Size optimization of MEMS gyroscopes using substructuring

In this paper we present an innovative approach to the automatic design of MEMS gyroscopes, based on structural size optimization. A novel design environment, called feMEMS, is fully developed in Matlab: it allows the parametric generation of the structure geometry, the simulation of its behaviour and the layout optimization by means of gradient based techniques. The gyroscope layout is parametrized by a set of design variables, that describe the geometry and position of the mechanical elements composing the structure, namely the internal masses and flexure springs. The dynamic behaviour of the gyroscope is simulated through a finite element discretization, focusing on the computation of the structure resonant frequencies and of the mechanical response to the external angular rate. Also, the use of substructuring techniques based on static reduction is suggested, in order to reduce the computational cost of the simulations and of the optimization procedure. The working scheme of feMEMS is demonstrated considering the mechanical design of a triaxial beating-heart MEMS gyroscope. Two possible formulations of the optimization problem are presented and compared: the design objectives are respectively the maximization of the sensor response to the external angular rate and the maximization of spurious modes frequencies, while constraints are imposed to properly tune the drive and sense resonant frequencies and to satisfy the requirements on the available design space.