Dipartimento di Meccanica

Structural optimization of MEMS gyroscopes and mechanical compensation of quadrature error

Introduction

• Growing importance of MEMS inertial sensors: more and more stringent market requirements
• Increasing complexity of the internal mechanical structure of MEMS gyroscopes
• Crucial design process: trial and error procedure based on the designer’s experience, time consuming and costly
• Impact of quadrature error: mechanical cross-coupling between the drive and sense axes due to non-vertical etching (wall angle)

Objectives

• Development of structural optimization algorithms to aid the design process of MEMS gyroscopes
  • Investigation of both size and topology optimization approaches

• Novel approach to reduce quadrature error
  • Passive mechanical layouts as an alternative to active electronic compensation
  • Aim: minimize the sensitivity of the structure to fabrication imperfections

Results

Structure size optimization (Fig.4, Fig.5, Fig.6):

• Development of an automatic design tool (feMEMS [1], [2]): parametric geometry definition, FE simulation and layout optimization
• Industrial application to complex triaxial gyroscopes

Structure topology optimization (Fig.7, Fig.8):

• Material distribution method to create non intuitive structure shapes
• Application to 2D in-plane single mass MEMS gyroscopes [3]

Reduction of the gyroscope quadrature error (Fig.9):

• Modelization of the effects of wall angle on the gyroscope dynamics [4] + identification of suitable conceptual solutions for their reduction
• Design of low quadrature gyroscopes + optimization with the proposed automatic tools
• Numerical investigation of the effects of local wall angle variations + design of test structures for experimental assessment.

Conclusions

• Valid aid to MEMS industry expected from the proposed optimization tools
• Future extensions: nonlinear and multiphysics simulations
• High reduction of quadrature error expected by the designed layouts
• Ongoing experimental tests to identify the shielding geometries that minimize local variations of wall angle

References

[1] D. Giannini, G. Bonaccorsi, F. Braghin, Size optimization of a triaxial beating-heart MEMS gyroscope using substructuring, under review
[2] D. Giannini et al., A novel approach to mechanical design optimization of triaxial MEMS gyroscopes at device-level, ESMC 2018
[3] D. Giannini, F. Braghin, N. Aage, Topology optimization of 2D inplane single mass MEMS gyroscopes”, under review
[4] M. Izadi et al, A comprehensive model of beams’ anisoelasticity in MEMS gyroscopes, with focus on the effect of axial non-vertical etching, IEEE Inertial 2018