Stability analysis and optimal absorber design for the two-degree-of-freedom gyroscope subjected to housing excitation.

摘要

This study deals with the dynamic analysis of the 2-D.O.F. gyroscope with Coulomb friction on the gimbal axes subjected to impulse or harmonic angular excitation on the gyro housing. The perturbation method is used to solve the nonlinear equations of the ideal gyro. These solutions allow better understanding of the significant properties of the ideal gyro. Closed form solutions are developed for the linearized equations of the 2-D.O.F. gyro in an undisturbed housing with dry friction on the gimbal axes. It is proved that appropriate dry friction on the gimbal axes will reduce the settling time when it is subject to an impulse on the inner gimbal axis. To minimize the effect of external disturbances, dynamic absorbers are attached to the axes of the inner and outer gimbals. The optimum tuning and damping ratios for the absorbers are determined with the objective of minimizing the settling time due to an impulse on the inner gimbal. The effects of the inertia, natural frequencies, and damping ratios of the optimal absorbers are discussed based on the numerical solutions of the non-linear system equations. It has been shown that incorporating optimally tuned absorbers and optimized dry friction in the design can considerably reduce the coning motion and drift of the ideal 2-D.O.F. gyro system.