the paper, and applying a second force to the paper sheet at a free section of the paper that is located at a second spacing from the point of the paper sheet that is being held, so as to cause the paper to deflect by a second deflection, (this being the socalled two point test);
d) recording the second deflection of the paper sheet that is attributable to the second force and recording the second force applied; and
e) using the first deflection, the first force, and the first spacing in a first equation having two unknown material properties of the paper sheet, and using the second deflection, the second force, and the second spacing in a second equation having the same unknown material properties, and solving the first and second equations to determine the two unknown material properties.
The two unknown material properties may be bending stiffness and shear modulus of the paper sheet.
Measuring the first force applied includes measuring the resistive force of the sheet of paper that causes the paper sheet to fail in shear between the supports.
Measuring the first force may include measuring the resistive force of the paper sheet 25 and determining the shear strength may include measuring the maximum force applied to the paper sheet.
The maximum resistive force may be measured over a range of deflections of the paper sheet.
The maximum resistive force of the paper sheet may occur at a point where the paper sheet has deflected by a first amount and begins to delaminate.
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The ability of the paper sheet to provide a resistive force can reduce, or will reduce, once the paper has begun to fail in shear or delaminate.
The first force applied to the paper sheet may be increased to the stage where the 5 paper sheet continues to deflect without the resistive force of the paper sheet increasing, at which stage the maximum resistive force has been attained.
The first force applied to the paper sheet may include continuing to applying the force to further increasing the deflection of the paper sheet to confirm that the resistive force 10 of the paper sheet is reducing and, in turn, that the maximum resistive force of the paper sheet has occurred.
Step b) may include continuously measuring the resistive force of the paper sheet from when the paper sheet begins to deflect and until a selected end point.
In other words, the maximum resistive force of the paper sheet may occur when the paper sheet has been deflected by the first amount, and the resistive force of the paper sheet may reduce when the paper sheet is deflect by an amount beyond the first amount. Deflecting the paper sheet beyond the first amount can further increase
0 delamination of the paper sheet.
Ideally the spacing between the supports is equal to or less than 10 times the thickness ofthe paper sheet. Suitably, the distance between the supports is less than 9 times the thickness of the paper sheet, and even more ideally, the distance between 2 5 the supports is in the range of 3 to 9 times the thickness of the paper sheet.
We have found that a spacing of 1mm between the supports allows most paper sheets, of various thicknesses, to fail in shear.
Step a) may include placing the paper sheet on the support without constraining the paper sheet in a longitudinal direction of the paper sheet. The longitudinal direction of the paper sheet is the orientation or direction between the supports.
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The first force may be applied laterally to the direction of the paper sheet, and preferably perpendicular to the longitudinal direction of the paper sheet.
The first and second deflections may be function of:
a shear deflection that is proportional to a ratio of the respective first spacing, to shear modulus of the paper sheet, and a bending deflection that is proportional to a ratio of the second spacing to bending stiffness of the sheet of paper.
PL
The shear deflection ratio (<5S) may be expressed as being proportional to — .
PL3
The bending deflection ratio (¾) may be expressed as being proportional to —.
In the above ratios:
b is the width of the paper sheet, t is the thickness of the paper sheet,
D the bending stiffness, μ is a shape factor,
L is spacing between the supports, and
G shear modulus of the sheet of paper.
The paper sheet may be freely supported on the pair of supports in step a) so as to be able to bend as desired at the supporting points.
The paper sheet may be held at a point of the paper sheet, as a fixed end, such that 2 5 the paper sheet cantilevers about the fixed end in step c).
In an embodiment the method for determining material properties of a paper sheet that can be used in, but by no means limited to, the manufacture of corrugated board, wherein the method including the steps of:
a) supporting the paper sheet on a pair of supports that are separated by a spacing, applying a force to the paper sheet intermediate of the supports to cause the paper to deflect between the supports;
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b) recording the deflection of the paper sheet between the pair of supports that is attributable to the force and recording the force applied, wherein the deflection varies according to a formulae in which the deflection is a function of the force applied to the paper sheets, the spacing between the supports, and two material properties of the paper sheet to be determined as unknowns;
wherein step a) is carried out at least twice, in which the spacing between 10 the supports is different when measuring the deflection according to step b), thereby providing two sets of input data, including deflection for the respective force and spacing between the supports;
c) using the input data and the formulae to create two equations in which the 15 material properties are unknowns, and solving the equations to determine the two material properties of the paper sheet.
