https://hal.archives-ouvertes.fr/hal-00935678/document

Nonlinear dynamics of a support-excited flexible rotor with hydrodynamic journal bearings.

Active vibration control of unbalanced flexible rotor–shaft systems parametrically excited due to base motion

The equations of motion of a rotor finite element subjected to six components of base excitation are developed by applying variational principles. The equations contain speed dependent gyroscopic terms, base rotation dependent parametric terms and several forcing function terms which depend upon the linear accelerations, rotational accelerations and a combination of linear and rotational velocities. To evaluate the importance of various terms, seismic response characteristics of a rotating machine subjected to simulated base excitations are studied. It is observed that even for strong rotational inputs the parametric terms in the equation of motion can be ignored without affecting the response. The rotational input terms in the forcing function, however, are quite important and can be ignored only when they are not very strong. Since the problematic parametric terms can be ignored, one can use a generalied modal analysis approach.

Seismic response of rotating machines

Nonlinear dynamic modeling of a simple flexible rotor system subjected to time-variable base motions

Random vibration of rotating machines subjected to seismic excitations is analyzed in which the six-component earthquake ground motions are modeled as nonstationary random processes. The six-component earthquake inputs, including the rotational components of base excitations, result in not only nonhomogeneous excitations but also parametric excitations. Thus, the classical spectral analysis of random vibration is not applicable. Furthermore, both nonhomogeneous and parametric random excitations are correlated random processes, making the problem even more difficult to solve analytically. To date random vibration of such a complicated problem has not been investigated. The method of Monte Carlo simulation is used to simulate the six-component nonstationary earthquake ground motions and to determine the statistics of the response of rotating machines. The significance of seismic base rotations on the overall structural response is examined. A numerical example is worked out to demonstrate the methodology employed.

Random Vibration of Rotating Machines under Earthquake Excitations

The seismic analysis of a rotor-bearing system is presented in the time domain. The governing equations of motion for the rotor are derived including the effects of rotatory inertia, shear deformation, gyroscopic effects, axial force, axial torque, stiffness and damping provided by the lubricants in the bearings, base translation and base rotation. A simple and efficient finite rotor element based on a Galerkin formulation is proposed to model the rotor. The effects of disks and flywheels mounted on the rotor are also included in the analysis. An example problem for a rotor-bearing system is solved using El Centro earthquake data. Four cases are investigated that will permit one to study the influence of spin, base rotation, comparison between rigid body model and beam model and the influence of axial force and axial torque. The results of the above study show that the gyroscopic effects amplify the response of the rotor-bearing system. The base rotations of the rotor-bearing system under seismic excitation contribute significantly to the response.

V. Srinivasan

Papers

Seismic analysis of a rotor‐bearing system