DEGREE PROJECT IN MECHANICAL ENGINEERING, SECOND CYCLE, 30 CREDITS STOCKHOLM, SWEDEN 2019

Prediction of paperboard thickness and bending stiffness based on process data

SACHA VANDENBOSSCHE

KTH ROYAL INSTITUTE OF TECHNOLOGY SCHOOL OF ENGINEERING SCIENCES

Degree project in Solid Mechanics, second cycle

Prediction of paperboard thickness and bending stiffness based on process data

by Sacha Vandenbossche, [email protected] June 2019

”...in theory there is no difference between theory and practice, while in practice there is...”

-BENJAMIN BREWSTER

Abstract

Bending stiffness is one of the most important mechanical properties in paperboard making, giving rigidity to panels and boxes. This property is currently only possible to measure by destructive measure off the production line. The current quality control method is deficient by assuming a non-realistic consistency of the paperboard properties along the machine direction. The objective of this thesis is to predict the thickness and bending stiffness of the final boards from process data.

Two modelling approaches are used: the first model calculates the bending stiffness from a calculated thickness, while the other one uses the measured baseboard thickness. Both models use common inputs such as material properties and grammage measurement. The grammage is taken from the online baseboard measurement. The material properties come from laboratory measurements and assumptions. It is assumed that the density ratio between the outer and middle plies is constant for all product lines, at all times. The TSI of each ply is defined from tensile testing experiments and nominal bending stiffness. It is also assumed that the coating does not contribute to bending stiffness. The two models use equations based on laminate theory assuming orthotropic layers and neglecting the interlaminar shear forces. The models use data of two different natures: i.e. laboratory data and online data. Laboratory data is used as a comparative to evaluate the models’ performance of calculated values from online data.

The results show various levels of prediction accuracy for different paperboard grades. The average thickness predictions are all underestimations within a 5% error while the bending stiffness estimations vary much more from product to product; varying from 9% underestima- tion to 32% overestimation. The bending stiffness prediction for CD is consistently higher than for MD for both models. Most product lines have better results with the calculated thickness, approach 1. The calculated thickness is always underestimated and bending stiffness is overes- timated, hence the better results with the first approach.

The most important conclusion from the models’ results is the spread of laboratory measure- ments, when compared to the predicted values. The large variation most likely comes from production, implying inconsistencies in the manufacturing process that are not accounted for by the models. These modelling approaches have failed to capture the production variations because of the lack of input parameters.

Keywords: Paperboard, bending stiffness, thickness, property prediction, laminate theory Sammanfattning

B¨ojstyvhet ¨aren av de viktigaste mekaniska egenskaperna i kartongtillverkning, vilken ger styvhet till paneler och l˚ador.Denna egenskap ¨arf¨orn¨arvarande endast m¨ojligatt m¨atamed de- struktiva off-line metoder utanf¨orproduktionslinjen. Den nuvarande kvalitetskontrollmetoden ¨arbristf¨alliggenom att den utg˚arfr˚anen icke-realistisk beskaffenhet hos kartongegenskaperna l¨angsmaskinriktningen. Syftet med denna avhandling ¨aratt f¨oruts¨aga tjocklek och b¨ojstyvhet hos den slutgiltiga kartongen fr˚anprocessdata.

Tv˚amodelleringsmetoder anv¨ands:den f¨orstamodellen ber¨aknar b¨ojstyvheten fr˚anen ber¨aknad tjocklek, medan den andra anv¨anderden uppm¨attabaskartongens tjocklek. B˚adamodellerna anv¨andervanliga indata som materialegenskaper och ytvikt. Ytvikten tas fr˚anonline-m¨atningar p˚abaskartong. Materialegenskaperna kommer fr˚anlaboratoriem¨atningaroch antaganden. Det antas att densitetsf¨orh˚allandetmellan de yttre och inre lagren i flerskiktskonstruktionen hela tiden ¨arkonstant f¨oralla produktlinjer. Dragstyvheten f¨orvarje skikt ¨ardefinierad fr˚andrag- prov och nominell b¨ojstyvhet. Det antas ocks˚aatt bestrykningen inte bidrar till b¨ojstyvheten. De tv˚amodellerna anv¨anderekvationer baserade p˚alaminatteori, antar ortotropa skikt och f¨orsummarinterlamin¨araskjuvkrafter. Modellerna anv¨andertv˚aolika typer av data: labo- ratoriedata och online-data. Laboratoriedata anv¨andssom en j¨amf¨orelsef¨oratt utv¨ardera modellernas prestanda f¨orv¨ardenber¨aknade fr˚anonline-data.

Resultaten visar olika niv˚aerav prediktionsnoggrannhet f¨orolika kartongkvaliteter. De genom- snittliga tjockleksuppskattningarna ¨aralla underskattningar med ett fel inom 5% till en ¨over- skattning p˚a32%. B¨ojstyvheten i CD ¨arkonsekvent h¨ogre ¨anin MD f¨orb˚adamodellerna. De flesta produktlinjer har b¨attreresultat f¨orber¨aknadtjocklek med tillv¨agag˚angss¨att 1. Den ber¨aknade tjockleken ¨aralltid underskattad och b¨ojstyvheten ¨overskattad, d¨arf¨ordet b¨attre resultatet f¨orf¨orstatillv¨agag˚angss¨attet.

Den viktigaste slutsatsen fr˚anmodellresultaten ¨arspridningen i laboratoriedata, j¨amf¨ortmed de uppskattade v¨ardena. Den stora variationen kommer sannolikt fr˚anproduktionen, vilket inneb¨arinkonsekvenser i tillverkningsprocessen som inte redovisas av modellerna. Dessa mod- elleringsmetoder har misslyckats med att f˚angaproduktionsvariationerna p˚agrund av avsak- naden av indata.

Nyckelord: Kartong, b¨ojstyvhet, tjocklek, uppskatta egenskaper, laminatteori Acknowledgements

This work was carried out at, and for, Iggesund Paperboard AB in Iggesund, Sweden. I wish to thank all of those who have helped and supported me through this tedious work.

First I would like to thank all the members of the development team at Iggesunds Bruk for their help and support. A special thanks goes to Staffan Berg, Tommy Str¨omand Johan Lindgren for their resourcefulness throughout my project as well as always taking the time to discuss and answer my numerous questions.

I would also like to thank my supervisors Hannes Vomhoff for his guidance and enthusiasm regarding the project and advice in my job research and applications. As well as S¨oren Ostlund¨ for his help in results interpretation and report writing.

Lastly, a special thank you goes to Malcolm MacDonald of Iggesund Paperboard AB in Work- ington, England, for his valuable work in making the ultrasonic measurements.

