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Research Papers: Fluid-Structure Interaction

Numerical Shape Optimization in Industrial Glass Blowing

[+] Author and Article Information
J. A. W. M. Groot

Department of Mathematics
and Computer Science,
Eindhoven University of Technology,
PO Box 513,
Eindhoven 5600, The Netherlands
e-mail: j.a.w.m.groot@tue.nl

C. G. Giannopapa

Department of Mathematics
and Computer Science,
Eindhoven University of Technology,
PO Box 513,
Eindhoven 5600, The Netherlands
e-mail: c.g.giannopapa@tue.nl

R. M. M. Mattheij

Department of Mathematics
and Computer Science,
Eindhoven University of Technology,
PO Box 513,
Eindhoven 5600, The Netherlands
e-mail: r.m.m.mattheij@tue.nl

Contributed by the Pressure Vessel and Piping Division of ASME for publication in the JOURNAL OF PRESSURE VESSEL TECHNOLOGY. Manuscript received May 16, 2013; final manuscript received July 20, 2014; published online September 4, 2014. Assoc. Editor: Haofeng Chen.

J. Pressure Vessel Technol 136(6), 061301 (Sep 04, 2014) (9 pages) Paper No: PVT-13-1082; doi: 10.1115/1.4028066 History: Received May 16, 2013; Revised July 20, 2014

Industrial glass blowing is an essential stage of manufacturing hollow glass containers, e.g., bottles, jars. A glass preform is brought into a mold and inflated with compressed air until it reaches the mold shape. A simulation model for blowing glass containers based on finite element methods, which adopts a level set method to track the glass–air interfaces, has previously been developed [Giannopapa and Groot, 2007, “A Computer Simulation Model for the Blow–Blow Forming Process of Glass Containers,” Paper No. PVP2007-26408, pp. 79–86; Giannopapa, C. G., 2008, “Development of a Computer Simulation Model for Blowing Glass Containers,” ASME J. Manuf. Sci. Eng., 130(4), p. 041003; Giannopapa and Groot, 2011, “Modeling the Blow–Blow Forming Process in Glass Container Manufacturing: A Comparison Between Computations and Experiments,” ASME J. Fluids Eng., 133(2), p. 021103]. A considerable challenge in glass blowing is the inverse problem: to determine an optimal preform from the desired container shape. In previous work of the authors [Groot et al., 2009, “Numerical Optimisation of Blowing Glass Parison Shapes,” ASME Paper No. PVP2009-77946; Groot et al., 2011, “Development of a Numerical Optimization Method for Blowing Glass Parison Shapes,” ASME J. Manuf. Sci. Eng., 133(1), p. 011010] a numerical method was introduced for optimizing the shape of the preform. The optimization method described the shape of the preform by parametric curves, e.g., Bezier-curves or splines, and employed a modified Levenberg–Marquardt algorithm to find the optimal positions of the control points of the curves. A combined finite difference and Broyden method was used to compute the Jacobian of the residual with respect to changes in the positions of the control points. The objective of this paper is to perform an error analysis of the optimization method previously introduced and to improve its accuracy and performance. The improved optimization method is applied to modeled containers of industrial relevance, which shows its usefulness for practical applications.

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Figures

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Fig. 1

Schematic drawing of glass blowing

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Fig. 2

Glass blowing problem description

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Fig. 3

Difference between designed and computed container

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Fig. 4

Parametrization of the unknown preform surface by a cubic spline with six control points

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Fig. 5

Typical structured mesh for glass bottle

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Fig. 6

Designed bottle with optimal wall thickness distribution

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Fig. 7

Initial guess of control points

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Fig. 8

Constrained domain of control points

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Fig. 9

Mold shapes for initial guess. (a) Computed with sagging and (b) computed without sagging.

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Fig. 10

Convergence of objective function

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Fig. 11

Optimal preform and mold shape for beer bottle. (a) Optimal preform and (b) optimal mold shape.

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