Modelling squeeze film effects in a MEMS accelerometer with a levitated proof mass

Abstract

A triaxial accelerometer is presented which employs as its proof mass a mechanically free micromachined disc that is electrostatically levitated. Air damping plays a critical role in the operation of the accelerometer, providing stability to an inherently unstable system. Systems that operate beyond the cut-off frequency, however, suffer reduced gain due to the spring component of the squeeze film damping, resulting in decreased sensitivity. A finite-element model for extracting squeeze film damping coefficients for transverse and rotational motion of the disc, via an analogy to heat transfer theory, is presented. The use of the analogy enables a reduction of the problem from a complex three-dimensional computational fluid dynamics domain to a two-dimensional heat transfer domain. The model is used to evaluate the effect of including damping holes in the proof mass. The high-frequency oscillation and physical size of the proof mass dictate that the accelerometer is operated well beyond its cut-off frequency and so the inclusion of damping holes in the proof mass can result in an increase rather than decrease in the damping coefficient. The resulting system-level model, implemented in Matlab/Simulink, is then used to evaluate the effect of the squeeze film damping on the device performance.

Optimal and Robust Design Method for Two-Chip Out-of-Plane Microaccelerometers

“…The BNEA is expressed as: $\text{italicBNEA}=\sqrt{\frac{4k_{B}T{\omega }_n}{\text{italicmQ}}}\left[m/s^2/H{z}^{1/2}\right]$where k B is the Boltzmann constant (1.38 × 10 −23 m 2 kg/s 2 /K), T is the absolute room temperature (300 K), ω n is the 1st mode natural frequency of the microacceleromter, m is the mass, and Q is the mechanical quality factor. For an analysis of the mechanical quality factor, the squeeze film damping model [20,21] is applied between movable proof mass and substrate. According to [22], the Stoke’s flow damping between the interdigitated comb electrodes is negligible compared to the squeeze film damping between two plates.…”

A Compact Squeeze-Film Model Including Inertia, Compressibility, and Rarefaction Effects for Perforated 3-D MEMS Structures

“…For higher values of σ, the compressibility leads to a significant air-spring effect, which can be undesirable as it can adversely affect the dynamic behavior of a device [10]. Contrary to this, the fact that perforations increase the cutoff frequency-the frequency at which the damping and spring forces are equal-can be exploited by suitably tuning both of these forces by varying the number and size of perforations [11]. Blech [12] and Allen et al [13] have also reported the use of squeeze-film damping to tailor the frequency response of a seismic accelerometer and that of micromachined sensors, respectively.…”

“…The coefficients A and B in (11) are evaluated by substituting the boundary conditions for the pressure cell approximated within a particular pattern. These boundary conditions can be taken as Φ| R i = 0 and ∂Φ/∂R| R o = 0, where R o and R i are the normalized outer and inner radii of the circular pressure cell, respectively.…”

Design and fabrication of a micromachined electrostatically suspended gyroscope

“…The stiffness and damping constants due to a squeeze-film effect were estimated from ANSYS simulations of the rotor under an operating pressure of 20 mtorr. The estimations were carried out using a method described in references [18,24]. All of the parameters are summarized in Table 1.…”