Contents

1 Introduction 1 1.1 Background ...... 1 1.2 Paper forming ...... 1 1.3 Quality control ...... 2 1.4 Purpose and structure of work ...... 4

2 Theory 5 2.1 Material properties ...... 5 2.2 Laboratory testing methods ...... 8 2.3 Online testing methods ...... 12 2.4 Quality control testing ...... 13

3 Assumptions and Simplifications 15

4 Models 18 4.1 Data ...... 18 4.2 Model 1 ...... 18 4.3 Model 2 ...... 20

5 Experimental Methods 21 5.1 Material ...... 21 5.2 Laboratory testing ...... 21 5.3 Determination of TSI of each ply ...... 24 5.4 Coating thickness ...... 25

6 Results and Discussion 27

7 Conclusions and Recommendations 29 7.1 Thickness prediction ...... 29 7.2 Bending stiffness prediction ...... 29 7.3 Recommendations for future work ...... 29

8 References 30

Appendices 32

A Coating thickness - Numerical experiment results 32

B Models results 34 B.1 Product A ...... 34 B.2 Product B ...... 37 B.3 product C ...... 38 B.4 Product D ...... 41 B.5 Product E ...... 44

1. Introduction 1.1 Background

Iggesund Paperboard is known for producing solid bleached boards (SBB) of very high quality. To maintain their leading position in paperboard manufacturing, an important step in process development is to ensure a high level of uniformity of the mechanical properties developed dur- ing the manufacturing process. In order to control the process accurately, a good understanding of the physical implications is necessary.

Bending stiffness is the most important mechanical property for packaging purposes, it is what gives boxes and panels their rigidity. The bending stiffness is developed throughout the paper forming process and is influenced by many parameters. The objective of this project is to build a robust and accurate model to predict the thickness and bending stiffness of the final product with process data. Controlling and predicting the bending stiffness is a complex task that has been done with various level of success in the past. Pettersson et al [1] developed a semi-physical model of type grey box to predict the bending stiffness with online measure- ments. The authors mention a limited success because of limited computational power (1997) and suggested to increase the number of inputs into the model, e.g. the drying section has been omitted. 1.2 Paper forming

The board machine is a complex system with several steps in series, see Figure 1.

Figure 1: Board machine diagram [2].

The main steps are the forming of the fibrous network right out of the headbox, dewatering, drying, surface sizing, calendering, coating and glazing. Each step will modify the structure in a way that will impact the mechanical properties of the finished paperboard.

During the fibre network formation, the goal is to distribute the pulp on the wire as evenly as possible to ensure homogeneity of the product properties along the width of the web. An uneven distribution of the pulp will cause local variation in the properties.

Dewatering, or wet pressing, consists of removing the excess water in the network prior to the drying section. Dewatering can be done with different methods, e.g. by pressing the paper- board between two felts. The main purpose of dewatering is to remove water for a faster and

1 more energy efficient drying process. Remove too much water and the board will be too fragile, not removing enough water will require a lot of energy to dry it. The usual dryness of the wet web after dewatering is about 40% [3]. The water content at which the plies merge will affect the amount of interlacing fibres.

The drying process consists of removing the excess moisture after the dewatering process by bringing the dryness level to about 95% [3]. The main difference between the dewatering and drying is that in the dewatering process the water is removed from the board in a liquid state, while during the drying process the water is removed by vaporization. Different drying tech- niques exist and the choice of drying method will have a great impact on the paper properties [3]. Previous work by Ostlund¨ [4] has shown that the drying process in multiply board will create internal stresses throughout the board thickness. Wahlstr¨om [5] has shown that drying conditions such as stretching and shrinking can influence the stiffness properties of paper.

Surface sizing consists of applying a starch solution, with or without pigments, on the board surfaces to create a more uniform surface by binding the fibres to the surface [2] and also in- crease the surface stiffness [6]. Surface sizing also helps the coating to adhere to the surface.

Calendering is a step where the board is pressed between rollers to increase surface smoothness and control the thickness. The calendering process ensures thickness uniformity, but will ac- centuate the local properties variations such as density and stiffness by compressing the spots with higher grammage more.

The surface coating consists of applying one or several layers of a liquid water-based solution containing mainly pigments particles and a binder [2]. This procedure can be done on one side only or on both sides of the board. A drying step, infrared drying in this case, is necessary between each applied coat. The coating increases furthermore the surface smoothness and con- trols the optical properties of the board.

The final step is the glazing where the coated board is calendered once again between hot rolls to, once more, increase the surface smoothness. Glazing is usually reserved for specific products requiring a pristine surface smoothness and is not performed on all boards. 1.3 Quality control

The current quality control procedure is to cut out a strip in the cross machine direction (CD), at the end of the reel, and perform quality control tests on the strip, see Figure 2. The reel is divided into positions of about 40 cm in CD, the number of positions varies in function of the width of the reel. The measured properties at each position on the sample strip are considered to be representative of the whole length, about 20 km, along the machine direction (MD).

2 Figure 2: Quality control procedure.

This process assumes that the properties in MD are constant, but online measurements prove that there is a notable variation in thickness and grammage along MD, see Figure 3.

(a) Thickness variation.

(b) Grammage variation.

Figure 3: Thickness and grammage variations along the MD direction (Time).

Understanding and controlling the bending stiffness from online data increases the non-destructive

3 testing capacity without extra manipulations. Having such a tool could also give the oppor- tunity of making instant adjustments of the production parameters to avoid drifting off target and minimizing the use of raw material. 1.4 Purpose and structure of work

The main goal of this thesis work is to predict the thickness and bending stiffness properties of the boards with process data, knowledge of the board structure and the material properties of the pulp. The goal is to predict the product property values before they are measured in the quality control lab.

This report presents the assumptions, methods and results of the thesis work. The main sections will cover the technical background, some material properties and their measurement methods, the assumptions and simplifications of the models and calculations, the models and their data flow, the experimental work and the results.

4 2. Theory 2.1 Material properties

Paper is a highly anisotropic material with three distinct orientations defined as machine direc- tion (MD), cross direction (CD) and thickness direction (ZD), see Figure 2. It is worth noting that for most paper products, the tensile stiffness ratio between MD and CD is around the order of two. For this work, the properties of interest are the grammage, thickness, density, tensile stiffness and bending stiffness. The properties in the thickness direction were not investigated. All properties will be defined and the measuring methods will be presented in the following sections.

Grammage

kg Grammage, or also called basis weight (w) is a measure of weight per unit area [ m2 ]. It is used to determine how much fibre there is in a specific area.

Thickness The thickness (d) can be defined in different ways: e.g. single sheet thickness (caliper), struc- tural thickness or bulk thickness. The caliper is the measure of one sheet only measured in a single spot, the bulk thickness is the average sheet thickness measured on a stack of sheets and the structural thickness is an average thickness of a single sheet considering the surface rough- ness, see Figure 7. These methods have different purposes. In this report, the term thickness will refer to the caliper thickness.

Density

kg Density is a measure of weight per unit volume [ m3 ]. The density is not a measured property, it is instead calculated from the measures of grammage and thickness. The relation between the parameters is shown by Equation (1). w ρ = . (1) d

Tensile stiffness In the paper industry, tensile stiffness (TS) is the modulus of elasticity or often called the Young’s modulus. The tensile stiffness is the ability of a material to withstand elastic deforma- tion under tensile stress. The tensile stiffness is a material parameter that is usually determined experimentally. When applying tensile load to a specimen, the applied force and displacement are measured and plotted against each other, like in Figure 4.

