Numerical Shape Optimization in Industrial Glass Blowing

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.