Non-linear dynamic response analysis of cylindrical roller bearings due to rotational speed

The dynamic behaviour of cylindrical roller bearings is presented, in both balanced and unbalanced conditions as a function of speed. The stiffness and damping non-linearities at the contact points (due to Hertzian contact force between rollers and races), radial internal clearance and unbalanced rotor force make the bearing system non-linear. Presently, the differential equations representing the dynamics of the cylindrical roller bearings have been obtained using Lagrange's equation and solved numerically using modified Newmark-beta method. The results of the analyses of various motion behaviours are presented as time-displacement responses, orbit plots, phase portraits, Poincare maps and Fast Fourier Transform plots. The obtained responses revealed the sensitive behaviour of the system from periodic to quasi-periodic and chaotic with speed variations for both balanced and unbalanced rotor conditions. Also, intermittent chaotic behaviour has been observed. A pattern of the interaction between rotational and variable compliance vibration is observed with speed variations. The frequency pattern analysis (with different techniques used like phase/orbit plots and Poincare plots) for healthy cylindrical bearing and different rotor conditions under different applied non-linearity consideration is a new attempt to analyse dynamic behaviour of the bearing. This analysis is helpful for online monitoring of fault-free cylindrical roller bearings and for studying the impact of speed on system's dynamical behaviour.