Optimization in high-precision glass forming

Summary. The question of interest in the present study is the inverse problem for high precision glass forming, i.e. 'How to design the mould and the temperature regime so that at the very end of the forming process we will get at room temperature a prescribed glass geometry with a precision in the order of the Micron? ' The aim is to eliminate from the manufacturing process the costly and time-consuming post-processing when the nal shape does not conform precisely to the desired one. Key words: glass forming, stress/structural relaxation, optimization 1 Description of the forward problem The present study focuses on the cooling stage of the glass forming process and provides a method based on computer-aided simulations to optimize the cooling treatment in order to keep the residual stresses below a given admis-sible threshold and identify the required initial geometry of the glass piece so that after cooling, it matches precisely the desired one. The case treated here corresponds to an optical device and the thermo-mechanical analysis is performed using the commercial Finite-Element code Ansys. The geometry and boundary conditions are shown on Figure 1. The glass piece has a symmetry of revolution and occupies the domain bounded by the surface = 1[2[3[4 at t = 0. It is assumed to be initially stress-free and with uniform temperature T0 = 873:15 K. Radiative heat transfer is ignored so that the temperature eld within the glass piece is dictated by the heat diusion equation. Moreover, heat is lost to the surrounding through convective heat transfer characterized by a constant coecient of heat trans-fer h. In this optimization problem, the time-dependent temperature of the surrounding Ta(t) is the control used to minimize an objective function yet to be dened. Upon cooling, the glass behavior undergoes drastic changes. At high tem-perature (T> Tg + 100 K) it behaves like a Newtonian liquid while at lowe