Affiliations: State Key Laboratory of Structural Analysis for
Industrial Equipment, Dalian, China | Department of Engineering Mechanics, Dalian University
of Technology, Dalian, China
Note: [] Corresponding author: State Key Laboratory of Structural
Analysis for Industrial Equipment, Dalian 116024, China. Tel.: +86 15840639767;
Fax: +86 411 84706571; E-mail: [email protected]
Abstract: The nonlinear vibration of a rotor excited by transverse
electromagnetic and oil-film forces is presented in this paper. The
rotor-bearing system is modeled as a continuum beam which is loaded by a
distributed electromagnetic load and is supported by two oil-film bearings. The
governing equation of motion is derived and discretized as a group of ordinary
differential equations using the Galerkin's method. The stability of the
equilibrium of the rotor is analyzed with the Routh-Hurwitz criterion and the
occurrence of the Andronov-Hopf bifurcation is pointed out. The approximate
solution of periodic motion is obtained using the averaging method. The
stability of steady response is analyzed and the amplitude-frequency curve of
primary resonance is illustrated. The Runge-Kutta method is adopted to
numerically solve transient response of the rotor-bearing system. Comparisons
are made to present influences of electromagnetic load, oil-film force and both
of them on the nonlinear vibration response. Bifurcation diagrams of the
transverse motion versus rotation speed, electromagnetic parameter and bearing
parameters are provided to show periodic motion, quasi-periodic motion and
period-doubling bifurcations. Diagrams of time history, shaft orbit, the
Poincaré section and fast Fourier transformation of the transverse
vibration are presented for further understanding of the rotor response.