5 Figure 4: Typical Force-Displacement curve for paper material.

The elastic modulus is represented by a linear section from the steepest calculated slope. For paper, the tensile stiffness is calculated from the modulus of elasticity and normalized by the width of the sample. The tensile stiffness is then calculated as [7] ∆F l h N i TS = , (2) b ∆l m where b and l are the nominal sample width and length, respectively. Since paper is a fibrous material containing a vast part of air, the tensile stiffness is usually normalized by the material density in order to have comparative values from one type of fibre to another. This property is called the tensile stiffness index (TSI), calculated as TS hNmi E∗ = · 1000 , (3) w kg ∗ g N where E represents the TSI, w is the grammage in [ m2 ] and TS is the tensile stiffness in [ m ]. As paper is an anisotropic material, this measure must be taken for each direction of interest.

Bending stiffness Bending stiffness is, much like the tensile stiffness, the resistance to elastic deformation, but to bending deformation in this case. The bending stiffness, often expressed as Sb is a measurable parameter, but can also be calculated with the tensile stiffness, grammage and thickness.

In solid mechanics, the bending stiffness is defined as

Sb = EI, (4) where E is the modulus of elasticity and I is the moment of inertia. In paper mechanics, assuming no property variation in the thickness direction [8], the bending stiffness is the same as for isotropic materials but normalized by the width of the board

EI Ed3 S = = , (5) b b 12

6 where d is the thickness of the board and b is the breadth of the sample. Equation (5) can be expressed differently using the paper parameters and relations defined above in Equations (1), (2) and (3). This reformulation is expressed by Equation (6).

E∗w3 S = (6) b 12ρ2 Here it is important to note the dependence of the density on the bending stiffness. Since paper is a porous material, the density is important to relate the strength of the material to the amount matter in the material. Equation (6) is not suitable for multiply boards since the different plies will have different properties, hence the requirement of uniformity in the thickness direction will not be met.

Figure 5: In a multiply board, di is the thickness of layer i, hi is the distance from the mid plane of layer i to the mid plane of the whole board and d z0 = − 2 , where d is the thickness of the whole board.

For multiply boards, see Figure 5, the laminate theory [8] can be used and the bending stiffness can be calculated with

B2 S = D − , (7) b A where

n X A = Ei(zi − zi−1) (8) i=1 n 1 X B = E (z2 − z2 ) (9) 2 i i i−1 i=1 n 1 X D = E (z3 − z3 ) . (10) 3 i i i−1 i=1 This model assumes constant material properties within each ply in the z direction and in the out of plane direction. It also does not take into account the interlaminar shear forces that are induced by the difference in deformation in the different materials.

7 Like the tensile stiffness, bending stiffness can also be normalized to make the property in- dependent of the amount of the fibres. The bending stiffness index is calculated by dividing the bending stiffness by the grammage cubed, expressed as

S hNm7 i S = b , (11) b,s w3 kg3 g where the units of Sb are [mNm] and w is in [ m2 ]. From Equations (7)-(10) it is noticeable that the parameter with the greatest influence on the bending stiffness is the thickness. While the modulus of elasticity has a linear effect on the bending stiffness, the thickness has a cubic dependence [8]. Because bending stiffness is a compound property that depends on the material and the geometry, a multiply laminate tries to imitate the principle of the I-beam, see Figure 6, where a considerable part of the material is positioned away from the centre. To imitate this principle, the key for a high bending stiffness board is to have high tensile stiffness outer plies and low density core, thus maximising the bending stiffness index.

Figure 6: I-beam principle: Considerable of the material (fibres) is posi- tioned away from the centre.

2.2 Laboratory testing methods

Material properties require different testing methods and equipment. The following section summarizes the testing methods for the properties described above, i.e. grammage, thickness, tensile stiffness and bending stiffness. As mentioned earlier, density is not a measured param- eter, but calculated from grammage and thickness with Equation (1). Conditioning will also be discussed as testing environment is of utmost importance in the paper industry because of the temperature and moisture sensitivity of the fibrous structure of paper. The test methods described below are based on the test standards of the International Organization for Standard- ization (ISO). Other governing bodies exist for paper testing such as the Technical Association of the Pulp and Paper Industry (TAPPI) or the Scandinavian Pulp, Paper and Board Testing Committee (SCAN), but will not be discussed in this report.

Conditioning Conditioning is a crucial step for comparable test results. As paper-based materials are highly sensible to temperature and moisture variations, exposing the samples to a standard and con- trolled atmosphere for a certain period of time ensures uniform test conditions. The standard

8 temperature stated by the standard ISO 187 [9] is 23◦C with a relative humidity (RH) of 50%. Samples must be placed in a controlled environment where all sides of the sample are in contact with the ambient air. The time of exposure depends of the grammage of the sample and its surface condition, e.g. type of coating. Samples are considered conditioned when the moisture content of the fibres is stabilized.

Grammage The grammage is calculated from two direct measurements: area of the sample and its weight. The usual procedure is to use a punch cutter of a known area and then weight the sample. The standard ISO 536 [10] dictates all the dimensions and quantities required, the recommended area is between 50 000 mm2 and 100 000 mm2. The grammage is then calculated from m g = , (12) A where m is the mean of the mass of the samples and A is the mean of the area of the samples. Note that the area is considered constant when using a punch cutter.

Thickness Thickness is a direct measurement of the distance that separates the two surfaces of the sheet. Thickness can be measured physically by two different methods: caliper and integrated mean. The caliper method is widely used in the industry for its simplicity and rapidity but tends to overestimate the thickness by measuring the peaks only, Figure 7a. The integrated mean thickness method, also called the STFI method or structural thickness, uses two hemispherical gauges that follow the surface roughness and average the measured thickness for a certain area, Figure 7b. In this study, the caliper method is the method of choice, mainly for reasons of equipement availability. Although previous work by Wretstam [11] showed a negligible difference between the two thickness measurement methods on Iggesund Paperboard AB boards.

(a) Caliper method. (b) Integrated mean thickness method [12].

Figure 7: Thickness measurement methods.

The test standard ISO 534 [13] describes a method suitable for both single sheet and bulk thickness, where the area of measurement in 200 mm2. The standard also describes how to calculate the apparent density from the thickness and grammage measurements.

9 Tensile stiffness Tensile stiffness can be calculated with two different methods: tensile testing and ultrasonic measurement. Both methods will be used in this study. The tensile testing method, Figure 8, calculates the stiffness from two measurements: force and displacement, as shown in section 2.1. The tensile testing method used, described in the standard ISO 1924-3 [14], consists of clamping both ends of a strip of paper of a known width, 15 mm, and pulling on it until rupture with a constant rate of deformation. ISO 1924-3 [14] requires a test length of 100 mm. While the specimen is being deformed, several measurements of force and displacement are made and a curve similar to Figure 4 is plotted. The tensile stiffness is defined as the steepest slope calculated.

Figure 8: Tensile testing method [2].

The ultrasonic measurement method is not yet regulated by a standard. The reference in ultrasonic measurements for paper products is the Lorentzen & Wettre (L&W) TSO measuring device [15], where TSO stands for tensile stiffness orientation. L&W published a book [12] where the method is well explained as well as the functioning of their measuring device, but in short; the stiffness of the material is related to the speed of sound in this same material.

