Characterisation of property variations in paperboard samples

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Characterisation of property

variations in paperboard samples

SOFIA WRETSTAM

KTH

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Investigation of variations in thickness, surface roughness and tensile properties in paperboard.

by

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Abstract

In today’s paper and board production, quality control is made on a single cross direction (CD) sample from each tambour. As several different properties are analysed, only a limited number of measurement results are obtained for one property. Therefore, the measurement results might not be representative for the properties of the entire width of the tambour. The first objective of the project was to investigate variations of thickness, surface roughness and mechanical properties with a much higher resolution and number of measurements. The results of the measurement were compared with the routine quality control of the mill. The second objective of the project was to evaluate the influence of the wire shake unit in the centre ply on the properties of the produced board. The measurements were performed on Iggesund paperboard samples.

The high-resolution measurements were performed using the STFI structural thickness measurement device, an OptiTopo topography measurement device and a modified Autoline device at RISE Bioeconomy. The statistical evaluation of the results was performed in Matlab. Standard deviation, local variance and a frequency analysis were calculated for the thickness measurements. Only standard deviation was considered for the topography data. For the mechanical properties, the distribution was evaluated using the Weibull distribution, since the results had a single-sided distribution. In addition, the properties were analysed as a function of their location, for example to identify deterministic deviations in cross direction.

The results of the first part of the project showed that the everyday control conducted in Iggesund is sufficient for most of the properties. Greatest difference was found at the edges of the samples, where Iggesund standard quality control does not detect a major variation in properties, as no measurements are performed that close to the edge of the web. For example, at one edge, the high frequent measurements showed a significant drop in thickness which were not detected with the everyday quality control.

In the second part of the project, the effect of a shake unit on the paper properties was evaluated. Here it was seen that the thickness variation were reduced, which also can be interpreted as an improvement of formation in the centre ply of the paperboard. As for the surface roughness a slight improvement was found. Also for the mechanical properties, the shake unit appeared to improve the uniformity of the product.

Keywords: Paperboard, variability, property, tensile strength, surface roughness, thickness,

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Sammanfattning

I dagens pappers- och kartongproduktion görs kvalitetskontroll på en enda tvärremsa (CD) från varje tambour. Eftersom flera olika egenskaper analyseras, erhålls endast ett begränsat antal mätresultat för en egenskap. Därför är informationen begränsad och kanske inte representativ för hela bredden av tambours egenskaper. Projektets första mål var att undersöka variationer i tjocklek, ytjämnhet och mekaniska egenskaper med mycket högre upplösning och antal mätningar. Resultaten av mätningen jämfördes med brukets rutinmässiga kvalitetskontroll. Det andra syftet med projektet var att utvärdera effekten av viraskaken på egenskaperna hos den producerade kartongen. Samtliga mätningar utfördes på kartongprover från Iggesunds Bruk.

Mätningarna med hög upplösning utfördes med hjälp av en STFI-mätare för strukturtjocklek, en OptiTopo-enhet och en modifierad L&W Autoline-enhet. Den statistiska utvärderingen av resultaten utfördes i Matlab. Standardavvikelse, lokal variation och en frekvensanalys beräknades för tjockleksmätningarna. Endast standardavvikelse utvärderades för ytråhetsdata. För de mekaniska egenskaperna utvärderades fördelningen med hjälp av Weibull-fördelningen, eftersom resultaten visade ett ensidigt beteende. Dessutom analyserades egenskaperna som en funktion av deras placering, till exempel för att identifiera deterministiska avvikelser i tvärriktningen.

Resultaten av projektets första del visade att den dagliga kontrollen i Iggesund är tillräcklig för de flesta egenskaperna. Den största skillnaden hittades vid provets kanter, där Iggesunds standardkvalitetskontroll Missar stora variationer för vissa egenskaper, eftersom inga mätningar utförs i det området på produkten. Vid ena sidan av nätverket visade de högfrekventa mätningarna en betydande minskning av tjockleken.

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Acknowledgements

This thesis was performed as a collaboration between Holmen AB and RISE Bioeconomy as the final examination of the Master of Science in Macromolecular materials at the Royal Institute of Technology in Stockholm, KTH. During the project I have gained a great understanding and a better knowledge about the pulp and paper industry. Furthermore, I have gained understanding about how research and industry cooperates and in the same time developed my abilities to work with different kinds of people to reach the goals in the project. Everyone I have interacted with in the course of the project has in every way assisted and supported me in an admirable way. Therefore, I would like to thank everyone in the staff at Iggesund and RISE Innventia who helped me during this time.

I want to give a special thanks to Mikael Lindström (KTH) and Hannes Vomhoff (Holmen Development) for the opportunity to do this project and for their important help and support during the whole process.

Many thanks to Thomas Grahn at RISE Bioeconomy for all the shared knowledge and guidance throughout my time at RISE.

Special thanks to Brita Timmermann at Iggesund who during the work has helped me with samples, knowledge, and providing guidance concerning the report.

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List of abbreviations

Table 1: List of abbreviations

Abbreviation Meaning

CTMP Chemi-thermomechanical pulp

TMP Thermomechanical pulp

CD Cross direction

MD Machine direction

DIN Deutsche Industrie Norm

TAPPI Technical Association of the Pulp and Paper Industry

SCAN Scandinavian Pulp, Paper and Board Testing Committee

ISO International organization of standardization

PPS Parker Print Surf

TEA Tensile Energy Absorption

FOA Fibre orientation anisotropy

TS Top side

BS Bottom side

OSD OptiTopo Surface Deviation

L&W ABB Lorentzen & Wettre

List of symbols

Table 2: Table of symbols, meaning and units of the quantity.

Symbol Meaning Unit

σw _{Tensile index} _Nm/kg FT Tensile force N b Width m w Grammage kg/m2 N Crowding factor Cv Volumetric concentration L Fibre length m d Fibre diameter m µ Mean value σ Standard deviation Cv Coefficient of variation

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1 Introduction

1.1 Background

Pulp and paper industry is one of the largest process industries in the world and the products from this industry is all around us in our daily life, packaging our food and goods but also for distributing information through newspapers and books. Generally, the raw material for paper products in the Nordic countries is softwood and hardwood, which consists of cellulose, hemicellulose, lignin and extractives. Cellulose is the component contributing with strength since it is a semi-crystalline polymer. Hemicellulose is amorphous and works as a binder between the components and plays an important role for the final properties of a paper. Lignin is the third major component and consists of phenolic-polymers. Lignin is often removed due to the tendency of yellowing as it interacts with light. Paper products are produced via pulping, a wide range of techniques, which leads to numerous products and applications. Paperboard, which is the main focus in the study, usually ranges from 180 g/m2_{up to 400 g/m}2 _in grammage. With the main application of packaging and information spreading, printability and folding properties are crucial. Some of the most important properties to monitor when producing paper board are: tensile strength, stiffness, optical properties and surface roughness. Therefore, these will influence the final product printability and folding behaviour, but also its processability for customers.

