Vibrations of continuous asymmetrical rotor bearing systems

Abstract

The practical rotors have some asymmetrical properties in bearings and/or rotors. The asymmetry in rotors and/or bearings affects the whirl speeds, the magnitude o forced responses, the mode shapes and the stability of rotor system. Vibration analysis method of rotor systems may be divided into two major classes according to modeling procedure, discretization method and analytical method. Some analytical solutions which treats a rotor system as a distributed parameter system were provided, and Modal Analysis was performed, but most works have considered only simple models such as Euler-Bernoulli shafts in geometric boundary conditions. The difficulties in Modal Analysis of rotor systems which include the effects of rotary inertia and gyroscopic moments arise from the fact that the resulting eigenvalue problems are characterized by the presence of skew symmetric matrices with differential operators as elements due to rotation, resulting in non-self-adjoint eigenvalue problem. Using Lagrangian formulation the equations of motion and boundary conditions of continuous anisotropic and asymmetrical rotor-bearing systems are evaluated. By writing the equations of motion of the rotor system which includes the effects of rotary inertia, gyroscopic moments and natural boundary conditions in state space the standard non-self-adjoint eigenvalue problem is obtained. The Modal Analysis of the anisotropic and asymmetrical rotor system is performed. Using the Modal Analysis the effects of the asymmetry in rotors and bearings are discussed. Solution methods for the vibration analysis of uniform rotor systems is various boundary conditions are also provided. The modal characteristics of forward and backward precesion modes of the continuous rotor systems having the asymmetry in rotors or bearings are clarified. The mode shapes of anisotropic rotor systems are composed of the mode shapes of the two different isotropic rotors, one rotating in the specified direction and another ...