Bending stiffness The bending stiffness can be measured with different methods: two, three and four points bending or by resonance method. The resonance method will not be discussed in this paper, but a good description of the method can be found in the book Pulp and paper testing [7]. For the bending methods, the bending stiffness is calculated from two measurements: force and displacement. The test specifications are presented in the standard ISO 5628 [16]. Note that the bending resistance and bending stiffness are two different material properties, but measured with the same method. The bending resistance, expressed in [mN], represents the reaction force recorded at a specific bending angle, usually 15◦. The bending stiffness, expressed in [mNm], is the moment calculated from the measured force and displacement. The bending stiffness is divided in two standard measurements: (15◦) and (5◦), the only difference is the deflection angle.

The two point bending method (Figure 9) is widely used in the paper and board industry for its mechanical simplicity and ease of use. The two point method consists of a clamp and a load cell separated by a known distance l, 50 mm in this case and a breadth b of 38 mm. If the clamp is rotating, Figure 9a, then the reaction force is recorded with the rotation angle. The bending stiffness is calculated with

60F l2 S = , (13) b πθb but if the clamp is fixed, Figure 9b, the load cell is pushed on the sample and the reaction force and displacement are recorded. The bending stiffness is then calculated with

10 F l3 S = . (14) b 3δb In Equations (13) and (14) F is the recorded force at maximum deformation, δ is the maximum deflection, θ is the rotation angle in degrees, b is the breadth of the sample and l is the testing length.

(a) Rotating clamp.

(b) Fixed clamp.

Figure 9: Two point bending method.

The three point bending method is simply a symmetry of the 2 point method, see Figure 10. The sample is simply supported on both ends and a load cell is applying a load point half way between the supports. The force and displacement are recorded. The bending stiffness is calculated with Equation (14).

Figure 10: Three point bending method.

11 The four point bending method is mostly used for thick boards or for corrugated boards because it does not cause interlaminar shear [17]. Interlaminar shear can cause warping of the cross section planes and lead to inaccurate measurements [17]. The four point method is then l preferred if the length to thickness ratio ( d ) is less than 40 [16], when referring to Figure 9. The test fixture consists of four point loads, see Figure 11, the applied force and displacement are recorded. The bending stiffness is calculated as

F l l2 S = 1 2 , (15) b 8δb where F is the recorded force at maximum deformation expressed in [mN], δ is the maximum deflection in [mm], b is the width of the sample in [mm] and l1 and l2 are distances between the point loads in [mm], see Figure 11.

Figure 11: Four point bending method.

2.3 Online testing methods

Some measurements are also taken throughout the paper forming process. These measurements are called online measurements; they are continuous measurements taken on the moving web on the board machine and are averaged over the time period desired. An array of properties are measurable online such as thickness, grammage, smoothness, gloss, filler content and more. The values used in both models are a one minute average taken 3 minutes before the end of the reel. This section will briefly present the thickness and grammage measurements, the only ones used for this project.

The different sensors are usually all mounted on the same moving head and move back and forth from one side to the other of the moving web which gives a zigzag path on the web, shown in Figure 12.

12 Figure 12: Online measuring device’s movement.

Online thickness measurement is a continuous measurement using two floating platens touching the surface and where an electric signal is converted into a distance between the platens [18].

Online grammage measurement is also a continuous measurement that uses two different instruments. The baseboard grammage is measured using the beta radiation principle [18] with Krypton-85 as a radiation source giving the total grammage because this type of radiation is sensible to mass.

Another sensor uses x-rays (gamma radiations) [18] to measure the coating grammage. Gamma radiations are sensible to the fillers, coating particles and latices. After each layer of coating, a sensor measures the total amount of coating on the board. 2.4 Quality control testing

The quality control testing is made on a CD strip of the whole width of the machine and 30 cm long, see Figure 2. This strip is fed into an automatic tester, in this case a L&W Autoline 400 [19]. This machine tests several different optical and mechanical properties. Figure 13 shows a section of the test strip with the different destructive tests made.

13 Figure 13: Section of quality control test strip.

The test section shown above is repeated 7 times along the cross-machine direction on a strip of about 4.6m long. Each measurement is made once per section, with the exception of bending stiffness which is measured twice. Figure 13 shows 4 specimens per direction for the bending stiffness but each pair corresponds to one measurement. The bending stiffness is measured once bending up and once bending down, the average of both test is recorded as one measurement. Each measurement is recorded with its position, but in this study only the average value for the whole strip is considered. Being only interested in the thickness and bending stiffness, one reel of paper is then defined by three averaged measurements: thickness, bending stiffness in CD and bending stiffness in MD. The Autoline 400 [19] measures the thickness using the single sheet caliper method and the bending stiffness using the 2-point bending method.

14 3. Assumptions and Simplifications

Based on the laminate theory, the model considers that the boards are made of three distinct layers with a sudden change in properties between each layer, although the manufacturing pro- cess will induce a certain transitional zone with interlaced fibres, see Figure 14. The laminate model does not account for interlaminar shear. The top and bottom plies are considered to be identical, even though the recipes of some products have different outer layers, regarding beating energy for example.

Figure 14: Cross section of paperboard [2].

The different plies are not only considered distinct from one another, but the properties of each ply are also considered constant throughout the plies in the thickness direction. The paper forming process creates internal stresses in the structure and these stresses are partially relieved by re wetting the fibres in steps downstream of the initial drying. The work of Ostlund¨ [4] suggests that there is a gradient in internal stresses changing from compressive stresses on the surfaces and tensile stresses in the centre, see Figure 15. This variation in internal stresses would mean a variation in plies properties, between the different plies but also within one ply itself.

Figure 15: Internal stress distribution [20].

15 Another assumption made is that the coating does not contribute to the mechanical properties of the board in any way. The coating is considered to have a modulus of elasticity much lower than the paper itself in a way that its effect on the bending stiffness is negligible. The coating as a material does not modify the board mechanical properties, but the process of adding coating contributes to the development of the final properties; by re wetting and drying the fibres for example. In multilayer coating, the different layers have a different purpose. The first layer (pre-coating), is usually used to increase the opacity and fill the small pores on the surface [6]. For this reason the first layer is not considered to contribute to the thickness. The other layers g are assumed to have a thickness of 1 μm per m2 of coating. The layers contributing to the thickness will be referred to as effective coating, see Figure 16.

(a) Effective layers: 2 & 3. (b) Effective layers: 2 & 4.

(c) Effective layer: 2. (d) Effective layers: 3 & 4.

Figure 16: Schematic representation of the effective coating on different products.

Other than the coating pattern variation between different products, the grammage share of each layer can vary. In the present work, the grammage shares are considered constant to the nominal values by neglecting the production variation.