Step a) may include supporting the paper sheet on the supports at the same or different spacings and measuring the force required to deflect the paper sheet by a
0 known deflection (displacement). In another instance, step a) may include supporting the sheet of paper on pairs of supports that are separated by different spacings, and applying a force to the paper sheet intermediate of the supports to cause the paper to deflect between the supports. The deflection may be the same or different for step a).
5 In an embodiment the method for determining material properties of a sheet of paper that can be used in, but by no means limited to, the manufacture of corrugated board, wherein the method includes the steps of:
a) supporting the sheet of paper on pairs of supports, the pairs of supports being separated at two different spacings, and applying a force to the paper sheet intermediate of the supports to cause deflection of the paper sheet between the supports;
b) recording the force applied to the paper sheet between pairs of supports that is attributable to the deflection, and thereby provide two sets of data
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- 132015202905 18 May 2020 including data on the force and deflection for respective spacings between the pairs of supports;
c) using the data obtained from step b) in a formulae defining that the deflection (δ) as a function of:
a shear deflection that is proportional to a ratio ofthe spacing between the supports (L) to shear modulus of the sheet of paper (G), namely the shear deflection (<5S), plus a bending deflection that is proportional to a ratio of the spacing between the supports cubed (L3) to bending stiffness of the sheet paper (D), namely the bending deflection (<5S), to form two equations in which the bending stiffness (D) and shear modulus (G) are 15 unknowns and solving the two equations to determine the bending stiffness (D) and shear modulus (G).
The shear deflection ratio (<5S) may include constants relating to the width (b) of the paper sheet in a direction transverse to the spacing between the supports, thickness of 2 0 the paper sheet (t), and the force applied (P). The shear deflection ratio (<5S) may be expressed as being proportional to .
PL3
The bending deflection ratio (¾) may be expressed as being proportional to —.
5 The method may also include determining the “shear” or delamination strength ofthe paper sheet, whereby the force applied to the sheet of paper is the force required to cause the paper sheet between the supports to fail in shear. Shear failure of the paper sheets may be defined as at least partial delamination of the sheet.
In an embodiment the method for determining the shear strength of a paper sheet, wherein the method includes the steps of:
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a) supporting the paper sheet on a pair of supports that are separated by a spacing;
b) applying a force to the paper sheet intermediate of the supports to cause the 5 paper sheet to deflect between the supports;
c) measuring the force applied to the paper sheet and determining the shear strength of the paper sheet based on the force measured that causes the paper sheet to fail in shear, and the dimensions of the sample of paper.
The “shear” or “shear strength” of the paper, is a function of the force applied, or the resistive force measured of the sheet of paper, that causes the paper sheet to fail in shear between the supports. In other words, measuring the force applied to the paper sheet may include measuring the resistive force of the paper sheet against deflecting 15 between the supports subjected to the force applied to the paper sheet.
Failing in shear may be characterised by at least partial delamination of the sheet.
When determining the shear strength of the paper sheet, ideally the spacing between 2 0 the supports is equal to or less than 10 times the thickness of the paper sheet.
Suitably, the distance between the supports is less than 9 times the thickness of the paper sheet, and even more ideally, the distance between the supports is in the range of 3 to 9 times the thickness of the paper sheet.
