On a deterministic approach for the evaluation of gas damping in inertial MEMS in the free-molecule regime

Frangi, Attilio; Ghisi, Aldo; Coronato, L.

doi:10.1016/j.sna.2008.09.018

Cited by 35 publications

(25 citation statements)

References 45 publications

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“…Figure 8. Tilting resonator from [7]: comparison between experimental and numerical quality factors.…”

Section: Experimental Validationmentioning

confidence: 99%

“…The first structure (Figure 7) is the tilting perforated mass addressed in [7] with a small-scale implementation of the integral approach. The mass is attached to the central circular anchor by means of four deformable beams and is suspended over a substrate.…”

Section: Rotational Resonatormentioning

confidence: 99%

“…The length scale and the working pressure are such that the collisions between molecules can be neglected; this regime is known as free-molecule flow [1][2][3][4][5][6]. The deterministic model implemented, proposed in [7,8], is an application of the collisionless Boltzmann equation which rests on the following assumptions: i) the mean free-molecule path is much larger than the typical dimension d of the flow (i.e. Kn 1); ii) molecules and solid surfaces interact according the diffuse-reflection model which basically states that molecules are re-emitted by the walls according to the wall equilibrium Maxwellian; iii) perturbations are small so that quadratic terms in the expansion of variables can be neglected.…”

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Integral equations for free-molecule ow in MEMS: recent advancements

Fedeli

Frangi

2017

Communications in Applied and Industrial Mathematics

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We address a Boundary Integral Equation (BIE) approach for the analysis of gas dissipation in near-vacuum for Micro Electro Mechanical Systems (MEMS). Inspired by an analogy with the radiosity equation in computer graphics, we discuss an efficient way to compute the visible domain of integration. Moreover, we tackle the issue of near singular integrals by developing a set of analytical formulas for planar polyhedral domains. Finally a validation with experimental results taken from the literature is presented.

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“…Figure 8. Tilting resonator from [7]: comparison between experimental and numerical quality factors.…”

Section: Experimental Validationmentioning

confidence: 99%

Section: Rotational Resonatormentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Integral equations for free-molecule ow in MEMS: recent advancements

Fedeli

Frangi

2017

Communications in Applied and Industrial Mathematics

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“…A lot of literature on air damping in micromachined gyroscopes is available, e.g. (Pasquale et al 2010;Veijola 2004;Frangia et al 2009;Kulygin et al 2008). Thermoelastic damping was concerned to be the limiting mechanism in micromachined gyroscopes due to the decreasing size and increasing frequency.…”

Section: Introductionmentioning

confidence: 99%

Effect of die attachment on key dynamical parameters of micromachined gyroscopes

Hou

Xiao

et al. 2012

Microsyst Technol

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This paper presents the effect of die attachment on the resonant frequency and quality factor of micromachined gyroscopes. Two types of epoxy die attachments are adopted in micromachined gyroscopes. A fourth order mass-spring-damper system is proposed to augment the dynamics of micromachined gyroscopes. Frequency response tests are implemented to analyze the quality factor and resonant frequency. Both maximums of the resonant frequency and quality factor are obviously much larger in the drive mode and sense mode when the more rigid die attachment is applied, due to the fact that rigid die attachment can minimize the energy loss through die substrate. Furthermore, the temperature dependence of the quality factor and resonant frequency on the die attachment is experimentally studied over the range -40°C to 60°C. Based on the experimental study, the rigidity, viscosity and temperature characteristics are the most considerable parameters for the die attachment in micromachined vibratory gyroscopes. Besides, the type of the mode shape is another factor determining the quality factor and temperature coefficient of resonant frequency. Balanced anti-phase mode operation can suppress the effect of die attachment.

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“…Although oscillatory Couette flow is a simple case, it has many related applications in a variety of MEMS devices, for example, the Tang resonator (Tang et al 1989). A proper understanding of flow phenomena in resonators will therefore help to improve the performance and quality factor (Frangi et al 2009). In this study, the extended continuum governing equations are employed to compute the details of Stokes' second problem and oscillatory planar Couette flow in the early transition regime.…”

Section: Introductionmentioning

confidence: 99%

Modeling oscillatory flows in the transition regime using a high-order moment method

Emerson

2010

Microfluid Nanofluid

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We present results using three different continuum-based models to study oscillatory flow in the transition regime. Data obtained from numerical solutions of the Boltzmann equation and the direct simulation Monte Carlo method, are used to assess the ability of the continuum models to capture important rarefaction effects. We further highlight the need to consider two Knudsen numbers: one based upon the length scale and the other upon the time scale. It is found that the regularized 26 moment model can follow kinetic theory in the early transition regime in terms of both Knudsen numbers but the regularized 13 moment equations can only be used up to the upper limit of the hydrodynamic regime. However, the subtle interplay of the length and time scales on oscillatory non-equilibrium flow causes the Navier-Stokes equations to fail even in the hydrodynamic regime. In addition, the effect of modifying the accommodation coefficient is also considered. It is found that reducing the accommodation coefficient on the stationary wall alone will increase the motion of the gas. However, gaseous movement will be reduced by changing both walls from diffusive to specular reflection.

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On a deterministic approach for the evaluation of gas damping in inertial MEMS in the free-molecule regime

Cited by 35 publications

References 45 publications

Integral equations for free-molecule ow in MEMS: recent advancements

Integral equations for free-molecule ow in MEMS: recent advancements

Effect of die attachment on key dynamical parameters of micromachined gyroscopes

Modeling oscillatory flows in the transition regime using a high-order moment method

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