Development of a Numerical Optimisation Method for Blowing Glass Parison Shapes

Abstract

Industrial glass blowing is an essential stage of manufacturing glass containers, i.e. bottles or jars. An initial glass preform is brought into a mould and subsequently blown into the mould shape. Over the last few decades, a wide range of numerical models for forward glass blow process simulation have 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 [1, 2]. 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 optimisation. This paper introduces a method to optimise the shape of the preform combined with the existing simulation model. In particular, the new optimisation method presented aims at minimising the error in the level set representing the glass-air interfaces of the desired container. The number of parameters used for the optimisation 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 optimisation method presented are the blowing of an axi-symmetrical ellipsoidal container and an axi-symmetrical jar.

Numerical Optimisation of Blowing Glass Parison Shapes

“…The simulation model presented in [6,7] is used to compute the container using the given preform with z 0 = [8]. Figure 5 compares the results of the analytical approximation and the simulation for the forward problem.…”

“…Furthermore, in [8] the constraint is added that the bottom of the preform at the symmetry axis is located at z = −h with respect to the mould entrance.…”

“…The inverse problem in [8] is formulated as follows: find the location of the initial glass surfaces,…”

“…A numerical optimisation method to find an optimal preform from the desired container shape has been previously developed [8]. The method uses a modified Levenberg-Marquardt algorithm combined with a secant method.…”

Mathematical Modelling of Glass Forming Processes

“…More recent papers focus on optimisation of glass forming processes [27]. For instance a numerical optimisation method to find the optimum tool geometry in a model for glass pressing was introduced in [44].…”