A flexible rotor bearing system is represented in detail utilizing the state of the art finite element technique. The mathematical model takes into account the gyroscopic moments, rotary inertia, shear deformation, internal viscous damping, hysteretic damping, linear as well as nonlinear stiffness, and damping for the finite bearing and the bearing support flexibility. Using a simple Timoshenko element and recognizing an analogy between the motion planes, a procedure is given that requires a construction of only three symmetric 4×4 matrices. As an application, the different effects of the bearing lining flexibility and the bearing support flexibility on the rotor stability behavior is studied and discussed. The necessary relation for general modal analysis is simply restated and integrated into the conventional spectral approach, thus developing a simple procedure for the calculation of the stochastic response of a general rotor dynamic system. An application to a light rotor bearing featuring a general spatial support and subjected to random disturbances is illustrated.

Stability analysis is performed on the linearized as well as the actual nonlinear finite bearing equations using the improved mathematical models for the hydrodynamic forces that are presented in Part I of this investigation. The results of the analysis using the linear equations show a significant trend, different from previous investigation, with respect to different L/d ratios and therefore can be considered as modified stability curves for the finite bearing. The nonlinear analysis, based on numerical integration of the equation of motion, is carried out for the commonly used L/d = 1. Details on the stability behavior of the finite bearing are established, including the orbital stability regions. It is also found that under certain light loading conditions, the supply pressure can introduce a high possibility of orbital stability to the system.

The linearized model of a rigid symmetric rotor with finite bearings is solved using modal analysis. Important parameters of the finite bearing system are evaluated and these include the logarithmic decrement, damped natural frequencies, complex frequency response functions, and inclination angles of the orbits with the load direction. A chart of error measures giving the deviation of the linearized bearing stiffness and damping from those of the actual nonlinear system is provided. This chart can assist in obtaining a knowledge of the quality of a rotor response as calculated using linearized stiffness and damping and can be used to set acceptance boundaries for the linear model in different industrial applications because of the mathematical difficulties involved in a complete solution of the actual nonlinear representation of the rotor bearing system.

Finite Journal Bearing With Nonlinear Stiffness and Damping. Part 1: Improved Mathematical Models Two mathematical models for the nonlinear hydrodynamic film forces in a finite bearing are developed including a practical adaptation of the cavitation phenomenon. Using the linearity of the Reynolds equation for incompressible film, the pressure components are effectively decomposed and the Reynolds equation is rearranged for general solution by a finite element program in which only the Lid ratio and the eccentricity ratio are to be specified. The different possibilities of partial film profile location in a general dynamic case are demonstrated. The two partial film models possess the required accuracy of the finite bearing approach with the simplicity of the known long and short bearing approximations which are shown as the upper and lower bounds for the present case. The finite bearing approach presented are particularly suitable for nonlinear dynamic analysis. Journal Equation of MotionThe journal equation of motion can be written for the radial direction as md r =F r + Wcos(fi -\j/) where d r is the journal acceleration in the radial direction and m is the journal mass and similarly for the tangential direction. The radial and tangential film forces F r and F, are