BRIEF DESCRIPTION OF THE DRAWINGS
A preferred embodiment of the method and apparatus will now be described with reference to the accompanying figures, of which:
Figures 1a and 1b illustrate means for graphically recording the results ofthe six data sets and using the data to determine an average bending stiffness and an average shear modulus;
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Figure 2a is photograph of prototype three-point testing apparatus comprising a pair of supports in which a paper sheet is supported and a force applied via a point probe;
Figure 2b is schematic illustration of a two-point test in which a paper sheet has a fixed 5 end and a force is applied to the paper sheet at a distance to the fixed end;
Figure 3 is a graph illustrating the results of a trial including deflection measurements and force (load) applied the paper sheet according to the three-point test;
Figure 4 a and 4b are graphs illustrating the results of a trial in which the paper sheet is oriented in a machine direction (MD) between the supports according to the three-point test, and the a cross direction (CD) between the supports according to the three-point test;
Figures 5a and 5b are graphs in which the slope is proportional to the inverse of the shear modulus in the MD and CD orientations based on the data shown in Figures 4a and 4b respectively;
Figure 6a and 6b are graphs in which the slope is proportional to the inverse of the
0 bending stiffness in the MD and CD orientations based on the data shown in Figures 4a and 4b respectively;
Figures 7a, 7b and 7c are photographs of cross-sections of paper sheets that have failed according to the shear strength test;
Figures 8 is a graph illustrating the shear strength measured using the three-point test method validated against an existing test method of concora;
Figure 9a is a graph illustrating the MD shear modulus calculated according to the multi-span three point method plotted, against MD shear modulus calculated via the 1 mm span three point bend with the two-point compliance replacing all other spans; and
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Figure 9b is a graph illustrating the MD bending stiffness calculated according to the multi-span three point method plotted, against MD shear modulus calculated via the 1 mm span three point bend with the two-point compliance replacing all other spans.
DETAILED DESCRIPTION
Figure 2a is a photograph of a pair of supports, a paper sheet in position on the supports, and a probe applying a force to the paper sheet intermediate of the supports according to the three-point test method. The probe may include a load cell for measuring the applied to the paper sheet and the resistive force of the paper.
Although not shown in figure 2a, a means for the measuring the deflection of the paper sheet may also be provided.
Generally, the formulae derived from the three-point test can be expressed as set out below. The total deflection of the paper sheet, subjected to force (P), may be 15 expressed as the sum of the bending deflection ratio (¾) and the shear deflection ratio (<5S). The bending deflection (δΒ) should vary with the cube of the span (L3), whereas the shear deflection (¾) should vary linearly with the spacing between the supports (L) as.
PL3 pPL . .
^-^ = 48^4^ (eqUa,l°n1) where:
b is the width of the paper sheet, t is the thickness of the paper sheet, D the bending stiffness, 25 μ is a shape factor,
L is spacing between the supports, and G shear modulus of the sheet of paper.
The method may include performing steps a) and b) at at least two different spacings 30 and thereby enable two equations based on formulae 1 to be solved.
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The method may also include performing steps a) and b) more than twice, for example to three, four, five or six times, each with different spacings between the supports. By measuring the deflection for various parameters, it is possible to obtain shear modulus and bending stiffness. In effect, this procedure should provide an average of the shear 5 modulus and bending stiffness by repeating steps a) and b) more than twice.
Specifically from equation 1, dividing the sample compliance (<5/P) by the cube of the spacing (L3) and plotting this against the inverse of the spacing squared (1/L2), gives a slope that is proportional to the inverse of a transverse shear modulus (see Figure 1a).
Similarly, dividing the sample compliance (<5/P) by the spacing (L) and plotting this against the spacing squared (L2), gives a slope that is proportional to the inverse of an average bending stiffness (see Figure 1b).
Accordingly, method may include using data, including the measurements of the 15 deflection and the first force, to plot in a graph points for (δ/PL3) against (1/L2) , forming a straight line based on the points shown in the graph, and determining the shear modulus by calculating the slope of the line, which is proportional to an inverse of the shear modulus.
0 Similarly, the method may include using the data to plot in a graph points for (5/PL) against L2, forming a straight line based on the points shown in the graph, and determining the bending stiffness by calculating the slope of the line, which is proportional to the inverse of the bending stiffness.
Figure 2b is a schematic illustration of a two-point test in which a paper sheet has a fixed end and a force (P) is applied to the paper sheet at a distance (L) to the fixed end. The total deflection of the paper sheet, as a result of the force (P), may be expressed as the sum of the bending deflection ratio (δΒ) and the shear deflection ratio (<5S). The bending deflection (δΒ) varies with the cube of the distance (L3), whereas the shear deflection (/)s) varies linearly with the distance (L) in accordance with the following expression.
δ = δΒ + δ5 = ^- + ^ (equation 2)
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b is the width of the paper sheet, t is the thickness of the paper sheet,
D the bending stiffness, μ is a shape factor,
L is spacing between the fixed cantilever support and the point of applied load, and
G shear modulus of the sheet of paper.
