A Comparative Analysis of Different Approaches to Determination of the Natural Frequencies of the MEMS Gyros

Abstract

The article is devoted to research different approaches used to determine the natural frequencies of the MEMS-gyro sensing element at the design stage. In a general case, the MEMS-gyro sensing element can be presented as one or more proof masses, which are connected with each other and with the gyro base by means of springs. Well-known mathematical models for the dynamics of the sensitive element consider it as a discrete system, where the proof masses are substituted by its mass center and the springs are substituted by their stiffness. The finite element modeling (FEM) allows us to consider the sensitive element as a system of linked solid deformable bodies. However, the results of the finite element simulation of the sensing element dynamics depends on the theory of bending supported in the elements used for modeling. Currently, the classical theory of bending of the Euler-Bernoulli and Timoshenko theory are widely used for the finite element simulation of the sensing element. Each of the three approaches (the mathematical models, FEM with Euler-Bernoulli theory, FEM with Timoshenko theory) has its advantages and disadvantages. In the paper the problem of the difference of the simulation results using one of the three approaches by the example for determination of the micromechanical gyroscope natural frequencies was investigated. Specific recommendations for the study of the micromechanical sensors and determination of their natural frequencies were formulated.