Equivalent Bryan's factor in hemispherical resonator gyroscopes with nonuniformities coupling

The precision of hemispherical resonator gyroscopes (HRGs) is critically dependent on resonator uniformity, yet is readily compromised by manufacturing defects. This paper presents a comprehensive investigation into the coupling effects of manufacturing-induced mass and residual stress nonuniformities in hemispherical resonators on the stability of equivalent Bryan's factor (BF), which determines HRGs accuracy. A novel dynamic model for the hemispherical resonator is developed, explicitly incorporating the fourth harmonic components of both mass and residual stress distributions to characterize their synergistic impact on vibrational behavior. Based on the equivalent mechanical model, the averaging method is employed to transform the fast-varying generalized coordinates into slow-evolving elliptical trajectory parameters, from which the expression for equivalent BF is analytically obtained. Simulations systematically quantify the individual and coupled effects of nonuniformity magnitude and spatial distribution, revealing that a tenfold reduction in the mass nonuniformity amplitude decreases equivalent BF fluctuation from 4.83% to 0.05%, and identifying the normal stress in the longitude direction as the most influential residual stress component. Experiments demonstrate that increased metallic film thickness exacerbates residual stress nonuniformity, thereby elevating equivalent BF fluctuation bounds, while greater mass nonuniformity further intensifies this instability. Excellent agreement between theoretical predictions and experimental results validates the effectiveness of the proposed model and methods, particularly under pronounced nonuniformity conditions. The quantitative statistical results validate that accounting for the coupling effects of residual stress and mass is essential for accurately predicting the behavior of hemispherical resonators. This study lays a foundation for the advancement of high-precision HRGs manufacturing.