The Effect of Stem on the Bryan's Factor of a Hemispherical Resonator

Abstract

• Bryan's factor of a hemispherical shell with stem is analytically investigated • Revised formulation of the Bryan's factor is presented with corrected shape functions considering the effect of stem • Existing values for the Bryan's factor are updated • Bryan's factor depends on the boundary condition at the interface between the stem and hemispherical shell • Stem/shell interface area of a HRG resonator should be cautiously designed to obtain high sensitivity • The effect of stem on the Bryan's factor is more significant as the non-dimensional stem size increases, especially for up-to-date MEMS or small-sized HRG HRG (Hemispherical Resonator Gyroscope) is a resonator gyroscope sensor which utilizes Coriolis effect for the resonant vibrational modes of a hemispherical shell-type resonator. HRG has a resonator that is composed of an axisymmetric hemispherical shell and a column structure that support the shell, usually called a stem. This paper investigates the effect of the stem on Bryan's factor of a hemispherical resonator. When a resonating structure is installed on a platform, which is under rotational motion, the vibrating pattern of the resonator rotates by the angle proportional to the rotational angle of the platform with respect to the rotating frame of reference. The Bryan's factor is the proportional constant, and so fundamental and important because it determines the physical sensitivity for the HRG to measure the rotational motion of the platform. Most of the previous studies on Bryan's factor have dealt with the hemispherical resonator without the stem for simplicity of mathematics or approximately neglecting the effect of the stem. Some of them considered the stem, however, used incorrect solutions for deflection shape function of the operational vibration mode. In this paper, the effect of the stem on the Bryan's factor is newly investigated by correctly deriving the deflection shape functions based on the thin shell theory and inextensional Rayleigh's mode assumptions. Then, the Bryan's factors are calculated with different non-dimensional diametrical sizes of the stem for various boundary conditions. This paper provides more correct and complete formulation for the Bryan's factor of a hemispherical resonator shell with considering the effect of stem, which could be a more solid foundation for the development of the HRG sensor.