Fluid Effects in Vibrating Micromachined Structures

Squeeze film damping and hydrodynamic lift for a micromechanical perforated proof mass are calculated and measured. This paper has resulted in closed-form expressions that can be used to design accelerometers, tuning-fork gyroscopes (TFGs), and other micromechanical devices. The fluid damping and lift are determined using finite-element analyses of the normalized and linearized governing equations where the boundary condition of the pressure relief holes is derived using pipe flow analysis. The rarefaction of gas is incorporated in the governing equations based on slip flow condition. As a further check, a one-dimensional (1-D) network model is developed to account for the boundary condition of the holes on a tilted proof mass. Both closed-form and numerical solutions are compared against experimental data over a range of pressures.