Effect of Unbalance with Bearing Flexibility on Vibration Phenomenon of Geometrically Nonlinear Rotating Shaft with Ball Bearing

Abstract

AbstractFree and forced vibration analysis of a geometrically rotating shaft supported on ball bearings has been studied using the numerical method and compared with the results obtained experimentally. This study is concerned with vibration analysis of geometrically nonlinear rotating model with a rigid disk. The shaft has been designed under the frame of Euler–Bernoulli beam theory with additional effects such as rotary inertia, gyroscopic effect, higher-order large deformations, and rotor mass unbalance in order to replicate an equivalent practical model of rotor-bearing system. The mathematical expressions have been derived to demonstrate the nonlinear free and forced vibrations of the rotating shaft coupled with rigid disk in two transverse planes. Solutions of the nonlinear equation are being obtained using method of multiple scales as well as numerical methods. Effects of rotor parameters such as bearing stiffness and damping coefficient are examined with help of this nonlinear mathematical model. The obtained results are portrayed for a better understanding free and forced vibration analysis with time response, FFT, phase portrait, and Poincare’s map. The present outcomes enable an understanding on how the system dynamics influenced with the variations in the values of different parameters.KeywordsFlexible rotorBearing flexibilityGeometric nonlinearityModal characteristicsUnbalance responsesNonlinear phenomena