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Modelling the dynamical behaviour of a paper web. Part I
KTH, School of Engineering Sciences (SCI), Solid Mechanics (Dept.), Solid Mechanics (Div.).ORCID iD: 0000-0003-3611-2250
2007 (English)In: Computers & structures, ISSN 0045-7949, E-ISSN 1879-2243, Vol. 85, no 3-4, 131-147 p.Article in journal (Refereed) Published
Abstract [en]

A new shell element has been proposed for geometrically non-linear, finite element analyses of axially moving paper web. Web instability problems of paper travelling in a printing system, such as wrinkling and fluttering, pose special challenges in the numerical analyses. For examples, theme are finite bending stiffness (as opposed to membrane), orthotropy, and non-uniform distributions of mechanical and hygro-properties (in different length scales). The new formulation has accounted for paper transport velocity and paper bending stiffness based on a mixed -1-agrangian-Eulerian description of the motion. A natural coordinate system has been employed in the analytical and finite element formulations. Benchmarking with different finite elements in various tests showed that the proposed element is indeed more stable and reliable for the chosen application than existing elements. The usability of the shell element has been successfully demonstrated by two example p:,-oblems: wrinkling of stretched isotropic and orthotropic membranes, and the vibration of a web showing a speedtensioning effect above a critical web transport velocity.

Place, publisher, year, edition, pages
2007. Vol. 85, no 3-4, 131-147 p.
Keyword [en]
axially moving materials, Hamilton's principle, one-point quadrature element, physical hourglass control
National Category
Other Materials Engineering
URN: urn:nbn:se:kth:diva-24376DOI: 10.1016/j.compustruc.2006.09.006ISI: 000244511600002OAI: diva2:349326

Tidigare titel: A shell finite element for geometrically non-linear analyses of axially moving paper webs QC 20100906

Available from: 2010-09-06 Created: 2010-09-06 Last updated: 2016-05-11Bibliographically approved
In thesis
1. Mechanics of paper webs in printing press applications
Open this publication in new window or tab >>Mechanics of paper webs in printing press applications
2006 (English)Doctoral thesis, comprehensive summary (Other scientific)
Abstract [en]

The mechanics of paper is a difficult subject because paper is a unique material. It is very thin, flexible at bending, unstable in compression and stiff at tension. Dealing with paper we have to account for orthotropy and heterogeneities created during the manufacturing process.

This thesis addresses two topics in mechanics of paper webs in printing press applications. First is the dynamic behaviour of the travelling webs. Second is so-called “fluting” after heat-set web-fed offset printing.

There are a number of challenges in simulating the dynamics of the paper web. It is necessary to include the influence of the paper web transport velocity. Due to initial sag or vibrations, gyroscopic forces affect the dynamics of the webs. Furthermore, the transport velocity reduces the stress stiffening of the web. A good theoretical model should account for large displacements and should be capable of simulating wrinkles, which is essentially a post-buckling phenomenon. Finally, the paper web is surrounded with air which reduces the natural frequencies substantially by “adding" mass to the paper. A non-linear finite element formulation has been developed in this study for simulation of travelling webs. The results of the studies shows that for the tension magnitudes used in the printing industry the critical web speed lies far above those used today. Speed limitations are rather caused by ink setting and tension control problems. If the web tension profile is skew, however, edge vibrations are inevitable even at small external excitations.

Fluting is a permanent wavy distortion of the paper web after heat-set web offset printing. It is often seen in high quality printing products, especially in areas covered with ink. It is generally accepted that tension and heat are required to create fluting. However, there have been certain disputes as to the mechanism of fluting formation, retention and key factors affecting this phenomenon. Most of the existing studies related to fluting are based on linear buckling theories. A finite element model, capable of simulating a post-buckling behaviour has been developed and experimentally verified. Studies show that none of the existing theories can consistently explain fluting. A new basic mechanism of fluting formation has been proposed and numerically demonstrated. Fluting was explained as a post-buckling phenomenon due to small scale moisture variations developing during through-air drying. It was concluded that air permeability variation is the key factor affecting fluting tendency. Fluting is retained due to inelastic deformations promoted by high drying temperatures.

Place, publisher, year, edition, pages
Stockholm: KTH, 2006. v, 18 p.
Trita-HFL. Report / Royal Institute of Technology, Solid mechanics, ISSN 1654-1472 ; 0404
Travelling webs, skew tension profiles, mixed dynamic formulation, fluting
National Category
Other Materials Engineering
urn:nbn:se:kth:diva-3863 (URN)
Public defence
2006-03-16, Fälldinsalen, Mittuniversitetet, Sundswall, 13:00

QC 20100906

Available from: 2006-03-03 Created: 2006-03-03 Last updated: 2013-01-14Bibliographically approved

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