Coupled FEM simulations of accelerometers including nonlinear gas damping with comparison to measurements

Abstract

Actuation or sensing in microdevices is often achieved through electro-mechanical coupling. In practice though, the electro-mechanical system is complicated by the effects influenced by the gas surrounding the system. The gas damping may be of the same order of magnitude as the electric and mechanical forces, and thus it needs to be accounted for in the design of the devices. Notably in microsensor design, controlling the amount of damping is crucial in achieving the desired measurement accuracy and sensitivity. A certain amount of damping is required to filter out high frequency oscillations, but too heavy damping reduces the sensitivity of the device. In this paper we present a modelling method based on the finite element method to simulate the behaviour of a planar gas-damped microdevice under electrostatic loading. The transient model takes into account the true nonlinear behaviour of the damping and includes effects from non-uniform gap height. The computational cost of the simulations has been significantly reduced by various reduced-order and reduced-dimensional methods utilized in the model development. The method is used to simulate an accelerometer prototype under voltage ramp loading, up to the pull-in. The results of the simulation are compared to capacitance measurements of the real device. The method is also suitable for other types of planar microdevices, such as pressure sensors, micromirrors or microswitches.

Curvilinear melting – A preliminary experimental and numerical study

“…We have four unknowns in total and the problem is now to solve the four derived Eqs. (16), (18)-(20) for U 0 and r. Since the system closure is formulated in terms of the pressure moments Eqs. (19) and (21), the system cannot be solved directly.…”

Numerical and experimental comparison of MEMS suspended plates dynamic behaviour under squeeze film damping effect

“…Pursula et al [10] simulated a planar gas-damped accelerometer behaviour under electrostatic loading by FE methods; the transient model combines electro-mechanical coupling to nonlinear squeeze film damping effects and utilizes various reduced-order and reduced-dimensional methods to significantly reduce the computational cost of the simulation. Nayfeh and Younis [11] presented a new approach to the modeling and simulation of flexible microstructures under the effect of squeeze film damping by expressing pressure distribution in terms of structural mode shapes.…”

Microelectromechanical systems (MEMS)

“…Numerical simulations and experimental measurements confirmed the validity of analytical model. Pursula et al [6] simulated the behaviour of a planar gasdamped accelerometer under electrostatic loading by finite element method; the transient model combines electro-mechanical coupling to nonlinear squeeze-film damping effects and utilize various reduced-order and reduced-dimensional methods to significantly reduce the computational cost of the simulation. Nayfeh and Younis [8] presented a new approach to the modeling and simulation of flexible microstructures under the effect of squeeze-film damping by expressing the pressure distribution in terms of the structural mode shapes.…”