ABSTRACT
In Chapter 2, we studied dynamic behaviors of rotors with a rigid disc and the flexible massless shaft. These simple rotor models have an advantage in that the mathematical modeling is simple and it predicts some of the vital phenomena with relative ease. However, in actuality, as the previous chapter has demonstrated, the supports of rotors, that is, bearings as well as the foundation, are flexible and have a considerable amount of damping. Consequently, they play a vital role in predicting the dynamic behavior of rotor systems. In the present chapter, we will incorporate bearing dynamic parameters in mathematical models of rotor systems. The previous chapter showed that a bearing has normally eight linearized dynamic parameters (four for the stiffness and four for the damping, with the direct and cross-coupled terms). To start with, first we will consider a long rigid rotor mounted on flexible anisotropic bearings (without damping and without cross-coupled stiffness terms). Next, in the long rigid rotor system, we will incorporate a more general bearing model with eight linearized bearing dynamic coefficients. Subsequently, along with the flexibility of the bearing, the shaft flexibility with rigid discs is considered. Finally, the flexibility of the shaft, bearings, and foundations has been included for predicting the dynamic behavior of a simple rotor system and the forces transmitted through the supports. Wherever equations are large, the matrix and vector forms are preferred. In fact, the aim of the present chapter is to demonstrate that for complex rotor-bearing-foundation systems, conventional modeling and analysis procedures are difficult to apply. A more systematic approach is required, like the transfer-matrix method and the finite element method.
