Analysis of quadrature and frequency split in a MEMS vibrating ring gyroscope with structural imperfections

Structural imperfections affect the performance of MEMS vibrating ring gyroscopes (VRGs), dominantly in terms of quadrature error and frequency split. We consider a VRG with a ring subjected to width nonuniformity and supported by an imperfect suspension. This reflects the scenario of nonuniform etching, common in microfabrication processes. We show that the ring's width nonuniformity mainly results in a rotation of the mode-shapes with respect to those of a perfect ring while an imperfect suspension induces frequency split between the modes. On this basis, we calculate the quadrature error in the gyroscope's output. As an example, a 4° mode-shape rotation and 15Hz frequency split in a 60kHz VRG generate an approximate quadrature error of 1000°/s.