Numerical Shape Optimisation in Blow Moulding

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Numerical Shape Optimisation in Blow Moulding
Hans Groot
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Overview

1. Introduction
2. Glass Blow Simulation Model
3. Optimization Method
4. Results
5. Conclusions

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Blow Molding

• e.g. glass bottles/jars

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Problem
Forward problem
Inverse problem
pre-form
container
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Forward Problem

• Interfaces ?1 and ?2 given
• Interface ?m fixed (mould wall)
• Interface ?i unknown

Forward problem
?m
?1
?i
?2
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Inverse Problem

• ?i and ?m given
• ?1 and ?2 unknown

?m
?1
?i
?2
Inverse problem
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Comparison
Inverse problem Forward problem
two unknown intefaces one unknown interface
Inverse problem under-determined or forward
problem over-determined?
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Volume Conservation

• Incompressible medium
• R(f) radius of interface G
• Simple example ? axial symmetry
• Either R1 or R2 should be known

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Inverse Problem

• ?1 given
• ?m, ?i given
• determine ?2

?1
?2

• Optimization
• Find pre-form for container with minimal
  difference in glass distribution with respect to
  desired container

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Parameterization of preform

• Describe interface by parametric curve
• e.g. spline, Bezier curve
• Define parameters