Influence of density error of hemispherical resonator on output accuracy of gyro

To study the influence of density distribution nonuniformity on the output of HRG, the position excitation's expression is derived, and the dynamic equations of resonator under the nonuniformity of density distribution are established by Bubonov-Galerkin method which is commonly used for solution of differential equations. According to the dynamic equations, the short time drift model with the 4^th harmonic density error is derived by averaging method. Finally the long time drift was simulated through the Runge-Kutta method. The calculation show that, when the 4^th harmonic density error is 0.0001 kg/m³, the angle drift reaches 0.03 (in one hour. So in the process of manufacturing, the 4^th harmonic density error should be smaller than 0.0001 kg/m³ or should be compensated for by other methods.