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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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References

Giannopapa, C. G., 2008, “Development of a Computer Simulation Model for Blowing Glass Containers,” ASME J. Manuf. Sci. Eng., 130(4), p. 041003. [CrossRef]
Giannopapa, C. G., and Groot, J. A. W. M., 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. [CrossRef]
César de Sá, J. M. A., 1986, “Numerical Modelling of Incompressible Problems in Glass Forming and Rubber Technology,” Ph.D. thesis, University College of Swansea, Swansea, UK.
César de Sá, J. M. A., 1986, “Numerical Modelling of Glass Forming Processes,” Eng. Comput., 3(4), pp. 266–275. [CrossRef]
Cormeau, A., Cormeau, I., and Roose, J., 1984, “Numerical Simulation of Glass-Blowing,” Numerical Analysis of Forming Processes, J. F. T.Pittman, O. C.Zienkiewicz, R. D.Wood, and J. M.Alexander, eds. Wiley, New York, pp. 219–237.
Williams, J. H., Owen, D. R. J., and César de Sá, J. M. A., 1986, “The Numerical Modelling of Glass Forming Processes,” Collected Papers of the XIV International Congress on Glass, H. C.Bharwaj, ed., Indian Ceramic Society, New Delhi, India, pp. 138–145.
DeLorenzi, H. G., and Nied, H. F., 1987, “Blow Molding and Thermoforming of Plastics: Finite Element Modelling,” Comput. Struct., 26(1–2), pp. 197–206. [CrossRef]
Warby, M. K., and Whiteman, J. R., 1988, “Finite Element Model of Viscoelastic Membrane Deformation,” Comput. Methods Appl. Mech. Eng., 68(1), pp. 33–54. [CrossRef]
Chung, K., 1989, “Finite Element Simulation of PET Stretch/Blow-Molding Process,” J. Mater. Shaping Tech., 7(4), pp. 229–239. [CrossRef]
César de Sá, J., Natal, R., Silva, C., and Cardoso, R. P., 1999, “A Computational Model for Glass Container Forming Processes,” Europe Conference on Computational Mechanics Solids, Structures and Coupled Problems in Engineering, Munich, Germany, August 31–September 3.
Hyre, M., 2002, “Numerical Simulation of Glass Forming And Conditioning,” J. Am. Ceram. Soc., 85(5), pp. 1047–1056. [CrossRef]
Diraddo, R. W., and Garcia-Rejon, A., 1993, “Profile Optimization for the Prediction of Initial Parison Dimensions From Final Blow Moulded Part Specifications,” Comput. Chem. Eng., 17(8), pp. 751–764. [CrossRef]
Diraddo, R. W., and Garcia-Rejon, A., 1993, “On-Line Prediction of Final Part Dimensions in Blow Molding: A Neural Network Computing Approach,” Polym. Eng. Sci., 33(11), pp. 653–664. [CrossRef]
Lee, D. K., and Soh, S. K., 1996, “Prediction of Optimal Preform Thickness Distribution in Blow Molding,” Polym. Eng. Sci., 36(11), pp. 1513–1520. [CrossRef]
Thibault, F., Malo, A., Lanctot, B., and Diraddo, R., 2007, “Preform Shape and Operating Condition Optimization for the Stretch Blow Molding Process,” Polym. Eng. Sci., 47(3), pp. 289–301. [CrossRef]
Gauvin, C., Thibault, F., and Laroche, D., 2003, “Optimization of Blow Molded Part Performance Through Process Simulation,” Polym. Eng. Sci., 43(7), pp. 1407–1414. [CrossRef]
Hsu, Y. L., Liu, T. C., Thibault, F., and Lanctot, B., 2004, “Design Optimization of the Blow Moulding Process Using Fuzzy Optimization Algorithm,” Proc. Inst. Mech. Eng., Part B, 218(2), pp. 197–212. [CrossRef]
Yu, J.-C., Chen, X.-X., Hung, T.-R., and Thibault, F., 2004, “Optimization of Extrusion Blow Molding Processes Using Soft Computing and Taguchi's Method,” J. Intell. Manuf., 15(5), pp. 625–634. [CrossRef]
Lochegnies, D., Moreau, P., and Guilbaut, R., 2005, “A Reverse Engineering Approach to the Design of the Blank Mould for the Glass Blow and Blow Process,” Glass Technol., 46(2), pp. 116–120. Available at: http://www.ingentaconnect.com/content/sgt/gt/2005/00000046/00000002/art00017
Moreau, P., Maréchal, C., and Lochegnies, D., 2001, “Optimum Parison Shape for Glass Blowing,” XIXth International Congress on Glass, Society of Glass Technology, Edinburgh, UK, July 1–6, pp. 548–549.
