Analysis of the Coupled Angular Motion in the Inertial Navigation System Induced by Nonlinear Vibration Isolation

Inertial navigation systems (INSs) are often equipped with rubber absorbers to prevent inertial sensors from being damaged under vibrations or shocks. Usually, coupled angular vibrations arise when the elastic center of the vibration isolation system (VIS) misaligns with the centroid of the INS. Unlike traditional methods that treat the VIS as linear, this work focuses on the influences of the nonlinear characteristics of the VIS and the corresponding dynamic behaviors. Specifically, we introduce the quadratic stiffness coefficient into the Duffing model for correcting the VIS stiffness model. Based on this, a coupled-angular-vibration model with a nonlinear VIS is established and numerically analyzed, showing that the nonlinearity causes angular vibrations in distorted forms and in high-order harmonics with respect to excitations. After the angular vibrations couple into the fiber optic gyroscope (FOG) (employed as the rotation-rate sensor of the INS in this work), significant bias error is generated through the beating among vibration-induced harmonic frequencies in demodulation. Experimentally, we select three sets of absorbers with different nonlinearities to examine their influence on the FOG performance. With a linear vibration of 30 Hz and 6g applied to the INS, the FOG bias error is suppressed from 0.048 °/h to 0.004 °/h as the amplitude of the second-order torsional harmonic (quantitative expression of the VIS nonlinearity) decreases from 2.31 to 0.34 arcsecond. The established theoretical and analytical models contribute to the fast and accurate optimization of the absorbers and the inertial sensors, which lays the foundation for designing and manufacturing high-precision INSs.