It is within the scope of the present invention that three point test and the two point test may be combined to allow the bending stiffness D and the shear modulus G of the paper sheet to be determined by solving equations 1 and 2. An advantage in this combination is that three point test can be carried once, that is at one spacing between the supports. Values for the spacing between the supports (L), the force applied (P), and the deflection δ can then be applied to equation 1. The two-point test can also be carried out once, in which the length (L) of the paper sheet between the fixed end and the force (P), the force itself (P), and the deflection δ can be applied to equation 2. Equations 1 and 2 can then be solved to the provide the bending stiffness D and the shear modulus G.
In other words, in order to determine the two unknown material properties for one of the paper sheets, steps a) and b) are carried out once at one first spacing between the supports, and steps c) and d) are carried out once at one second spacing
The steps of the method and any other features described herein may be carried using any suitable apparatus, for example, by an automated apparatus in which step a) includes feeding the paper sheet over a series of spaced supports and an actuator is operable to located a probe onto the paper sheet with a load cell operably connected to the load probe to measure the forces applied to the paper sheet. Examples of existing automated machines that may be modified to carry out the method include machines known as the Lorentzen & Wettre “Autoline” and the Metso “Paper Lab”.
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In an embodiment, there is also provided an apparatus for determining material properties of a paper sheet that can be used in, but by no means limited to, the manufacture of corrugated board, the apparatus including:
a pair of supports for supporting the paper sheet a span between the supports;
a load cell for applying a force to the paper sheet intermediate of the supports to cause the paper sheet to deflect between the supports;
a displacement sensor for measuring the deflection of the paper sheet between the pair of supports that is attributable to the force, wherein the deflection is expressed by a formulae in which deflection is a function of the force applied to the paper sheets, the spacing between the supports, and two unknown material properties of the paper sheet, whereby is use, the displacement sensor measures the deflection of the paper sheet at least twice where the spacing between the supports is different thereby providing two sets of data, including deflection for the
0 respective force and spacing between the supports;
a processor in which each set of data is inputted into the formulae to create two separate equations, and the processor is operable to solve the equations and thereby determine the two material properties of the paper
5 sheet.
In another embodiment, there is also provided an apparatus for determining material properties of a paper sheet that can be used in, but by no means limited to, the manufacture of corrugated board,the apparatus including:
a pair of supports that supports the paper sheet over a first spacing between the supports;
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-202015202905 18 May 2020 a cantilever assembly that locates a fixed end of the paper sheet and from which a free end of the paper sheet extends over a second spacing of the paper sheet;
at least one load cell that is operatable to (I) measure a first force that is applied to the paper sheet intermediate of the supports to cause the paper sheet to deflect between the supports and (ii) measure a second force that is applied to the free end of the paper sheet held by the cantilever assembly;
at least one displacement sensor that is operable to (I) measure the first deflection of the paper sheet between the pair of supports that is attributable to the first force, and (ii) measure the second deflection the deflection of the paper sheet at the free end of the paper sheet that is subject to the second force; and a processor that is receives data on the first force and the second force, on the first deflection and the second deflection, and the processor is arranged to use the data solve two equations, to provide two unknown material
0 properties of the paper sheet.
The processor may be, for example, a hard wired processing chip or a computer CPU capable of running computer software.
5 The processor may receive data from the load cell or the displacement sensor.
The apparatus may also include an input device for inputting any one or a combination of: the equations, know properties of the paper sheet such as thickness and width of the paper sheet, and the first spacing and the second spacing. The equations (1) and 30 (2) mentioned herein.
The apparatus described herein may include any one or a combination of the features of the method also described herein. And vice versa, the method described herein
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-21 2015202905 18 May 2020 may also include any one or a combination of the features of the apparatus described herein.
It will be appreciated that the spacing between the supports shown in Figure 2 can be 5 reduced to spacing less than or equal to 10 time the thickness of the paper sheet. In one embodiment, the three point bending method can be applied to the paper sheet to calculate a quantitative value for shear strength. Existing methods, such as concora, can provide an empirical value that is related to the shear strength of the paper sheet, but is not quantitative value.
