Dynamic Characteristics Research Of Rotating Flexible Blade

In this paper, a flexible blade attached to a moving central rigid body undergoing large overall rotating motion is discussed. This is a coupling system about a rigid body and a flexible body. It not only changes with time but also has the highly coupled and nonlinear characteristics. This model has wide application in many areas, for example the airplane, spacecraft, high-speed vehicles, robotic arm, the robot areas and so forth.Firstly, the effects of the transverse deformation induced longitudinal deformation were also included in the whole longitudinal deformation. The dynamic equations including the dynamic stiffening terms was established by utilizing the Hamilton theory. The flexible blade is discretized by employing the approach of assumed modes method. This is called for the first-order approximation coupling (FOAC) model taking the second-order coupling quantity. If the second-order coupling quantity is neglect, the model is called for zero-order approximation coupling (ZOAC) model. The simplified first-order approximation coupling (SFOAC) model which neglects the effect of axial deformation of the blade is also studied. Two cases are considered in the simulations. One is the dynamics study in non-inertia system which the large motion of a system is known and the other is that the large motion of a system is unknown. The simulation indicated that the FOAC is stable in any angle velocity, but the ZOAC is emanative in high angle velocity. The SFOAC model is valid for the description of a rotating blade in dynamics and control by numerical comparisons made between the results SFOAC and FOAL.Then nonlinear stability of hub-leaf model in large overall motions is studied by Lyapunov direct method. Lyapunov direct method can be used in linear models and nonlinear models. This is a rife method in judging the stability. Utilizing the Energy-Momentum method, nonlinear stability of the equilibrium in the first-order approximation coupling (FOAL) model and the zero-order approximation coupling (ZOAC) model is analyzed. The results show that the ZOAC will lose stability when the rotating angular velocity is greater than its fundamental frequency. However, the FOAC can keep stable in any rotating angular velocity in the coupling dynamical model.At last, the linearization model is the linearization treatment for the SFOAC model. Active controller is designed using optimal tracking control theory. Since the controller designed is a function of modal coordinate of the blade, a modal filter used to extract tire modal coordinate from actual physical measurements is presented. Two cases are studied, the one is trajectory given, the other is angle given. By the optimal tracking controller, the desired motion target may be obtained and the vibration of flexible blade can be suppressed.