Bifurcation Analysis and Vibration Signal Identification for a Motorized Spindle with Random Uncertainty

Abstract

A nonparametric model is established to investigate the vibration characteristics of a motorized spindle system, where the bearing restoring force, the unbalanced magnetic pull, and the external bounded noise excitation are taken into account. Based on the Monte Carlo simulation, several numerical examples are used to study the effect of dispersion parameters from model uncertainty and strength of external bounded noise excitation on the whirl frequency and bifurcation behavior of the spindle. It is shown that the whirl frequency fluctuates due to the random uncertainty, and the fluctuation range grows wider as the dispersion parameters increase as anticipated. In the randomly uncertain case, the vibration of the spindle also exhibits periodic-dominant and bifurcation phenomena, of particular interest is the delay of bifurcation point following the increase of the rotation speed. Towards the vibration condition monitoring on the spindle system, the phase space reconstruction technique is also applied to identify the vibration signals by comparing the reconstructed deterministic phase-space orbits with those from the random uncertainty and the bounded noise excitation, and the inherent dynamical behavior can be revealed from the irregular one-dimension time series effectively.