Numerical prediction of stress evolution during blowtorch reflow of fused silica micro-shell resonators

Micro-blowtorching is a new, fast and reliable fabrication process to form 3D hollow fused silica shell structures such as high Q-factor birdbath resonators. The performance of the fabricated shell as a resonator can be significantly degraded due to the thermal residual stress during the early cooling phase after fabrication. A multi-step finite element analysis is developed for a qualitative prediction of residual stresses and deformation of the birdbath shells. First, a novel non-isothermal model is used to simulate the reflow and molding process. In the next step, the calculated temperature field is used to conduct a transient heat transfer analysis to mimic the cooling phase up to a designated temperature. Finally, the non-uniform temperature field from the heat transfer simulation is used to conduct a thermoelastic analysis to predict the residual stresses and deformation that would exist at ambient temperature in the birdbath shell structure. The predicted internal stresses can usefully be employed to optimize the coarse and fine annealing processes to reduce the stresses in a fabricated shell to a desired level.