Two-dimensional axisymmetric winding model for finite deformation |
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Authors: | K Ärölä R von Hertzen |
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Affiliation: | (1) Smart Machines, Structural Dynamics, VTT–Technical Research Centre of Finland, P.O.Box 1000, 02044 VTT Espoo, Finland;(2) Laboratory of Fatigue and Strength, Lappeenranta University of Technology, P.O.Box 20, 53851 Lappeenranta, Finland |
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Abstract: | A two-dimensional axisymmetric winding model for wound rolls of thin web is developed. The model accounts for radial and axial
displacements and radial, circumferential, axial and shear stresses. The roll build-up is modeled as an incremental accretion
process. The material behaviour of the roll is considered as hyperelastic, orthotropic and radially nonlinear. The numerical
solution is developed using the finite element method and the total Lagrangian formulation. The model is applied to the winding
of paper rolls. It is shown that centrifugal forces may considerably affect the resulting stress distributions. For nonzero
Poisson’s ratios significant edge effects in the roll stresses are found. In particular, high shear stresses and shear stress
gradients are discovered in the vicinity of the core near the roll ends. A remarkable stress leveling phenomenon is found
where the effect of a non-constant incoming web tension is evened out in the roll axial direction. |
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Keywords: | Winding Paper roll Axisymmetric Large deformation |
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