Compact damping models for laterally moving microstructures with gas-rarefaction effects

Compact models for the viscous damping coefficient in narrow air gaps betwe en laterally moving structures are reported. In the first part of the paper , a simple frequency-independent first-order slip-flow approximation for th e damping coefficient is derived and compared with a more accurate expressi on obtained from the linearized Boltzmann equation. The simple approximatio n is slightly modified and fitted to match the accurate model, The resultin g simple approximation has a maximum relative error of less than +/-6% at a rbitrary Knudsen numbers in viscous, transitional and free molecular region s, In the second part of the paper, dynamic models for the damping force ar e derived, considering again gas rarefaction, by applying various boundary conditions. The damping admittance of the first-order slip-flow model is im plemented also as an electrical equivalent admittance, constructed of RC se ctions, to allow both frequency and time domain simulations with a circuit simulator. The dependence of the damping admittance on pressure and gap dis placement is demonstrated with model simulations. The accuracy and validity range of the model are verified with comparative numerical simulations of the Navier-Stokes equation. Finally, the damping coefficient in a lateral r esonator is calculated using the compact model and compared with measured d ata with good agreement.