Modelling and numerical simulation of the wrinkling evolution for thermo-mechanical loading cases
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1 Modelling and numerical simulation of the wrinkling evolution for thermo-mechanical loading cases Georg Haasemann Conrad Kloß 1 AIMCAL Conference 2016
2 MOTIVATION Wrinkles in web handling system Loss of product quality Down time of manufacturing operation Foundation for a solution Experience Profound understanding Analytical models Numerical simulations Analytical models Easy to apply Fast to compute Limited if the problem is too complex to be solved 2 AIMCAL Conference 2016
3 MOTIVATION Numerical simulations of wrinkles Challenging and time consuming Large displacement Contact with friction Strong non-linear problem Structural stability Convergence of numerical calculation Solution of complex problems Any geometry Multiphysics: mechanics, thermo-dynamics, fluid-dynamics Web-material: anisotropy, layer-stack, nonlinear material law Evaluation of results Large range of data: stress, strain, contact pressure, sliding etc. 3 AIMCAL Conference 2016
4 NONLINEAR MODELLING OF WEB TRANSPORT GEOMETRY, FE-MODEL AND BOUNDARY CONDITIONS Geometry Initial shape Finial shape A B AIMCAL Conference 2016 Web travel Radius rr zz yy Modification: crowned or concave rollers No symmetry Non-symmetric boundary conditions Unconstrained generation of wrinkles Web span LL Web width WW xx 4
5 NONLINEAR MODELLING OF WEB TRANSPORT GEOMETRY, FE-MODEL AND BOUNDARY CONDITIONS FE-mesh Flexible web: shell elements Rollers: rigid elements Element size: ~2x2 mm² Contact definition Frictional contact Normal stiffness reduction improved numerical stability Boundary conditions Prevent free body rotation of rollers Torsion spring attached to master node Nonlinear behavior of spring element 5
6 NONLINEAR MODELLING OF WEB TRANSPORT GEOMETRY, FE-MODEL AND BOUNDARY CONDITIONS Boundary conditions Movement of the web ends 1. Step: plane web U-shaped web uu xx φφ = LL 0 rr φφ cos φφ + rr sin φφ LL 0 uu zz φφ = LL 0 rr φφ sin φφ + rr(cos φφ 1) Definition of warp angle φφ tt end Subdivision into load steps = φφ max 2. Step: web tension uu LL = 0, uu RR = uu TT 3. Step: web transport uu LL = uu CC, uu RR = uu CC 6
7 NONLINEAR MODELLING OF WEB TRANSPORT GEOMETRY, FE-MODEL AND BOUNDARY CONDITIONS Generation of imperfection Problem Perfect geometry no buckling Instable result Solution Introduction of imperfect geometry or FE-mesh Linear eigenvalue buckling analysis Displacement distortion of unloaded mesh 7
8 NONLINEAR MODELLING OF WEB TRANSPORT THERMO-MECHANICAL PROPERTIES OF THE WEB MATERIAL General assumptions Material: PET Large displacement, small strain No plastic or rate-dependent deformations Medium velocity no inertial effects Elastic behavior Isotropic linear elasticity Temperature dependent YOUNG s modulus Poisson s ratio: νν = 0.4 Glass transition between 70 C and 80 C 8 AIMCAL Conference 2016
9 NONLINEAR MODELLING OF WEB TRANSPORT THERMO-MECHANICAL PROPERTIES OF THE WEB MATERIAL Thermal expansion Thermomechanical analysis (TMA) Strain in MD and TD depending on temperature Strong anisotropy if temperature of glass transition is exceeded Computation of CTE Definition of a custom material in the FE-Program 9 AIMCAL Conference 2016
10 RESULTS AND DISCUSSIONS MODEL WITH CROWNED OR CONCAVE ROLLERS Dimension of the model Radius of Roller: 60 mm Free span: 500 mm Web width: 200 mm Web thickness: 12 µm Crowned roller Geometry of crowned roller: Δrr rr max = 2% Web deformation Changing configuration of waves due to web transport y [mm] 10 AIMCAL Conference 2016
11 RESULTS AND DISCUSSIONS MODEL WITH CROWNED OR CONCAVE ROLLERS Contact behavior between web and roller Pressure Sliding distance Crowned roller Concave roller 11 AIMCAL Conference 2016
12 RESULTS AND DISCUSSIONS MODEL WITH TRANSVERSE SHIFT OF THE WEB Boundary conditions Misalignment angle of 0.2 Results Formation of wrinkles Smallest principle stress σσ II Orientation of σσ II uu zz in mm σσ II in MPa 12 AIMCAL Conference 2016
13 RESULTS AND DISCUSSIONS MODEL WITH INHOMOGENEOUS TEMPERATURE DISTRIBUTION Boundary conditions Thermal simulations temperature distribution TT(xx) Mapping of TT(xx) Results uu zz in mm Formation of wrinkles Dependency on maximum web temperature y [mm] 13 AIMCAL Conference 2016
14 SUMMARY AND OUTLOOK Summary Geometrical and physical modeling of web transport including wrinkle formation Definition of appropriate boundary conditions Formulation of a thermo-mechanical material model Set-up of numerical parameters fast convergent solution Application to different models and load cases Outlook Verification Advanced material models Anisotropy Elastic visco-plastic behavior Web-material with coatings Dynamic thermal-structural interactions 14 AIMCAL Conference 2016
15 Thank you for your attention 15 AIMCAL Conference 2016
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