Bifurcation and chaos of the bladed overhang rotor system with squeeze film dampers

To study the nonlinear dynamic behavior of the bladed overhang rotor system with squeeze film damper (SFD), a blade-overhang rotor-SFD model is formulated using the lumped mass method and the Lagrange approach. The cavitated short bearing model is employed to describe the nonlinear oil force of the SFD. To reduce the scale of the nonlinear coupling system, a set of orthogonal transformations is employed to decouple the one nodal diameter equations of blades, which are coupled with the dynamical equations of the rotor, with other equations of blades. In this way, the original system with 16+4n (n≥3) degrees of freedom (DoF) is reduced to a system with 24 DoF only. Then the parametric excitation terms in the blade-overhang rotor-SFD model are simplified in terms of periodic transformations. The coupling equations are numerically solved and the solutions are used to analyze the dynamic behavior of the system in terms of the bifurcation diagram, whirl orbit, Poincaré map and spectrum plot. A variety of motion types are found such as multi-periodic, quasi-periodic, and chaotic motions. Moreover, the typical nonlinear dynamic evolutions including the periodic-doubling bifurcation and reverse bifurcation are noted. It is noticed that there exist apparent differences in the dynamic behavior between the blade-overhang rotor-SFD models without and with considering the effect of blades. Supported by the National Natural Science Foundation of China (Grant No. 10632040), the Natural Science Foundation of Hei-Long-Jiang Province of China (Grant No. ZJG0704), and the Harbin Science & Technology Innovative Foundation of China (Grant No. 2007RFLXG009)