1.2 Pulp preparation

Pulping starts with a stem of the tree, debarking it and chipping it into smaller pieces, so called chips, these can be introduced to the fibre line in the mill (1). There are two main types of pulps; chemical and mechanical pulp. In mechanical pulping the fibres are defibrillated by mechanical force, and therefore all components remain in the pulp. During chemical pulping the wood chips are delignified, meaning that most of the lignin and a smaller share of hemicellulose are removed. This is performed by oxygen delignification and cooking chemicals which mainly consist of sodium hydroxide and sodium sulphide, also called white liquor. This specific pair is also called Kraft chemicals. This is the most common pulping technique used for paperboard since it provides preferable mechanical properties. The aim of the pulping is to produce a bright and strong pulp that can be feed to the paper machine in a homogeneous mixture of fibres, additives and water. To improve the mechanical properties further beating is performed. Here the fibres are mechanically treated between two refiner plate, and the more flexible fibres will form a stronger fibre network with stronger fibre bonds (1).

1.3 Paper forming

When the pulp has been prepared, it is fed to the paper machine, where the forming of a fibrous network, dewatering and drying are the main steps. One of the most important sections in the paper machine is the headbox. Its main purpose is to evenly distribute the fibres on the wire. How successful the distribution is will greatly influence the mechanical properties of the product, and in particular how the properties vary over the produced area. When the fibres have been deposited on the wire, dewatering and drying is performed, starting with the drainage of the redundant water which occurs at the dewatering section. In the press section, water is forced out of the network using mechanical forces. In the press section the mechanical properties are enhanced due to the densification of the network, consequently leading to more fibre-fibre interactions. Finally drying with heat is utilized for the last percentages of water. This is the most energy demanding part of the paper machine.

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Figure 1: Schematic of a paper machine (2).

During the drying, the paper shrinks in all three directions of the network due to the removal of water out of the fibres. This effect is greatest in the cross direction, especially at the edges of the web. The center parts is exposed to restrained drying while the edges are freely dried. Thus, extensive shrinkage may occur at the outer regions of the web. Most commonly the shrinkage is a few percent, but unevenly distributed over the cross direction, affecting several physical properties related to the fibre-fibre joints (3).

1.4 Variations and control

As an effect of the increasing demand on process control, several parameters and properties are measured online during production. Better control gives a larger ability to correct and resolve troubles that arises in the production, making it possible to deliver paperboard with a higher and more even quality. The goal is to produce a homogeneous product which has the same properties over the entire produced area. Thus, it is important to detect and control variations in both MD and CD. These online measurements are performed by a scanning sensor moving in a zig-zag pattern across the machine, providing information of the product properties continuously (4). This transverse movement provides a combination of cross direction (CD) and machine direction (MD) information(see definition in Figure 2) , which complicates the separation of CD variations and MD variations.

Variations both in MD and CD (see Figure 2) are of interest when evaluating process induced variations as well as random ones. Machine direction variations are an effect of variations in the stock if they occur randomly, whereas frequently appearing deviations in MD arise from process variations in the approach flow system, for example pressure pulsation of pumps. In cross direction deviances arise due to the distribution of pulp onto the wire from the headbox or are induced during the drying procedure in the paper machine.

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2 Objective of the thesis

Since the production rate is very high, the techniques used to control each tambour needs to be fast and easy but at the same time accurate enough to ensure sufficient validation. Thickness is measured continuously online, but many other properties such as strength or bending properties can only be measured after the production on manually taken samples. This both increases the reaction time considerably and limits the number of measurements that can be performed. Furthermore, alternative production processes can be used the make the product more even. These structural changes occur on a small length scale, which can only be detected by a measurement method that has a higher spatial resolution than the standard measurement method.

The present project had two parts based on the following two objectives:

(1) Investigate paperboard samples with high resolution measurement methods and compare with today’s standard measurement method.

(2) Quantify the influence of the newly installed shake unit at the breast roll at Iggesunds Bruk and investigate the influence on the product variations.

The properties investigated were the tensile strength, thickness and surface roughness for several samples of paperboard. The property variation was analysed in both machine direction (MD) and cross direction (CD) of the board machine.

In the first part, the following questions were in focus:

• How much do the properties (tensile strength, thickness and surface roughness) vary in paperboard products?

• How does the high-frequency measurements compare to standardized measurements? • Is the result obtained industrially comparable to lab-scale results?

Therefore, several tests on paperboard with different basis weights and qualities were performed to obtain statistically correct results.

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3 Technical background

A common quality control equipment in industry is the ABB L&W Autoline device, which is an automatic system for paper testing that is used in the production and feeds information to the mill by the results provided. Its advantages are the fast measurements and the broad number of properties that can be controlled. In general, 20 positions across of the tambour are tested for selected properties, giving a sense of the properties of the entire tambour. For each property in question a module can be built-in to the instrument and the software program can be modified to suit a specific costumer (5). The measurement results are the core of the quality assessment of the produced product, and therefore the most important information for the quality control of the entire process.

3.1 Grammage

Grammage is a property that is widely used when characterizing paper and board products. It is defined as the mass per unit area and often spans from 12 gm-2_{to 1000 gm}-2_{(6). Measuring} the grammage is done by weighing a specimen of known area (7). Strength properties are often related to the grammage of the sheet, a higher grammage often provides a higher strength.

3.2 Thickness

Paper which is a porous structure, is compressible and therefore the thickness measurements are preferred to do as little impact as possible on the network measured. Therefore, in standars methods, a larger area is measured at the same time to minimize the compression; this can be performed with a micrometre device, applying a constant load over a pre-set area. The micrometre method is the most common method and is also the module often found in the Autoline. Measurements are performed by a pressure head moving towards the surface and registering the distance between the upper and lower head, that is in contact with the sample. The method is considered accurate and the indication errors are considered below ±1 µm or 0.1 % of the readings. The area measured with the micrometre is 2 cm2_{, which does not allow a} study of the smallest variations of the thickness, i.e. caused by flocculation. Since the area of the heads is quite large, the value will be a mean thickness of an area (4) (8).

In addition, the STFI-structural thickness method is available (Figure 3). Two spherical probes, each with a radius of 2 mm are moving over the surface while the sample is transported forward by feeder wheels. The measuring probes register the thickness at a constant load along the entire sample at a pre-set rate (9). The latter technique is considered to be the most accurate since it is an average, including both craters and hills and therefore measure the true thickness of the paperboard (4) (10) (11)].

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Another aspect of the thickness measurements is to analyse the thickness variance of a product. This is interesting since the thickness is assumed to be related to the material distribution in the product. For a multi-ply board grade with a much higher grammage in the middle ply, the thickness variation can be assumed to be primarily dependent on the material variation in the middle ply. If a lowering of the variance in the thickness measurements is found, this can be an effect of a better formation, i.e. a more even material distribution, which is desirable since it would improve properties such as tensile strength and surface roughness.