The shear strength of a sheet of paper can be an important factor in the failure of a paper product, including corrugated paper boards. For instance, a paper sheet is an order of magnitude stronger in compression than in shear, and is double the strength again in tension relative to compression. This means that paper is pre-disposed to fail 15 in shear relative to other modes. In addition, we have realised that paper is well adapted to three point shear testing in which the supports are spaced at a short distance on account that paper is relatively “soft” and has a “rough” surface that should conform somewhat to a loading tip by which the force is applied and the tips of the supports/load application surfaces. The roughness of the paper sheet is relative to the 2 0 thickness of the paper sheet. The sheet of paper may be relatively rough on both sides, or may be rougher on one side than the other. We have now realised that the roughness and/or softness of the paper sheet minimises the risk of stress concentrations forming at the loading/supporting structure that can occur in, for example, more rigid materials being tested.
The shear strength of the sample of paper is calculated as a function of maximum resistive force and the dimensions of the sample of paper being tested, namely the width and thickness of the sample.
In particular, the shear strength of the paper sheet may be determined or calculated as the maximum resistive force for a paper sheet having particular dimension according to the following formula:
Y = — bh where
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F is the maximum resistive force ( eg N) b is the width of the sample of the paper (eg mm) h is the thickness of the sample of the paper (eg mm)
Y is the shear strength ( eg MPa).
Examples
Shear modulus and bending stiffness
A sample of a corrugating medium was pre-conditioned overnight at 25°C, 25%Relative Humidity (RH) then conditioned at 23°C, 50%RH. The sample had a thickness of 259 pm, and a basis weight 171 gsm. The sample was cut in approximately A4 sized sheets. The A4 sheets were stored under load at 50%RH to flatten the slight mechanical curl from being wound on a roll in the machine direction (MD).
A purpose built aluminium three point bend jig, as shown in Figure 2a, was fitted to an Instron 5500R universal testing machine with 100N load cell operating at 10 mm/min crosshead speed. Crosshead displacement was used as a measure of beam midpoint deflection (5 ) and logged every 4 pm, along with load (P) and test duration. A total of four test spans were used (3.5mm, 6mm, 9mm and 12mm) giving span-to-thickness
0 ratios (L/t) ranging from 14 to 46.
A typical load-deflection (P-5) curve is shown in Figure 3 (blue line) for a cross direction (CD) using a 3.5mm spacing (L). A centred 0.1mm (25 point) moving linear least squares fit was used to calculate the slope (red line) at all points along the load25 deflection curve. The sample compliance (5/P) was calculated as the inverse of the maximum slope (red circle, solid black line) and used for further analysis.
Typical load-deflection curves in the MD and CD for the four different spans are shown in Figures 4a and 4b. Note that, although the maximum loads for the MD and CD are similar, the CD test pieces are twice as wide as the MD test pieces (50mm c.f. 25mm).
Figures 5a and 5b illustrate the average test compliance for each span to determine MD and CD transverse shear modulus. Figures 6a and 6b illustrates the average test
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-232015202905 18 May 2020 compliance for each span to determine MD and CD bending stiffness for four different deckle positions.
Table 1 summarises the results in the Figures 5a, 5b, 6a and 6b.
Table 1.
| Average Shear modulus MD (MPa) | Average Shear modulus CD (MPa) | Average Bending stiffness MD (mNm) | Average Bending stiffness CD (mNm) |
| 4 | 9 | 5.6 | 2.6 |
A standard (off-the-shelf) industry two-point bend unit was set to 10mm bending length 10 (equivalent to 20mm for three-point bend) and bending rate of 57sec (equivalent threepoint bend cross-head speed of approximately 52mm/min). Standard dimension twopoint bend samples were used (38mm width, 76mm total length). The sample compliance (5/P) measured from the two-point bend test was used in conjunction with the compliance measured from the previous 1mm short span three-point bend test to 15 calculate both the Shear modulus and bending stiffness of the sample.
Figure 9a is a graph illustrating the MD shear modulus calculated according to the multi-span three point method plotted, against MD shear modulus calculated via the 1mm span three point bend with the two-point compliance replacing all other spans.
Figure 9b is a graph illustrating the MD bending stiffness calculated according to the multi-span three point method plotted, against MD shear modulus calculated via the 1mm span three point bend with the two-point compliance replacing all other spans
The shear moduli were calculated, that is, an inverse of the slope of the linear best fit from Figure 9a. The slope ofthe plots is dominated by the short 1mm span data. The plot is highly insensitive to fluctuations in the two-point test results. We assume that this is the result of the relatively long length of the paper sample tested according to the two point test and subsequent reduction in shear stress.