The true thickness of a board can be calculated by rearranging Equation (1) giving: w d = . (16) ρ By expanding Equation (16) to a multiply board that has the same outer plies density the true thickness becomes

ftop + fbot fmid  dtrue = w + . (17) ρout ρmid To calculate the plies density, the grammage shares are assumed to be applicable to the density so that if, for example, the top ply represents 25% of the grammage, its density will contribute to 25% of the board density. This assumptions gives the following equation:

16 ρ = (ftop + fbot)ρout + fmidρmid , (18) given that the density of the top and bottom plies is the same and where f is the grammage share of a ply. Equation (18) above is only true if the ratio between the outer plies and middle ply density, defined by Equation (19), is equal to 1. ρ κ = out . (19) ρmid

Using the assumption presented in Equation (18) and using Equation (16) the approximate thickness of the board thickness is calculated with w dapprox = . (20) (ftop + fbot)ρout + fmidρmid

Inserting the density ratio from Equation (19) into Equation (20) gives w dapprox = . (21) (ftop + fbot)κρmid + fmidρmid

Equation (21) will induce an error in the thickness calculation. This method will cause an underestimation of the true thickness as κ increases. Figure 17 shows the influence of κ on the thickness error, for a symmetrical 3-ply board.

Figure 17: Influence of the density ratio κ on the thickness error.

This figure is for a 3 plies symmetrical board. Figure 17 shows that with a κ value of 1.18, used as a constant in the models, the underestimation will be limited to 0.69%.

17 4. Models

The calculation models use the bending stiffness model based on laminate theory presented in section 2.1, but with two different approaches. This section shows the data flow of the two calculation models used, where the data comes from, how it is processed and how it is used. Two similar models with different inputs and outputs were used with the unique goal of trying to match the calculated values as closely as possible to the measured values. The first model calculates the thickness and the bending stiffness from the online baseboard and coating grammage while the second model only calculates the bending stiffness using the online thickness, baseboard grammage and coating grammage as inputs. 4.1 Data

On the production line and in the quality control laboratory of the mill, several measurements are made. These measurements are here divided in either online measurements or laboratory measurements. The models use the two different types of data. The data used for all calculations is all the usable data of the year 2018 limited to products A, B, C, D and E.

Online data refers to measurements that are taken on the production line. For the models, coating grammage, baseboard thickness and baseboard grammage are taken from online data.

Laboratory data is used as a comparative to evaluate the models’ performance. The model generates values for bending stiffness (MD and CD) and thickness. The predictions are then compared to the measurements taken in the quality control laboratory with a L&W Autoline 400. 4.2 Model 1

The first model (Figure 18) uses product specific plies densities and TSIs determined experi- mentally to calculate the baseboard thickness and bending stiffness.

Figure 18: Data flow Model 1.

From the different laboratory measurements, a set of two densities, outer and middle plies, and four TSI values, one per ply per direction, were determined for each recipe. By knowing the

18 product, the only measurement needed in the model is the baseboard grammage. The model performance is then evaluated by comparing the calculated values with the measured values by the quality control laboratory.

The lowest cell in Figure 18 introduces the term: hardening factor. The hardening factor is a compensation factor added to the bending stiffness measurements. This factor compensates for the ageing phenomenon that will occur over the course of several weeks, where the bending stiffness will increase with time up to a certain point where it stabilises.

Model 1: Calculations In this model, the only input is the baseboard grammage measured online. Note that this grammage measurement also includes the starch from the sizing press. Knowing the grammage share of each ply, the plies weight can be calculated with

wtop = ftopw

wmid = fmidw (22)

wbot = fbotw , where w is the online grammage and f are the grammage shares. With the grammage of each ply and by knowing the density of each ply from Equation (30), the thickness of each ply is then calculated with

wtop dtop = ρout wmid dmid = (23) ρmid wbot dbot = . ρout The baseboard thickness is calculated by a summation of all the plies’ thickness with Equation (24).

dbaseboard = dtop + dmid + dbot (24) The bending stiffness model presented in Equations (7) to (10) uses Young’s modulus as a stiffness parameter. Young’s modulus can be calculated from the TSI measurements and the plies density with Equation (25).

∗ h N i Eout = Eoutρout 2 mm (25) h N i E = E∗ ρ mid mid mid mm2 With a calculated value for the board thickness from Equation (24) and two bending stiffness values, CD and MD, from Equations (7) to (10), the calculated bending stiffness values can be compared to the Autoline measurements, but not the thickness since the Autoline measures a coated board and the calculated values are for uncoated boards. To be able to compare the calculated and measured thickness, the thickness of the coating is subtracted from the Autoline measurement using the online measured coating weights and Equation (27).

For each reel a set of three calculated values and three measured values are compared to get three ratios:

19 MD SbModel RatioSbMD = MD SbAutoline SbCD Model (26) RatioSbCD = CD SbAutoline dModel Ratiod = . dAutoline These three ratios are used to evaluate the performance of the model; a ratio of 1 meaning an exact match, < 1 meaning an underestimation and > 1 meaning an overestimation. 4.3 Model 2

The second model (Figure 19) is somewhat similar to the first model in a sense that it uses the same laminate model for the bending stiffness calculation.

Figure 19: Data flow Model 2.

The main difference is that the thickness is not calculated, but set to the real baseboard thickness measured online meaning that the plies density are not fixed for a specific product but the ratio between the outer and middle plies, κ, is fixed. The experimentally measured, product specific, stiffness values are still used in this model. Once again, the model performance is evaluated by comparing the calculated values with the measured values by the quality control laboratory.

Model 2: Calculations This model takes two online measurements as inputs, grammage and thickness, both of which are measured on a calendered and uncoated board. Knowing the grammage and the thickness from the online measurements, the baseboard density can be calculated with Equation (1). The density of each ply can also be calculated with Equation (30). With Equation (22), the grammage of each plies can be calculated. With the grammage and the density of all plies the individual thicknesses can be calculated with Equation (23). The plies Young’s Modulus are calculated the same way as in the first model with Equation (25) and the laboratory measured TSI. The comparison is made the same way as in the previous model, see Equation (26), but without the thickness this time since it is used as an input and not calculated. This model then generates two bending stiffness ratios to evaluate its performance.

20 5. Experimental Methods

To determine the boards and plies properties, a series of experimental testing and calculations were used. The laboratory measurements were all made according to the testing standards described in section 2.2. The tests and measurements performed are: thickness, grammage, tensile testing and TSO measurement. 5.1 Material

The different laboratory measurements were performed on a variety of multiply solid bleached boards. The samples’ grammages are shown in Table 1. All samples have a composition and coating structure that correspond to one of the images in Figure 16.

Table 1: Products’ nominal grammage

Products Grammage [ g ] m2 A1 270 A2 220 A3 240 A4 280 B1 180 C1 260 C2 300 C3 380 D1 220 D2 300 E1 270

5.2 Laboratory testing

All laboratory measurements were performed internally and locally with the exception of the ultrasonic measurements that were made at another Iggesund Paperboard AB mill in Work- ington, England. Conditioning was ensured before all testing according to ISO 187 [9].

Thickness Measurements The thickness measurements were made using a L&W micrometer (caliper method), according to the ISO 534 [13]. The measured thickness is a measure of the coated samples, the uncoated thickness is calculated with

dbaseboard = dmeasured − dcoating , (27)

where dcoating is the thickness of the effective coating, as discussed in section 3.

