Modelling of a rotor-ball bearings system using Timoshenko beam and effects of rotating shaft on their dynamics

This study has focused on the influence of rotating shaft on the dynamics of rotor-ball bearings system. A mathematical modelling of the system has been carried out by considering shaft as rotating Timoshenko beam model. The radial force of rotor unbalance varied with rotating speed. The contact between balls and races is considered as nonlinear spring, whose stiffness is obtained by using Hertzian contact deformation theory. After the modelling for shaft, the governing equation of bearing are derived. The proposed mathematical model is validated experimentally. Moreover, the proposed model is also validated with previous published studies. The bifurcation diagram and Lyapunov exponent are presented to define the state of the system as a function of rotational speed. Fast Fourier transform (FFT) and phase trajectory are used to investigate the influence of the shaft under dynamics of the system.