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The bending stiffness was calculated from the inverse of the slope of the linear best fit from Figure 9b. The slope of the plot is dominated by the two point test results. The slope of the plot is highly insensitive to fluctuations in the three-point test data from 1mm span.
By combining three-point test data, for example 1mm spans, and two-point test data, for long lengths such as 20mm, equations 1 and 2 can be used to provide equally good values of the shear modulus, compared to just using the previous trials of the multispan three point test.
Shear strength
Three samples of multiply paper board have been tested using the three-point test method in which the spacing between the supports is 1mm and the force applied increased until failure of the paper substrate. As described above, the shear strength 15 was measured using the apparatus shown in Figure 2 which includes a 100N load cell for measuring the resistive force of the paper sheer. The load cell was operated at a speed of 10 mm/min which deflects the paper sheet and continuously reads the resistive force of the paper sheet. The supports were spaced at a spacing of approximately 1mm.
Five samples were tested, one sample being a “starch off sample”, which had no added starch content, another sample was a “bad sample” which had delaminated during corrugating in the box plant, and the final three samples were “good samples” having the required starch application. The samples had a weight or grammage of 2 5 approximately 100 gsm and the thickness of approximately 150pm.
Figures 4a, 4b and 4c plot the resistive force measurements (N) of the paper sheet against the deflection of the paper sheet. Extension of the paper sheet in Figure 4c is the same deflection. Each line on the graph represents the continuous measurements 30 of the load cell for particular spans/spacings between the supports. In the case of
Figures 4a and 4b, the supports were separated by spacings of 3.5mm, 6mm, 9mm and 12mm. In the case of Figure 4c, the supports were separated by spacings of 1mm, 3mm, 6mm, and 12mm. The paper had a weight of 100 gsm and was approximately 150 pm. We concluded that in order to best determine the maximum
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-252015202905 18 May 2020 shear strength of the paper sheet, was better to maintain the spacing between the support being the on the range of the 2 to 9 time the thickness of the paper sheet. Moreover, a spacing of 1mm enables accurate shear strength measurements to be obtained for a broad range of paper grammages.
Figure 4d plots stress against displacement for a 1mm span/spacing between the supports for various paper samples. Some has a grammage of 100grm, and other had a grammage of 112 gsm.
All samples appeared to fail in shear with delamination of the middle layers of the sheet. Figures 7a, 7b and 7c are photographs of the cross-sections of the three sample types and the arrows in the photographs point toward sections of the sample where the plies delaminated, i.e. failed.
The ‘starch off’ and ‘bad’ samples had MD shear strengths less than 1.77 MPa, while the ‘good’ samples had MD shear strengths above 1.93 MPa.
In order to validate the test method, the three samples, were then assessed against an existing test method, specifically the Concora Medium Test (CMT).
Figure 8 graphically illustrate the different values of shear strength comparison obtained according to the three-point beam test and the Concora test method.
It was seen that there was a strong correlation (r2=98%) between MD Short Beam 25 Shear strength and concora. An advantage of the preferred test method is that threepoint test method can be carried out using automated machinery, which is not possible in the case of the Concora test method.
Moreover, an advantage of the preferred method is that shear modulus, bending 30 stiffness and shear strength can each be measured in a single automated test action, and thereafter used to the predict performance characteristics of corrugated board and corrugated board products. These are important benefits as prior to this invention it has not been possible to easily measure these specific properties for a sheet of paper, particularly to measure these properties using a mechanism which is entirely suitable
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-262015202905 18 May 2020 to automated or semi-automated paper testing lines sometimes used in paper mills to monitor the quality of the paper produced.
Furthermore, the measure of these intrinsic engineering properties can be used to 5 support engineering modelling of paper and corrugated board.
Those skilled in the art of the present invention will appreciate that many variations and modifications may be made to the preferred embodiment without departing from the spirit and scope of the present invention.
In the claims which follow and in the preceding description of the invention, except where the context requires otherwise due to express language or necessary implication, the word “comprise” or variations such as “comprises” or “comprising” is used in an inclusive sense, i.e. to specify the presence of the stated features but not to 15 preclude the presence or addition of further features in various embodiments of the invention.
