Theoretical prediction of soft-forming micro-hemispherical shells from fused silica substrates in reclining mold

Abstract

A reclining mold can support the soft forming of fused silica substrates into micro-hemispherical shells with the same height, which makes the processing of micro-hemispherical shells attractive. Currently, it is difficult to determine the optimal process parameters for machining micro-hemispherical shells, and several iterations of experiments are required. This process wastes large amounts of substrate material, experimental consumables, and machining time, and increases the cost of the experiments. In this paper, we report a reflow process for soft-forming micro-hemispherical shells from fused silica substrates supported by a reclining mold. The shapes of the shells formed from the fused silica substrates in reclining and non-reclining molds were analysed by building a two-dimensional model. Moreover, we predicted the effects of varying the process parameters on the shell-forming time and geometrical parameters, as well as the stresses and deformations of the shells after cooling. The effect of the eccentricity of the central support column of the mold on the symmetry of micro-hemispherical shells was also investigated, and the influence of the mold and substrate heating inhomogeneity on micro-hemispherical shell formation was analysed. Additionally, the heat uniformity of the substrate in the rotating state was examined. Finally, we investigated the temperature field and thickness distribution during the shell-forming process through 3D modelling to verify the 2D modelling results. Analysing and predicting the parameters helps to reduce the number of trial-and-error processes in experiments, and we expect this work to provide a theoretical parametric basis for micro-hemispherical shell machining.