Nonlinear Dynamics of Flexible Rotors Supported on Journal Bearings - Part 2: Numerical Bearing Model

[+] Author and Article Information
Mohammad Miraskari

Mechanical Engineering Department, University of British Columbia, 2054-6250 Applied Science Lane, Vancouver, BC, V6T 1Z4, Canada

Farzad Hemmati

Mechanical Engineering Department, University of British Columbia

Mohamed S. Gadala

Mechanical Engineering Department, University of British Columbia, and Abu Dhabi University, Abu Dhabi, UAE

1Corresponding author.

ASME doi:10.1115/1.4037731 History: Received January 17, 2017; Revised August 14, 2017


The nonlinear stability of a flexible rotor-bearing system supported on finite length journal bearings is addressed. A perturbation method of the Reynolds lubrication equation is presented to calculate the bearing nonlinear dynamic coefficients, a treatment that is suitable to any bearing geometry. A mathematical model, nonlinear coefficient-based model, is proposed for the flexible rotor bearing system for which the journal forces are represented through linear and nonlinear dynamic coefficients. The proposed model is then used for nonlinear stability analysis in the system. A shooting method is implemented to find the periodic solutions due to Hopf bifurcations. Monodromy matrix associated to the periodic solution is found at any operating point as a by-product of the shooting method. The eigenvalue analysis of the Monodromy matrix is then carried out to assess the bifurcation types and directions due to Hopf bifurcation in the system for speeds beyond the threshold speed of instability. Results show that models with finite coefficients have remarkably better agreement with experiments in identifying the boundary between bifurcation regions. Unbalance trajectories of the nonlinear system is shown to be capable of capturing sub and super-harmonics which are absent in the linear model trajectories.

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