Grammage Measurements The grammage measurements were made using a L&W 100 cm2 square punch cutter for the area measurement. The samples were then weighted on a Mettler-Toledo MS303TS precision laboratory scale. The uncoated grammage is calculated with the measured grammage and the target coating weights with Equation (28).

21 wbaseboard = wmeasured − wcoating (28)

Ply Densities The plies’ density are calculated from the baseboard density and results of previous laboratory experiments. The results for the ply densities are presented in Table 2. The values shown are an average of three specimens from the same A4 sheet.

Table 2: Ply densities

Density [ kg ] Products m3 Outer plies Middle ply A1 811 689 A2 962 818 A3 900 765 A4 878 746 B1 948 806 C1 843 717 C2 806 685 C3 795 676 D1 825 701 D2 813 691 E1 803 682

The results show a significant variation with products of the same line and with the same recipe; density decreases as the grammage increases.

The baseboard density is calculated using Equation (1) with the results of Equations (27) and (28). Measures taken on laboratory sheets (undocumented internal experiment) for the plies density on both uncalendered and calendered hand sheets, showed that the outer plies will increase their density by 14% during calendering and the middle ply will increase by 19%. For the calculation of the production board density, the density ratio, κ, of laboratory sheets is used so that ρ 1.14ρ κ = out = labout = 1.18 , (29) ρmid 1.19ρlabmid

where ρout and ρmid represent the plies density for the production board and ρlabout and ρlabmid represent the plies density for the laboratory sheets. From Equations (18) and (29), the different ply densities can be calculated with Equation (30).

 −1 ρ = ρ f κ + f mid avg out mid (30) ρout = ρmidκ

Tensile Testing Tensile tests were performed on a L&W Alwetron TH1 according to ISO 1924-3 [14] specifi- cations with a sample width of 15 mm, a test length of 100 mm and a constant deformation speed of 100 mm/s. Three specimens per direction were used and the results were averaged. The machine measures the tensile stiffness in N/m. To convert the tensile stiffness into a TSI,

22 Equation 3 is used. The density used in this case is the baseboard density.

The results from the tensile testing are presented in Table 3. The values shown are an average of three specimens from the same A4 sheet.

Table 3: Tensile test stiffness measurements

TSI [ MNm ] Products kg MD CD A1 6.5 3.0 A2 7.5 4.0 A3 7.5 3.7 A4 8.8 3.4 B1 10.4 4.5 C1 9.4 4.0 C2 9.5 3.3 C3 8.7 3.1 D1 10.2 4.4 D2 8.3 4.1 E1 7.9 4.7

TSO Measurements The ultrasonic measurements were performed externally in Workington. The device used was a L&W TSO measuring device. The grammage measurements’ instrument and conditions are unknown. Unfortunately not all products were tested with the TSO measuring device, Table 4 shows the results for the six products tested:

Table 4: Ultrasonic stiffness measurements

TSI [ MNm ] Products kg MD CD A2 9.7 5.9 A3 9.8 5.6 A4 10.8 5.5 B1 12.3 6.2 C1 11.0 5.3 C2 10.7 5.0

The results of the ultrasonic measurements in Table 4 are higher than those of the tensile test in Table 3. Table 5 shows the ratio between the two measuring methods, where the ultrasonically measured stiffness is divided by the mechanically measured stiffness.

Table 5: Ratio of TSI evaluated by TSO device and TSI value from tensile testing

Products MD CD A2 1.18 1.36 A3 1.15 1.59 A4 1.23 1.60 B1 1.30 1.50 C1 1.30 1.53 C2 1.23 1.63

23 The difference in TSI between the two methods is significantly higher for the cross-machine direction. 5.3 Determination of TSI of each ply

The plies TSI were calculated with three different methods using two different measurements, tensile testing and TSO, for a total of three sets of values. The sought values are:

∗MD • Eout : outer plies in MD

∗CD • Eout : outer plies in CD

∗MD • Emid : middle ply in MD

∗CD • Emid : middle ply in CD

The first method is to use the experimental results of the tensile testing and the ultrasonic measurements combined with the nominal grammage shares hMNmi E∗ = (f + f )E∗ + f E∗ , (31) avg top bot out mid mid kg ∗ ∗ where Eavg is the tensile test result and Eout is the TSO measurement, one equation per direc- tion (MD and CD).

The second method is by using the laminate theory presented in Equations (7) to (10), but written differently [21]

n X Sb = Sb,i , (32) i=1 where Sb is the nominal bending stiffness from product specification and Sb,i is the bending stiffness for the layer i and is calculated with

 d3  S = E i + d (z − z )2 . (33) b,i i 12 i i 0

In Equation 33 above, Ei is the modulus of elasticity of layer i, di and zi are the layer i’s thickness and mid plane distance to the 0 surface, respectively (Figure 5).

From Tables 3 and 4, the tensile stiffness indexes of each plies can be calculated and are presented in Table 6.

24 MNm Table 6: Plies TSI [ kg ]

TSI + TSO TSI + S TSO + S Product b b Outer Middle Outer Middle Outer Middle MD -- 11.1 2.2 -- A1 CD -- 6.3 0.5 -- MD 10.2 5.0 11.8 3.6 10.6 9.8 A2 CD 6.2 1.9 6.4 1.9 5.4 7.5 MD 10.2 5.0 10.8 4.5 9.7 10.7 A3 CD 5.8 1.6 6.1 1.9 5.1 7.0 MD 11.2 6.6 10.2 7.5 9.2 13.1 A4 CD 5.7 1.2 6.0 1.4 5.1 7.0 MD 14.2 7.3 11.5 9.5 9.7 18.0 B1 CD 7.1 2.4 5.3 3.9 4.1 9.7 MD -- 11.9 7.5 -- C1 CD -- 5.8 2.6 -- MD 12.5 7.1 13.1 6.7 11.7 13.3 C2 CD 6.0 1.1 5.8 1.3 4.5 7.2 MD 11.8 6.2 11.0 7.0 9.5 13.8 C3 CD 5.5 1.2 4.6 1.9 3.4 7.2 MD -- 16.7 5.0 -- D1 CD -- 8.1 1.3 -- MD -- 16.9 1.3 -- D2 CD -- 8.0 0.9 -- MD -- 13.1 3.6 -- E1 CD -- 5.9 3.8 --

Table 6 above shows that by using the ultrasonic measurements and the nominal bending stiffness (column 4) to calculate the TSI values for the different plies, this method gives stiffer middle plies than outer plies. Because the strength and stiffness of a fibrous material is related to the density, having denser outer plies cannot lead to a stiffer middle ply. This set of results is then improbable and disregarded. These results can have several meanings. One of which is that the tensile stiffness values measured by the ultrasonic method do not represent the board average property but are instead influenced by the higher density of the outer plies, it could even be a measurement of the outer plies itself. Comparing the results of columns 2 and 3 of Table 6 showing very similar results strengthens this hypothesis. The results of column 4 could also be explained by the fact that the TSI of each ply was calculated from values of two different origins, the tensile stiffness was measured on a specific sample, while the bending stiffness comes from the product specification. The samples used for the ultrasonic measurements could have had a higher bending stiffness than the specifications, ideally the tensile stiffness and the bending stiffness would be measured on the same sample. 5.4 Coating thickness

In section 3 some assumptions regarding coating thickness were presented. In order to verify this assumption, the online thickness measurements before and after coating were compared. By knowing how much coating goes on the board, the coating thickness can be estimated. The coated thickness is plotted against the uncoated thickness on a scatter plot. The slope of the trend line should be around 1, while the y-intercept will give the average coating thickness.