3.3 Surface roughness

One parameter that is important for the printability of a paper is the roughness of the surface. Since the network is not completely uniform the fibres will form a certain roughness that needs to be quantified. To measure the surface roughness there are several methods such as OptiTopo, Bendtsen, PPS or Sheffield instruments.

One of the most common techniques in the industry is the air-leak methods including Bendtsen

(Figure 4) and PPS. The instrument generates a constant air pressure inside the ring and the

Bendtsen surface roughness is estimated depending on the flows of air that can pass through the contact land. For a sample with a rougher surface, more air escapes to the surrounding atmosphere. The value of the surface roughness is measured in ml/min (13).

Figure 4: Principle of Bendtsen method.

More recently the OptiTopo has been developed for the characterisation of the surface topography of paper and board samples (Figure 5). It is a non-contact technique that utilizes light sources illuminating from opposite sides, and two images are combined to obtain results of the topography of the sample. It analyses the height map and can therefore relate darker areas to the surface roughness.

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Figure 5: Image generation for the OptiTopo measurements. (16)

The OptiTopo expert software is used to filter the different bands, scale of the surface variations, and evaluate all bands separately. The three bands OptiTopo Surface Deviation (OSD) (0.063-0.5 mm), mid- scale ((0.063-0.5-2mm) and large-scale variations (2-8 mm) are the standard setting using the software. Additionally, user-defined intervals can be chosen and evaluated based on requirements. Usually the OSD value is related to the printability of the surface since such small variations cannot be reached by the print press or cylinder, causing non-printed spots (16).

3.4 Strength properties

Mechanical properties are often very important for the utilization of a material and for paperboard it is no exception. Paper is an anisotropic material which means that the properties are strongly dependent on the direction of stress on the sampleThe properties are tested both in MD and CD, as in-plane properties are strongly related to the fibre orientation and therefore both directions are interesting for packaging and printing purposes (17). Since pulp fibres are sensitive to moisture and temperature, the mechanical properties of the produced paper and board is also influenced by temperature and moisture. As the RH increases the tensile strength decreases and the elongation increases. Therefore, the evaluation of the properties must be conducted in a controlled climate (Figure 6).

Figure 6: Strength properties of paper at different humidity (12).

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consequently the location of the fracture must be monitored (10). Despite this, the strip geometry is most commonly used since it is more convenient. Other factors that may impose uncertainties are slipping during the test, and therefore the alignment and a relaxed sample is crucial in the setup of the testing (18).

3.4.1 Tensile strength

The setup for a standard in-plane tensile test consists of two clamps pulling the specimen in opposite directions at the same time as the drag force applied is registered. At the point of fracture, the maximum tensile stress is obtained, defined as the tensile strength of the specimen. The strain obtained at the point of fracture can be defined as the stain at break (17). These values are related to the inter-fibre bonds which each fibre contributes to, which are strongly affected by the water content of the fibre matrix and the number of fibres in the network (6). As mentioned earlier, paper is not homogeneous, and additionally it is porous, which affects the value of tensile properties. Since the fibre network strength is related to the number of fibres per unit area, the number of fibre joints is important for the strength properties. To minimize the influence of fibre density on the specific strength is often used for a paper sample, relating the tensile force to the width and basis weight of the specimen. This means using tensile index (Equation 1) instead of tensile strength, which also allows conclusions to be drawn for results from sample with different grammages (6). For paper, values are typically in a range between 10 to 100 Nm/g. This value is a function of the elongation rate. Paper becomes stronger at higher elongation rates (19).

Equation 1: Tensile index per unit width and grammage

𝜎"#=

𝐹"

𝑏𝑤 * 𝑁𝑚

𝑔 .

Furthermore, the Autoline is utilizing a different method of tensile testing since space is limited. Instead of pulling the sample in opposite directions, a small cylinder pushes up against the paper, causing a small deformation in the z-direction, which also implies an elongation of the sample. This, according to L&W, does not affect the results and the method can be compared to standardized mechanical testing (5).

3.4.2 Tensile Energy Absorption (TEA)

Tensile energy absorption values are the area under the stress-strain curve, which is the energy needed to deform the sample. (Equation 2) The TEA value is useful to accurately determine the toughness of a sample, an important consideration in paperboard production.

Equation 2: Tensile energy adsorption

𝑊"#= 𝑊"/ 𝑤 * 𝐽 𝑘𝑔. 3.5 Variability

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is performed in frequent time intervals assuring that the instrument is still reliable, is required (5).

3.5.1 Statistical evaluation

To be able to correctly interpret the data given by the experiments, statistical tools are applied to the data giving information about trends, outliers and providing a way of comparing the results to each other. The most common statistical tools to quantify variations in a set of data are standard deviation, variance and coefficient of variation.

First, Equation 3 is used to calculate the standard deviation for all data sets. Secondly, to further describe the outcome of an experiment, the variance of the data is interesting to quantify and is calculated by taking the square of the standard deviation (Equation 4).

Equation 3: Definition of standard deviation Equation 4: Definition of variance.

𝜎 = 2∑:6;< (𝑥6− 𝑥)9 𝑁

𝜎9₌∑:6;< (𝑥6− 𝑥)9

𝑁

Since samples of various grammage are evaluated the spreading is normalized by the mean, giving the coefficient of variation, also called relative standard deviation. The coefficient of variation is calculated by Equation 5 (20).

Equation 5: Coefficient of variation. Normalizing the standard deviation, 𝝈 , by the mean, 𝝁.

𝐶A=

𝜎 𝜇

The standard deviation gives an indication of how spread the data are compared to the mean, a low standard deviation implies small spreading from the mean (Figure 7).

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3.5.2 Frequency analysis

For the STFI-structural thickness measurements the amount of raw data becomes very high and requires filtering and processing. The goal with this is to find a frequency at which the thickness varies over the length of the sample. By transferring a position dependent signal to a frequency function, the variations in the sample can be assigned some sinusoidal and cosine wavelengths. This conversion is done by the FFT function in Matlab, which computes the Fast Fourier transform of a vector by implementing the Fourier transform in Equation 6. Filtering and sorting the time dependent signal into domains of individual simple sine and cosine functions (22).

Equation 6 : Fourier transform used in Matlab function FFT.

𝒀(𝒌) = E 𝑿(𝒋)𝑾_𝒏(𝒋J𝟏)(𝒌J𝟏)

𝒏 𝒋;𝟏

𝒘𝒉𝒆𝒓𝒆: 𝑾_𝒏= 𝒆J𝟐𝝅𝒊𝒏

In order to identify possible sources for property variation, it is interesting to look for periodic variation in properties that can be linked to variations in the process. Variations in CD occur on a much longer time scale than the ones in MD. Variations in the MD can be seen as time-dependent fluctuations in the process while CD variations are more constant (23).