Claims (5)
1. A method for determining material properties of a paper sheet, the method including:
5 a) supporting the paper sheet on a pair of supports that are separated by a first spacing, and applying a first force to the paper sheet intermediate of the supports to cause the paper sheet to deflect between the supports by a first deflection;
10 b) measuring the first deflection of the paper sheet between the pair of supports that is attributable to the first force and measuring the first force applied, wherein the deflection of the paper sheet during step a) can be expressed as the sum of the bending deflection ratio (δΒ) and the shear deflection ratio (<5S) according to equation 1:
PL3 pPL S = Sl,+Ss = WbD + lGbt (equation 1) wherein:
P is the first force, b is the width of the paper sheet,
2 0 b) recording the force applied to the paper sheet between pairs of supports that is attributable to the deflection, and thereby provide two sets of data including data on the force and deflection for respective spacings between the pairs of supports;
25 c) using the data obtained from step b) in equation 1 defining the deflection (δ) as a function of:
a shear deflection that is proportional to a ratio of the spacing between the supports (/_) to shear modulus of the paper sheet (G),
30 namely the shear deflection ratio (<5S), plus a bending deflection that is proportional to a ratio of the spacing between the supports cubed (L3) to bending stiffness of the paper sheet (D), namely the bending deflection ratio (<5S):
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PL3 μΡΕ e = e,s + Ss = 4SbD + 4Gbl (equation 1) wherein:
P is the force, b is the width of the paper sheet,
2 0 a processor that receives data on the first force and the second force, on the first deflection and the second deflection, and the processor is arranged to use the data to solve equations 1 and 2, to provide the bending stiffness (D) and shear modulus (G) of the paper sheet.
25 13. The apparatus according to claim 12, wherein the apparatus includes an input device for inputting any one or a combination of: the equations, known properties of the paper sheet such as thickness and width of the paper sheet, the spacing between the supports, and the spacing between the fixed cantilever support and the point of applied load.
14. A method for determining material properties of a paper sheet, wherein the method includes the steps of:
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a) supporting the paper sheet on a pair of supports that are separated by a spacing, applying a force to the paper sheet intermediate of the supports to cause the paper sheet to deflect between the supports;
5 b) recording the deflection of the paper sheet between the pair of supports that is attributable to the force and recording the force applied, wherein the deflection varies according to equation 1 in which the deflection is a function of the force applied to the paper sheet, the spacing between the supports, and bending stiffness (D) and shear modulus (G) of the paper sheet to be
10 determined as unknowns, wherein the deflection of the paper sheet during step a) is expressed as the sum of the bending deflection ratio (¾) and the shear deflection ratio (<5S) according to equation 1:
PL3 gPL S~S‘ + Ss-A8bD + Wbi (equation 1)
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15. The method according to claim 14, wherein step a) includes supporting the paper sheet on the supports at the same or different spacings and measuring the force required to deflect the paper sheet by a known deflection, namely a predetermined
5 displacement.
16. The method according to claim 14, wherein step a) includes supporting the paper sheet on the supports that are separated by different spacings, and applying a force to the paper sheet intermediate of the supports to cause the paper sheet to deflect
10 between the supports.
17. A method for determining material properties of a paper sheet, wherein the method includes the steps of:
15 a) supporting the paper sheet on pairs of supports, the pairs of supports being separated at two different spacings, and applying a force to the paper sheet intermediate of the supports to cause deflection of the paper sheet between the supports;
2 5
2. The method according to claim 1, wherein measuring the first force applied includes measuring the maximum resistive force of the paper sheet.
2 0 t is the thickness of the paper sheet,
D is the bending stiffness of the paper sheet, μ is the shape factor of the paper sheet, L is the first spacing between the supports, and G is the shear modulus of the paper sheet;
c) holding the paper sheet so as to provide a fixed end and a free section, and applying a second force to the paper sheet at the free section of the paper sheet that is located at a second spacing from the fixed end, so as to cause the paper sheet to deflect by a second deflection;
d) measuring the second deflection of the paper sheet that is attributable to the second force and measuring the second force applied, wherein the
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-282015202905 18 May 2020 deflection of the paper sheet during step c) can be expressed as the sum of the bending deflection ratio (δΒ) and the shear deflection ratio (<5S) according to equation 2:
(equation 2) wherein:
P is the second force, b is the width of the paper sheet, t is the thickness of the paper sheet,
D is the bending stiffness of the paper sheet, μ is the shape factor of the paper sheet,
L is the spacing between the fixed cantilever support and the point of applied load, and
G is the shear modulus of the paper sheet;
e) using the first deflection, the first force, and the first spacing in equation 1, and using the second deflection, the second force, and the second spacing in equation 2, and solving equations 1 and 2 to determine the bending stiffness (D) and shear modulus (G) of the paper sheet.
