Unveiling the Effects of Viscous Friction on the Full Annular Rubs in a Piecewise Smooth Rotor/Stator Rubbing System

Abstract

Experimental evidences show that friction during rotor/stator rubbing may not always obey the Coulomb friction law, which is predominantly adopted in the studies of these kinds. This work is devoted to unveiling the effects of viscous damping in the friction model on forward and backward full annular rubbing responses in a piecewise smooth rotor/stator rubbing system. The effects induced by the viscous friction, which are exclusively different from those with pure Coulomb friction, may possibly be used as the signatures for identifying the presence/extent of viscous friction in rotor/stator rubbing tests. In this work, the boundaries of both forward and backward full annular rub motions are analytically derived based on the stability and bifurcation theory. Due to the introduction of viscous friction, the rotor/stator system changes from a piecewise smooth continuous system to a Fillipov one. The results show that the viscous friction has little influence on the region of backward full annular rubbing responses but has significant effects on the region of forward full annular rub motion. With the increase of the viscous friction, the parameter region of the forward full annular rub shrinks significantly, and the boundary of Hopf bifurcation changes increasingly from supercritical to subcritical. This leads to more complex behaviors in the global response characteristics in comparison with those of the rotor/stator rubbing system with Coulomb friction, for instance, two new quasiperiodic rubbing responses appear beside the quasiperiodic partial rub bifurcating from the synchronous full annular rub, including a new quasiperiodic full annular rub motion that is different from the traditional full annular rubs mentioned above.