3.6 Mechanisms causing material property variations

Material property variations can have their origin from numerous sources in the paper process. Every parameter from the colloidal stability of the pulp to the mass flows in the stock preparation is essential when searching for process variations. Some of the deviations arise from flocculation, flow instabilities, gradient and streakiness as the paper is formed on the wire (24).

3.6.1 Flocculation

Fibre flocculation is a phenomenon when fibres mechanically entangles in the stock. These forms since collisions between fibres occur frequently which leads to aggregation. These flocs are commonly occurring, and larger flocs should be dispersed when entering the headbox. Even though the headbox is highly optimized to dilute and disintegrate the flocs, fibres will agglomerate and flocs will remain when the stock is deposited onto the wire. The formation of flocculation depends on the crowding factor, fibre length, fibre flexibility, and concentration of the suspension. The crowding factor is a measurement of number of fibres present in a spherical volume, set by the length of a single fibre. The crowding factor, N, is determined by how many fibres present in a spherical volume, cv, the length of the fibres present, L, and their diameter, d and is calculated according to Equation 7.

Equation 7: Crowding factor equation quantifying the tendency of fibers to flocculate based on process conditions and fibre morphology.

𝑁 =2 3𝑐AW

𝐿 𝑑Z

9

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be dispersed and will cause variations in the formation and network of the paper. These variations of formation, i.e. the variation in the local grammage, are expected to be encountered in the measurement of the local thickness, linking the variation in thickness to formation. A table of other variations, their origin and their interpreted wavelength can be seen in Figure 8 (4).

Figure 8: Table of how the wavelength in grammage variations is related to process conditions (4).

There are models on how to interpret the effect of flocs when considering paper strength, such as the chain model (Figure 9), where the weakest link between element will limit the paper strength. There are several reasons for weak spots in the network, but formation is one of them. The bundle model (Figure 10) is another approach, where the elements are acting parallel using both global and local stresses to predict the behaviour and the maximum strength that the network can resist (25).

Figure 9 : Chain model. Figure 10: Bundle model.

Considering this, a theoretical model for a Weibull distribution can be applied to make a statistical evaluation of results. The Weibull model is suited for a single-sided distribution, for example a tensile index distribution for a paper. The reason for using a single-sided distribution is that the stock, of which the paper is made, has a certain strength. This strength cannot be exceeded. However, the above-mentioned process variation will cause a local reduction in strength. The target for the paper and board making process is to produce a product that has a strength of the entire paper web that is as close as possible to that of the stock.

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Equation 8: Weibull probability density function. 𝑓(𝑥; 𝛼; 𝛽) =𝛽 𝛼_ 𝑥 𝛼` aJ< 𝑒J_cd` e

In the Weibull probability density function (Equation 8), 𝜷 is the shape parameter, affecting the shape of the probability curve, and 𝜶 is the scale parameter which indicates the spreading of the values within the distribution. A larger scale parameter indicates a larger spreading. The behaviour of the curve can be seen in Figure 11.

Using the Matlab function wblfit to estimate the shape- and scale parameter for each data set provides the most likely parameters which enables generation of the Weibull plots.

Figure 11: Examples of Weibull plots for 2 samples illustrating the effect of the shape (𝜷) and scale

parameter (α). Model one is the lower curve and model two the upper curve.

3.6.2 Gradients

When the fibre suspension leaves the headbox a large share of the flocs has been desintegrated and the fibres align in the direction of the flow due to a difference in speed between the jet and the wire. When the jet of low concentrated pulp fibres is leaving the headbox the distribution onto the wire is controlled by the slice lip thus controls the grammage and thickness in CD. If the pressure in the headbox across the full width of the machine is deviating, the pulp flow out from the slice lip will distribute unevenly, which give rise to gradients and grammage deviations in CD. Fibre orientation gradients and grammage abnormalities in CD is primarily an effect of such abnormities. The strength properties in the final product are influenced by gradients in the CD direction, areas with less fibre joints exhibits a lower tensile index and most fractures will occur at these regions (26).

Variations in the MD are mainly induced by concentration variation in the pulp and pressure pulses in the headbox. These are controlled and reduced by dilution control, pressure chambers and the tube bank in the headbox (4).

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network, which entails unpredictable mechanical properties, thickness and surface roughness (27).

3.7 Shake unit

Since the properties of the final products are strongly related to the formation step in the paperboard machine, even small improvements here could affect the mechanical properties and formation significantly. As previous mentioned, these properties are dependent on the amount and size of flocs present in the final product, and an improvement of formation would thus increase the overall product evenness and quality. One approach to improve formation is to install a shake unit at the breast roll in the beginning of the wire section after the headbox, to improve the formation of the paperboard (Figure 12). A shake unit provides a vibrating motion in the cross direction to the wire, breaking up flocs by a shear force in the liquid state pulp at the forming stage. But also, this motion is changing the fibre orientation created in the jet out from the headbox, decreasing the amount of fibres in the machine direction in the fibre web. Assuming that variation in the headbox jet can be reduced by the transverse oscillation, it could result in a less anisotropic material with a smaller difference between the MD to CD properties (28).

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4 Methods

All samples supplied by Iggesund were conditioned at 23 °C and 50 % RH for 24 h before the measurement were performed. To statistically evaluate the results the Matlab function std, standard deviation (Equation 3), was applied on all data obtained. Samples in CD were taken from the top of the tambour direct after winding, meanwhile MD strips were for practical reasons taken after winding. All MD samples from each tambour are taken directly after each other in the machine direction so that they form one long sample. In Table 3 the direction and grammage of each sample is presented, also the samples coating is stated. Before the majority of the experiments were conducted a smaller number of samples were tested to compare and evaluate results.

Table 3 : Samples studied in the report. Sample Number of

samples

Grammage

(gm-2₎

Direction Position Coating

Initial tests for learning the methods and evaluation

2327 1 260 CD Single sided 2328 1 260 CD Single sided 2329 1 260 CD Single sided 2330 1 260 CD Single sided 2333 1 240 CD Single sided 2704 2 350 CD Double sided 2727 1 400 CD Double sided 2732 2 400 CD Double sided

3358 6 330 MD Center Single sided

Main trials

3582 (w

shake) 9 380 MD & CD Center & Edge Single sided 3583 (w/o

shake) 9 380 MD & CD Center & Edge Single sided

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4.1 STFI-structural thickness

All samples were fed at 20 mm/s and the thickness was registered every 0,1 mm. For the first test each roll of paperboard was measured two times, one from each direction along the sample, with 3 cm in between the readings. For all following tests, three parallel measurements were conducted, all in the same direction with 3 cm between each measurement line. Besides the standard deviation, the variance was also calculated. Additionally, the variation was used to compare if the thickness of the centre ply became more stable when a shake unit was used. The variance was calculated in segments of 1 cm (100 data points) to reduce the influence of the CD trends originating from shrinkage. The CD trends have a much larger length-scale which otherwise would affect the evaluation greatly. Outliers and extreme values due to creases on the samples were removed when such come across.

