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.
Issue Section:
Research Papers
Keywords:
blow moulding,
bottles,
finite element analysis,
glass manufacture,
glass products,
inverse problems,
optimisation,
shapes (structures),
optimization,
level set methods,
finite element methods,
glass forming
Topics:
Glass,
Inverse problems,
Optimization,
Preforms,
Shapes,
Glass containers,
Glass jars,
Containers
1.
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
.2.
Cséar de Sá
, J. M. A.
, 1986, “Numerical Modelling of Glass Forming Processes
,” Eng. Comput.
0177-0667, 3
, pp. 266
–275
.3.
Hyre
, M.
, 2002, “Numerical Simulation of Glass Forming and Conditioning
,” J. Am. Ceram. Soc.
0002-7820, 85
(5
), pp. 1047
–1056
.4.
César de Sá
, J. M. A.
, Natal Jorge
, R. M.
, Silva
, C. M. C.
, and Cardoso
, R. P. R.
, “A Computational Model for Glass Container Forming Processes
,” Europe Conference on Computational Mechanics Solids, Structures and Coupled Problems in Engineering
.5.
Giannopapa
, C. G.
, 2008, “Development of a Computer Simulation Model for Blowing Glass Containers
,” ASME J. Manuf. Sci. Eng.
1087-1357, 130
, p. 041003
.6.
Giannopapa
, C. G.
, and Groot
, J. A. W. M.
, 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
.7.
Sethian
, J. A.
, 1999, Level Set Methods and Fast Marching Methods
, Cambridge University Press
, Cambridge
.8.
Sussman
, M.
, Smereka
, P.
, and Osher
, S.
, 1994, “A Level Set Approach for Computing Solutions to Incompressible Two-Phase Flow
,” J. Comput. Phys.
0021-9991, 114
, pp. 146
–159
.9.
Adalsteinsson
, D.
, and Sethian
, J. A.
, 1995, “A Fast Level Set Method for Propagating Interfaces
,” J. Comput. Phys.
0021-9991, 118
, pp. 269
–277
.10.
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. Comput. Phys.
0021-9991, 124
, pp. 449
–464
.11.
Moreau
, P.
, Lochegnies
, D.
, and Oudin
, J.
, 1999, “Optimum Tool Geometry for Flat Glass Pressing
,” Int. J. Form. Processes
1292-7775, 2
, pp. 81
–94
.12.
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.
0924-0136, 148
, pp. 342
–352
.13.
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. J Mech. Eng. Sci
, 212
, pp. 7
–11
.14.
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.
0017-1050, 46
(2
), pp. 116
–120
.15.
Moreau
, P.
, Marechal
, C.
, and Lochegnies
, D.
, 2001, “Optimum Parison Shape for Glass Blowing
,” Proceedings of the 19th International Congress on Glass
, pp. 548
–549
.16.
Bernard
, T.
, and Ebrahimi Moghaddam
, E.
, 2006, “Nonlinear Model Predictive Control of a Glass Forming Process Based on a Finite Element Model
,” Proceedings of the 2006 IEEE International Conference on Control Applications
.17.
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.
0098-1354, 17
(8
), pp. 751
–764
.18.
Lee
, D. K.
, and Soh
, S. K.
, 1996, “Prediction of Optimal Preform Thickness Distribution in Blow Molding
,” Polym. Eng. Sci.
0032-3888, 36
(11
), pp. 1513
–1520
.19.
Laroche
, D.
, Kabanemi
, K. K.
, Pecora
, L.
, and Diraddo
, R. W.
, 1999, “Integrated Numerical Modeling of the Blow Molding Process
,” Polym. Eng. Sci.
0032-3888, 39
(7
), pp. 1223
–1233
.20.
Huang
, G. Q.
, and Huang
, H. X.
, 2007, “Optimizing Parison Thickness for Extrusion Blow Molding by Hybrid Method
,” J. Mater. Process. Technol.
0924-0136, 182
, pp. 512
–518
.21.
Gauvin
, C.
, Thibault
, F.
, and Laroche
, D.
, 2003, “Optimization of Blow Molded Part Performance Through Process Simulation
,” Polym. Eng. Sci.
0032-3888, 43
(7
), pp. 1407
–1414
.22.
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.
0032-3888, 47
, pp. 289
–301
.23.
Ranjbar
, A. A.
, and Mirsadeghi
, M.
, 2008, “An Inverse Estimation of Initial Temperature Profile in a Polymer Process
,” Polym. Eng. Sci.
0032-3888, 48
(1
), pp. 133
–140
.24.
Bordival
, M.
, Schmidt
, F.
, Le Maoult
, Y.
, and Velay
, V.
, 2009, “Optimization of Preform Temperature Distribution for the Stretch-Blow Molding of PET Bottles: Infrared Heating and Blowing Modeling
,” Polym. Eng. Sci.
0032-3888, 49
(4
), pp. 783
–793
.25.
Fourment
, L.
, and Chenot
, J. L.
, 1996, “Optimal Design for Non-Steady-State Metal Forming Processes—I. Shape Optimization Method
,” Int. J. Numer. Methods Eng.
0029-5981, 39
, pp. 33
–50
.26.
Fourment
, L.
, Balan
, T.
, and Chenot
, J. L.
, 1996, “Optimal Design for Non-Steady-State Metal Forming Processes—II. Application of Shape Optimization in Forging
,” Int. J. Numer. Methods Eng.
0029-5981, 39
, pp. 51
–65
.27.
Srikanth
, A.
, and Zabaras
, N.
, 2000, “Shape Optimization and Preform Design in Metal Forming Processes
,” Comput. Methods Appl. Mech. Eng.
0045-7825, 190
, pp. 1859
–1901
.28.
