Analytic damping model for an MEM perforation cell

Abstract

The concept of the perforation cell is specified for compact modelling of perforated gas dampers with micromechanical dimensions. Both, analytic expressions and FEM simulations, are used to derive its flow resistance. An extensive set of FEM simulations is performed to characterize the flow resistance of the cell, and to derive approximations for different flow regions by fitting simple functions to them. Sinusoidal small-amplitude velocities are assumed, and micromechanical dimensions are considered with rare gas effects in the slip flow regime (Knudsen number <0.1). The model is capable of modelling all practical combinations of the perforation cell dimensions in a wide range of perforation ratios (1,...,90%). Its validity is verified with a Navier-Stokes solver, and it is shown to be accurate (relative error <4.5%) in the continuum and slip flow regimes. Estimates for cut-off frequencies due to inertial and compressibility effects are specified in a way that the maximum operation frequency of the model can be easily tested. Using a harmonic FEM solver, these estimates are verified. The perforation cell model is also applied to estimate the damping in a perforated rectangular damper (4,...,64 square holes). The damping predicted by the simple model is in moderate agreement with that obtained with 3D FEM simulations.

Experimental validation of compact damping models of perforated MEMS devices

“…The second model M2 has been also presented in (Bao et al 2003), but now an arbitrary rectangular surface is assumed. Next, the model M3 in (Veijola 2006a) is used. The air gap flow resistance model, the circular perforation flow channel model, and four different elongations of the flow channels, that vary depending on the ratios of the cell dimensions, are included in the model.…”

“…The measurement setup, the testing procedure and specimens characteristics are presented in (Somà and De Pasquale 2007); here it is observed that dynamic parameters of the microsystem characterizing the fluidic and structural coupling can be extracted from the experimental frequency response function (FRF). The dynamic performance of microstructures are discussed ) based on the analytical solutions to perforated parallel-plate problems in (Bao et al 2003;Veijola 2006a;Veijola 2006b). Since the perforation is uniform, the motion is almost translational, and also since the shape of the surface is rectangular, analytic damping models are applicable.…”

Optimal damping of the infinite-dimensional vibrational systems: commutative case

“…An important class of vibrational systems are systems with so-called analytic damping (see [12], [4], [20]). Analytic damping corresponds to the case where C = βM α , hence it is a special case of the modal damping.…”

Viscous damping and spring force in periodic perforated planar microstructures when the Reynolds’ equation cannot be applied

“…As a result there is an extensive literature dedicated to the study of squeeze-film damping in perforated MEMS. [3][4][5][6][7] While the squeeze-film damping is reduced by incorporating holes in one plate, the vertical motion of the air within the holes gives a new viscous resistance which adds to the squeeze-film damping. A rigorous solution of the total damping problem requires the solution of the Navier-Stokes' ͑NS͒ system in the three-dimensional ͑3D͒ domain comprised of the space between the plates and the volume of the holes, which is not at all a simple task.…”

“…A rigorous solution of the total damping problem requires the solution of the Navier-Stokes' ͑NS͒ system in the three-dimensional ͑3D͒ domain comprised of the space between the plates and the volume of the holes, which is not at all a simple task. Three-dimensional flow simulations are not practical for the entire microstructure geometry 5 due to the complexity of the implementation and the computational resource requirements.…”