Bifurcation onset delay in magnetic bearing systems by time varying stiffness

We study the nonlinear dynamics behaviours of a rigid rotor supported by magnetic bearings. In particular, we consider the effect of rotor unbalanced mass and geometric coupling. Existing works in literature have mostly focused on a single value of parameter or a smaller range of the nonlinearities introduced by rotor imbalance and geometric coupling. This is partly due to the use of a linear PD controller which limits the system performance. In this paper, we use a nonlinear PD controller by adopting a time varying stiffness term. The control gains are chosen according to the stability chart for a Mathieu's equation. Consequently, we observe a delay in the onset of bifurcation indicating an improved rotor performance.