Transient Analysis of Flexible Rotors with Nonlinear Bearings, Dampers and External Forces

General rotor-bearing systems often display nonlinear behavior due to hydrodynamic effects and external nonlinear forces. Linear methods based on finite element methods are the most common methods for performing rotor dynamic analyses. Nonlinear bearing/damping forces are often linearized into equivalent stiffness and damping coefficients. This method often works well for weakly nonlinear systems, but has limits for strongly nonlinear systems. To more accurately describe rotor behavior, transient analysis and nonlinear models are often used. Analytical solutions for Jeffcott rotors with nonlinear springs or numerical solutions for complex rotors with plain journal bearings have been developed for nonlinear rotor dynamic analyses. However, systems with complicated bearings/dampers and coupled lateral and torsional analyses of rotor-bearing systems have not been involved.

This dissertation provides time transient methods for solving nonlinear dynamic behavior of flexible rotor-bearing systems including gyroscopic effects, complicated bearings, squeeze film dampers, and external nonlinear forces/torques. The rotor is modeled as linear; and the supporting components, including bearings and dampers, are modeled as nonlinear. The nonlinear bearing forces, which depend on instantaneous nodal displacements and velocities, are calculated at each time step through nonlinear bearing/damper models. To describe the coupled motion of shaft, bearing pads/pivots and squeeze film dampers, a method of assembling both the linear rotor and the nonlinear components is developed. An implicit Runge-Kutta method to solve coupled lateral and torsional analysis of rotor-bearing systems is approached.

The developed methods are verified against published data. Vibration amplitudes of a linear system under different rotational speeds from transient analysis are exactly same as from linear analysis based on steady state. The tiling pad bearing full dynamic coefficients obtained via transient analysis and small perturbation method (for verification purpose only) at different rotational speeds match those from THPAD (maximum difference of 6% on stiffness). Comparisons to previous torsional analysis are made to verify the nonlinear transient torsional solver.

The transient analyses are applied to a 3-disk rotor supported with nonlinear short plain journal bearings and nonlinear short squeeze film dampers first, and then to an industrial 8-stage back-to-back compressor supported with nonlinear tilting pad bearings and nonlinear finite length squeeze film dampers under severe unbalance conditions. Coupled lateral and torsional transient analyses of the 3-disk rotor with nonlinear supporting system including acceleration effects are solved directly using an implicit 4th order Runge-Kutta method. The effects of support flexibility in series of nonlinear bearings and nonlinear squeeze film dampers are examined. Squeeze film dampers introduced to the system increase dynamic stability of the system under high range rotational speed, decrease the bearing forces, and avoid the possible touch between the shaft and the bearings under severe unbalance conditions. Different nonlinear behavior, such as sub-harmonic, super-harmonic and torus are shown in transient analyses.