Numerical Modelling of the Cross Direction Shrinkage Profile in a Dryer Section, a First Approach, 1999 International Paper Physics Conference Proceedings

Torbjörn Wahlström, Klas Adolfsson, Sören Östlund, Christer Fellers

Paper properties are dramatically affected if the paper is stretched or allowed to shrink during drying. In the dryer section of a conventional paper machine transportation over heated cylinders dries the paper. During this process the paper acquires different properties at the edges compared to the middle of the web as a result of an uneven shrinkage in the cross machine direction. The aim of the present work was to study the physics behind the shrinkage profile and how the profile depends on the geometry of the dryer section. As a first approach an orthotropic hypoelastic constitutive model for plane stress was proposed. The total strain was assumed to be the sum of mechanical strain and hygroscopic strain due to water evaporation. When the paper web is on the cylinders it was assumed to be restrained from shrinkage by the pressure imposed by the drying fabric. In the free draw between the dryer cylinders no forces were acting on the edges of the web. The finite element method was used to simulate in-plane stresses and strains in the paper. Laboratory scale experiments were used for calibration of the model and creation of input data. The analysis showed that it was possible to qualitatively simulate the stresses and strains that develop in a paper web during its transportation through a cylinder dryer section. The shrinkage profile was measured on two paper machines and their respective geometry simulated. The results showed that the model gives a qualitative understanding of how the studied variables influence the shrinkage profile. If the length of the free draw was reduced the shrinkage in the middle of the paper web decreased significantly. At the edges the shrinkage also decreased but to a smaller extent. The part in the middle of the web with low shrinkage also became wider if the free draw was shortened, which means that the shrinkage gradient at the edges of the web became steeper. Shorter free draws reduced the total web width shrinkage but the difference in shrinkage between the edge and the middle increased.