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

Abstract

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-β method. The results of the analyses of various motion behaviours are presented as time–displacement responses, orbit plots, phase portraits, Poincaré 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 Poincaré 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.