Research On Nonlinear Dynamic Characteristics And Stability Of Gyroscope Rotor System

As a key device of inertial navigation system, gyroscope is widely used in satellite and other space craft. The performance of gyroscope largely depends on the performance of gyroscope rotor system. It is necessary to research nonlinear dynamic characteristics of gyroscope rotor system to improve the performance of satellite gyroscope. In this paper, a nonlinear dynamic model of rolling element bearing rotor system is presented and nonlinear dynamic characteristics and stability of gyroscope rotor system is investigated.The main research works can be described as follows:1. Analysis of nonlinear dynamic characteristics of gyroscope rotor system. With multiple nonlinear factors such as varying compliance and Hertzian elastic contact force considered, a dynamic model of rolling element bearing rotor system is presented. A new method to calculate stiffness of rolling element bearing is proposed, by which the time-varying stiffness matrix can be obtained. The effect of structure and running parameters on nonlinear dynamic characteristics and stability of gyroscope rotor system is studied. Simulation results show that abundant kinds of periodic and non-periodic (quasi-periodic and chaotic) responses exist in the system. The main route to chaos is doubling bifurcation. Instability of the system can be reduced by adopting reasonable structure parameters and running parameters in the system.2. Study on nonlinear dynamic characteristics of gyroscope rotor system due to surface defect.With the sources of nonlinearity such as inner and outer race surface waviness, Hertzian elastic contact force and localized defect considered, an analytical model of rolling element bearing rotor system is presented. With the aid of numerical algorithm, Poincarémaps, frequency spectrum diagrams, the bifurcation and chaos behaviors of gyroscope rotor system are analyzed. The effect of number and amplitude of waves, impact factor of localized defect on nonlinear response of gyroscope rotor system is studied. Simulation results show that the severe vibration occurs when the number of balls is equal to the number of waves. There is a definitely functional relationship between the number of waves and frequencies of vibration produced by inner race waviness. A method to spot defect by vibration time domain parameters is proposed.3. Analysis of nonlinear dynamic stability of gyroscope rotor system. The stability of rolling element bearing rotor system is analyzed by means of Floquet theory. With the aid of fixed-point method, numerical algorithm, Poincarémaps and frequency spectrum diagrams, the bifurcation, chaos and stability behaviors of gyroscope rotor system are analyzed. The effect of damping on stability of gyroscope rotor system is investigated. It is found that damping plays a significant role in stability of system. Three routes to unstable periodic solution are found: doubling bifurcation, quasi-periodic bifurcation and intermittent bifurcation.4. Analysis of nonlinear vibration of gyroscope rotor system subject to parametrical and external excitations.The rolling element bearing rotor system in practice is essentially a nonlinear system under parametrical and external excitations. With unbalance force and the sources of nonlinearity such as Hertzian elastic contact force, internal radial clearance and varying compliance considered, the governing differential equations of motion of a rolling element bearing rotor system are derived first and then solved by numerical algorithm. Meanwhile the nonlinear dynamic behaviors of gyroscope rotor system are illustrated by means of bifurcation diagrams, Poincarémaps and frequency spectrum diagrams. Numerical results show that various periodic responses with frequencies of the external forcing one, the parametrical forcing one, or the linear combinations of them, and even chaotic responses may exist. When the unbalance is weak and the parametrical vibration is the dominating one, proper increase of the unbalance force may relieve the risk of parametrical vibration instability. On the other hand, increase of unbalance force makes forced vibration stronger, and an improper increase of unbalance force may induce chaotic response.5. The effect of axial preload on nonlinear dynamic characteristics and stability of gyroscope rotor system.A 3-dimention freedom dynamic model of rolling element bearing rotor system is presented and the effect of axial preload on nonlinear response, bifurcation and stability of gyroscope rotor system is analyzed. Experiments have been conducted to study relationship between axial preload and natural frequency of system, and relationship between axial preload and rotating speed of bearing cage. Numerical results are in agreement with experimental ones. It is found that axial preload is an important parameter. It is also shown that increase of axial preload may decrease the amplitude value of varying compliance vibration, increase natural frequency of system, and enhance stability of the system.