Zhao
, G.
, Wright
, E.
, and Grandhi
, R. V.
, 1997, “Preform Die Shape Design in Metal Forming Using an Optimization Method
,” Int. J. Numer. Methods Eng.
0029-5981, 40
, pp. 1213
–1230
.29.
Chung
, S. H.
, and Hwang
, S. M.
, 1998, “Optimal Process Design in Non-Isothermal, Non-Steady Metal Forming by the Finite Element Method
,” Int. J. Numer. Methods Eng.
0029-5981, 42
, pp. 1343
–1390
.30.
Zhao
, X.
, Zhao
, G.
, Wang
, G.
, and Wang
, T.
, 2002, “Numerical Modeling of Dynamic Sealing Behaviors of Spiral Groove Gas Face Seals
,” J. Mater. Process. Technol.
0924-0136, 128
, pp. 25
–32
.31.
Ou
, H.
, Armstrong
, C. G.
, and Price
, M. A.
, 2003, “Die Shape Optimisation in Forging of Aerofoil Sections
,” J. Mater. Process. Technol.
0924-0136, 132
, pp. 21
–27
.32.
Shim
, H.
, 2003, “Optimal Preform Design for the Free Forging of 3D Shapes by the Sensitivity Method
,” J. Mater. Process. Technol.
0924-0136, 134
, pp. 99
–107
.33.
Ponthot
, J. P.
, and Kleinermann
, J. P.
, 2005, “Optimisation Methods for Initial/Tool Shape Optimisation in Metal Forming Processes
,” Int. J. Veh. Des.
0143-3369, 39
(1/2
), pp. 14
–24
.34.
Boffi
, D.
, Brezzi
, F.
, and Fortin
, M.
, 2008. “Finite Elements for the Stokes Problem
,” Mixed Finite Elements, Compatibility Conditions, and Applications (FM 2009)
(Lecture Notes in Mathematics
Vol. 1939
), D.
Boffi
and L.
Gastaldi
, eds., Springer
, Berlin
, pp. 45
–100
.35.
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. Softw.
0098-3500, 31
, pp. 363
–396
.36.
Allaart-Bruin
, S. M. A.
, Linden
, B. J. v. d.
, and Mattheij
, R. M. M.
, 2006, “Modelling the Glass Press-Blow Process
,” Mathematics in Industry/The European Consortium for Mathematics in Industry
, Progress in Industrial Mathematics at ECMI 2004, Proceedings of the 13th European Conference on Mathematics for Industry
, Eindhoven, The Netherlands, Jun. 21–25, Vol. 8, A.
Di Bucchianico
, R. M. M.
Mattheij
, and M. A.
Peletier
, eds., Springer
, Berlin
, pp. 351
–355
.37.
Kimmel
, R.
, and Sethian
, J. A.
, 1998, “Computing Geodesic Paths on Manifolds
,” Proc. Natl. Acad. Sci. U.S.A.
0027-8424, 95
, pp. 8431
–8435
.38.
Carroll
, C. W.
, 1961, “The Created Response Surface Technique for Optimizing Nonlinear Restrained Systems
,” Oper. Res.
0030-364X, 9
, pp. 169
–184
.39.
Schnur
, D. S.
, and Zabaras
, N.
, 1992, “An Inverse Method for Determining Elastic Material Properties and a Material Interface
,” Int. J. Numer. Methods Eng.
0029-5981, 33
, pp. 2039
–2057
.40.
Gelin
, J. C.
, and Ghouati
, O.
, 1994, “An Inverse Method for Determining Viscoplastic Properties of Aluminium Alloys
,” J. Mater. Process. Technol.
0924-0136, 45
, pp. 435
–440
.41.
Marquardt
, D. W.
, 1963, “An Algorithm for Least-Squares Estimation of Nonlinear Parameters
,” J. Soc. Ind. Appl. Math.
0368-4245, 11
(2
), pp. 431
–440
.42.
Broyden
, C. G.
, 1965, “A Class of Methods for Solving Nonlinear Simultaneous Equations
,” Math. Comput.
0025-5718, 19
(92
), pp. 577
–593
.43.
Broyden
, C. G.
, 1967, “Quasi-Newton Methods and Their Application to Function Minimisation
,” Math. Comput.
0025-5718, 21
(99
), pp. 368
–381
.44.
Moré
, J. J.
, and Trangenstein
, J. A.
, 1976, “On the Global Convergence of Broyden’s Method
,” Math. Comput.
0025-5718, 30
(135
), pp. 523
–540
.45.
Dennis
, J. E.
, and Schnabel
, R. B.
, 1996, Numerical Methods for Unconstrained Optimization and Nonlinear Equations
, SIAM
, Philadelphia, PA
.46.
Martinez
, J. M.
, 2000, “Practical Quasi-Newton Methods for Solving Nonlinear Systems
,” J. Comput. Appl. Math.
0377-0427, 124
, pp. 97
–121
.47.
Martinez
, J. M.
, and Ochi
, L. S.
, 1982, “Sobre dois métodos de broyden
,” Mathemática Aplicada e Computacional
, 1
, pp. 135
–141
.48.
Ruan
, B.
, 2002, “Numerical Modeling of Dynamic Sealing Behaviors of Spiral Groove Gas Face Seals
,” ASME J. Tribol.
0742-4787, 124
, pp. 186
–195
.49.
Dierckx
, P.
, 1993, Curve and Surface Fitting With Splines
, Oxford Science
, New York
.50.
Prautzsch
, H.
, Boehm
, W.
, and Paluszny
, M.
, 2002, Bézier and B-Spline Techniques
, Springer
, Berlin
.Copyright © 2011
by American Society of Mechanical Engineers
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