# Om kantbuckling av pappersbanan vid pappersproduktion

Sammanfattning: Web wrinkling is one of the more common web handling problems, caused by shear forces, resulting from in-plane misaligned rollers. Several analytical models have been derived, mainly based on the theory of beams or membranes and isotropic material properties. Paper is a highly anisotropic material but can be assumed orthotropic for thin structures as paper web. For this reason, an orthotropic plane stress model based on the von Kármán theory of plates have been derived. Further, an investigation has been performed on the mechanics that is the origin of the shear forces due to misaligned rollers. It is believed that the differential equation proposed by von Kármán does not have a simple solution in closed form for the proposed problem. Therefore, energy methods and double Fourier series are used to calculate the critical load by solving the corresponding eigenvalue problem. It is then shown that the use of an isotropic material model to estimate the critical load could be as much as thirty percent wrong. Thus, it is concluded that orthotropy should not be neglected in the analysis of buckling of paper webs. The shear force causes the web to deflect from its original path in the machine direction according to the normal entry law. Thus, the web tension becomes non-uniform and the stresses are redistributed so that only a small part of the web caries the load. The highest stresses are then found near the load carrying edge. Because high stresses causes permanent deformation, it has been assumed that misalignment causes the characteristic waviness that often can be seen on paper web edges in manufacturing plants. In this licentiate thesis, a model has been derived that is based upon difference in material properties across machine direction. The model shows that above mentioned waviness, not necessarily is caused by misaligned rollers, but may very well be the result of the differences in material properties, such as yield strength and Young’s modulus.

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