This experiment was a numerical experiment to verify the assumption that the coating adds 1 g [µm] per [ m2 ] of coating, see section 3. The results for product C are presented in Figure 20.

25 Figure 20: Coating thickness evaluation for product C.

Knowing the coating pattern for product C and the nominal weight of each coating layer, the expected y-intercept is 14 µm.

The figures for the other products can be found in Appendix A, but Table 7 shows the results of the experiment. Note that for technical reasons, this experiment could not be done for both machines. Moreover, product E goes through a second calender after coating which will reduce the thickness, hence the expected y-intercept is unknown. product D has been separated in two sub lines because the amount of coating is different for the lower and higher grammages.

Table 7: Coating thickness experiment

Product line Expected y-intercept Measured y-intercept Slope r2 n B 14 8.3 1.00 0.96 227 C 14 18.6 0.98 0.99 4205 D Low grammage 18 28.7 0.91 0.98 397 D High grammage 24 38.7 0.92 0.99 1168 E - 17.5 0.98 0.98 236

The expected y-intercepts correspond to the effective coating thickness as presented in section 3. All the measured y-intercepts are higher than the expected ones with the exception of product B, which also presents the highest slope, i.e. 1.00. A higher y-intercept means a higher coating thickness. A thicker coating could be explained by either a contribution to the thickness by the pre-coating and/or a lower density of the dry coating. These results do not present any valuable information on that matter but that the coating thickness could be higher than expected. For this study, the initial assumption was maintained.

26 6. Results and Discussion

This section presents some of the results of the two calculation models, more detailed results can be found in Appendix B. The two models have shown various level of success on the different products where in some cases the average predictions were a near perfect match, but the spread of the values is too high to consider accuracy. Figure 21 shows the results for both models on product A.

(a) Model 1. (b) Model 2.

Figure 21: Results for models 1 and 2 on product A.

Model 1 shows an underestimation of the thickness, a good average estimation of the bending stiffness in MD and an overestimation in CD. As the bending stiffness is calculated from that calculated thickness, this indicates faulty TSI values and/or density ratio. As expected, with model 2 using the true thickness, the calculated bending stiffness values increase, but the spread remains.

The results show the gravity of the spread, especially for the bending stiffness. The spread is more easily visualised with the histograms in Figure 23.

(a) Thickness spread. (b) Bending stiffness CD.

Figure 22: Difference in spread between thickness and bending stiffness.

27 The thickness distribution has a much lower spread because of the calendering operation where the high spots are compressed, resulting in a more uniform thickness. However, this will also increase the local variation in density because on an uncalendered board, the high spots, as in thicker spots, will correlate with the high grammage spots therefore increase the density by compressing the material. While the local density variation increases, the variation in tensile stiffness will remain the same. Consequently, the variation in bending stiffness by the calen- dering process will only be reduced as an effect of the reduced thickness.

The deviation of the average predictions means that the plies TSI calculated with the prod- uct specifications are probably not accurate; these calculations should be done on a sample of known tensile and bending stiffness.

Model 1 has only one input: grammage. For a given product and a given grammage, the model will always return the same value; the nature of the spread is not a measurement variation, but a production variation. Meaning that changing the density ratio or the plies’ TSI will only modify the average performance.

Similar results are observed for the other products. Figure 23 shows the results for product C.

(a) Model 1. (b) Model 2.

Figure 23: Results for models 1 and 2 on product C.

In Figure 23, model 1 shows an underestimation of all properties, but in this case the estimation for CD is the same as for MD. Model 2 has a near perfect average estimation, but there is a variation of almost 60% for one specific product. product C can be subdivided in two recipes, Figure 23b shows a clear division in these recipes where the model seems to overpredict at lower grammages and underpredict for the heavier boards, meaning a potential wrong assumption of the density ratio. The density ratio is the only value that was not measured on production boards and is assumed constant for all products.

28 7. Conclusions and Recommendations

The objective of this work was to predict the thickness and the bending stiffness using process data. The models show various levels of precision accuracy, showing that some assumptions need to be revised, but despite that show promising results. This work demonstrates the presence of strong property variations in the current paperboard making process. Iggesund Paperboard AB collects currently a lot of interesting data throughout the paper forming process, but most of these data are not used to their full potential. Some of the questionings raised during this study can be answered by analysing the current measurements, but in some cases more measurements are required to monitor the property, e.g. tensile stiffness. 7.1 Thickness prediction

The thickness predictions of model 1 has constant underprediction of less than 5%, but its performance evaluation is based on two assumptions: the density ratio and the coating thick- ness. These assumptions were kept constant for all the products, but will in reality change for each different product. For example, the density ratio is more than likely to be different for each product because the beating energy and composition of the different plies differs from one product to another. The coating thickness could also differ from product to product in function of the baseboard surface roughness and the weight of the pre-coat. More experiments could be made to get more exact values and bring the average prediction equal to the Autoline measurements, i.e. bring the average prediction to one, but the spread of the input cannot be changed. 7.2 Bending stiffness prediction

The bending stiffness has the distribution that shows the most variation; variation that is most likely attributed to production instability. The models have a fixed set of parameters for each specific product, meaning that the only varying inputs from production are the grammage and the thickness. This model can then not really adapt to all the different parameters that vary on a board machine, e.g. fibre orientation, wet pressing, drying, etc. Meaning that the parameters defined in a laboratory can only be attributed a specific combination of conditions. Before attempting to control the effect of these parameters, detecting and understanding the instabilities as well as the influence of the parameters are mandatory steps. 7.3 Recommendations for future work

A possible next step would be to detect and investigate the local property variations, for example: detecting the density variation induced by the calendering process from grammage variations and the tensile stiffness variations in CD and MD. The online sensors could be fixed to a specific point and measure the properties at only one CD position throughout a whole reel generating an MD profile by eliminating the variations along CD. To improve the model results it is important to quantify the density ratio (κ) and the thickness of the coating applied on the boards. The coating thickness could be measured with an experiment where the coating is added one layer at the time, while waiting to reach steady state, and measuring the increase in thickness after each layer. Increasing the model complexity could help adapt to process variations by considering some property influencing steps, e.g. the drying section and also by considering the grammage share variation. Lastly, to help characterise the material and improve the quality control, it would be relevant to measure the tensile stiffness on a regular basis, for example: as part of the reel quality control.

29 8. References [1] J. Pettersson, P.-O. Gutman, T. Bohlin, and B. Nilsson. A grey box bending stiffness model for paper board manufacturing. Proceedings of the 1997 IEEE International Conference on Control Applications, pages 395–400, 1997.

[2] Iggesund Paperboard AB. Iggesund Paperboard Reference Manual. Iggesund Paperboard AB, 2010. URL https://www.iggesund.com/en/knowledge/knowledge-publications/ the-reference-manual/.

