Study Of The Nonlinear Characteristics Of The Cracked Rotor Maneuvers

In this dissertation, some investigations of the nonlinear response of cracked rotor in maneuver flight are carried out, and the methods to characterize the nonlinear response are discussed. It aims to reveal the influence of maneuver load on the nonlinear response of cracked rotor.The maneuver load model for hover and dive-hike are set up, and the motion equations for Jeffcott rotor in maneuver flight are derived. The simulation results show that rotor is apparently deformed under maneuver load.Two novel methods, Periodic sampling peak-to-peak value diagram and Modified Poincare map, are presented for distinguishing nonlinear responses. The nonlinear response of a Duffing equation, a Pendulum in circular orbit, an oscillating circuit and Lorenz system are studied by these methods. Simulation results show that the suggested methods are more effective for characterizing nonlinear responses.The stiffness matrix of cracked rotor is derived basing on fracture mechanics, and the relationships between the stiffness and some parameters are investigated. It is concluded that the shaft is weaker as the crack is deeper, and the stiffness influenced by crack is more sensitive as the slenderness ratio increased. When the crack is smaller, the influence in the ζ axis (perpendicularity crack) is only needed to be considered. When the crack is deeper, the influence both in the ζ axis and η axis (parallel crack) are needed to be considered.Numerical method was employed to analyze the nonlinear response of cracked rotor in maneuver flight. The switching crack model is easier to give rise to nonlinear response than cosine crack model. The nonlinear responses are more apparent when rotor is runing above the critical speed in flat flight. There are three ways leading to chaos, quasi-periodic bifurcation, intermittence bifurcation and instability period-3 motion to chaos. The maneuver flight will depress the nonlinear response;however the position of axis center will be obviously deflected. It will also lead to nonlinear response or peak-to-peak value jump near the fraction frequency of swing critical speed.