4.2 OptiTopo

Samples were pre-marked at every 5 cm and at each mark an area of 32 x 32 mm was examined. For the final samples the interval of measurements was changed to intervals between 3 cm and 10 cm depending on position. Since the variation is larger at the edges, the interval was decreased to 3 cm. For the centre regions was increased to 10 cm due to lack of time. At first the three standard scales of variations were evaluated: OSD (0.063-0.5 mm), mid- scale (0.5-2mm) and large-scale variations (2-8 mm). After the first measurements a user defined scale of 0,5-7 mm was added, this to match Iggesunds own apparatus to measure surface roughness, “STURE”. Since the OptiTopo Expert software was used, these users defined setting could be applied on already conducted measurements afterwards. Outliers due to joints and creases in the paperboard were removed.

Since the OptiTopo was not located in a conditioned room at the beginning of the project, the samples were not conditioned for these measurements.

4.3 Autoline

For the automatic tensile test and the Bendtsen surface roughness the Rise Bioeconomy Autoline was programmed to implement the sequence shown in Table 4.

Table 4: Intervals for measuring modules in the Rise Bioeconomy Autoline. Measurement Intervals

(Initial tests)

Intervals (Main test)

Bendtsen Roughness TS & BS 10 cm 10 cm

Bendtsen Roughness TS & BS Traditional 10 cm 10 cm

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The clamp distance during the tensile test was 100 mm and the rate was approximately 3,5 mm/s, which according to L&W gives consistent result to regular laboratory methods. Error values were removed if occurring. To control the accuracy of the Autoline at Rise Bioeconomy, manual tensile test was performed on the 10 first samples. The measurement interval in MD was increased to 6 cm, which allows for a sample to be cut out between the Autoline measurements. These samples were analysed manually. In the main experimental series, the interval of the tensile strength in MD direction was decreased to 3 cm to get more measurements, the sequence of testing can be seen in Table 4.

4.4 Laboratory tensile test

The tensile test were conducted according to ISO 1924-3:2011, which means that the clamps were 100 mm apart, rate of extension 100mm/min and the samples were 15 mm wide. Samples were taken every 6 cm of the same paperboard as used in the Rise Bioeconomy Autoline, in-between each automatic tensile test earlier completed (see Figure 13). This procedure was only conducted on the first samples 2327-2732.

Figure 13: Illustration of the position where the strips for laboratory tensile testing were retrieved. At the bottom the Rise Bioeconomy Autoline MD test strips can be seen. Red marking shows where

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5 Results and discussion

5.1 Initial tests

5.1.1 STFI Structural thickness

For each measurement with the STFI structural thickness apparatus data was evaluated by looking at the thickness values, the variance and also the frequency of the thickness variation. In Figure 14, a typical plot of the thickness data can be seen. What can be seen in Figure 14 is that the left side is experiencing a considerable decrease in thickness. This trend is the same for all grammage, indicating some deviation in the production.

Figure 14: Unfiltered data from STFI structural thickness measurements compared with Iggesund routine analysis. Sample 2704, 350 gm-2_.

The same procedure was conducted on all samples and the mean value and standard deviation was calculated using Matlab built in functions mean and std. Notable is that for the 3358 1-2 sample, one of the three measurements had to be redone since the instrument was not correctly reset at the first attempt. The new measurement was conducted at the same position as the previous, thus the results should not have been affected.

In Table 5 mean values of the tests are presented together with thickness data provided by

Iggesund. Detailed results for all separate samples can be found in Appendix STFI Structural thickness.

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thickness measurements cannot be detected by the Iggesund routine analysis, as there is no thickness measurement at that location.

Table 5: Results of thickness measurements.

Sample (gm-2₎ Sample Grammage (gm-2₎ Thickness (µm) STD Cv Iggesund data (µm) 240 2333 246.1 282.1 6.8 0.024 288.7 260 2327 2328 2329 2330 _267.3 _314.1 _6.5 _0.021 _320.4 350 2704 349.7 406.3 5.9 0.015 402.3 400 2727 2732 401.0 481.4 5.6 0.012 476.9 330 3358 334.3 421.3 6.7 0.016 429.0

To evaluate the local variance of the data, the Matlab function var was used. The results of this are summarized in Table 6 and Figure 15. It can be seen that the variance is fluctuating between the different grammages and no clear relationship could be found. The edges are showing larger variations than the center parts of the tambour. For detailed results for each sample see Appendix STFI Structural thickness .

Table 6: Calculated mean values of thickness and variation for all samples.

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Figure 15: Local variance in the thickness measurements for sample 2333, 240 g/m2_{with a}

variance of 12.5.

Additionally, the frequency at which the thickness variance was varying was studied with a Matlab script provided by RISE Bioeconomy. In Figure 16, the variance data used as an input to the Matlab script can be seen.

Figure 16: Average thickness profile that the Matlab script utilizes to estimate the frequency.

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Figure 17: Example of graph provided by the Matlab script for frequency analysis. For the example plot is sample 3358-1.

From the graphs generated by the Matlab script, the mean value of the frequency wavelengths calculated for each grammage was and presented in Table 7.

Table 7: Wavelengths from graphs provided by the Matlab script. Table shows mean values of the frequency found in the thickness data.

Sample Sample Wavelength

(mm) Number of samples 240 2333 11.2 1 260 2327 2328 2329 2330 13.1 4 350 2704 7.5 2 400 2727 2732 9.3 3 330 3358 10.1 6

By looking at the range of the wavelengths found in the obtained thickness data it is indicated that the source of the thickness variation in MD is probable to be caused by flocculation. In CD the variation might be caused by the geometry of the headbox, has been shown in Figure 8. 5.1.2 OptiTopo

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Figure 18: Results OptiTopo measurements on samples of 260 gm-2_.

For the sake of simplicity, only the user-defined scale of roughness will be compared to the “STURE” value provided by Iggesund. As can be seen in Figure 18 the edges exhibit a higher surface roughness, probably induced by the shrinkage of the paperboard as it dries. To see detailed results for each sample, see Appendix OptiTopo. A summary of all the grammages studies can be seen in Table 8.

Table 8: Summary of mean values from OptiTopo results compared to the value provided by Iggesunds STURE. OptiTopo refers to the user defined interval of 0.5-7 mm.

