UBC Theses and Dissertations
Identification of the fluid induced instability phenomenon in journal bearings Miraskari, Seyed Mohammad
The demand for high pressure injection of natural gas in underground has been an incentive for a growing interest in the design and manufacture of multistage compressors. Many of such compressors suffer from violent sub-synchronous whirl. If the spin-speed of the rotors exceed the “threshold speed of instability,” the rotor-bearing system experiences sub-synchronous whirling known as oil whirl/whip. For rotors supported on journal bearings, oil whirl is the most common cause of instability. Existing models fall short in predicting the nature of sub-synchronous instabilities in journal bearings with a finite length. In this thesis, a new nonlinear rotor-bearing model is introduced to characterize the phenomenon of oil whirl for rotors supported on finite length journal bearings. As a first step in constructing a rotor-bearing model, this research introduces a modified scheme for performance predictions of cavitated journal bearings. The resulting algorithms are then used throughout the thesis to obtain solutions to the Reynolds equation in original and perturbed form in order to calculate journal induced pressure and pressure gradients. The pressure gradients are used as a basis for the calculation of bearing linear and nonlinear dynamic coefficients. Dynamic coefficients are widely used to represent the journal bearing reaction forces exerted on the rotating shaft. These coefficients are implemented to construct mathematical models of the system that are suitable for studying dynamics and stability. Analytical treatments are introduced wherever possible to provide a means for verification purposes. The linear and nonlinear stability of flexible shafts supported on finite length journal bearings is studied. As linear models are not suitable for bifurcation analysis, a simple yet versatile nonlinear rotor-bearing model is proposed such that the journal force is represented by first and higher order dynamic coefficients. Results show that the implementation of nonlinear coefficients can enable the application of nonlinear analysis methods. Nonlinear stability analysis is carried out by implementing a variety of techniques including the Hopf bifurcation theorem and eigenvalue analysis of the Monodromy matrices. The versatility of the techniques used made it possible to study the existence and directions of Hopf bifurcations for rotors supported on finite length journal bearings.
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