Dynamics And Control Of Random Rotor System And Dynamics Of Spinning Flexible Circular Disk

Dynamic behaviors and active vibration control of a rotor system subjected to random excitations and dynamic behaviors of a spinning flexible circular disk system were investigated considering the engineering background. The dissertation consists of three parts, i.e. introduction, dynamics and active vibration control of the rotor system under random excitations, and dynamics of the spinning flexible circular disk.In the first part, the research status of dynamics and active vibration control of the rotor system under random excitations and dynamic behaviors of a spinning flexible circular disk were reviewed in detail. The significances, methods and contents of the research work were proposed.In the second part, the dynamics and the active vibration control of the rotor system under random excitations were investigated systemically.The equations of the motion of a rotor dynamic system with random excitation and random parameters were presented. General formulations of the statistical variables of displacement response of the linear rotor system under random excitation were obtained by the analysis method of random vibration of the linear system.In order to understand the dynamic behaviors of the linear rotor system subjected to random excitations, seismic responses of a balance and an unbalance linear rotor-bearing system and linear rotor-bearing-casing system were analysed by using the pseudo excitation method and numerical integration scheme. The power spectral density and time-dependent variance of the displacement response of the rotor-bearing system and rotor-bearing-casing system under nonstationary Kanai-Tajimi seismic excitation were obtained. The influence of rotational speed and rotor imbalance on the time-dependent variance of the displacement response was discussed. The results show that the rotor imbalance cannot be disregarded in seismic response analysis of a high speed rotating machinery, new resonance of the rotor system was produced by the base excitation. An effective analysis method for reliability of a linear rotor-bearing-casing system subjected to random excitation was presented, and the reliabilities of the rotor-bearing-casing system were analysed.In order to study the dynamic behaviors of the nonlinear rotor system subjected to random excitations, the impact-rub nonlinear characteristics of a flexible rotor system supported on plain bearings and nonlinear squeeze film dampers subjected to evolutionary Kanai-Tajimi seismic excitation were studied by the Monte-Carlo method and the numerical integration scheme. The rotor orbits, displacement responses of the center of the disk, impact-rub force between the rotor and the stator, and phase angle of the disk were obtained. The effects of the rotor system parameters on the impact-rub nonlinear characteristic of the flexible rotor system supported on nonlinear squeeze film dampers were discussed. The rotor system can endure seismic excitation with large intensity by properly selecting the dynamics parameters of the rotor system.In order to study the vibration control of the linear rotor system subjected to random excitation, stochastic optimal vibration control strategies of the linear rotor system under the white noise and the coloured noise excitations were, respectively, proposed based on the Linear-Quadratic Gaussian (LQG) control theory. Then, stochastic optimal strategies for active vibration control of the rotor system with imperfect state information under the white noise and the coloured noise excitations were developed based on the LQG control and Kalman-Bucy filter theory. The stochastic optimal control strategies presented were applied to investigate the effectiveness of the active vibration control for the rotor system under nonstationary El. Centro seismic excitation. The results show that the vibration of the rotor system subjected to random seismic excitation can effectively be suppressed by the stochastic optimal control strategies presented. The effectiveness of the active vibration control of the stochastic optimal strategies presented to the rotor system can be changed by changing the corresponding elements of the weighting matrices.In order to resolve the vibration control of the linear rotor system with model error subjected to random excitation, the H₂, H_∞and mixed H₂/H_∞state and output feedback control laws were presented, respectively, by means of Linear Matrix Inequality to attenuate the vibration of the rotor system under seismic excitation. The H₂, H_∞and mixed H₂/H_∞state and output feedback control laws presented were applied to an active vibration control problem for the rotor system under nonstationary El. Centro seismic excitation. The effect of the H_∞, performance on the control effectiveness of the mixed H₂/H_∞control to the rotor system was discussed. It is shown that the mixed H₂/H_∞control can effectively suppress the vibration of the rotor system in both the frequency and the time domains.Dynamic characteristics of a spinning flexible circular disk, i.e., free vibration, forced vibration and coupled vibration with air were studied theoretically and experimental study of the vibration of the disk was carried out in the third part.In order to study the free vibration characteristics of the spinning flexible circular disk, the partial differential equation of the motion of the disk with the effect of centrifugal force and bending stiffness was discretized by the Finite Element Method (FEM). The eigenfrequencies, eigenmodes and critical speeds of the spinning flexible circular disk were analysed. The effects of disk parameters on the eigenfrequencies and critical speeds were discussed. The vibration mode characteristics of the spinning flexible circular disk were changed under rotation. The eigenfrequencies, forward traveling wave frequencies and critical speeds of the spinning flexible circular disk increase with the increase of the spinning speed, clamped radius and thickness of the disk, but decrease with the increase of the disk's density. The backward traveling wave frequencies of the spinning flexible circular disk decrease with the increase of the spinning speed.The steady responses of the spinning flexible circular disk under different constant transverse loads were studied numerically, respectively. The effects of location and magnitude of the transverse applied loads and rotating speed on the steady displacement response were analysed. The steady responses of the spinning flexible circular disk under different time-dependent harmonic transverse loads were studied, respectively. The effects of frequencies of the applied time-dependent transverse loads on the displacement response of the disk were analysed. Results show that the circular disk partially deformed under point and radial line constant transverse loads and wholly deformed under constant circumferentially line constant transverse loads. The resonance with high vibration will occur when the rotating speed is close to the critical speed of the spinning flexible circular disk under the constant transverse loads. The spinning flexible circular disk partially deformed under time-dependent transverse harmonic point load when the frequencies of the applied loads are very low. Vibration mode corresponding to the eigenfrequency mainly occur when the frequency of the applied load equal to the eigenfrequency of the spinning flexible circular disk. And high vibrations occur. Vibration mode close to the frequency of the applied loads easily occur when the frequency of the applied load away from the eigenfrequency of the spinning flexible circular disk. The displacement response of the spinning disk increases with increasing the magnitude of the transverse applied load and the distance of the location from the center of the disk in the radial direction.In order to study the coupled vibration characteristics of the flexible circular disk spinning on the thin air film, the dynamic characteristics of a flexible circular disk coupled to a thin air film between the disk and the rigid boundary was studied and the effect of different parameters on the disk's steady response was analysed.The experiments of vibration of the spinning flexible circular disk at the non-rotating and steady rotating cases were carried out in order to partially verify the theoretical results. The experiments were good agreement with the theoretical results.Finally, the work was summarized, the existing problems were explained and the problems that need more investigation were presented.