Sample (gm-2₎ Sample OptiTopo (o.5-7 mm) STD STURE (o.5-7 mm) 240 2333 1.54 0.31 1.53 260 2327 2328 2329 2330 1.62 0.56 1.68 350 2704 1.56 0.44 - 400 2727 2732 1.75 0.44 - 330 3358 0.97 0.19 -

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5.1.3 Autoline

As the last stage in the analysis, the samples were measured by the Rise Bioeconomy Autoline and evaluated. All tensile strengths obtained were indexed using the grammage of each sample. Grammage data provided from Iggesunds Autoline was used for indexation. For the first four grammages (240-400 gm-2_{) 76-77 MD and 38 CD tensile tests were conducted. For the 330 gm} -2_{sample in MD direction, the variation of quantity of tests performed was greater since the} length of the samples was varying more; 33-37 MD and 136-151 CD tensile tests were managed. By comparing the tensile index in MD versus CD direction the ratio can be calculated to approximately 1.8 for all strips.

Table 9: Results from mechanical testing in Rise Bioeconomy Autoline. All values are mean values. Sample

(gm-2₎

Direction Tensile index MD

(Nm/g) STD Tensile index CD (Nm/g) STD MD/CD ratio 240 CD 58.4 2.9 33.8 1.5 1.7 260 CD 57.8 2.6 32.7 1.3 1.8 350 CD 55.6 2.9 32.6 1.5 1.7 400 CD 53.7 2.4 29.8 1.1 1.7 330 MD 53.6 1.8 29.2 0.8 1.9

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Figure 19 : Tensile index of the CD samples for 350 g/m2_{samples. Dots represent data provided by}

Iggesund.

For the tensile index results all samples follow the same trend, edges show significant lower strength properties while MD profile are more stable over the tambour. This is also an effect of the shrinkage during drying but can also be linked to the lower thickness earlier found at the same position. It is clear from Figure 19 that the Autoline measurements in Iggesund misses the large deviation on the edges but gives otherwise a good representation of the remaining parts of the tambours. All graphs can be seen in Appendix Autoline. From Table 10 it is clear that the samples show a trend that the paperboard becomes stiffer at higher grammage, thus the extension decreases in both MD and CD direction.

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Figure 20: Tensile stretch in MD and CD direction for 350 g/m2_.

Furthermore, extension of samples before the point of break is stable in MD direction while the CD shows an increase of elongation at the edges. This effect is very clear looking at Figure 20, the stretch in CD direction increases significantly at the outer parts, while MD are stable over the full width. This is also an effect of the shrinkage; more shrinkage gives a higher value for the stretch results. For the TEA and Bendtsen values see Appendix Autoline.

To be able to evaluate the distribution of data points, MiniTab was used. To confirm that Weibull distribution was a suitable approach. Distribution was compared to normal distribution, the Weibull distribution and evaluate the p-value (probability value) was evaluated; the one with the highest probability can be considered true.

Figure 21: Probability plot generated in MiniTab for a Weibull distribution. P-value for each series of 0.195 and 0.247.

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Results from the comparison of the probability plots are depicted in Figure 21 and Figure 22 which shows, that the probability for a Weibull distributed turn out is higher than for a normal distributed. This trend was observed for all of the initial results, which allows the conclusion that the variation in strength properties is better described by a Weibull distribution than by a normal distribution.

For visualization of the spread of the results, Weibull plots are presented below in Figure 23 a-d. The Matlab function wblfit was used to estimate the shape and scale parameters in order to generate the Weibull graphs and generate Weibull plots for all samples.

(a) (b)

(c) (d)

Figure 23 a-d: Weibull distribution for (a-b) sample 2704 and (c-d) sample 3358. On the left-hand side tensile index in MD direction is presented, on the right-hand CD direction. 2704 is a CD sample and sample 3358 a MD, increasing the number of data point from 77 to 105 in MD and from 38 to 430 in CD.

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Gradients in the MD could be evaluated by measuring the distance from the edge to where the break occurs and see if specific values were recurrent. Only one of the MD strips was suitable for this since it required a perfectly straight cut sample, which only one was considered to be.

Figure 24: Histogram of the point of fracture for sample 3358 MD. The samples size that the Rise Bioeconomy Autoline is using for the mechanical testing is 10 cm long, which means that the rupture at 0 cm is due to special conditions at the clamp.

From Figure 24 it can be speculated that there are two main locations where the sample is breaking, at 3-4 cm and at 7-8 cm from the edge. This could be associated with local peculiarities in the sheet structure, for example caused by local fibre orientation artefacts causing streaks with weaker CD strength, caused by the geometry of the headbox. The breaks occurring at the 0 cm range are considered to be caused by the special conditions at the clamps and are therefore not considered to be a gradient induced break.

5.1.4 Laboratory tensile testing

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Figure 25: Comparison between Tensile index for the 260 g/m2 _{samples. Data from Rise}

Bioeconomy’s Autoline, Laboratory measurements and values provided by Iggesund.

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5.1.5 Evaluation

Starting with only two thickness measurements from opposite direction, to eliminate the possible fault from the feeding, it could be concluded that this did not appear to be a problem. After this, more data was preferred, and three parallel measurements were made, without switching direction of the sample. Starting with the frequency analysis on the STFI-structural thickness apparatus raw data, a new approach was used, considering the variance data instead. This was due to the problems finding a frequency in the large number of data at the beginning. Concerning the interval of the surface roughness measurements, since the edges showed the most variation, more frequent measurements were desired there. Due to this the measurement distance was decreased to 3 cm at the first 30 cm of each CD strip, while the MD samples and the center parts of the CD samples will be measured every 10 cm.

For the results obtained from the Rise Bioeconomy’s Autoline a few conclusions could be made. After the first samples both TEA values and Bendtsen results were considered less important for the following measurements and were considered outside the scope of the project. For the MD sample, the measuring of distance to the point of breakage was continuingly interesting to see if property variations occur in this direction. The graphs demonstrate a great loss of information at the edges when comparing the high frequent measurements to the Iggesund ones.

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5.2 Main tests

Several samples from the same product and the same grammage were evaluated in the main tests. The aim was to investigate if the use of the installed shake unit resulted in a reduction of the property variation. Sample 3582 was produced with the shake unit and sample 3583 without. When comparing samples within the same grammage and product, variations from the entire production becomes more significant. Therefore, data from three different production occasions the past year are displayed in Figure 27 below, showing the typical variance during production. This provides a good estimate of which types and deviation magnitudes can be expected from the process itself. From the graphs it can be read that the values was stable also in 2017, before the shake unit at the breast roll was installed.

(a) (b)

Figure 27: Tensile index (a), and thickness and grammage (b) in typical production of 380 g/m2_.

Tambours from 2017 were produced without shake unit and those in 2018 with shake unit. All data was provided by Iggesund.

5.2.1 STFI Structural thickness

Using the same evaluation method as previous, 5.1 Initial tests, for the thickness determination, measurements and calculation of the thickness and variance were performed.

Table 11: Results from thickness measurements together with calculated local variance.

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(a)

(b)

Figure 28: Graphs showing thickness data for all (a) sample 3582 (w shake) and (b) sample 3583 (w/o shake) samples in cross direction.

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provided by Iggesunds Autoline. But over-all the STFI structural thickness apparatus correlate well with the results from Iggesund Autoline.

