Analysis of a rotor supported in bearing with gyroscopic effects

Abstract

Rotors with one or more offset disks and supported on bearings are common in high speed turbomachinery. During start up, these rotors have to cross through several critical speeds before reaching their operating speed. At critical speeds, the spin speed of the rotor matches with one of its natural frequency leading to the condition of resonance and large vibration amplitude. In rotating systems, these natural frequencies depend on the support stiffness. Also, they are a function on the spin speed because of the phenomenon of gyroscopic effect. The gyroscopic effects on critical speeds of a rotor system supported in bearing can be studied by means of a Campbell diagram, which has been used in the design of turbines. In this paper, gyroscopic effects of a rotor with an offset disk and supported on bearing is studied by means of Campbell diagrams. The numerical study is carried out by modelling of the rotor-bearing system using finite element mass, stiffness and gyroscopic matrices. The solution is obtained by solving the assembled equations of motion; following application of geometric boundary conditions and representing the second order differential equations of motion in statespace form. The results of critical speed obtained are compared with those of the results obtained through modal analysis using FE tool (ANSYS). The analysis of the results can be used to extend the study for a multi-disk rotor with different bearing supports.