Robust optimal design of a vibratory microgyroscope considering fabrication errors

Abstract

A robust optimal design of shape and size is formulated for vibratory microgyroscopes that can reduce the effect of variations from uncertainties in microelectromechanical systems fabrication. The important objective in the design of vibratory microgyroscopes is to reduce the difference between the resonance frequencies of the vertical (detecting) and lateral (driving) modes in order to attain high mechanical detecting sensitivity. The deterministic optimization for this goal results in good performance but is sensitive to fabrication errors. The basic idea of the present formulation is to obtain robustness of the objective function by minimizing the gradient of the objective function with respect to uncertain variables through a proper selection of shapes and sizes. The beam width, length and thickness of vibratory microgyroscopes are adopted as design variables and are simultaneously regarded as uncertain variables in the optimization problems. A robustness check using a newly defined yield through the Monte Carlo simulation has shown that the robust optimal design obtained has generated twice the number of acceptable designs than the deterministic optimum. The important point is that the formulation of minimizing the maximum sensitivity of the objective function requires no statistical information on the uncertainties and yet achieves robustness.

Simulation of a novel lateral axis micromachined gyroscope in the presence of fabrication imperfections

“…Understanding the behavior of gyroscopes in the presence of fabrication imperfections is essential for improving their performance (Shkel et al 1999). Although theoretical model and Monte-Carlo simulation can be used to analyze such non-ideal performances (Ha et al 2006;Han and Kwak 2001;Iyer and Mukherjee 2002;Shkel et al 1999), the deducing process makes many approximations, so errors brought by the theoretical deduction itself are difficult to be distinguished from the errors caused by the fabrication imperfections. Moreover, most analyses above used models built from lumped mass-damp-spring systems, which could not simulate the asymmetric performances caused by asymmetric defects and imperfections within a design.…”

Robust Design of a Decoupled Vibratory Microgyroscope Considering Over-Etching as a Fabrication Tolerance Factor

“…However, since it needs to calculate the standard deviation, it requires excessive calculation time. Han et al (15) obtained the robustness of the objective func-tion by minimizing the gradient of the response to uncertain variables in the coupled vibratory microgyroscope. However, the proposed objective formulation, which minimizes the maximum sensitivity of the frequency difference, is not adequate for the decoupled vibratory microgyroscope.…”

Identification of material and geometrical parameters for microstructures by dynamic finite element model updating

“…The finite element method (FEM) has been widely employed to simulate the static and dynamic behavior of microstructures (Meroni and Mazza 2004;Edler et al 2004;Huber and Aktaa 2003;Liu et al 2003;Han and Kwak 2001). Applying FEM to analyze a microstructure requires the geometrical and material properties of the structure as input parameters.…”