(a) (b)

(c) (d)

Figure 29 a-d: Thickness data for sample 3582 in MD. In (a), center of the tambour and (b), edge is presented. 3583 presented below in (c-d), center roll in (c) and edge in (d).

It can be seen that the thickness variation is larger at the edge samples compared to the center parts, see Figure 29 b and d. Also it can be seen that the three individual measurements vary more at the edge samples compared to the samples from the center of the board machine. When comparing the results for sample 3582 and the ones for sample 3583, it can be seen that the thickness becomes more uniform when the shake unit is active and also that the edges experience more outliers and a greater instability than the center samples. This is in line with the previous conclusions from the data in Table 11.

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(a) (b)

Figure 30: Graph from frequency analysis, for sample 3582 MD Center (a) and sample 3583 MD Center (b).

The results in Table 12 are compiled from the graph in Figure 30 and indicate the dominating frequencies occurring in the samples. As it can be seen the frequencies have a short wavelength, that suggests that the source of the variations is flocculations, this is in line with the previous results from the first group of samples. As mentioned before, the CD samples are a result of the geometry of the headbox while the MD direction is a result of the stock and the deposit onto the wire. There are also several other peaks in the graphs suggesting that other frequencies are occurring, frequencies with longer wavelengths with probable origin from the headbox.

Table 12: Dominating wavelength from the frequency analysis graphs. The table shows mean values for all samples.

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5.2.2 OptiTopo

All samples were examined at the same wavelengths as previous, see 5.1.2 OptiTopo.

Table 13: Results in the user-defined interval from the OptiTopo together with the values provided by Iggesunds STURE. Sample OptiTopo (o.5-7 mm) STD STURE 3582 CD 1.50 0.53 - 3582 MD Center 1.04 0.12 - 3582 MD Edge 0.97 0.05 - 3583 CD _1.62 _0.45 _2.09 3583 MD Center 1.12 0.07 - 3583 MD Edge 1.13 0.34 -

As Table 13 shows, the surface roughness was higher for the CD samples than for the MD samples, this due to the fact that the OptiTopo is a one dimensional technique. When

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(a)

(b)

Figure 31 a-b: Comparison of surface roughness measured with the OptiTopo. To the left (a), showing sample 3582 with shake unit and to the right (b), sample 3583 without shake unit.

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(a) (b)

Figure 32 a-b: Gradient maps obtained with the OptiTopo. Figure 28(a) shows a MD sample from the edge of the tambour, Figure 28(b) represents a CD sample.

In Figure 32 the difference between the cross and machine direction of the samples are shown. This particularly shows the wrinkles cross the machine that the OptiTopo lack the ability to detect. This is expected since the OptiTopo is designed to measure in one direction and detect surface roughness perpendicular to the illumination source. Notable is that it is not the same area in MD and CD, only the same tambour.

5.2.3 Autoline

At last, all samples were mechanically tested in Rise Bioeconomy Autoline. The results for tensile index in both MD and CD together with MD/CD ratio are shown in Table 14.

Table 14: Obtained results from the Rise bioeconomy’s Autoline mechanical tests. Table shows mean values from all mechanical tests.

Sample Tensile index MD

(Nm/g) STD Tensile index CD (Nm/g) STD MD/CD ratio 3582 CD 56.6 2.6 24.2 0.9 3582 MD Center 55.8 1.7 25.1 0.8 2.1 3582 MD Edge 56.1 2.1 24.4 0.6 2.4 3583 CD 57.4 3.4 23.1 0.9 3583 MD Center 56.2 1.7 23.9 0.6 2.4 3583 MD Edge 56.2 1.7 22.8 0.9 2.5

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(a)

(b)

Figure 33 a-b: Tensile test of cross directional samples. Black marks represent values provided by Iggesund.

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other hand, the bottom graphs, displays an increase of tensile index at the center region and a more pronounced profile for sample 3582. This shows, that the shake units uplifting characteristics is greater at the center that at the outermost regions. Also here the tensile test performed by the Autoline in Iggesund seems to miss out on the outermost parts of the tambour neglecting the edge effect seen by the high frequent measurements.

(a)

(b)

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As shown above, the shake unit increases the tensile index in the CD which is noticable in Figure 34 as well. Another aspect clearly seen in Figure 34 is that the edge experiences a lower tensile index in CD, especially for sample 3583 to the right. This is also indicated for the sample 3582, nevertheless the trend is not as prominentThe fact that the values are stable in MD indicates that other parameter have been stable between the two tambours. This supports the theory that the improvement in the CD would be an effect of the shake unit.

a b

c d

Figure 35 a-d: Weibull distribution for the CD samples, 3582 on top (a-b) and 3583 at the bottom (c-d). Left ones represent tensile index in MD and right illustrates tensile index in CD.

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a b

c d

Figure 36 a-d: Weibull distribution for the MD samples, 3582 on top (a-b) and 3583 at the bottom (c-d). Left ones represent tensile index in MD and right illustrates tensile index in CD.

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a b

c d

Figure 37 a-d: Histogram illustrating the point at which the fracture occurs in the Autoline at Rise Bioeconomy. 3582 at the top and 3583 below. These histogram were normalized by the number of measurements.

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6 Conclusions

6.1 STFI Structural thickness

What can be seen from the results is that edges exhibit large disparity from the central parts, one side displays a thinner than the average result and the other a more similar behaviour to the centre regions. To large extent recurrent for all samples in large extent, even though deviant cases exist. The variance of the thickness measurements varies quite a lot over the different grammages, with little or no relation to the average grammage of the sample. As the results show, for the main tests, the variance decreases for the samples for which the shake unit was applied which appears to be the case for both CD and MD direction, and might indicate that the shake unit is improving the structural evenness, and thus the formation of the center ply. However, the decrease in thickness at one of the sides exhibits no improvement when comparing the samples with and without the shake unit, which indicates that the source of this deviation is further back in the production line. Most likely, the jet out from the headbox is not completely uniform over the whole width of the machine.

According to the results of this study, the thickness measurements performed at Iggesund was very accurate at the positions where they are performed. But the largest issue is the edges where the outermost parts are overlooked. But, the positive in these results are that trends seen with the STFI structural thickness apparatus is in line with trends from the Autoline. This provides a lot of valuable information to the mill nevertheless.

6.2 OptiTopo

The largest consern with the illumination technique is the fact that MD and CD direction of samples will not be comparable due to that the illumination direction will only detect surface variation the have a certain contribution perpendicular to the direction of the illumination of the sample. This is important to take into account when using the OptiTopo.The reason for using an additional bandwidth is to easier compare the high-frequent measurements to the ones made at the Iggesund mill. However, the comparison to STURE is still an uncertainty without further investigations due to the small number of STURE values available. Regarding the shake unit does not seem to affect the surface roughness extensively, even though the difference between the center and the edge is decreasing. The reason for this behaviour could depend on the fact that the paperboard is coated, which smoothens the surface efficiently even if the plies have a deviating surface roughness from the beginning.

