Lu Yanjun

Yu Lie

Liu Heng

Theory of Lubrication and Bearing Institute,

Xi’an Jiaotong University,

Xi’an 710049, China

ISTICS OF HYDRODYNAMIC

Abstract: The nonlinear dynamic behaviors of flexible rotor system with hydrodynamic bearing supports are analyzed. The shaft is modeled by using the finite element method that takes the effect of inertia and shear into consideration. According to the nonlinearity of the hydrodynamic journal bearing-flexible rotor system, a modified modal synthesis technique with free-interface is represented to reduce degrees-of-freedom of model of the flexible rotor system. According to physical character of oil film, variational constrain approach is introduced to continuously revise the variational form of Reynolds equation at every step of dynamic integration and iteration. Fluid lubrication problem with Reynolds boundary is solved by the isoparametric finite element method without the increasing of computing efforts. Nonlinear oil film forces and their Jacobians are simultaneously calculated and their compatible accuracy is obtained. The periodic motions are obtained by using the Poincaré-Newton-Floquet (PNF) method. A method, combining the predictor-corrector mechanism to the PNF method, is presented to calculate the bifurcation point of periodic motions to be subject to change of system parameters. The local stability and bifurcation behaviors of periodic motions are obtained by Floquet theory. The chaotic motions of the bearing-rotor system are investigated by power spectrum. The numerical examples show that the scheme of this study saves computing efforts but also is of good precision.

Key words: Nonlinear dynamics  Bearing-rotor system  Stability Bifurcation  Chaos Finite element method