Choi, J., Ha, D., Kim, J., and Grandhi, R. V., 2004, “Inverse Design of Glass Forming Process Simulation Using an Optimization Technique and Distributed Computing,” J. Mater. Process. Technol., 148(3), pp. 342–352. [CrossRef]
Moreau, P., Lochegnies, D., and Oudin, J., 1998, “An Inverse Method for Prediction of the Prescribed Temperature Distribution in the Creep Forming Process,” Proc. Inst. Mech. Eng., Part C, 212(1), pp. 7–11. [CrossRef]
Groot, J. A. W. M., Giannopapa, C. G., and Mattheij, R. M. M., 2009, “Numerical Optimisation of Blowing Glass Parison Shapes,” ASME Paper No. PVP2009-77946. [CrossRef]
Groot, J. A. W. M., Giannopapa, C. G., and Mattheij, R. M. M., 2011, “Development of a Numerical Optimisation Method for Blowing Glass Parison Shapes,” ASME J. Manuf. Sci. Eng., 133(1), p. 011010. [CrossRef]
Giannopapa, C. G., and Groot, J. A. W. M., 2007, “A Computer Simulation Model for the Blow–Blow Forming Process of Glass Containers,” ASME Paper No. PVP2007-26408. [CrossRef]
Sethian, J. A., 1999, Level Set Methods and Fast Marching Methods, Cambridge University, New York.
Sussman, M., Smereka, P., and Osher, S., 1994, “A Level Set Approach for Computing Solutions to Incompressible Two-Phase Flow,” J. Comp. Phys, 114(1), pp. 146–159. [CrossRef]
Adalsteinsson, D., and Sethian, J. A., 1995, “A Fast Level Set Method for Propagating Interfaces,” J. Comp. Phys, 118(2), pp. 269–277. [CrossRef]
Chang, Y. C., Hou, T. Y., Merriman, B., and Osher, S., 1996, “A Level Set Formulation of Eulerian Interface Capturing Methods for Incompressible Fluid Flows,” J. Comp. Phys., 124(2), pp. 449–464. [CrossRef]
Groot, J. A. W. M., Mattheij, R. M. M., and Laevsky, K., 2011, “Mathematical Modelling of Glass Forming Processes,” Mathematical Models in the Manufacturing of Glass (Lecture Notes in Mathematics), A.Fasano, ed., Vol. 2010, Springer, Berlin, pp. 1–56.
Bathe, K., 1996, Finite Element Procedures, Prentice Hall, Englewood Cliffs, NJ.
Hindmarsh, A. C., Brown, P. N., Grant, K. E., Lee, S. L., Serban, R., Shumaker, D. E., and Woodward, C. S., 2005, “SUNDIALS: Suite of Nonlinear and Differential/Algebraic Equation Solvers,” ACM Trans. Math. Software, 31(3), pp. 363–396. [CrossRef]
van der Vorst, H. A., 1992, “Bi-CGSTAB: A Fast and Smoothly Converging Variant of Bi-CG for the Solution of Nonsymmetric Linear Systems,” SIAM J. Sci. Stat. Comput., 13(2), pp. 631–644. [CrossRef]
Kimmel, R., and Sethian, J. A., 1998, “Computing Geodesic Paths on Manifolds,” Proc. Natl. Acad. Sci. USA, 95(15), pp. 8431–8435. [CrossRef]
Haagh, G. A. A. V., 1998, “Simulation of Gas-Assisted Injection Moulding,” PhD thesis, Eindhoven University of Technology, Eindhoven, Netherlands.
Carroll, C. W., 1961, “The Created Response Surface Technique for Optimizing Nonlinear Restrained Systems,” Oper. Res., 9(2), pp. 169–184. [CrossRef]
Schnur, D. S., and Zabaras, N., 1992, “An Inverse Method for Determining Elastic Material Properties and a Material Interface,” Int. J. Numer. Methods Eng., 33(10), pp. 2039–2057. [CrossRef]
Gelin, J. C., and Ghouati, O., 1994, “An Inverse Method for Determining Viscoplastic Properties of Aluminium Alloys,” J. Mater. Process. Technol., 45(1–4), pp. 435–440. [CrossRef]
Broyden, C. G., 1965, “A Class of Methods for Solving Nonlinear Simultaneous Equations,” Math. Comput., 19(92), pp. 577–593. [CrossRef]
Moré, J. J., and Trangenstein, J. A., 1976, “On the Global Convergence of Broyden's Method,” Math. Comput., 30(135), pp. 523–540. [CrossRef]
Dennis, J. E., and Schnabel, R. B., 1996, Numerical Methods for Unconstrained Optimization and Nonlinear Equations, SIAM, Philadelphia, PA.
Nocedal, J., and Wright, S. J., 1999, Numerical Optimization, Springer, New York.

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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