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.

A simple numerical methodology for thermal-fluid-structural interactions of air damping over heated micro-cantilevers

“…Therefore, the heating of the micro-cantilever increases the quality factor by 5.49%. The main reason for this is the change of the fluid density and viscosity with temperature, which is in good agreement with the semi empirical expression for the quality factor obtained by Lee et al (2007). A qualitative comparison of both oscillations is found in Fig.…”

“…The current numerical methodology is validated against the experimental and numerical results published in (Lee et al 2007). These results analyse the size effect on quality factor associated with the first mode of isothermal silicon micro-cantilever oscillation in 1 atm air with.…”

“…The fluid density and viscosity are constant, having values of 1.2 kg/m 3 and 1.85 9 10 -5 kg/(m s). Table 2 defines the two selected cases according to the micro cantilever dimensions, the undamped natural frequency and the quality factors obtained from (Lee et al 2007) and the current CFD model. The agreement between the quality factors obtained from the numerical models and experimental tests is quite good, as is further demonstrated by Fig.…”

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

“…Lee et al [16] investigated the size effect on quality factor associated with the first vibration mode of microcantilever in ambient air, by the comparison between numerical models, analytical analysis and experimental measurements; existing approximate models for air damping evaluation are modified to account geometry effects, demonstrating that quality factors are proportional to geometrical dimensions. The introduction of an 'effective damping width' of the structure allows to Bao et al [17] the easy treatment of boundary effect on damping; they found an analytical expression of damping pressure for rectangular plates with holes by the modification of Reynolds equation with a term related to the damping effect of gas flow through the holes.…”

Microelectromechanical systems (MEMS)

“…An other comparison between squeeze film damping effects on an inertial sensor at high and low pressure of surrounding fluid is performed by Braghin et al [13], that used a multi-physic code for numerical simulations and experimental measurements. Lee et al [14] investigated the size effect on the quality factor associated with the first mode of microcantilever vibration in ambient air, by the comparison between numerical models, analytical analysis and experimental measurements; existing approximate models for air damping evaluation are modified to account geometry effects, demonstrating that quality factors are proportional to geometrical dimensions. The introduction of an 'effective damping width' of the structure allows to Bao et al [16] the easy treatment of boundary effect on damping; they found an analytical expression of damping pressure for rectangular plates with holes by the modification of Reynolds equation with a term related to the damping effect of gas flow through holes.…”