Telefono: 02.2399.8671
Skype: daniele.giannini7
E-mail: daniele.giannini(at)

Sustainable Mobility

Relatore: Prof. Francesco Braghin

Tutor: Prof. Mario Guagliano

Università di Provenienza: Politecnico di Milano - Ingegneria Meccanica

Titolo della Tesi: Structural optimization of MEMS gyroscopes and mechanical compensation of quadrature error

Structural optimization of MEMS gyroscopes and mechanical compensation of quadrature error


  • 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)


  • 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


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.


  • 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


[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