The fully decoupled configurations integrating high-aspect-ratio flexible beams and proof masses are a widely adopted design in micro-electromechanical systems (MEMS) vibratory gyroscopes. However, such structures are extremely sensitive to microfabrication errors, particularly beamwidth deviations. To address this issue, this article proposes a high-order nonlinear dynamic modeling method and a robust optimization strategy for fully decoupled MEMS gyroscopes, explicitly accounting for microfabrication errors. Nonlinear stiffness expressions are derived for double-folded beams, V-shaped coupling beams, and composite beams, and a high-order dynamic model is established incorporating both geometric and electrostatic nonlinearities. Theoretical natural frequencies agree well with finite element simulations, with deviations below 3.3%. Assuming that all beamwidth deviations are normally distributed, the direct probability integration method (DPIM) is used to quantify gyroscope performance uncertainties in mechanical sensitivity and quadrature output. Robust optimization is conducted using beam structural parameters and drive voltage as design variables, aiming to improve sensitivity while minimizing deviations in sensitivity and quadrature output. The optimized gyroscope structure demonstrates strong robustness against beamwidth deviations, achieving a 3.75 times improvement in sensitivity and a 31% reduction in quadrature output. The 1 sigma standard deviation of sensitivity and quadrature output is significantly reduced by 78.1% and 40.2%, respectively, effectively suppressing the impact of fabrication errors on device performance.

In this study, the air damping ratios of an unsealed chip of a capacitive accelerometer subjected to different pressures were measured by a special designed circuit in a static state test. There are total eight trapezoid grooves on the top and bottom electrode wafers aiming at reducing air damping effect. Finite element method based on energy balance method and transient blade row model is used to simulate in ANSYS/CFX with a new formula of effective viscosity of the air derived from simulation and validated by experimental results. The numerical results are in good agreement with the experimental results. With the same method and the new formula of effective viscosity, the air damping ratio of a new chip without trapezoid grooves is simulated as well. The comparison of the two kind of chips shows that the air damping ratio decreases 63.4% after four trapezoid grooves were engrooved on the top and bottom electrode wafers. As a result, engrooving on the top and bottom electrode wafers provides a new way to reduce air damping effect.

This paper presents a robust optimal model of Micro Electro Mechanical Systems(MEMS) gyroscope and its design procedure.The proposed method adopts the sensitivity analysis considering the worst-case tolerance instead of statistical information about uncertainties.The genetic algorithm with the advantage of global optimization is employed.Sensitivity analysis shows the robust design is less sensitive to errors.Monte Carlo analysis is also performed,whose result indicates 88.35% of samples are acceptable.The gyroscope is fabricated using bonding and deep etching bulk micromachining process.

A z-axis decoupled micromachined gyroscope with dual frames is designed, fabricated and tested. The robust structure considering fabrication errors is obtained by the use of optimal robustness of design and process compensation. The gyroscope is packaged in vacuum, and test results show that quality factor of driving and sensing modes are 2000 and 800, respectively. In the range of 0~2400 deg/sec, sensitivity and linearity of the fabricated gyroscope are 1 deg/sec and 0.3%, respectively.

A decoupled-sense-mode z-axis micromachined gyroscope is presented.The sense mode is restricted to be only one degree of freedom for vibration,which restrains the effect from the drive mode and reduces the undesired sense mode bias.Using double masses allows both matched natural frequencies and decoupled modes.A U-shaped beam is utilized for meeting the requirements on the degrees-of-freedom of the drive and sense modes.In order to create a high-aspect ratio structure,a Deep Reactive Ion Etching(DRIE) process is used to achieve a larger proof mass,reduce the thermomechanical noise floor and provide high sensitivity.The area of the fabricated gyroscope is 2 100 μm×2 100 μm,with a thickness of 60 μm.The gyroscope is vacuum-packaged for a high mechanical quality factor.Measured results show that the drive and sense mode quality factors are 2 000 and 1 800,respectively,and the thermomechanical noise floor is 3.76(°)/h·Hz-12.The scale factor is 21 mV/(°)·s-1 in a range of ±200(°)/s,with a full-scale nonlinearity of 1.426 %FS.The bias drift is 0.057 9(°)/s over a 1 h measurement period.

A robust design applied to microgyroscope using tolerance analysis was presented,and the optimal robust design procedure was developed.The proposed robust model was formulated through estimating the nominal values and perturbation of the objective function and constraints,considering the worst-case tolerance as the perturbation in design parameters.Automatic design procedure based on such an approach was developed for microgyroscope structure design,and it was realized in a design environment integrating device modeling and optimization.And the genetic algorithm with the advantage of global optimization was employed.A comparison of different robust designs shows that the presented method can obtain a higher quality result at a moderate computational cost.Sensitivity analyses show that the robust optimum is less sensitive to errors than the optimal design.Moreover,Monte Carlo analysis was performed to check the yield of robust design,which indicates that 88% of samples are acceptable,whereas the percentage is only 50% for the deterministic optimization.The gyroscope has been fabricated using bonding and deep reactive ion etching technique.

A robust design method applied to microgyroscope is presented which is of automation, efficiency and accuracy. The design target is to maximize the microgyroscope performance, within minimum variation of performance due to uncertainties caused by fabricating errors. Analysis of the tolerance is used to calculate the nominal value and the transmitted variation of the objective function, and the genetic algorithm with advantage of global optimization is employed for the optimal process. Compared with stochastic optimization and sensitivity analysis investigated in previous studies, proposed method in this paper can reach more accurate results with lower computational cost. Robustness analyses of optimization and robustness show robust optimum is less sensitive to errors than deterministic optimization. Also, Monte Carlo simulation is performed to check yield of robust design, and the result indicates 90% of samples are acceptable, whereas, only 50% in the deterministic optimization.

This paper reports on a robust optimal design of MEMS gyroscope. Proposed robust design method uses perturbation method, which doesn't need to calculate derivative compared with method based on sensitivity analysis, considering the worst-case tolerance instead of statistical information about uncertainties. Monte Carlo analyses of robust and deterministic optimization are also studied, and results indicate that more than 80% of the objective function samples with standard deviation 0.4μm is acceptable with respect to the robust design. System-level based on macromodels and physical level based on finite element model simulation verifications show that the MEMS gyroscope designed using presented method is acceptable.

This paper reports on an efficient robust optimal design of MEMS gyroscope. Proposed method uses sensitivity analysis considering the worst-case tolerance instead of statistical information about uncertainties. The robust optimal models based on macromodels consider electro-mechanical couple-field analysis. Monte Carlo analysis and physical level verification are also studied.