0
Research Papers

Development of a Numerical Optimization Method for Blowing Glass Parison Shapes

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

Department of Mathematics and Computer Science, Eindhoven University of Technology, P.O. Box 513, 5600 MB Eindhoven, The Netherlandsj.a.w.m.groot@tue.nl

C. G. Giannopapa

Department of Mathematics and Computer Science, Eindhoven University of Technology, P.O. Box 513, 5600 MB Eindhoven, The Netherlandsc.g.giannopapa@tue.nl

R. M. M. Mattheij

Department of Mathematics and Computer Science, Eindhoven University of Technology, P.O. Box 513, 5600 MB Eindhoven, The Netherlandsr.m.m.mattheij@tue.nl

J. Manuf. Sci. Eng 133(1), 011010 (Feb 08, 2011) (10 pages) doi:10.1115/1.4003331 History: Received November 23, 2008; Revised December 08, 2010; Published February 08, 2011; Online February 08, 2011

Industrial glass blowing is an essential stage of manufacturing glass containers, i.e., bottles or jars. An initial glass preform is brought into a mold and subsequently blown into the mold shape. Over the past few decades, a wide range of numerical models for forward glass blow process simulation has been developed. A considerable challenge is the inverse problem: to determine an optimal preform from the desired container shape. A simulation model for blowing glass containers based on finite element methods has previously been developed (Giannopapa, 2008, “Development of a Computer Simulation Model for Blowing Glass Containers,” ASME J. Manuf. Sci. Eng., 130, p. 041003; Giannopapa and Groot, 2007, “A Computer Simulation Model for the Blow-Blow Forming Process of Glass Containers,” 2007 ASME Pressure Vessels and Piping Conference and 8th International Conference on CREEP and Fatigue at Elevated Temperature). This model uses level set methods to track the glass-air interfaces. The model described in a previous paper of the authors showed how to perform the forward computation of a final bottle from the given initial preform without using optimization. This paper introduces a method to optimize the shape of the preform combined with the existing simulation model. In particular, the new optimization method presented aims at minimizing the error in the level set representing the glass-air interfaces of the desired container. The number of parameters used for the optimization is restricted to a number of control points for describing the interfaces of the preform by parametric curves, from which the preform level set function can be reconstructed. Numerical applications used for the preform optimization method presented are the blowing of an axisymmetrical ellipsoidal container and an axisymmetrical jar.

Copyright © 2011 by American Society of Mechanical Engineers
Your Session has timed out. Please sign back in to continue.

References

Figures

Grahic Jump Location
Figure 1

Schematic of the final blow stage

Grahic Jump Location
Figure 2

Approximation of a preform by parametric curves

Grahic Jump Location
Figure 4

The 2D axisymmetrical ellipsoidal container design

Grahic Jump Location
Figure 5

Bezier curves with five control points per interface

Grahic Jump Location
Figure 6

Cubic splines with five control points per interface

Grahic Jump Location
Figure 7

Constraints on the variable control points

Grahic Jump Location
Figure 8

((a)–(c)) Optimal preform and (d)–(f) resulting glass container; Bezier curves are used with three ((a) and (d)), four ((b) and (e)), and five ((c) and (f)) control points per interface

Grahic Jump Location
Figure 9

((a)–(c)) Optimal preform and ((d)–(f)) resulting glass container; cubic splines are used with three ((a) and (d)), four ((b) and (e)), and five ((c) and (f)) control points per interface

Grahic Jump Location
Figure 10

Convergence of the optimization method

Grahic Jump Location
Figure 11

Bar graph of the residuals

Grahic Jump Location
Figure 13

Typical mesh representation for a jar

Grahic Jump Location
Figure 14

Initial guess for an axisymmetrical jar

Grahic Jump Location
Figure 15

Optimal preform for an axisymmetrical jar

Grahic Jump Location
Figure 3

A typical mesh representation for a 2D axisymmetrical ellipsoidal mold

Tables

Errata

Discussions

Some tools below are only available to our subscribers or users with an online account.

Related Content

Customize your page view by dragging and repositioning the boxes below.

Related Journal Articles
Related eBook Content
Topic Collections

Sorry! You do not have access to this content. For assistance or to subscribe, please contact us:

  • TELEPHONE: 1-800-843-2763 (Toll-free in the USA)
  • EMAIL: asmedigitalcollection@asme.org
Sign In