ABSTRACT
In a previous chapter, we studied the instability in a single mass rotor emanating from various kinds of sources—for example, fluid-film bearings, seals, asymmetrical shafts, hysteretic or material damping of the shaft, and steam whirl. We also studied instability in an asymmetrical rotor with distributed mass and stiffness properties by the continuous approach by including higher effects like the gyroscopic effect and rotary inertia. Predictions of the instability regions due to fluid-film bearings for practical rotors are a great challenge. The disadvantage of the Routh–Hurwitz stability criteria is that it is difficult to apply to multi-degree-of-freedom (DOF) rotor-bearing systems. In Chapters 9 and 10, the multi-DOF rotor system was analyzed using the finite-element method (FEM) without considering the dynamic characteristics of flexible supports. The main complexities in only rotors were considered—for example, the rotary inertia, shear deformation, and gyroscopic couples. In the present chapter, the multi-DOF rotor-bearing system will be analyzed for obtaining natural whirl frequencies, critical speeds, logarithmic decrements, and forced responses. The main tool for such analyses will be finite-element methods; in previous chapters (Chapters 7, 9 and 10) we have already seen the versatility of finite-element methods in rotors for difficult boundary conditions such as multiple rigid supports. In Chapter 4, it was demonstrated that even for a single mass rotor and mounted on two bearings, the analysis using the conventional method becomes very complex. For modeling of fluid-film bearings, the short bearing approximation (refer to Chapter 3) is taken. The stiffness and damping coefficients of fluid-film bearings are speed-dependent and lead to the natural whirl frequency being speed-dependent. To obtain critical speeds, the Campbell diagram is very useful; moreover, in the Campbell diagram apart from the natural whirl frequencies, logarithmic decrements are also provided, which predicts the instability behavior of the rotor at different speeds.
