Simulated analysis of forming imperfection for micro shell resonators

Abstract

High-precision micro shell resonator fabricated from the micro glassblowing process shows great potential in inertial sensors with acceptable cost. The finite-element analysis indicates that the 4th radius and thickness harmonic of geometric imperfections significantly increases frequency split of resonator. In order to investigate more details about the rapidly high-temperature molding of glass, a two-dimensional axisymmetric model and a three-dimensional shell model are built based on a numerical approach. The common sources of imperfections in the fabrication are analyzed including non-planarity of initial fused silica substrate’s surface, non-circularity of mold and misalignment of blowtorch with respect to mold. First, the simulation results show that different shell contours form from the fused silica substrates with nonuniform thickness, which affects the physical parameters of resonator, such as angular gain and anchor loss. The case that four protrusions or depressions evenly distributed on the circumference of the fused silica substrate is believed that will cause severe frequency split of resonator. Second, the results show that the non-circularity of the mold completely reproduce at the rim of resonator through the molding process, which is another source of the frequency split. However, the mapping effect gradually declines along the axis of shell. Finally, height variation along the circumference is generated due to the misalignment error of blowtorch. Radial uniform heat flux is considered to be helpful to improve the robustness to misalignment.