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Stability in Film Casting

Stability in Film Casting. Olena Zavinska. Outline. Problem Statement Project Goal Modeling Solution Method Validation Results Conclusions. 1. Early Film Breakage. 2. Draw Resonance. Width. Thickness. Die. Web. Air Gap. Chill Roll. Off-Set. Problem Statement. Project Goal.

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Stability in Film Casting

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  1. Stability in Film Casting Olena Zavinska

  2. Outline Problem Statement Project Goal Modeling Solution Method Validation Results Conclusions

  3. 1. Early Film Breakage 2. Draw Resonance Width Thickness Die Web Air Gap Chill Roll Off-Set Problem Statement

  4. Project Goal Design and implement a method for analysis of stability of the film casting process Determine the tolerance values of system parameters to keep the process stable Reference:Silagy, D. et.al., Study of the Stability of the Film Casting Process, Polymer Engineering and Science, 36, no.21, 1996.

  5. Outline Problem Statement Project Goal Modeling Solution Method Validation Results Conclusions

  6. Assumptions • Polymer flow: • Isothermal • Elongational • Inertia, gravity, and surface tension are neglected • Kinematics’ Hypothesis (Silagy) • membrane approximation • 1D model • Velocity (u) • Length (X) • Coordinates (x,y,z) • Width (L) • Thickness (e) Reference:Silagy, D. et.al., Study of the Stability of the Film Casting Process, Polymer Engineering and Science, 36, no.21, 1996.

  7. 1. Mass Conservation: 4. Stress F.S. condition: 2. Forces: Solving Unknowns 5. Kinematics F.S. Condition: 6. Boundary Conditions: 3. Constitutive Eq.: Governing Equations Modeling

  8. Outline Problem Statement Project Goal Modeling Solution Method Validation Results Conclusions

  9. 1. Unknown Variables: 2. Independent Variables: Step 1: Scaling 3. Unknown Parameter: 4. Input Parameters: Solution Method

  10. Scaled: + inhomogeneous boundary conditions Stationary Solution Procedure Solution Method

  11. Step 2: Stationary Solution + inhomogeneous b.c.’s 1. Shooting method is applied to find the parameter E 2. RK4 is applied to solve the system, when E is given Solution Method

  12. - process is stable - process is unstable Step 3: Dynamic Solution + homogeneous b.c.’s Parameter - indicates instability Solution Method

  13. Outline Problem Statement Project Goal Modeling Solution Method Validation (Newtonian model) Results Conclusions

  14. Comparison with literature reference NEWTON: Method vs Literature

  15. Outline Problem Statement Project Goal Modeling Solution Method Validation Results (PTT model) Conclusions

  16. STABLE UNSTABLE LLDPE (eps=0.1) : Stability Curves

  17. STABLE UNSTABLE LDPE (eps=0.01) : Stability Curves

  18. Conclusions • A numerical algorithm for the resolution of linear stability analysis was developed • It shows excellent performance (precision, low calculation time) • The material rheological model explains the stabilization effect of LDPE • The algorithm can be applied to other similarly mathematical described processes.

  19. Acknowledgment • Angela Sembiring (TU/e) • Hong Xu (TU/e) • Andriy Rychahyvskyy (TU/e) • Jerome Claracq (Dow) • Stef van Eijndhoven (TU/e)

  20. the end

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