[3] M. Ek, G. Gellerstedt, and G. Henriksson. Paper Products Physics and Technology. Pulp and Paper Chemistry and Technology. Berlin/Boston, 2009. ISBN 9783110213454.

[4]M. Ostlund,¨ S. Ostlund,¨ L.A. Carlsson, and C. Fellers. Residual stresses in paperboard through the manufacturing process. Journal of Pulp and Paper Science, 31-4:197–201, 2005.

[5] T. Wahlstr¨om. Influence of shrinkage and stretch during drying on paper properties. Trita- PMT 1999:15. Stockholm, 1999. ISBN 91-7170-486-8.

[6] E. Lehtinen. Pigment coating and surface sizing of paper. Papermaking science and tech- nology. Finnish Paper Engineers’ Association, 2000. ISBN 9789525216004.

[7] J.E. Levlin and L. S¨oderhjelm. Pulp and Paper Testing. Papermaking science and tech- nology. Finnish Paper Engineers’ Association, 1999. ISBN 9789525216004.

[8] C. Fellers, A. de Ruvo, M. Htun, L. Carlsson, and R.r Lundberg. Carton Board: Profitable use of pulps and processes. Swedish Forest Products Research Laboratory (STFI), 1983.

[9] ISO 187:1990. Paper, board and pulps – Standard atmosphere for conditioning and testing and procedure for monitoring the atmosphere and conditioning of samples. Standard, International Organization for Standardization, Geneva, CH, dec 1990.

[10] ISO 536:2012. Paper and board – Determination of grammage. Standard, International Organization for Standardization, Geneva, CH, jul 2012.

[11] S. Wretstam. Characterization of property variations in paperboard samples. Master’s thesis, KTH, Stockholm, June 2018.

[12] G. Lindblad, T. F¨urst,and I. Rosengren. The Ultrasonic Measuring Technology on Paper and Board: A Handbook. Lorentzen & Wettre, 2007. ISBN 9197378100.

[13] ISO 534:2011. Paper and board – Determination of thickness, density and specific volume. Standard, International Organization for Standardization, Geneva, CH, nov 2011.

[14] ISO 1924-3:2005. Paper and board – Determination of tensile properties – Part 3: Con- stant rate of elongation method (100 mm/min). Standard, International Organization for Standardization, Geneva, CH, jul 2005.

[15] AB Lorentzen & Wettre. L&W TSO Tester, 2019. URL https://new.abb.com/ pulp-paper/abb-in-pulp-and-paper/products/lorentzen-wettre-products/ laboratory-paper-testing/paper-strength-testing/l-w-tso-tester.

[16] ISO 5628:2012. Paper and board – Determination of grammage. Standard, International Organization for Standardization, Geneva, CH, jan 2012.

30 [17] Handbook of physical testing of paper. Vol. 1. Dekker, New York, 2. ed., rev. and expanded. edition, 2002. ISBN 0-8247-0498-3v.

[18] K. Leivisk¨a. Process Control. Papermaking science and technology. Finnish Paper Engi- neers’ Association, 1999. ISBN 9525216144.

[19] AB Lorentzen & Wettre. L&W Autoline 400, 2019. URL https://new.abb.com/ products/4LB4110001/lw-autoline-400.

[20] M. Ostlund.¨ Experimental determination of residual stresses in paperboard. Trita-HFL, 0349. Stockholm, 2003.

[21] K. Niskanen. Paper physics. Papermaking science and technology. Finnish Paper Engi- neers’ Association, 1998. ISBN 9525216160.

31 Appendices

A. Coating thickness - Numerical experiment results This appendix presents the results of the numerical experiment to measure the coating thickness for each product.

Figure A.1: Coating thickness evaluation for product B - Expected y-intercept: 14 µm.

Figure A.2: Coating thickness evaluation for product D low grammage - Expected y-intercept: 18 µm.

32 Figure A.3: Coating thickness evaluation for product D High grammage - Expected y-intercept: 24 µm.

Figure A.4: Coating thickness evaluation for product E High grammage - Expected y-intercept: 14 µm.

33 B. Models results This appendix presents the result plots for both models and all products. B.1 Product A

Figure B.1: Results for Model 1 - product A.

(a) Histogram for thickness (b) Contour plot for thickness.

Figure B.2: Results for Model 1 - product A - Thickness.

34 (a) Histogram for Bending stiffness CD. (b) Contour plot for Bending stiffness CD.

Figure B.3: Results for Model 1 - product A - Bending stiffness CD.

(a) Histogram for Bending stiffness MD. (b) Contour plot for Bending stiffness MD.

Figure B.4: Results for Model 1 - product A - Bending stiffness MD.

35 Figure B.5: Results for Model 2 - product A.

(a) Histogram for Bending stiffness CD. (b) Contour plot for Bending stiffness CD.

Figure B.6: Results for Model 2 - product A - Bending stiffness CD.

36 (a) Histogram for Bending stiffness MD. (b) Contour plot for Bending stiffness MD.

Figure B.7: Results for Model 2 - product A - Bending stiffness MD.

B.2 Product B

Figure B.8: Results for Model 1 - product B.

37 Figure B.9: Results for Model 2 - product B.

B.3 product C

Figure B.10: Results for Model 1 - product C.

38 (a) Histogram for Thickness. (b) Contour plot for Thickness.

Figure B.11: Results for Model 1 - product C - Thickness.

(a) Histogram for Bending stiffness CD. (b) Contour plot for Bending stiffness CD

Figure B.12: Results for Model 1 - product C - Bending stiffness CD.

(a) Histogram for Bending stiffness MD. (b) Contour plot for Bending stiffness MD.

Figure B.13: Results for Model 1 - product C - Bending stiffness MD.

39 Figure B.14: Results for Model 2 - product C.

(a) Histogram for Bending stiffness CD. (b) Contour plot for Bending stiffness CD.

Figure B.15: Results for Model 2 - product C - Bending stiffness CD.

40 (a) Histogram for Bending stiffness MD. (b) Contour plot for Bending stiffness MD.

Figure B.16: Results for Model 2 - product C - Bending stiffness MD.

B.4 Product D

Figure B.17: Results for Model 1 - product D.

41 (a) Histogram for Thickness. (b) Contour plot for Thickness.

Figure B.18: Results for Model 1 - product D - Thickness.

(a) Histogram for Bending stiffness CD. (b) Contour plot for Bending stiffness CD.

Figure B.19: Results for Model 1 - product D - Bending stiffness CD.

(a) Histogram for Bending stiffness MD. (b) Contour plot for Bending stiffness MD.

Figure B.20: Results for Model 1 - product D - Bending stiffness MD.

42 Figure B.21: Results for Model 2 - product D.

(a) Histogram for Bending stiffness CD. (b) Contour plot for Bending stiffness CD.

Figure B.22: Results for Model 2 - product D - Bending stiffness CD.

43 (a) Histogram for Bending stiffness MD. (b) Contour plot for Bending stiffness MD.

Figure B.23: Results for Model 2 - product D - Bending stiffness MD.

B.5 Product E

Figure B.24: Results for Model 1 - product E.

44 Figure B.25: Results for Model 2 - product E.

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