3. The method according to claim 1 or 2, wherein measuring the first force applied includes measuring the resistive force of the paper sheet that causes the paper sheet to fail in shear between the supports.
4. The method according to any one of claims 1 to 3, wherein the first force applied to 30 the paper sheet can be increased to the stage where the paper sheet continues to deflect without the resistive force of the paper sheet increasing, at which stage the maximum resistive force has been attained.
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5. The method according to any one ofthe preceding claims, wherein the paper sheet is freely supported on the pair of supports in step a) so as to be able to bend as desired at the supporting points.
5
6. The method according to any one of the preceding claims, wherein the first spacing between the supports is equal to or less than 10 times the thickness of the paper sheet.
7. The method according to any one of claims 1 to 5, wherein the first spacing between
10 the supports is in the range of 3 to 9 times the thickness of the paper sheet.
8. The method according to any one ofthe preceding claims, wherein the first spacing between the supports is in the range from 0.5 to 1.5mm.
15
9. The method according to any one of claims 1 to 7, wherein the first spacing between the supports is 1.0mm.
10. The method according to any one ofthe preceding claims, wherein in order to determine the bending stiffness and shear modulus for one of the paper sheets, steps 2 0 a) and b) are carried out once at one first spacing between the supports, and steps c) and d) are carried out once at one second spacing.
11. The method according to any one of the preceding claims, wherein the method includes determining the shear strength of the paper sheet based on the first force of 25 step b) being a maximum resistive force for a paper sheet according to the following formula:
Y = — bh where
F is the maximum resistive force of the paper sheet,
30 b is the width of the paper sheet, h is the thickness of the paper sheet, and
Y is the shear strength of the paper sheet.
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12367277_1 (GHMatters) P98597.AU.1 18/05/20
-31 2015202905 18 May 2020 δ = δΒ + 5S = — + — (equation 2) ΰ 5 3bD Gbt \ 'Λ / wherein:
5 Ρ is the second force, b is the width of the paper sheet, t is the thickness of the paper sheet, D is the bending stiffness of the paper sheet, μ is the shape factor of the paper sheet,
10 L is the spacing between the fixed cantilever support and the point of applied load, and
G is the shear modulus of the paper sheet;
at least one displacement sensor that is operable to (i) measure the first
15 deflection of the paper sheet between the pair of supports that is attributable to the first force, and (ii) measure the second deflection of the paper sheet at the free end of the paper sheet that is subject to the second force; and
5 t is the thickness of the paper sheet,
D is the bending stiffness of the paper sheet, μ is the shape factor of the paper sheet, L is the first spacing between the supports, and G is the shear modulus of the paper sheet;
to form two equations in which the bending stiffness (D) and shear modulus (G) are unknowns and solving the two equations to determine the bending stiffness (D) and shear modulus (G).
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| AU2014904264A AU2014904264A0 (en) | 2014-10-24 | A method and apparatus | |
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Citations (3)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| US5171403A (en) * | 1989-11-07 | 1992-12-15 | Measurex Corporation | Method for determining the bending stiffness of a moving sheet |
| JPH063236A (en) * | 1992-06-24 | 1994-01-11 | Fujitsu Ltd | Measuring device for young's modulus and measuring method for young's modulus |
| EP1787102B1 (en) * | 2004-08-19 | 2013-12-11 | New Zealand Forest Research Institute Limited | Method and apparatus for testing of shear stiffness in board |
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2015
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Patent Citations (3)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| US5171403A (en) * | 1989-11-07 | 1992-12-15 | Measurex Corporation | Method for determining the bending stiffness of a moving sheet |
| JPH063236A (en) * | 1992-06-24 | 1994-01-11 | Fujitsu Ltd | Measuring device for young's modulus and measuring method for young's modulus |
| EP1787102B1 (en) * | 2004-08-19 | 2013-12-11 | New Zealand Forest Research Institute Limited | Method and apparatus for testing of shear stiffness in board |
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