Bifurcation onset delay in magnetic bearing systems by time varying stiffness

•System dynamic responses are analyzed using bifurcation diagrams for different unbalance parameters and geometric couplings.•The results for a system with a time varying stiffness are compared with a system without it.•Delayed bifurcation onsets are observed which indicate an improved rotor performance. 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.