Controlling bifurcations in high-speed rotors utilizing active gas foil bearings

Abstract

High-speed rotors on gas foil bearings (GFBs) are applications of increasing interest due to their potential to increase the power-toweight ratio in machines and also formulate oil-free design solutions. The gas lubrication principles render lower (compared to oil) power loss and increase the threshold speed of instability in rotating systems. However, self-excited oscillations may still occur at circumferential speeds similar to those in oil-lubricated journal bearings. These oscillations are usually triggered through Hopf bifurcation of a fixed-point equilibrium (balanced rotor) or secondary Hopf bifurcation of periodic limit cycles (unbalanced rotor). In this work, an active gas foil bearing (AGFB) is presented as a novel configuration including several piezoelectric actuators that shape the foil through feedback control. A finite element model for the thin foil mounted in some piezoelectric actuators (PZTs), is developed. Second, the gas-structure interaction is modelled through the Reynolds equation for compressible flow. A simple physical model of a rotating system consisting of a rigid rotor and two identical gas foil bearings is then defined, and the dynamic system is composed with its unique source of nonlinearity to be the impedance forces from the gas to the rotor and the foil. The third milestone includes a linear feedback control scheme to stabilize (pole placement) the dynamic system, linearized around a speed-dependent equilibrium (balanced rotor). Further to that, linear feedback control is applied in the dynamic system utilizing polynomial feedback functions in order to overcome the problem of instability.

Keywords

• bifurcation control
• hopf bifurcation
• active gas foil bearings
• high speed rotors
• nonlinear control