Stability in Film Casting

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Presentation transcript:

Stability in Film Casting Olena Zavinska

Outline Problem Statement Project Goal Modeling Solution Method Validation Results Conclusions

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

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.

Outline Modeling Problem Statement Project Goal Solution Method Validation Results Conclusions

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

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

Outline Solution Method Problem Statement Project Goal Modeling Validation Results Conclusions

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

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

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

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

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

Comparison with literature reference NEWTON: Method vs Literature

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

STABLE UNSTABLE LLDPE (eps=0.1) : Stability Curves

STABLE UNSTABLE LDPE (eps=0.01) : Stability Curves

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.

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

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