6.3 Autoline

When comparing the results from the high frequent measurements to the data points provided by Iggesund it can be seen, that the edge behavior is not captured by the quality control measurements, meaning that the quality control does not detect a part of the characteristic of the paperboard. Except these outer region deviations, the overall results correlate well to the average of each tambour. A solution to this problem might be to change the sequence at which the measurements are performed, if it is logistically possible. This might however come at a cost of losing information about another property instead. This trade-off is a constant matter in paper production since an increase of measurements of one property often leads to a decrease of another.

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the graphs (poor thickness and strength properties), most likely depends on a problem in one or several of the three headboxes.

When comparing the results for samples produced with and without the shake unit it can be concluded that the tensile index across the machine increases which is an effect of the decreasing alignment of fibres. This effect is greatest in the middle part of the tambour indicating that the shrinkage, imposed by the drying, still affects the CD direction strength significantly. This also contributes to the decrease in MD/CD ratio, which appears when the shake unit is active. Additionally, the strength along the machine is very stable which indicates that the process itself has been stable during the production. It is however important to be aware that the trends found in this study are on the order of variations found during normal production. Therefore, the results can only be seen as a first evaluation for a further and broader investigation of the effect of the shake units. Furthermore, the operating parameters of the shake unit were not investigated.

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7 Future work

• More measurements on the same grammages and products are required to ensure that the indications found actually point towards the real case. This would reduce the uncertainties and provide knowledge if the variations are coincidence or actual process defects.

• Longer samples in MD could be of interest to further investigate the time dependence of variation over a longer period than the few seconds in the present work. It would give more information of periodic variations, and also a base for finding the root cause of these variations.

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8 References

1. Ullmann, Fritz. Ullmann's Encyclopedia of industrial chemistry . New York : Wiley InterScience, 2000.

2. Brännvall, E. Lennholm, H. Lindstr, T. Norman, B. Introduktion till Cellulosateknologi. Stockholm : Institutionen för Fiber och Polymerteknologi, 2011.

3. Walker, John C.F. Primary wood processing - Principles and Practice. University of Canterbury, Christchurch,New Zealand : Springer, 2006.

4. J. A. Bristow, C. Fellers, U-B. Mohlin, B.Norman, M. Rigdahl, L.Ödberg. Pappersteknik . Stockholm : Avdelningen för Pappersteknik Kungl Tekniska Högskolan, 1996.

5. Lorentzen and Wettre. Pappers och massaprovning. Stockholm : Lorentzen and Wettre, 2011. 6. Alava, M. and Niskanen, K. The physics of paper. s.l. : INSTITUTE OF PHYSICS PUBLISHING, 2006.

7. Kriwan, M.J. Paper and paperboard - raw materials, processing and properties. Oxford, UK : Blackwell Publishing, 2005.

8. Lorentzen & Wettre. L&W Micrometer. [Online] J 2018. [Cited: 01 29, 2018.]

https://library.e.abb.com/public/8c3d3d9fdf71429faae4033596cc94bc/251_LW_Micrometer_v2.0.pd f?x-sign=8qjkyj/SbNbJFglsJ5Hix/ZGNScteEkmfxzJ0E2Y7eSxjX+pjBe35hjun1xDWPb3.

9. Ek, M. Pulp and paper chemsitry and technology. Berlin,Boston : De Gruyter, 2016.

10. Yoshihara, H. Yoshinobu, M. Effects of specimen configuration and measurement method of strain on the characterization of tensile properties of paper. s.l. : Official journal of the Japan wood research society, 2014.

11. Hagman, A. Influence of inhomogeneties on the tensile and compressive mechanical properties of paperboard. Stockholm : KTH Royal Intstitute of Technology, 2016.

12. Nygårds, Mikael. Paper mechanics. Föreläsning Pulp and Paper processes KTH. Stockholm : s.n., 2017.

13. Lorentzen & Wettre. L&W Bendtsen Tester. [Online] ABB, 2018. [Cited: 01 29, 2018.] http://new.abb.com/pulp-paper/abb-in-pulp-and-paper/products/lorentzen-wettre-products/laboratory-paper-testing/l-w-bendtsen-tester.

14. Barros, G.G and P.-Å Johansson. The OptiTopo Technique for Fast Assessment of Paper Topography - Limitations, Applications and Improvements. Journal of Imaging Science and technology. 2005, Vol. 49(2).

15. Mettänen, M. Comparison of registered paper surface representations from microtomography and photometric stereo. Graz, Austria : Progress in Paper Physics Seminar, 2011.

16. Christiansson, H. OptiTopo - Measuring the surface of paper and board. [Online] [Cited: 02 01, 2018.]

http://www.innventia.com/Documents/Produktblad/Material%20processes/Pappersyta/OptiTopo%2 0-%20the%20technique%20and%20fields%20of%20application.pdf.

17. Takashi Yokoyama, Kenji Nakai. Orientation Dependence of In-Plane Tensile Properties of Paperboard and Cardboard: Eperiments and Theories. Okayama : Department of Mechanical Engineering, Okayama University of Science, 2010.

18. Tryding, J. Experimental and theoretical analysis of in-plane cohesive testing of paperboard. s.l. : International Journal of Damage Mechanics, 2017.

19. Kungliga tekniska högskolan. Institutionen för fiber- och polymerteknologi. The Ljungberg textbook. Paper physics. Stockholm : Kungliga tekniska högskolan. Institutionen för fiber- och polymerteknologi, 2005.

20. Mandel, J. The Statistical analysis of Experimental data . s.l. : Dover Publications, 1964. 21. Wikipedia. Wikipedia-Variance. [Online] [Cited: 04 24, 2018.]

https://en.wikipedia.org/wiki/Variance.

22. H. Kaper, H Engler. Mathematics and Climate. Chapter 11, pp. 123-139. Mathematics and Climate. s.l. : SIAM eBooks (Society for Industrial and Applied Mathematics), 2013.

23. Ohenoja, Markku. One- and two-dimensional control of paper machine: A literature review. s.l. : University of Oulu, Control Engineering Laboratory, 2009.

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25. Mathen, R. Niskanen, K. Strength distribution of running paper webs. Journal of pulp and paper science. 2006, Vol. 32, 2.

26. Lundell, F. Söderberg, D. Alfredsson, H. Fluid mechanics of papermaking. Stockholm, Sweden : Annual Reviews, 2011.

27. Östlund, M. Modeling the influence of drying conditions on the stress buildup during drying of paperboard. Stockholm, Sweden : Journal of Engineering Materials and Technology, 2006.

28. Buchanan, John Gordon. PAPER MACHINE SHAKE . United States Patent , Dec 23, 1976. 29. Voith. [Online] [Cited: 07 23, 2018.]

Characterisation of property variations in paperboard samples