Numerical Investigation of non-linear Phenomenon in Rotor Bearing System

Abstract

The present work deals with nonlinear free vibration analysis and resulting critical speeds of a highly flexible rotor-bearing system consisting a rotating shaft with higher order of deformation modeled as an Euler-Bernoulli beam and a rigid disk located at positions along the shaft. The rotary inertia and gyroscopic effect combined with inextensible geometric condition for pinned guided shaft element has been taken into account in deriving the governing equation of motion. The method of Galerkin decomposition has been applied followed by method of multiple scales to analyze the nonlinear free vibration of rotor-disk system for undamped and damped systems. The closed-form expressions for determining linear and nonlinear forward and backward frequencies have been obtained and their behavioral pattern on changing the influenced parameters such as rotational speed, mass of the disk and location of the disk have been graphically portrayed. Results obtained numerically have been compared with published research and found good in agreement. Then rotor system with mass unbalance is also considered and same procedure is applied to obtain time response for two transverse directions to axis of shaft. The results obtained are compared with experimental data recorded in vibration lab at Indian Institute of Technology Jodhpur and found in good agreement. Outcomes enable significant theoretical understanding of free vibration analysis and obtaining critical speeds of rotating system which are of great experiment importance for investigating dynamic analysis.