Mechanism of the bias error for fiber optic gyroscopes induced by the damping-system nonlinearity

When fiber optic gyroscopes (FOGs) are installed in the inertial navigation system (INS), significant FOG bias errors may appear under vibration environments, even if the FOG is free from angular motion and violent linear vibrations are greatly attenuated by the damping system in the INS. The reason lies in the unclarified nonlinear behavior of the damping system, which has impeded the deployment of FOGs in high-precision applications. In this work, the mechanism of the FOG bias error induced by the damping-system nonlinearity is comprehensively analyzed, including the generation of higher-order harmonic stresses induced by the damping-system nonlinearity, the transmission of mechanical stresses inside the FOG, and the propagation of errors in the FOG optical and electrical signals. Particularly, we found that, as multiple-frequency harmonic stresses induced by the damping-system nonlinearity simultaneously act on the FOG, significant bias errors are generated through the beating among multiple frequencies in the demodulation process. Experimentally, the bias error of the FOG is evaluated under different damping-system nonlinearities. Under the 30 Hz/6g sinusoidal vibration, as the nonlinearity ratio declines from 1.71 × 104 m−2 to 1.00 × 102 m−2, the amplitude of the third-harmonic stress acting on the FOG decreases from 1.6 g to 0.1 g, consequently reducing the FOG bias error from 0.0445 °/h to 0.0118 °/h, which coincides with numerical simulation results. This work lays theoretical foundations for optimizing the damping system as well as the FOGs in the INS under vibration and is also applicable to the mechanical and material design of absorbers in the damping system.