Two-dimensional axisymmetric winding model for finite deformation

Kilwa Ärölä (Corresponding Author), R. Von Hertzen

Research output: Contribution to journalArticleScientificpeer-review

7 Citations (Scopus)

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.
Original languageEnglish
Pages (from-to)933-947
JournalComputational Mechanics
Volume40
Issue number6
DOIs
Publication statusPublished - 2007
MoE publication typeA1 Journal article-refereed

Fingerprint

Finite Deformation
Shear stress
Shear Stress
Poisson ratio
Stress concentration
Model
Finite element method
Edge Effects
Centrifugal Force
Accretion
Poisson's Ratio
Stress Distribution
Finite Element Method
Numerical Solution
Gradient
Formulation

Keywords

  • Axisymmetric
  • Large deformation
  • Paper roll
  • Winding

Cite this

Ärölä, Kilwa ; Von Hertzen, R. / Two-dimensional axisymmetric winding model for finite deformation. In: Computational Mechanics. 2007 ; Vol. 40, No. 6. pp. 933-947.
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Two-dimensional axisymmetric winding model for finite deformation. / Ärölä, Kilwa (Corresponding Author); Von Hertzen, R.

In: Computational Mechanics, Vol. 40, No. 6, 2007, p. 933-947.

Research output: Contribution to journalArticleScientificpeer-review

TY - JOUR

T1 - Two-dimensional axisymmetric winding model for finite deformation

AU - Ärölä, Kilwa

AU - Von Hertzen, R.

PY - 2007

Y1 - 2007

N2 - 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.

AB - 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.

KW - Axisymmetric

KW - Large deformation

KW - Paper roll

KW - Winding

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DO - 10.1007/s00466-006-0152-8

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JF - Computational Mechanics

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