Influence of elasticity modulus on the natural frequency in hemispherical resonator

For any Coriolis vibratory gyroscopes, symmetrically perfect resonator is their core component. In order to analyze the influence of non-uniform elasticity modulus on the natural frequency in resonator, the finite element model of hemispherical resonator is established by using finite element analysis software (ANSYS). The second-order natural frequency of ideal resonator and resonator with elastic modulus non-uniform is analyzed. The relationship between elasticity modulus and natural frequency is established. The first fourth harmonics of elasticity modulus along the circumferential direction in resonator are mainly investigated that dominates mainly the amplitude of uneven elasticity modulus. The influence of the first fourth harmonic of non-uniform elastic modulus on the natural frequency is deeply analyzed, which will cause the natural frequency difference. The influence of the first four harmonics on the frequency difference is almost the same, which will bring approximately equal frequency difference. In order to reduce the influence of elasticity modulus non-uniform on the precision and performance of the HRG, the relative values of first fourth harmonics of elasticity modulus should be less than 1×10
⁻⁷
, which provides a theoretical basis for the manufacturing design and error analysis of resonator.