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Prediction of Paperboard Thickness and Bending Stiffness Based on Process Data

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Prediction of Paperboard Thickness and Bending Stiffness Based on Process Data 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
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