Thermoelastic damping is one of the key factors affecting the quality factor of vacuum-encapsulated resonant devices. In order to suppress the influence of thermoelastic damping, vertical slots are introduced to the MEMS resonant beams. The heat flux inside the beams are expected to be reduced through local structural optimization, thus improving the quality factor. To verify the feasibility of the proposed method, the software of COMSOL is employed to explore the inhibition effect of structural parameters such as length, width and quantity of the slots on thermoelastic damping. The simulation results show that the thermoelastic damping decreases sharply and the quality factor are improved after the slots are introduced, and the effects are strongly related to the characteristic parameters of the slots.
This paper mainly focuses on the sphericity evaluation based on the minimum zone sphere (MZS) method in the Cartesian coordinate system. An asymptotic search method is proposed to search for the homocentric centre of MZS model and calculate the sphericity error. The search process of the proposed method consists two parts: geometric area search is implemented to obtain a quasi-MZS centre (close to the MZS centre) and 3+2 and 2+3 mathematical models dominating the minimum zone sphere are solved to obtain the MZS centre. The geometric area search is employed to fast convergence to the quasi-MZS centre by constructing a search sphere model. Some characteristic points distributed on the search sphere are selected to determine the search direction. A threshold is set to terminate the search process and the quasi-MZS centre is determined as a result. The quasi-MZS centre is employed as a reference centre to solve the 3+2 and 2+3 models to determine the MZS centre. According to the minimum conditions, the mathematical models are established to solve the two models. Then the judgment is implemented to ensure all the measured points are enveloped between the two homocentric spheres. As a result, the centre of two homocentric spheres is the MZS centre. The MZS sphericity error can be obtained as well. To verify the performance of the proposed method, simulation experiments and comparison experiments are implemented. The results demonstrated that the proposed method is effective, reliable and meet the requirement of sphericity evaluation.