Nonlinear coupled dynamics of flexible blade–rotor–bearing systems

The nonlinear dynamic behavior of a rotor–bearing system with interaction between blades and rotor is addressed in this paper. Using the Lagrange equation, a time-dependent nonlinear model of a flexible blade–rotor–bearing system is established, in which the rotor is supported by journal bearings and the blades are modeled as pendulums in order to analyze the dynamic coupling between the elastic blades and the flexible shaft. To emphasize the gyroscopic effect of the rotor, the disk is assumed to be located at an arbitrary position of the shaft. Employing the orthogonal transformations, the 1-nodal diameter equations of motion of the blades, which are coupled with the dynamic equations of the rotor, are decoupled with other equations of the blades. Then the parametric excitation terms in the blade–rotor–bearing system are simplified in terms of periodic transformations. The dynamic equations with nonlinear oil-film forces are numerically solved using the Runge–Kutta method. Bifurcation diagrams, three-dimension spectral plots, and Poincaré maps are employed to analyze the dynamic behavior of the system. The numerical results show that the nonlinear dynamic behavior of the system varies with the increase of the rotational speed. And the effect of the nonlinear vibration of the rotor on the blade vibration is discussed.