Comments on the size effect on the microcantilever quality factor in free air space

Abstract

This study presents a numerical approach to investigate the size effect on the quality factor associated with the first mode of microcantilever vibration in 1 atm air. The numerical simulation results are verified by experiments and compared with the approximate analytical solutions. Bulk micromachined cantilever arrays are employed as the test vehicles. Based on the experimental and numerical results, this paper proposes a modification to the existing approximate models for air damping analysis by taking into account the geometry effects of the microcantilevers. The arrived semi-empirical equation suggests that the quality factors of the microcantilevers are approximately proportional to L −1.62 and b 0.62 at a low kinetic Reynolds number. Thus, the quality factor of the microcantilever resulting from the free space air can be precisely predicted for design purposes.