Uncertainty quantification models for micro‐scale squeeze‐film damping

Abstract

SUMMARYTwo squeeze-film gas damping models are proposed to quantify uncertainties associated with the gap size and the ambient pressure. Modeling of gas damping has become a subject of increased interest in recent years due to its importance in micro-electro-mechanical systems (MEMS). In addition to the need for gas damping models for design of MEMS with movable micro-structures, knowledge of parameter dependence in gas damping contributes to the understanding of device-level reliability. In this work, two damping models quantifying the uncertainty in parameters are generated based on rarefied flow simulations. One is a generalized polynomial chaos (gPC) model, which is a general strategy for uncertainty quantification, and the other is a compact model developed specifically for this problem in an early work. Convergence and statistical analysis have been conducted to verify both models. By taking the gap size and ambient pressure as random fields with known probability distribution functions (PDF), the output PDF for the damping coefficient can be obtained. The first four central moments are used in comparisons of the resulting non-parametric distributions. A good agreement has been found, within 1%, for the relative difference for damping coefficient mean values. In study of geometric uncertainty, it is found that the average damping coefficient can deviate up to 13% from the damping coefficient corresponding to the average gap size. The difference is significant at the nonlinear region where the flow is in slip or transitional rarefied regimes.

Quantitative model validation techniques: New insights

“…Despite the superior performance provided in terms of signal loss and isolation compared with silicon devices [37], the use of RF MEMS switches in applications requiring high reliability is hindered by significant variations in device lifetime [38]. Rigorous quantification of the uncertainty sources contributing to the observed life variations is necessary in order to achieve the design of reliable devices.…”

“…For the purpose of illustration, this study considers damping prediction using the Navier-Stokes slip jump model [41]. Two major sources of uncertainty have been shown to affect the prediction of gas damping [38]. The first one is epistemic uncertainty related to the lack of understanding of fundamental failure modes and related physical models.…”

Application of the Immersed Boundary Method to Fluid, Structure, and Electrostatics Interaction in MEMS

“…These aspect ratios can cause shear-locking problems in typical finite-element solvers unless properly addressed [8]. The uncertainties of material properties, residual stress, and geometric parameters due to microfabrication processes must be taken into account [9,10]. Typical electrostatic force computations based on the parallel-plate assumption, though sufficient for first-order analyses, are insufficient for more accurate characterization even if fringing field effects are included [11].…”

“…(6),(7),(8), and(10)] are integrated over the control volume and the conservation laws enforced in a discrete sense on the control volume. The discretized governing equations are written in the form of linearized algebraic equations with respect to the discrete unknowns.…”

Robust Design Optimization of Dual Thrust Solid Propellant Motors due to Burning Rate Uncertainties

“…The random uncertainties mostly account for initial operating conditions such as temperature, pressure, velocity, loading conditions and manufacturing tolerances etc. On the other hand, epistemic uncertainties account for lack of knowledge, model error due to lack of design information and numerical error and erratic behavior of some parameters with fix quantity 1, 2. If unaccounted during design, these uncertainties can cause the product to deviate from its expected performance.…”